HA-UVC: Hybrid approach for unmanned vehicles cooperation

Abstract

This paper addresses the problem of ecological ocean pollution by using semi-autonomous unmanned vehicles. A hybrid approach for unmanned vehicles cooperation (HA-UVC) is presented for unmanned aerial vehicles (UAV) to monitor ocean regions and clean up their dirty areas with a swarm of unmanned surface vehicles (USV). Thus, the proposed HA-UVC addresses the problem of trajectory planning, where unmanned vehicles must find a trajectory from the starting position to the goal position while avoiding static obstacles. Consequently, two solutions are proposed in order to manage the trajectory planning problem for the semi-autonomous USV Swarm. The first solution is performed by a modified genetic algorithm (GA). However, the second one is achieved by a proposed Cartesian coordinate algorithm (CCA). In order to optimize the applicable performance, the proposed solutions make it possible to detect and reduce the level of pollution in ocean regions, while avoiding obstacles and failures of unmanned vehicles.

Keywords

Unmanned aerial vehicle unmanned surface vehicle swarm genetic algorithm Cartesian coordinate algorithm fault tolerance

1. Introduction

Marine pollution is defined as the direct or indirect introduction of wastes, substances, or energy. Basically, it includes underwater sound sources of human origin, that causes or is likely to cause adverse and undesirable effects on living resources and marine ecosystems. It negatively touches and disturbs bio diversity, risks to human health, obstacles to maritime activities such as: fishing and tourism, recreation and other uses of the sea, an alteration of water quality from the point of view of their use, and a reduction in the amenity value of the marine environment.

The pollution of the oceans, particularly that of coastal waters, is due to terrestrial as well as marine activities. Fertilizers and pesticides are used in agricultural operations, industrial and nuclear waste, exhaust gases emitted in streets and on roads, sewage and garbage, spread into rivers and streams, that end up in the ocean. Releases to the atmosphere either by industry, or transport is another important source of pollution from the land. Once emitted, many chemical compounds (copper, nickel, mercury, cadmium, lead, zinc, etc.) remain in the air for weeks, see more. It is mainly through the winds that they travel and fall back into the oceans. All these pollutants and waste are then redistributed around the world by the marine currents. Marine activities such as: mining, transportation, fishing, and cruise ships discharge large quantities of toxic substances into the ocean. Noise pollution, which strongly disrupts the behavior of certain animal species such as large marine mammals, is also a growing problem. Oil pollution, which is caused by the stranding and collisions between ships, which has been a major international problem for long time. In this term, the oil spill is a good example of this pollution, which results in the flow of oil slicks into the coastal zone. This slick, which results from the deliberate or accidental release of a significant amount of crude oil or heavy petroleum products into the sea, is then brought back to the coast by tides, winds, or currents.

While looking at the frequency and quantities of oil spilt, it should be noted that a few large spills are responsible for a high percentage of the oil spilt. For example, in the recent decades can be seen in the 1990s, in which there were 358 spills of 7 ton and over, resulted in 1,134,000 ton of oil lost; 73% of this amount was spilt in just 10 incidents. In the ninth year period 2010–2018, there have been 59 spills of 7 tones and over, resulted in 163,000 ton of oil lost; 92% of this amount was spilt in just 10 incidents. One incident is responsible for about 70% of the quantity of oil spilt in this decade. In terms of the volume of oil spilt, the figures of a particular year may be severely distorted by a single large incident. This is clearly illustrated by incidents such as: Atlantic Empress (1979), 287,000 ton spilt; Castillo De Bellver (1983), 252,000 ton spilt; Abt Summer (1991), 260,000 ton spilt; and Sanchi (2018), 113,000 ton spilt (see Fig. 1) [10].

Figure 1.

Location of major spills [10].

The fight against this pollution is very difficult to be implemented and no ‘ultimate’ solution exists up to date. As a result, industry sectors have been encouraged to develop an unmanned vehicle, or drone solution to protect marine environments and help the human being. A ‘Bio-Cleaner’ drone design was designed to clean the oceans of oil slicks [12]. By the use of this drone, a solution based on swarms of semi-autonomous unmanned vehicles is proposed to clean up the oil slicks of a coast of the city of Oran, Algeria (oil port). The oil slicks illustrated in black, are positioned between the maritime region of the ‘anastel Forest’ and the beach ‘The dunes’ as shown in Fig. 2.

Figure 2.

Oil slicks at ORAN (Western Algeria, Source: Google Maps).

Fundamentally, the interest of this work is to present a hybrid approach that can successfully allow an easy management between the different unmanned vehicles. Moreover, this architecture allows fault tolerance and scalability compared to the self-organized approach [18] that does not allow or hardly allows scalability with increased complexity for efficient management of its entities [19]. Centralized management includes a central node with deterministic decision-making capability and easy to implement coordination. This coordinator has a global view of the unmanned vehicle activities of its appropriate system. These unmanned vehicles are: surveillance vehicles and swarms of cleaning vehicles. They cooperate with each other to carry out a mission of monitoring the ocean regions, cleaning up their dirty zones, and follow the requests of its coordinator. Distributed management begins when the surveillance vehicle is assigned to a region. The surveillance vehicle has a lower decision than that of its coordinator. It has the ability to coordinate its own cleaning swarms to properly accomplish the cleansing mission. These swarms plan their movements to go to the dirty zones from their bases of life. In this context, two solutions are proposed to the problem of trajectory planning. Furthermore, these solutions are based on two algorithms, ‘Modified Genetic Algorithm (GA)’ and ‘Proposed Cartesian Coordinate Algorithm (CCA)’. Besides, these algorithms propose a calculation method avoiding obstacles calculation method that quickly provides a workable solution to the planning problem. Several trajectories will be generated and the best will be selected for the cleaning vehicle swarm according to each proposed solution. As this cleaning vehicle is a mechanical, electronic, and computer system which may at some point fail at the hardware/software level while performing its tasks, a solution is proposed to allow the selection and replacement of failed cleaning vehicles by the competent cleaning vehicles during the realization of the cleaning mission.

This present paper proposes a hierarchical hybrid approach for heterogeneous unmanned vehicles cooperation (HA-UVC). The HA-UVC includes various and effective methods to manage the trajectory planning and fault tolerance problem for the unmanned surface vehicle (USV) swarm. Moreover, the proposed HA-UVC permits a cooperation of an unmanned aerial vehicle (UAV) to monitor an oceanic region and a USV swarms to clean dirty ocean zones. The UAV is assumed to be equipped with on-board sensors that allow it to locate dirty zones by using the proposed movement methods. UAV discretizes its environment map and updates it with the collected information related to dirty zones. UAV sends its environment map to its general coordinator (represented by a laptop and guided by a human operator). After an analysis of the collected data, the general coordinator assigns the explored map to the USV swarm to clean each dirty zone. This swarm navigates to the assigned dirty zone and cleans it based on the proposed solutions for trajectory planning. The first solution is based on the modified GA, whereas the second one relies on a proposed CCA. Also, these solutions incorporate a method to avoid static obstacles during the movement of a USV swarm. In addition, the proposed HA-UVC is complemented by a failure managing method of a USV during the execution of its cleaning task.

The paper is organized as the following: Section 2 presents some related works in the literature; Section 3 describes the proposed HA-UVC for the different unmanned vehicles with the trajectory planning and failure managing method, and model them by logical formalization; Section 4 illustrates an example to simulate the operation of HA-UVC; in Section 5, the proposed HA-UVC is compared to the related works; finally, Section 6 concludes this paper and provides some future research directions.

2. Literature review

The occurrence of natural disasters is an important problem in all world’s regions, either developed, or developing.The problem arises from the physical extent of the disaster, which makes it out of scope of human possibilities to react to it. Accordingly, efforts are being made to recognize and predict the possibility of a disaster, especially to respond effectively to the ongoing disaster, and to assess and repair the damage as quickly as possible. Several efforts are based on the use of different unmanned vehicles in several applications, namely, environmental monitoring applications, disaster prediction, cleaning, mapping, etc. For example, the work of [7] described a vision of leveraging the latest advances in UAV and wireless sensor (WSN) network technology to enhance the ability of network-assisted disaster prediction, assessment, and response. UAV networks in conjunction with WSN and cellular network are showed to be a promising future technology for the applications in a disaster management.

Thus [1], the authors proposed a model system and a performance evaluation of UAVs to map an affected area during a Japan Tohoku of Tsunami disaster in 2011. The city of Sendai in Japan has been mapped using a multi-heterogeneous UAV. The flight plan designs are based on the information recorded after the disaster and on the mapping capabilities of the UAVs. The numerical and statistical results of the mapping missions were validated by executing the missions on real-time flight experiments in a hardware-in-the-loop simulator (HITL) that developed and analysed the flight logs of the UAVs. Multi-rotor UAVs are suitable for monitoring small urban areas because their complexity and manoeuvrability enable obstacles avoidance in these areas. The flooded and remote areas should be monitored by fixed-wing UAVs because they have longer flight times than multi-rotor UAVs.

Additionally, the work of [2] addressed the problem of monitoring the pollution of unknown ocean regions, the detection, cleaning of dirty zones, and the breakdown of unmanned autonomous vehicles. The authors proposed a centralized decision-making approach for air-sea cooperation and coordination, which is composed of a UAV to monitor an oceanic region and an USV in order to clean up a dirty zone. The color has been chosen as a degree of dirt, so that UAV can detect the dirty zones and initiate the cleaning. The geo-referenced images of UAV are collected through using its sensory sensors to create an exploration map of the region with a path a priori known and determine the positions of dirty zones. UAV sends the explored map and dirty zone data to the general coordinator (represented by an artificial agent). After an analysis of the captured data, the USV uses its sensors and the map provided by UAV via the general coordinator to access the assigned dirty zone and clean it. Each USV has the LEDs to measure the amount of energy. Mainly, the measured metrics are the total energy consumption, the average cleaning energy consumption, and the number of cells cleaned by the selected USV.

Furthermore, in terms of cleaning vehicles, a Waste Hunter Surface cleaning robot [6] was developed for rivers that allows real-time monitoring of water cleanliness. Waste Hunter Surface is a tele-operated robotwith three main functions: surface cleaning, purification process, and water quality monitoring.In addition, the robot is a semi-automatic control robot, where it will be turned on and off. It can also make a movement from the input gain of the user. This robot has a flexible design, which is built by several functions on the mobile application, namely: wireless controllers (WIFI) to communicate between the user and the robot, a smart phone application for the remote control, a Nodemcu microcontroller module for the interface between the user and the robot, a virtual gauge for data quality monitoring (PH value), etc. An automation system is put in place to monitor the water cleanliness 24/7. Also, it can trap the physical waste that flows there. During the test, Waste Hunter Surface is examined with four movement conditions, namely: forward, backward, left, and right movement. The result shows that the robot was able to reach the desired location in minimum wind conditions. However, Waste Hunter Surface is difficult to clean in an open environment with strong water comparing the clam water environment.

Furthermore, a prototype [19, 21] of a USV based on two gas sensors was developed to locate the gas source of an oil spill in the sea. The gas concentration received by the two sensors, applied to a fuzzy logic controller, determines the rate at which each propeller motor approaches the gas target. The result shows that the USV prototype is able to approach and locate the target with average accuracy obtained when searching for the location of the gas source of 90.1%. Thus, a new robotic system swarm [19, 22] was proposed to locate and pick up an oil spill on the surface of the water (ocean, river, lake). A coordinator determines the position and the center of the spill using a GPS receiver, then a barge carrying the robots moves to the workplace. Depending on the state of the spill, the coordinator can send a swarm of robots to surround and collect the oil spill, then place the barge with oil suction equipment and move it to another location to remove the oil more safely. This new system saves money and time.

On the other hand, the heterogeneous unmanned vehicles must plan their displacements to accomplish a given mission based on several approaches and methods of trajectory planning. A synthesis was proposed in the article [11], which systematically examined optimal approaches to trajectory planning adopted for a single or a USV swarm. Initially, the optimal approaches for trajectory planning currently adopted in the literature for unique USVs are analysed with the ‘reactive obstacle avoidance (ROA)’, ‘deliberative obstacle avoidance (DOA)’ and ‘simultaneous localization and mapping (SLAM)’ techniques in two aspects: the static and dynamic environment. This is followed by path planning approaches adopted for swarm of USVs. Among these approaches, an evolutionary approach to the path planning of coverage region (PPCR) was presented in [15]. This approach is based on a genetic algorithm (GA) for a vacuum cleaner robot, where GA is used to generate an efficient path to clean all accessible areas in the room environment. In the proposed model, the map is built on a disk shape, which represents the robot position that is connected to each other with only local lateral connections. The model works in real time and in a dynamic environment. GA consists of several steps to get the solutions. Each gene represents the robot position and some of the chromosomes also represent the mini-path. The authors demonstrated the effectiveness and robustness of this algorithm to help the robot navigate a zigzag path in the entire work space by avoiding obstacles using different sensors. The simulations are implemented in C #. The simulations prove advantages in reducing the length of the trajectory, the number of turns, and the cells, which are revisited for the GA compared to the other ‘scan matching’ algorithms and combined with ‘oriented rectilinear decomposition (ORD)’ and ‘spatial cell diffusion (SCD)’.

Another genetic algorithm [3] was proposed for the trajectory planning problem to handle the problem of fault tolerance for USV swarms while performing their tasks. They proposed a hybrid approach that represents a cooperation of a semi-autonomous UAV and a semi-autonomous USV swarm and their coordination by a general coordinator. A UAV is assigned to a region and a swarm of USV is allocated to a dirty zone for cleaning. The color is chosen as the degree of dirt, so that UAV can detect dirty zones with its on-board sensors. UAV discretizes its environment card and updates it with the collected information about dirty zones. Also, it sends its environment card to its general coordinator (represented by a laptop, guided by a human operator). After an analysis of the data collected, the general coordinator assigns the scanned map to the swarm. This swarm plans its movement via the proposed GA to reach its dirty zone. Each swarm of USV measures its amount of energy by a threshold of energy, and then sends its information to its leader. This latter sends back information to its supervisor to make the decision to find a free USV, and to replace USV in unloaded state. The measured metrics are the average total energy consumption of the USV swarm and the average total energy consumption of the selected USV.

Besides, the authors in [4] presented a GA for autonomous mobile robots, where GA is used to find a sequence of actions that robots must perform to reach the goal as quickly as possible. A coding based on specific actions has been tested in a realistic robotic simulator. In the proposed approach, the robot did not know in advance the disposition of the environment and only had a rough estimate of starting positions and goal. At first, a set of actions is generated randomly. The robots execute these actions, and then their aptitude is evaluated. The fitness function is based on the distance travelled and the Euclidean distance from the goal. Individuals are selected by tournament to reproduce. Then, a new sequence of actions is generated by applying crossover and mutation operators. However, the evolution continues only for the sequence of actions related to the robots that did not reach the goal.GA has a higher average performance than that proposed by the algorithms A* and its improvement (C*), and the smallest distances travelled by the solutions returned by GA are always better than the solutions returned by A* and C*.

Thus, a multi-domain inversion strategy based on the ‘conventional genetic algorithm (CGA)’ to solve the trajectory planning problem was presented in [14]. This strategy increases the number of offspring in order to improve a local search capability and to increase the probability of generating excellent individuals. Monte Carlo simulations for several examples from the library for the travelling salesman problem were conducted to analyse the feasibility and effectiveness of the improved algorithms. These improved algorithms, namely, ‘Single-Domain Inversion-based Genetic (SDGA)’, ‘Multi-Domain Inversion-based Genetic Algorithm (MDIGA)’, and ‘Double-Domain Inversion-based Genetic Algorithm (DDGA)’, have been applied to the navigation, guidance, and control system of an USV in a real maritime environment. A comparative study reveals that MDIGA algorithm is superior with a desirable balance between path length and time cost, and it has a shorter optimal path, a faster convergence speed, and a higher robustness than the others.

Furthermore, a new method of trajectory planning for mobile robots in an uncertain dynamic environment was presented by [16]. Through this method, the positions of the moving obstacles are sampled by the robot sensor system, and the sampling position information on dynamic obstacles is treated as instantly static. Moreover, with the current sampling positions, an autoregressive (AR) model predicts the future positions of the obstacles in the next sampling period. Then, the trajectory of the robot is planned with such predicted positions. With the integration of global planning and local planning, an online real-time approach has been based on polar coordination which the desirable steering angle is taken into account as an optimization index. Unlike the different traditional methods of trajectory planning, this approach does not concern the length of the robot’s movement, but the direction in which it moves.

Thus, a new state feedback based back stepping control algorithm to solve the trajectory tracking problem of an under actuated USV in the horizontal plane was proposed in [5]. The well-known Persistent Exciting (PE) conditions of yaw velocity is completely relaxed for tracking control of both the curve and straight line trajectories of USV with high accuracy. This controller is designed on the basis of the overall system and the overall stability, and it is proved by Lyapunov Theory and Barbalat’s Lemma. In order to verify and illustrate the performance of the proposed control schemes for the tracking of the under-actuated USVs, computer simulations were performed on a USV model with hydrodynamic parameters, which are derived from the hydrodynamic calculation based on the FLUENT software.

Principally, an offline 3D path planner for a single UAV in a real space of uncertain mission is introduced in [17]. A new coordinate system is used to remedy the drawbacks of two coordinate systems by rotating the Cartesian coordinate system and dividing the whole mission space into several subspaces, which heavily reduces the search space. Based on this new coordinate system, an estimation of the distribution algorithms (EDA) is used to build a new path planner for UAV. This EDA is introduced for saving the fine-tuning time of reproductive parameters and guide the search for optimal waypoint in each subspace. The results have showed the effectiveness of this new proposed path planner.

This article deals with the marine pollution problem by proposing a cooperative hybrid approach (HA-UVC). This proposed HA-UVC allows cooperation between the heterogeneous semi-autonomous air-sea vehicles that is presented to monitor ocean regions and clean dirty zones. Thus, two solutions are proposed to find an optimal trajectory and avoid static obstacles between the starting position of an unmanned cleaning vehicles (USV) swarm and the objective. The first solution is based on a modified GA, and the second is relies on a proposed CCA. This trajectory planning between the base of life and the dirty zone is made from the metric map of an oceanic region. This map is built by an unmanned surveillance vehicle (UAV). Eventually, a fault tolerance service is introduced for USV swarms.

3. Proposed cooperative hybrid approach and formulation

This paper presents a HA-UVC based on the cooperation and the coordination of unmanned vehicles. This cooperation minimizes the work overload by breaking down the mission into tasks. These tasks are allocated or distributed on the various unmanned vehicles based on air-sea coordination. This coordination facilitates and reduces the execution, competition and conflicts of these tasks between the different unmanned vehicles. Thus, the approach proposed in the article Bella et al. [3, 19] is developed by describing the architecture and the constituent entities of the system, the solutions proposed for trajectory planning, and fault tolerance as well as their operation. In addition, a logical formalization is defined to broadly encompass the steps used in this HA-UVC and to illustrate them in a formal way based on a representation of classical planning.

3.1 Proposed cooperative hybrid approach

3.1.1 Architecture of the system

The hybrid architecture of the proposed system, shown in Fig. 3, consists of a central unit, surveillance vehicle to monitor maritime region, swarms of cleaning vehicles to clean dirty zones, and recovery vehicles are presented to recover defective vehicles. The central unit is composed of a general coordinator, a base of life and a database. The general coordinator stores and consults the data in the database. It interacts with the base of life and the surveillance vehicle via a communication link of the IEEE.802.11a standard (5000 m outside range) of the name Wi-Fi 5. While the Wi-Fi network of the IEEE.802.11b standard (35 m–140 m indoor range). Also, it allows messages to be connected between the surveillance vehicle and the swarm of cleaning vehicles.

Figure 3.

Hybrid architecture of the system.

3.1.2 Hierarchical role of each vehicle

The decision-making hierarchy of the proposed approach, illustrated in Fig. 3, is made up at the first level of a general coordinator. It represents the central memory which has the highest decision for the execution of various tasks like the launching and controlling of the unmanned vehicles used that are located in the base of life, the use (processing) and storage of data in the database. The monitoring drone is loaded of a lower decision in a second level. It represents a central memory that has the role to supervise and monitor its cleaning vehicles swarms. These swarms are located in the third level and are composed of leaders’ vehicles with their followers. Their objective is to carry out the cleaning operation of the dirty zone according to the energy availability of each member. Each leader can represent a central memory of its followers. It has two necessary roles; it is responsible for the tasks/characteristics of it followers, and also, it shares (cooperates) with them the cleaning action. Finally, each USV in the swarm has a local memory building the fourth level, and they can communicate with each other. The coordinator launches a recovery vehicle to recover the failing vehicles.

Table 1
Descriptive table of the different vehicles

Unmanned vehicle	Definition	Tasks	Hard/soft components
$\textit{UAV}_{mr}$	Monitoring, homogeneous and semi-autonomous aerial vehicle	• Monitoring the regions, the dirty zones, the cleaning vehicles swarm. • Supervising the cleaning vehicles swarm ( $\textit{USV}_{cz}$ ). • Asking/Informing the leader of each swarm by tasks. • Launching/Return the data and the results to the general coordinator ( $\textit{General}_{\textit{crd}}$ ).	• A camera. • An ultrasonic sensor. • A GPS (Global Positioning System). ———————————— • An autopilot software. • A speed. • An energy capacity.
$\textit{USV}_{cz}$	Cleaning, homogeneous and semi-autonomous surface vehicle.	• Cleaning the dirty zones. • Following/Request the tasks of its leader ( $\textit{Leader}_{cz}$ ). • Informing/Returning the data and the results to its leader. • Coming-back to the base of life.	• An ultrasonic sensor. • A GPS. ———————————— • An autopilot software. • A speed. • An energy capacity.
$\textit{Leader}_{cz}$	Cleaning, homogeneous and semi-autonomous surface vehicle.	• Cooperate with followers to clean dirty zones. • Sending the requests for its followers ( $\textit{USV}_{cz}$ ). • Receiving/Saving the characteristics of each follower ( $\textit{USV}_{cz}$ ) (and save its features). • Informing/Returning the data and the results to its supervisor ( $\textit{Sup}_{mr}$ ). • Coming-back to the base of life.	• An ultrasonic sensor. • A GPS. ———————————— • An autopilot software. • A speed. • An energy capacity.
$\textit{Vehicle}_{rec}$	Vehicle homogeneous sur-face and semi autonomous. It is a special vehicle named recovery vehicle.	Bringing back the faulty vehicles (out of order) towards the base of life (The detailed description of this vehicle is presented in our article [2]).	• An ultrasound sensor. • GPS. ———————————— • An autopilot software. • A speed and • An energy capacity.

3.1.3 Environment modeling

This section defines the modeling of this work environment. It is described by the set of components listed below and the parameters used (Table 3).

Set of tasks: Five high level tasks are defined and used by the general coordinator, the monitoring and cleaning vehicles: task of allocating ( $t_{a}$ ) unmanned vehicle to different regions and dirty zones; task of monitoring ( $t_{mr}$ ) the region r; task of cleaning ( $t_{cz}$ ) a dirty zone z; task of supervising ( $t_{sz}$ ) the cleaning of a dirty zone z; task of launching ( $t_{l}$ ) of the different previous tasks (monitoring, cleaning, supervising cleaning and allocating).

Descriptive table of the different vehicles: Table 1 lists the different vehicles used in this HA-UVC with their tasks.

Descriptive table of the different agents: Table 2 shows the different types of agents with their names and roles.

Set of regions: The monitored maritime space is divided into maritime regions. The region is composed of two sub-spaces; an atmosphere sub-space where $\textit{UAV}_{mr}$ can be found and a maritime sub-space with the swarm of $\textit{USV}_{cz}$ , $\textit{Vehicle}_{\textit{rec}}$ , base of life and dirty zones.

Set of base of life: It is a zone (can be a boat, ship, or an island) to store a fixed number of $\textit{UAV}_{mr}$ , $\textit{USV}_{cz}$ and $\textit{Vehicle}_{rec}$ .

Set of database: These are basics for storing and saving all the data and features of the maritime space as well as the different unmanned vehicles used.

Set of dirty zones: With water pollution, for example oil slicks or plastic waste; the proposed metric in this work is the degrees of dirt for each zone with four types: strong dirt, average-strong dirt, average dirt, and low dirt. Each zone is characterized by a list ‘ $\textit{Lis}_{tzone}$ ’ which delimits its borders by the coordinates. These last are composed by the list of degrees of dirt ‘ $\textit{List{\_}Degree}_{cell}$ ’, list of cell positions of these degrees ‘ $\textit{List{\_}Position}_{cell}$ ’ and they are attached to a zone by ‘ $\textit{Position}_{zone}$ ’.

Set of obstacles: They represent obstacles that float on the surface of the water such as ships, boats, marine mammals like dolphin and whale, birds, fish, excessive growth of sea plants, natural scum, etc. The position of these obstacles ‘ $\textit{Pos}_{\textit{Obs}}$ ’ are saved in a list ‘ $\textit{List{\_}Obs}_{mr}$ ’ of each maritime region presented by its identifier ‘ $\textit{Id}_{region}$ ’.

Table 2
Descriptive table of defined agents

Agent type	Agent name	Description/agent roles
$\textit{General}_{crd}$	General coordinator	It is represented by a laptop that contains a coordination software, guided by a human operator. It is responsible for: the base of life, data of the regions and the dirty zones, use (treatment) and the storage of data in the database, launch of the tasks/missions and allocate tasks to vehicles.
$\textit{Leader}_{cz}$	Leader vehicle	It is an unmanned surface vehicle that has two roles: it is an intermediary between the supervisor $\textit{Sup}_{mr}$ and $\textit{USV}_{cz}$ of the swarm, and also cooperates in the cleanup operation.
$\textit{USV}_{cz}$ (discharge)	Cleaning vehicle in discharge state	It is a cleaning vehicle, that has not yet completed its task and energy capacity are low during cleaning.
$\textit{USV}_{cz}$ (free)	Cleaning vehicle in free state	It is a cleaning vehicle that has completed its task.
$\textit{USV}_{cz}$ (prepared)	Cleaning vehicle in prepared state	It is a cleaning vehicle prepared in the base of life by the $\textit{General}_{crd}$ which will replace $\textit{USV}_{cz}$ (discharge).
$\textit{Sup}_{mr}(\textit{USV}_{cz}\_\textit{discharge})$	Supervisor of $\textit{USV}_{cz}$ (discharge)	It is the surveillance vehicle ( $\textit{USV}_{cz}$ ) of the cleaning vehicle in discharge state.
$\textit{Sup}_{mr}(\textit{USV}_{cz}\_\textit{free})$	Supervisor of $\textit{USV}_{cz}(\textit{free})$	It is the surveillance vehicle ( $\textit{USV}_{cz}$ ) of the cleaning vehicle in free state.
$\textit{Sup}_{mr}(\textit{USV}_{cz}\_\textit{prepared})$	Supervisor of $\textit{USV}_{cz}(\textit{prepared})$	It is the surveillance vehicle ( $\textit{USV}_{cz}$ ) of the cleaning vehicle in prepared state.
$\textit{Leader}_{cz}(\textit{USV}_{cz}\_\textit{discharge})$	Leader of $\textit{USV}_{cz}$ (discharge)	It is the leader of the cleaning vehicle in discharge state.
$\textit{Leader}_{cz}(\textit{USV}_{cz}\_\textit{free})$	Leader of $\textit{USV}_{cz}(\textit{free})$	It is the leader of the cleaning vehicle in free state.
$\textit{Leader}_{cz}(\textit{USV}_{cz\_prepared})$	Leader of $\textit{USV}_{cz}(\textit{prepared})$	It is the leader of the cleaning vehicle in prepared state.

Table 3

Descriptive table of used parameters

Parameters	Description
Threshold	Fixed threshold that allows classifying the zone coordinates according to the degrees of the cells ‘ $\textit{List{\_}Degree}_{cell}$ ’.
$\textit{Threshold}_{\textit{average\_energycap}}$	Threshold of the average energy capacity that has a fixed value and it allows to determine the average energy capacity.
$\textit{Threshold}_{\textit{low\_energycap}}$	Threshold of low energy capacity that has a fixed value and it allows to determine the low energy capacity.
$\textit{List}_{\textit{ID}}(\textit{Id}_{\textit{USV\ cz}})$	List of USV identifiers composing the swarm.
$\textit{List}_{\textit{energy\_usv(t)}}(\textit{Id}_{\textit{USV cz}}$ , $\textit{Cap}_{\textit{energy}}\textit{CZ})$	List of the USV energy capacity in instant t during cleaning as well as its identifier.
$\textit{List}_{\textit{zone}}(\textit{List{\_}Degree}_{\textit{cell}}$ , $\textit{List{\_}Position}_{\textit{cell}}$ , $\textit{Position}_{\textit{zone}})$	List of coordinates of the dirty zone.
$\textit{List}_{\textit{zoneS}}$	$\textit{List}_{\textit{zone}}$ sorted by the degree of dirt.
$\textit{List}_{\textit{threshold\_degree}}Z$	Coordinates list of the dirty zone that is compared with the threshold of dirt compared to the dirty degrees ( $\textit{List{\_}Degree}_{\textit{cell}})$ .
$\textit{List{\_}Obs}_{mr}(\textit{Pos}_{\textit{Obs}}$ , $\textit{Id}_{\textit{region}})$	List of obstacles in each region.
$\textit{Nbr}_{\textit{CZ}}$	A function that gives the number of selected $\textit{USV}_{cz}$ by $\textit{General}_{crd}$ .
$\textit{Pos}_{\textit{Start}}(x,y)$	Starting position that $\textit{USV}_{cz}$ can start from the base of life. This position is a Cartesian coordinate (X, Y). Each $\textit{USV}_{cz}$ at its own starting position.
$\textit{Pos}_{\textit{End}}(x,y)$	End position represents the arrival of $\textit{USV}_{cz}$ to the dirty zone. This position is a Cartesian coordinate (X, Y). Each $\textit{USV}_{cz}$ to its own ending position.
$\textit{Pos}_{\textit{Gol}}(x,y)$	Goal position means the next position of $\textit{USV}_{cz}$ in its move. This position is a Cartesian coordinate (X, Y).
$\textit{List}_{\textit{PosE}}(x,y)$	List of Cartesian coordinates (X, Y) representing the final positions (to arrive at the dirty zone).
$\textit{List{\_}tabooPos(Id}_{\textit{USv}}$ , $\textit{Pos}_{\textit{Gol}}(x,y))$	List of positions to save positions that are already traversed by $\textit{USV}_{cz}$ . It contains the identifier of USV ‘Id ${}_{\textit{USV}}$ ’ which has already visited the position $\textit{Pos}_{\textit{Gol}}(x,y)$ where its Cartesian coordinate is the pair (x, y) in the grid.
$\textit{List{\_}tabooCell}(\textit{Id}_{\textit{US}}$ , $\textit{Cell}(x;y))$	List of dirty cells to memorize cells that are already cleaned by $\textit{USV}_{cz}$ . It is constituted by the identifier of USV ‘Id ${}_{\textit{US}}$ v’ and its cleaned cell Cell(x, y). This cell represented by the Cartesian couple (x, y) in the grid.
$\textit{List{\_}distCost}(\textit{link}_{ij}$ , $\textit{Cost}_{ij})$	List of distances between positions that are marked as an energy cost. It is composed of: $\textit{link}_{ij}$ is the link between the position i and the position j thus its energy cost $\textit{Cost}_{ij}$ .
$\textit{Parameters}_{\textit{start-up(M)}}(\textit{Id}_{\textit{region}}$ , $\textit{Position}_{\textit{region}}$ , $\textit{Path}_{\textit{region}}$ , $\textit{Map}_{\textit{region}})$	A triplet of start parameters for each $\textit{UAV}_{mr}$ which represents the identifier, position, trajectory and map of a region.
$\textit{Parameters}_{\textit{start-up(C)}}(\textit{Id}_{\textit{region}}$ , $\textit{Id}_{\textit{zone}}$ , $\textit{Id}_{\textit{SUPMR}}$ , $\textit{Id}_{\textit{LeaderCZ}}$ , $\textit{Position}_{\textit{zone}}$ , $\textit{Pos}_{\textit{Start}}(x,y)$ , $\textit{Pos}_{\textit{End}}(x,y)$ , $\textit{List}_{\textit{PosE}}(x,y)$ , $\textit{List{\_}Obs}_{mr})$	Triplet of the start parameters for each $\textit{USV}_{cz}$ which represents the identifier of its region, zone, supervisor, leader and the position of zone with the starting and end position, the list of end positions and obstacles.
$\textit{Parameters}_{\textit{cleaning}}(\textit{PosUSV g, Cell}_{cz}$ , $\textit{Id}_{\textit{region}}$ , $\textit{Id}_{\textit{zone}}$ , $\textit{Position}_{\textit{zone}}$ , $\textit{Trajectory}_{\textit{zone}}$ , $\textit{Id}_{\textit{SUPMR}}$ , $\textit{Id}_{\textit{LeaderCZ}})$	Cleanup parameters for the $\textit{USV}_{cz}$ that replaces the $\textit{USV}_{cz}$ in discharge state. This list contains: the position of $\textit{USV}_{cz}$ in the grid, the cell to be cleaned, the identifier, the position and the trajectory of the zone, the identifier of the region, the identifier of $\textit{Sup}_{mr}$ and $\textit{Leader}_{cz}$ .
$\textit{List}_{\textit{characteristics}}(\textit{Id}_{\textit{zone}}$ , $\textit{Id}_{\textit{USV CZ}}$ , $\textit{Dur}_{\textit{EC}}$ , $\textit{Cons}_{\textit{EC}}$ , $\textit{Dur}_{\textit{ED1}}$ , $\textit{Cons}_{\textit{ED1}}$ , $\textit{Dur}_{\textit{ED2}}$ , $\textit{Cons}_{\textit{ED2}})$	List of the $\textit{USV}_{cz}$ characteristics: the identifier of an zone ( $\textit{Id}_{\textit{zone}}$ ), identifier of a USV ( $\textit{Id}_{\textit{USVCZ}}$ ), the duration and the energy consumption of displacement of the base of life towards the dirty zone ( $\textit{Dur}_{\textit{ED1}}$ , $\textit{Cons}_{\textit{ED1}})$ , the duration and the energy consumption of displacement in the dirty zone ( $\textit{Dur}_{\textit{ED2}}$ , $\textit{Cons}_{\textit{ED2}})$ and the duration and the energy consumption of cleaning ( $\textit{Dur}_{\textit{EC}}$ , $\textit{Cons}_{\textit{EC}})$ .

3.1.4 Key steps of cooperative hybrid approach

This section describes the key steps of HA-UVC with proposed solutions for the trajectory planning problem and the fault tolerance problems. To this end, the HA-UVC is based on two essential steps: monitoring and cleaning. The proposed solutions are applied in the cleaning step. To better understand the proposed HA-UVC, a pseudo code of the complete procedure and the structure (flowchart) of this approach are illustrated in Algorithm 1 and Fig. 4 respectively.

Figure 4.

Structure of the hybrid approach for unmanned vehicles cooperation (HA-UVC).

Step 1: Monitoring

This step presents the monitoring actions performed by each $\textit{UAV}_{mr}$ . These actions are presented in two phases: the monitoring setup and the monitoring execution.

Algorithm 1: Approach procedures

Begin

for all ((int) id_region

\in

region space) do

execute monitoring setup();

execute monitoring execution();

execute cleaning setup();

execute obstacle avoidance();

execute GA-based trajectory planning();

execute CAA-based trajectory planning;

for all ((int) id_dirty_A setup();

execute GA-based trigger process();

execute CAA-based trigger process();

end for

execute cleaning operation();

execute cleaning finalization();

end for

Phase 1. Monitoring setup: the monitoring step is performed, for example, twice a week in the maritime region to be monitored. The $\textit{General}_{crd}$ prepares the monitoring drones according to the regions numbers, allocating a $\textit{UAV}_{mr}$ for each region. In addition, $\textit{General}_{crd}$ checks periodically the maritime space statistics that are saved in the database. So, if it finds a region statistic that shows that this last contains a high percentage of dirty zones in certain period. Consequently, it launches a $\textit{UAV}_{mr}$ for a full day to monitor this dirty zone.

Phase 2. Monitoring execution: this phase is executed when the $\textit{General}_{crd}$ prepare each $\textit{UAV}_{mr}$ with a startup parameters $\textit{Parameters}_{\textit{start-up(M)}}(\textit{Id}_{\textit{region}}$ , $\textit{Position}_{\textit{region}}$ , $\textit{Path}_{\textit{region}}$ , $\textit{Map}_{\textit{region}})$ , energy (battery charged) and associated speed before starting. Then, $\textit{UAV}_{mr}$ is launched via $\textit{General}_{crd}$ from the base of life from a starting position to the end position according to the assigned path $\textit{Path}_{\textit{region}}$ and the map of the region (a discreet space of dimension 2 of square shape). $\textit{UAV}_{mr}$ follows this path with a rectilinear movement (see Fig. 5 to reach its region). Once the $\textit{UAV}_{mr}$ arrives at its region, it can plan its movement based on its field of vision. So it uses its sensory sensors(a camera and an ultrasonic sensor) to know the number of cells on which it can fly or move on the grid, it sweeps repeatedly until the final cleaning, as shown in Fig. 5. Then, with this movement, it prepares a second map (square grid 2D) of the maritime space (lower level) with its captured data, it records these data in the $\textit{List}_{\textit{zone}}(\textit{List{\_}Degree}_{\textit{cell}}$ , $\textit{List{\_}Position}_{\textit{cell}}$ , $\textit{Position}_{\textit{zone}})$ . Once the maritime level data collection is completed, the $\textit{UAV}_{mr}$ sorts the collected list and saves it in a list $\textit{List}_{\textit{zoneS}}$ and compares the $\textit{List{\_}Degree}_{\textit{cell}}$ of this $\textit{List}_{\textit{zoneS}}$ with a fixed threshold Threshold. After, it saves the result in list $\textit{List}_{\textit{threshold\_degree}}Z$ and sends it to $\textit{General}_{\textit{crd}}$ .

Figure 5.

Unmanned aerial vehicle (UAV) movements to achieve.

Step 2: Cleaning

This step is illustrated the cleaning actions in three phases: the cleaning setup, operation and the cleaning finalization.

Phase 1. Cleaning setup: two proposed solutions for trajectory planning are applied in this phase. The first solution is based on a modified GA, and the second is used by a proposed CCA. In addition, they guide the swarm of $\textit{USV}_{cz}$ to execute the phase of moving to dirty zones. Before applying the two solutions, $\textit{General}_{crd}$ analyzes the received data (the $\textit{List}_{\textit{threshold\_degree}}Z)$ from each $\textit{UAV}_{mr}$ . Then, $\textit{General}_{crd}$ determines the $\textit{USV}_{cz}$ number containing the swarm for each dirty zone. This action is described by Algorithm 2. After the execution of Algorithm 2, a decision is made to trigger the cleaning step. Then, the main phases of the two proposed solutions are presented so that the $\textit{USV}_{cz}$ swarm can plan its way to its dirty zone:

Algorithm 2: Calculate the needed number of $\textit{USV}_{cz}$
Inputs
$\text{List}_{\textit{threshold\_degreeZ}}$ [C]: list which contains the degree of dirty cells of an zone compared with Threshold, where C represents the length of this list;
M: represents the number of $\textit{USV}_{cz}$ in base of life (constant);
Outputs
y: solution variable to find the number of $\textit{USV}_{cz}$ ;
$\text{List}_{\textit{average}}$ [A]: list of average of $\text{List}_{\textit{threshold\_degreeZ}}$ , where A represents the length of $\text{List}_{\textit{average}}$ [];
$\text{List}_{X}$ [X]: list of value x, where X represents the length of $\text{List}_{X}$ [];
$\text{Nbr}_{\textit{CZ}}$ [U]: list which contains the $\textit{USV}_{cz}$ numbers, where U represents the length of $\text{Nbr}_{\textit{CZ}}$ [];
Begin
for all (List ${}_{\textit{threshold\_degreeZ}}$ received ) do
calculate average(List ${}_{\textit{threshold\_degreeZ}})$ ;
save List ${}_{\textit{threshold\_degreeZ}}$ in List ${}_{\textit{average}}$ ;
end for
calculate min(List ${}_{\textit{average}})$ ;
% calculate the solution variable to find the number of $\textit{USV}_{cz}$
(int) y $=$ 0, sum $=$ 0, X $=$ A;
for all ((int) x $=$ 0 to X) do
List ${}_{X}$ [X] $\leftarrow$ List ${}_{\textit{average}}$ [a]/min;
sum $=$ sum $+$ List ${}_{X}$ [X];
end for
% calculate the solution of equation (y) M sum * y;
y $=$ M/sum;
for all (x $\in$ List ${}_{X}$ [X]) do
Nbr ${}_{CZ}$ [x] $\leftarrow$ y * List ${}_{X}$ [x]; end for

Detection and avoidance of the obstacle for the $\textit{USV}_{cz}$ swarm: Detection and avoidance of the obstacle is the most important factor in the trajectory planning. To this, an obstacle avoidance technique is proposed in the ‘modified GA’ and ‘proposed CCA’ algorithms as mentioned in Fig. 6. $\textit{Leader}_{cz}$ of each $\textit{USV}_{cz}$ swarm knows at the start the list of obstacles positions of its maritime region. After that, it checks the new position selected according to the algorithm used. If it does not belong to the list of obstacles then $\textit{Leader}_{cz}$ moves to this new position. Otherwise, it looks for another position closer to it that is different from the obstacle positions.

Figure 6.

Detection and avoidance of the obstacle.

Solution 1. Modified GA trajectory planning: This phase is presented as the first solution modified to the trajectory planning problem. The different actions of this solution are mentioned so that the selected $\textit{USV}_{cz}$ swarm can build its trajectory towards its dirty zone:

Genetic algorithm setup: the modified GA is inspired by the algorithm presented in [3, 15, 19]. In this GA, the $\textit{USV}_{cz}$ swarm must search for an optimal trajectory between the starting position (the base of life) and the goal (the dirty zone). The novelty of this algorithm is to allow the leader to plan a trajectory for its swarm of $\textit{USV}_{cz}$ while avoiding obstacles compared to GA proposed in [15, 3, 19]. The setup is prepared by the following stages:

Environment modeling, the environment modeling depends on the map of the discretized region (metric map) by the supervisor $\textit{UAV}_{mr}$ . Workspace is discretized by a square grid G, which is composed of square cells. A node is located inside each cell to facilitate the movement of $\textit{USV}_{cz}$ . These nodes build a dynamic graph where the arcs are presented by $R_{ij}$ connection links. $R_{ij}$ between two neighboring cell-nodes represents the distance between two positions as illustrated in Fig. 7. This distance is represented by the energy value $E_{ij}$ that the $\textit{USV}_{cz}$ can consume in the displacement. Each cell-node $i_{th}$ represents a free/occupied position by a position or an obstacle in the environment. These positions are identified by Cartesian coordinates (X, Y) in a 2D plane. These positions have a maximum of eight links ( $R_{ij})$ with the neighboring positions $j_{th}$ .

Figure 7.

Environment modeling of modified GA.

Trajectory planning method, General ${}_{crd}$ assigns a start position $\textit{Pos}_{\textit{Start}}(x,y)$ and the list of end positions $\textit{List}_{\textit{PosE}}(x,y)$ to $\textit{Leader}_{cz}$ of each swarm. This list sets the positions to arrive at the dirty zone. Then, the trajectory travelled by the $\textit{Leader}_{cz}$ from a $\textit{Pos}_{\textit{Start}}(x,y)$ to a $\textit{Pos}_{\textit{End}}(x,y)$ passing through all accessible positions and avoiding obstacles, this is called the global trajectory planning for the region. To get this global trajectory, it should be divided into a mini-trajectory, the latter must not exceed the sensor range of $\textit{Leader}_{cz}$ (an ultrasonic sensor), as shown in Fig. 8.

Figure 8.

Trajectory planning method.

The range of the sensor represents a detection region Rs of s * s boxes that allows $\textit{Leader}_{cz}$ to capture its neighboring positions relative to its current position. A $\textit{Leader}_{cz}$ can move by one step between cells. The mini-trajectory contains the start position $\textit{Pos}_{\textit{Start}}(x,y)$ and the gol position $\textit{Pos}_{\textit{Gol}}(x,y)$ . If $\textit{Pos}_{\textit{Gol}}(x,y)$ belongs to the list of obstacles ‘List_Obs’ then $\textit{Leader}_{cz}$ looks for another position closer to it. If $\textit{Pos}_{\textit{Gol}}(x,y)$ is equal to one of $\textit{List}_{\textit{PosE}}(x,y)$ , then $\textit{Leader}_{cz}$ has arrive in the dirty zone. The mini-trajectory contains $\textit{Pos}_{\textit{Gol}}(x,y)$ positions which are occupied by the $\textit{USV}_{cz}$ when it moves. These positions are scanned, but the others remain un-browsed until they are taken into account during the next planning of the mini-trajectory. Each $\textit{Leader}_{cz}$ shares its positions travelled with its followers. The aim is to obtain an efficient global trajectory between $\textit{Pos}_{\textit{Start}}(x,y)$ and $\textit{Pos}_{\textit{End}}(x,y)$ . To this end, the mini-trajectory should also be automatically effective and it will have a short distance, less obstacle, and a minimum of consumed energy.

Evolutionary approach, an evolutionary approach based on GA is proposed to minimize the energy consumption, obstacle and trajectory distance. GA helps the $\textit{Leader}_{cz}$ to find an efficient trajectory from the $\textit{Pos}_{\textit{Start}}(x,y)$ to $\textit{Pos}_{\textit{End}}(x,y)$ . This consists of several steps whose first step is the initialization of solution (genome or chromosome). Then, the evaluation of these populations is launched by using the fitness functions. The lowest fitness value allows to switch to a new generation. This passage makes it possible to replace the existing chromosomes with new ones in order to preserve a constant number of chromosomes. This passage is made by operators inspired by biological genetic variation, namely: selection, crossover, and mutation.

Encoding and representation, each node has its own number after the environment modeling is finished. The gene is made of one part which represents these nodes. In the trajectory planning of the region, the gene corresponds to a position of $\textit{Leade}_{rcz}$ . The chromosome is consisted of genes, which represent a mini-trajectory. In this study, the chromosome contains a number of genes; this latter should belong to the rayon of the sensors. To better clarify, an example is shown in Fig. 9, in which any gene that is located between the position of $\textit{Leader}_{cz}$ and the circular zone is taken into consideration to form a chromosome. For example, if any mini-trajectory is taken, the $\textit{Leade}_{rcz}$ must pass on 4 nodes/positions (e.g. [5, 8, 9, 12]), which allows the creation of a new chromosome that should contain 4 genes, so the code of each gene should match one of the nodes/positions and take its number. The order of genes in chromosomes should be obligatory because it represents the different positions that take the $\textit{Leader}_{cz}$ .

Figure 9.

Gene presentation.

Generation of initial population, the population has a fixed length of p individuals and each individual has a sequence of initial positions of length l. The positions represent the cell-nodes that the $\textit{Leader}_{cz}$ can explore in the known environment. In this phase, the mini-trajectory planning is random by choosing neighboring positions. As a result, individuals (chromosomes) have their sequences of positions, which are filled randomly. Each sequence is executed by the $\textit{Leader}_{cz}$ and associated with that individual. Different proposed trajectories can get with a standard sweep or zigzag movement for the mini-trajectory, as shown in Fig. 10. Among these mini trajectories, a mini trajectory is chosen for $\textit{Leader}_{cz}$ in order to execute it. Once the $\textit{Leader}_{cz}$ has the sequence of positions, a fitness value will be updated based on the trajectory travelled in the environment.

Figure 10.

Two ways of motion.

Fitness function and selection, fitness function is necessary to know the details of description and solution of the problem. It is directly related to the constraints of navigation coverage, i.e. the energy reduction, the obstacle and the trajectory size. Two parameters are taken into consideration to evaluate the fitness of the mini-trajectories: the total distance of mini-trajectory, the direction cost for $\textit{Leader}_{cz}$ . An appropriate fitness function of mini-trajectory $(i)$ is constructed as:

$\displaystyle F_{i}=A*\textit{Dist}_{\textit{Trajectory(i)}}+B*\Sigma\textit{% Cost}_{\textit{Dir(i)}}$ (1) $\displaystyle\textit{Cost}_{\textit{Dir(i)}}=\textit{Direct}_{\textit{Cost}}+% \textit{Left}_{\textit{cost}}+\textit{Right}_{\textit{cost}}$ (2)

where two equilibrium parameters (constant numbers) and $\textit{Dist}_{\textit{Trajectory(i)}}$ and $\textit{Cost}_{\textit{Dir(i)}}$ are the distance of the mini-trajectory $(i)$ and the direction cost for $\textit{Leader}_{cz}$ respectively. Total distance of mini-trajectory ( $\textit{Dist}_{\textit{Trajectory(i)}})$ is calculated by the sum of each distance between two cell-nodes in which this distance is represented by a value of energy. Direction cost for each USV ${}_{cz}$ ( $\textit{Cost}_{\textit{Dir(i)}}$ ) is calculated according to the direction of the $\textit{USV}_{cz}$ when it moves to another node. The displacement of the $\textit{Leader}_{cz}$ is composed in three directions: Direct direction ( $\textit{Direct}_{\textit{cost}}$ ) where $\textit{Leader}_{cz}$ moves from its position to another position in the same direction; Right direction ( $\textit{Right}_{\textit{cost}}$ ) where $\textit{Leader}_{cz}$ turns to the right of its position to get to another position; Left direction ( $\textit{Left}_{\textit{cost}}$ ) where $\textit{Leader}_{cz}$ turns to the left of its position to reach another position. The management costs are fixed in advance and the ideal form is the solution that does not contain redundant cells visited.

Genetic operators, the new position sequences (new individuals) are created by applying crossover and mutation operators. Crossover is performed positions sequence provided by two parents. These parents (two mini-trajectories) are selected by tournament [20], where they (the individuals) are chosen at random and who with a low fitness value becomes a parent. One-point crossover technique was chosen for this approach; the two children are then added to the population. An example of a crossover operator is shown in Fig. 11. In which, the crossover point is the first three genes of two trajectories selected (parents) by the tournament. Then, the child 1 takes the first part of the parent 1 chromosomes plus the second part of the parent 2 from the crossover point. Thus, the child 2 takes the first part of parent 2 and the second part of parent 1. Therefore, two new mini-trajectories are provided.

Figure 11.

Crossover operator.

The mutation randomly defines a quantity of genes that is randomly chosen to be mutated. In this case, the gene that builds a problem in the trajectory. It is replaced by one’s neighbor’s previous neighbor gene in the trajectory. The neighboring gene is also randomly selected. Figure 12 shows the mutation operation on child 1 of the previous example. At each generation, applied elitism can be created by new individuals (children) of length l who have a low fitness to replace previous individuals (parents). Each new position sequence is executed by an associated $\textit{Leader}_{cz}$ , so that the fitness value of each new individual is calculated.

Figure 12.

Mutation operator.

Modified GA based trigger process: the modified GA based process is triggered when the $\textit{General}_{\textit{crd}}$ chooses the swarm of $\textit{USV}_{cz}$ ; so it sends the list of their identifiers $\textit{List}_{\textit{idusv}}(\textit{Id}_{\textit{USV CZ}})$ to their $\textit{Sup}_{mr}$ . Upon receipt of this message, $\textit{Sup}_{mr}$ sends its discrete maritime space exploration map to $\textit{General}_{crd}$ . This latter, $\textit{General}_{crd}$ prepares a leader for each swarm with a strong energy capability compared to other $\textit{USV}_{cz}$ of the swarm. Then, $\textit{General}_{crd}$ broadcasts a set of parameters to the selected swarm, namely: $\textit{Parameters}_{\textit{start-up(C)}}(\textit{Id}_{\textit{region}}$ , $\textit{Id}_{\textit{zone}}$ , $\textit{Id}_{\textit{SUPMR}}$ , $\textit{Id}_{\textit{LeaderCZ}}$ , $\textit{Position}_{\textit{zone}}$ , $\textit{Pos}_{\textit{Start}}(x,y)$ , $\textit{Pos}_{\textit{End}}(x,y)$ , $\textit{List}_{\textit{PosE}}(x,y)$ , $\textit{List{\_}Obs}_{mr})$ , Explored map (EM), Energy capacity (EC) and speed (S); $\textit{List{\_}tabooPos}(\textit{Id}_{\textit{USV}}$ , $\textit{Pos}_{\textit{Gol}}(x,y))$ , $\textit{List{\_}tabooCell}(\textit{Id}_{\textit{USV}}$ , Cell(x, y)); $\textit{List{\_}distCost}(\textit{link}_{ij}$ , $\textit{Cost}_{ij})$ ; and it just sends this leader the start position $\textit{Pos}_{\textit{Start}}(x,y)$ and end position $\textit{Pos}_{\textit{End(x,y)}}$ (N.B. these fields are empty for other $\textit{USV}_{cz}$ of the same swarm). After, $\textit{General}_{crd}$ just sends this leader the start position $\textit{Pos}_{\textit{Start}}(x,y)$ and end position $\textit{Pos}_{\textit{End}}(x,y)$ and these fields are empty for other $\textit{USV}_{cz}$ of the same swarm). Then, $\textit{General}_{crd}$ starts the execution of GA and each $\textit{Leader}_{cz}$ of the swarm plans its trajectory according to the steps mentioned above until reaching the end position. At first, $\textit{Leader}_{cz}$ finds a new position from its starting position, it sends its first position to its first follower. After, when it finds a third position, it sends its second position to its follower, and it sends its first position to its follower, and so on. $\textit{USV}_{cz}$ of the swarm move together in the grid in a rectilinear shape and at the same time they change their positions in the start parameter, and each $\textit{USV}_{cz}$ follows its neighbor $\textit{USV}_{cz}$ . When $\textit{Leader}_{cz}$ arrives at $\textit{Pos}_{\textit{End}}(x,y)$ , checks whether the last position of each $\textit{USV}_{cz}$ of the swarm belongs to $\textit{List}_{\textit{PosE}}(x,y)$ . If it is not, it executes a small instruction so that all $\textit{USV}_{cz}$ are positioned in the end positions. When all USVcz are in their final positions, the Leadercz sends the list of information (PosStart(x,y), PosEnd(x,y)) of each USVczto Generalcrd.

Solution 2- proposed CCA trajectory planning: this phase is presented as a second appropriate solution to the trajectory planning problem. Different actions of this solution are mentioned, so that the selected $\textit{USV}_{cz}$ swarm can build its trajectory towards its dirty zone.

TPCC setup: this solution of trajectory planning algorithm is based on a Cartesian coordinates. This proposed CCA algorithm can model the behaviour of a $\textit{USV}_{cz}$ swarm to find an optimal trajectory between the starting position (base of life) and the goal (dirty zone). In addition, this CCA is used to select a leader for this $\textit{USV}_{cz}$ swarm. The discretized grid G is composed of cells. The cells contain the positions. These positions are presented as cities. Each city represents a free/occupied position by a $\textit{USV}_{cz}$ or obstacle. Also, they are identified by Cartesian coordinates (X, Y) in a 2D plane. They can have links between their neighboring positions. The connection links $R_{ij}$ represent the distance between the cities, as shown in Fig. 13. This distance is represented by an energy cost $E_{ij}$ that $\textit{USV}_{cz}$ will be able to consume when moving between cities. On the basis of the proposed algorithm, named ‘Proposed CCA’, each $\textit{USV}_{cz}$ will be placed in a departure city. It moves from one city to another by using the connection links between cities to reach the goal. Cities are composed of three positions,namely the start city $\textit{Pos}_{\textit{Start}}(x,y)$ , goal city $\textit{Pos}_{\textit{Gol}}(x,y)$ and the list of end cities $\textit{List}_{\textit{PosE}}(x,y)$ . If the goal city $\textit{Pos}_{\textit{Gol}}(x,y)$ is equal to one of the end cities $\textit{List}_{\textit{PosE}}(x,y)$ , $\textit{USV}_{cz}$ arrives at the dirty zone.

Figure 13.

Environment modeling of proposed Cartesian coordinate algorithm (CCA).

Algorithm 3 presents the method of ‘proposed CCA’ where $\textit{General}_{crd}$ prepares a List Nv_Pos_USV $\textit{(List\_idZone}[\textit{idUSV},(u_{x},u_{y})])$ , List_PE_Zone $([(i1,i2),(j1,j2)]$ , $\textit{List}_{\textit{PosE}}(x,y))$ and $\textit{List{\_}Obs}_{mr}$ $(\textit{Pos}_{\textit{Obs}}$ , $\textit{Id}_{\textit{region}})$ . This list of lists contains all the identifiers of the USV containing the swarm with their running positions as Cartesian coordinates $(u_{x},u_{y})$ of each dirty zone. This list is empty at the beginning. The List_PE_Zone constructed by the Cartesian Coordinates in matrix representation ‘[i1, i2),(j1,j2)], the list ‘ $\textit{List}_{\textit{PosE}}(x,y)$ ’ of positions of its borders and the list’ $\textit{List{\_}Obs}_{mr}$ ’ of obstacle positions. $\textit{General}_{crd}$ assigns a $\textit{Pos}_{\textit{Start}}(x,y)$ presented by $(u_{x},u_{y})$ to each selected $\textit{Leader}_{cz}$ for each swarm. $\textit{General}_{crd}$ launches Algorithm 3 for each USV swarm to find the best trajectory. The flow is started by filling the ListNv_Pos_USV (1). Three conditions are proposed to arrive at the dirty zone by using $u_{x}$ abscissa of $\textit{Leader}_{cz}$ and the couple of the abscissa (i1, i2) of the dirty zone and also avoiding the obstacles. The conditions are applied as follows: If (( $u_{x}>i1$ ) && ( $u_{x}>i2$ )) then dirty zone is located at the top of $\textit{Leader}_{cz}$ position (2). Else if (( $u_{x}<i1$ ) && ( $u_{x}<i2$ )) then dirty zone is found at the bottom of $\textit{Leader}_{cz}$ position (4). Else $\textit{Leader}_{cz}$ is positioned either in the same line of i1 or i2 of dirty zone (5). Within these conditions, each $\textit{Leader}_{cz}$ must check every time the obstacles positions to avoid it by the list ‘List_Obs’, and check whether the Pos ${}_{\textit{Gol}}(x,y)$ is equal to one of the end positions of $\textit{List}_{PosE}(x,y)$ through the list ‘List_PE_Zone’. At the same time, it sends the traversed positions to its neighbor $\textit{USV}_{cz}$ and so on (3). The modification of ListNv_Pos_USV is done when $\textit{Leader}_{cz}$ find sa new Pos ${}_{\textit{Gol}}(x,y)$ (3).

Proposed CCA based trigger process: the proposed CCA based process is triggered when the $\textit{General}_{crd}$ chooses the $\textit{USV}_{cz}$ swarm, so it sends the identifiers list ‘ $\textit{List}_{ID}(\textit{Id}_{\textit{USVcz}})$ ’ from $\textit{USV}_{cz}$ to its $\textit{Sup}_{mr}$ . On receipt of this message, $\textit{Sup}_{mr}$ sends its discrete sea space exploration map to $\textit{General}_{crd}$ . Then, $\textit{General}_{crd}$ prepares a leader for each swarm with a strong energy capability compared to other swarm $\textit{USV}_{cz}$ , and broadcasts a set of parameters to the selected swarm, namely: $\textit{Parameters}_{\textit{start-up(C)}}(\textit{Id}_{\textit{region}}$ , $\textit{Id}_{\textit{zone}}$ , $\textit{Id}_{\textit{SUPMR}}$ , $\textit{Id}_{\textit{LeaderCZ}}$ , $\textit{Position}_{\textit{zone}}$ , $\textit{Pos}_{\textit{Start}}(x,y)$ , $\textit{Pos}_{\textit{End}}(x,y)$ , $\textit{List}_{\textit{PosE}}(x,y)$ , $\textit{List{\_}Obs}_{mr})$ , Explored map (EM), Energy capacity (EC) and speed (S); List_tabooPos(Id ${}_{\textit{USV}}$ , $\textit{Pos}_{\textit{Gol}}(x,y))$ , $\textit{List{\_}tabooCell(Id}_{\textit{USV}}$ , Cell(x, y)); $\textit{List{\_}distCost(link}_{ij}$ , $\textit{Cost}_{ij})$ with $\textit{Pos}_{\textit{Start}}(x,y)$ and $\textit{Pos}_{\textit{End}}(x,y)$ positions are empty at the beginning. Then, $\textit{General}_{crd}$ sends $\textit{Leader}_{cz}$ the start city $\textit{Pos}_{\textit{Start}}(x,y)$ and launches the CCA execution and each $\textit{Leader}_{cz}$ of the swarm plans its trajectory according to the steps mentioned above until reaching the end position. At first, $\textit{Leader}_{cz}$ finds a new city from its starting position through avoiding obstacles, and thenit sends its first city to its first follower. After that, when it finds a third city, it sends its second city to its follower, and this latter sends its first position to its follower, and so on. The $\textit{USV}_{cz}$ of swarm moves together and follows its neighbor in the grid following a rectilinear shape, and at the same it modifies its positions in its starting parameters.

Algorithm 3: Proposed Cartesian coordinate algorithm (CCA)
Inputs
ListNv_Pos_USV[sizePU]: list of lists which contains the new cartesian coordinates ( $u_{x}$ , $u_{y}$ ) of each USV of swarm of each dirty zone, where sizePU represente the length of ListNv_Pos_USV [sizePU].
ListPE_Zone[sizePE]: list of lists which contains the cartesian coordinates [( $i_{1}$ , $i_{2})$ ; ( $j_{1}$ , $j_{2}$ )] of each dirty zone with the positions list of its borders ( $\textit{List}_{\textit{PosE}}(x,y)$ ), where sizePE represente the lenght of this list.
List_Obs[sizeOb]: list of list which contains the positions of obstacles ( $\textit{Pos}_{\textit{Ob}}$ ) found in the region, where sizeOb represente the lenght of this List_Obs[sizeOb].
Outputs
(newUx, newUy): cartesian coordinate pair that represents the new position of each USV of swarm. ListNv_Pos_USV[sizePU].
begin
fill_list(ListNv_Pos_USV[sizePU], ( $u_{x}$ , $u_{y})$ , $z$ ); (1)
while ((int) $z==$ 0 $<$ sizeZ) do
(3) $\left\{\begin{array}[]{l}\text{{if} (($u_{x}>i_{1}$) {\&}{\&} ($u_{x}>i_{2}$))% {then} {(2)} }\\ \text{\quad search{\_}Pos{\_}End((u${}_{x}$, u${}_{y})$, z, ListPE{\_}Zone[% sizePE]); }\\ \text{\quad{while} ((boolean) End $==$ false ) {do} }\\ \text{\qquad select neighboring couple (newUx, newUy) that is has minimal % distance with of (u${}_{x}$, u${}_{y})$, not dirty and }\\ \text{\qquad(newUx, newUy) !$=$ PosOb; }\\ \text{\qquad$u_{x}=$ newUx; $u_{y}$ newUy; }\\ \text{\qquad add(($u_{x}$, $u_{y}$), ListNv{\_}Pos{\_}USV [sizePU]); }\\ \text{\qquad send(($u_{x}$, $u_{y}$), followers{\_}USV); }\\ \text{\quad{end while} }\\ \text{ajustement{\_}position{\_}end(ListNv{\_}Pos{\_}USV [sizePU], z);}\end{% array}\right.$
(3) $\left\{\begin{array}[]{l}\text{{else if} (($u_{x}<i_{1}$) {\&}{\&} ($u_{x}<i_{% 2}$)) {then} {(4)} }\\ \text{\quad search{\_}Pos{\_}End(($u_{x}$, $u_{y}$), z, ListPE{\_}Zone[sizePE]% );}\\ \text{ \quad{while} ((boolean) End $==$ false) {do} }\\ \text{ \qquad select neighboring couple (newUx, newUy) that is has minimal % distance with of ($u_{x}$, $u_{y}$), not dirty and }\\ \text{ \qquad(newUx, newUy) !$=$ PosOb;}\\ \text{ \qquad$u_{x}=$ newUx; $u_{xy}=$ newUy; }\\ \text{ \qquad add(($u_{x}$, $u_{y}$), ListNv{\_}Pos{\_}USV[sizePU]); }\\ \text{ \qquad send(($u_{x}$, $u_{y}$), followers{\_}USV); }\\ \text{ \quad{end while} }\\ \text{ajustement{\_}position{\_}end(ListNv{\_}Pos{\_}USV [sizePU], z); }\end{% array}\right.$
(3) $\left\{\begin{array}[]{l}\text{{else} % {(5)} }\\ \text{\quad search{\_}Pos{\_}End(($u_{x}$, $u_{y}$), z, ListPE{\_}Zone[sizePE]% ); }\\ \text{\quad{while} ((boolean) End $==$ false ) {do}}\\ \text{\qquad select neighboring couple (newUx, newUy) that is has minimal % distance with of ($u_{x}$, $u_{y}$), not dirty and }\\ \text{\qquad(newUx, newUy)!$=$PosOb;}\\ \text{\qquad$u_{x}=$ newUx; $u_{y}=$ newUy; }\\ \text{\qquad add(($u_{x}$, $u_{y}$), ListNv{\_}Pos{\_}USV[sizePU]); }\\ \text{\qquad send(($u_{x}$, $u_{y}$), followers{\_}USV); }\\ \text{\quad{end while} }\\ \text{ {end if} }\\ \text{ ajustement{\_}position{\_}end (ListNv{\_}Pos{\_}USV [sizePU], z); }\end% {array}\right.$
z $++$ ; end while

When $\textit{Leader}_{cz}$ arrives at $\textit{Pos}_{\textit{End}}(x,y)$ , it checks whether the last position of each $\textit{USV}_{cz}$ of the swarm belongs to $\textit{List}_{\textit{PosE}}(x,y)$ . If it does not, it executes a small function (adjustment_position_end ()), so that all $\textit{USV}_{cz}$ are positioned in the end positions. Then, when all $\textit{USV}_{cz}$ of the swarm are in their final positions, $\textit{Leader}_{cz}$ sends the information’s list ( $\textit{Pos}_{\textit{Start}}(x,y)$ , $\textit{Pos}_{\textit{End}}(x,y))$ of each $\textit{USV}_{cz}$ to $\textit{General}_{crd}$ . To this end, the sequence diagram below (Fig. 14) generally describes this cleaning process.

Figure 14.

Sequence diagram ‘CCA-based cleaning trigger process for USVcz swarm’.

Phase 2. Cleaning operation: this phase allows the $\textit{USV}_{cz}$ swarm to move into the dirty zone and clean it. The maritime space is discretized in square grid (G). Each box of the G can contain an object (a dirty cell/a clean cell). Objects are points in a numerical space with M dimensions. These objects to be partitioned are positioned. $\textit{USV}_{cz}$ move on G and perceive a detection region Rs in their neighborhood (see Fig. 8). These $\textit{USV}_{cz}$ can clean the dirty cell type objects. To this end, an Algorithm 4 is proposed and applied by the swarm to clean the dirty zone. Using this algorithm, the swarm can move in the dirty zone and clean its dirty objects. This phase is started when the swarm arrives at its dirty zone. $\textit{General}_{crd}$ stops the execution of modified GA and proposed CCA. Subsequently, $\textit{General}_{crd}$ selects another $\textit{Leader}_{cz}$ from the $\textit{USV}_{cz}$ composing the swarm, and at the same time shares this information with the other USVs. This leader has a very high energy capacity compared to other $\textit{USV}_{cz}$ . After, $\textit{General}_{crd}$ launches Algorithm 3 on the swarm and at the same time $\textit{Leader}_{cz}$ launches the recording of the characteristics of himself and its followers. $\textit{USV}_{cz}$ of the swarm follow the algorithm so that they can properly position and move between the clean cells, select the cells to be cleaned afterwards, and share their positions between them.

Algorithm 4: Cleaning operation
Input
List ${}_{\textit{Crd\_USV}}$ [sizeU]: list which contains the cartesian coordinate of each USV ( $u_{x}$ , $u_{y}$ ), where sizeU represente the length of List ${}_{\textit{Crd\_USV}}$ [];
ListCrd ${}_{\textit{threshold\_degreeZ}}$ [sizeD]: list which contains the cartesian coordinates of the dirty cells of zone ( $d_{x}$ , $d_{y}$ ), where sizeD represente the lenght of this list;
Outputs
(NewU ${}_{x}$ , NewU ${}_{y}$ ): cartesian coordinate pair that represents the new position of each USV;
List ${}_{\textit{TabooCelU}}$ [sizeC]: list which represent the memory of dirty cells that are already cleaned by USV;
List ${}_{\textit{NearbyCrdU}}$ [sizeN]: list which contains the neighboring coordinates ( $v_{x}$ , $v_{y}$ ) of USV ( $u_{x}$ , $u_{y}$ ), where sizeN represente the length of
List ${}_{\textit{NearbyCrdU}}$ [];
Begin
while ((int) $u<$ sizeU && (int) $d<$ sizeD) do
for all ((int) d ListCrd ${}_{\textit{threshold\_degreeZ}}$ [sizeD]) do
calculate the distance between ( $u_{x}$ , $u_{y}$ ) and ( $d_{x}$ , $d_{y}$ );
end for
select couple ( $d_{x}$ , $d_{y}$ ) which it has a minimal distance with ( $u_{x}$ , $u_{y}$ );
if (( $u_{x}-d_{x}==$ 0) && ( $u_{y}-d_{y}==$ 0)) then
NewU ${}_{x}=d_{x}$ ; NewU ${}_{y}=d_{y}$ ;
update((NewU ${}_{x}$ , NewU ${}_{y})$ , List ${}_{\textit{Crd\_USV}}$ [sizeU]);
delete((dx, dy), ListCrd ${}_{\textit{threshold\_degreeZ}}$ [sizeD]);
save((NewU ${}_{x}$ , NewU ${}_{y}$ ), List ${}_{\textit{TabooCelU}}$ [sizeC]);
else if (( $u_{x}-d_{x}==$ 0) && ( $u_{y}-d_{y}==$ 1)) then
NewU ${}_{x}=d_{x}$ ; NewU ${}_{y}=d_{y}$ ;
update((NewU ${}_{x}$ , NewU ${}_{y})$ , List ${}_{\textit{Crd\_USV}}$ [sizeU]);
delete((dx, dy), ListCrd ${}_{\textit{threshold\_degreeZ}}$ [sizeD]);
save((NewU ${}_{x}$ , NewU ${}_{y}$ ), List ${}_{\textit{TabooCelU}}$ [sizeC]);
else if (( $u_{x}-d_{x}==$ 1) && ( $u_{y}-d_{y}==$ 0)) then
NewU ${}_{x}=d_{x}$ ; NewU ${}_{y}=d_{y}$ ;
update((NewU ${}_{x}$ , NewU ${}_{y})$ , List ${}_{\textit{Crd\_USV}}$ [sizeU]);
delete((dx, dy), ListCrd ${}_{\textit{threshold\_degreeZ}}$ [sizeD]);
save((NewU ${}_{x}$ , NewU ${}_{y})$ , List ${}_{\textit{TabooCelU}}$ [sizeC]);
else
find nearby positions((ux;uy); ListNearbyCrdU[sizeN]);
for all (( $v_{x}$ , $v_{y})$ && List ${}_{\textit{NearbyCrdU}}$ [sizeN]) do
if (( $v_{x}$ , $v_{y}$ ) ! $=$ occupied_another ( $u_{x}$ , $u_{y}$ ) && ( $v_{x}$ , $v_{y}$ ) ! $=$ dirty) then
calculate the distance between ( $u_{x}$ , $u_{y}$ ) and ( $v_{x}$ , $v_{y}$ );
end if
end for
select couple ( $v_{x}$ , $v_{y}$ ) which it has a maximal distance with ( $u_{x}$ , $u_{y}$ );
NewU ${}_{x}=v_{x}$ ; NewU ${}_{y}=v_{y}$ ;
update((NewU ${}_{x}$ , NewU ${}_{y})$ , List ${}_{\textit{Crd\_USV}}$ [sizeU]);
end if end if end if
$u++$ ;
if (( $u==$ sizeU) && (d! $=$ sizeD)) then $u=$ 0;
end if
end while

Phase 3. Cleaning finalization: this phase consists in identifying the finalization of cleaning with the different proposed cases. These cases are illustrated based on two states. The first state is defined when the $\textit{USV}_{cz}$ finishes the execution of its cleaning task. Thus, the second is presented when $\textit{USV}_{cz}$ breaks down during the execution of its task (i.e. its energy is average/low). Also, the situations are defined in the second state to search for a competent $\textit{USV}_{cz}$ which will replace the $\textit{USV}_{cz}$ in discharge state. To this end, the characteristics of $\textit{USV}_{cz}$ are collected and saved in each proposed case.

Case 1: the cleaning task is completed. When the $\textit{USV}_{cz}$ finishes its cleaning task, it informs $\textit{Leader}_{cz}$ by its mission completeness by sending a message. Upon reception of the message, $\textit{Leader}_{cz}$ informs the $\textit{USV}_{cz}$ to return to the base of life. Then, when $\textit{USV}_{cz}$ arrives at the base of life, it informs $\textit{Leader}_{cz}$ by sending a message. This latter stops saving the characteristics of this $\textit{USV}_{cz}$ , then, it sends $\textit{List}_{\textit{characteristics}}(\textit{Id}_{\textit{zone}}$ , $\textit{Id}_{\textit{USV CZ}}$ , $\textit{Dur}_{\textit{EC}}$ , $\textit{Cons}_{\textit{EC}}$ , $\textit{Dur}_{\textit{ED1}}$ , $\textit{Cons}_{\textit{ED1}}$ , $\textit{Dur}_{\textit{ED2}}$ , $\textit{Cons}_{\textit{ED2}})$ of $\textit{USV}_{cz}$ to its $\textit{Sup}_{mr}$ for recording. $\textit{Sup}_{mr}$ sends this list $\textit{List}_{\textit{characteristics}}$ to the $\textit{General}_{crd}$ for the record.

Case 2: The cleaning task is not completed and Energy ${}_{\textit{cap CZ}}$ is average. In this case, two situations are available:

The first situation is presented by Algorithm 5 where the energy capacity ( $\textit{Energy}_{\textit{cap CZ}}$ ) of $\textit{USV}_{cz}$ is greater at a given time than a $\textit{Threshold}_{\textit{average\_energycap}}$ , i.e. its energy capacity is average. So, $\textit{USV}_{cz}$ sends its $\textit{List}_{\textit{energy\_usv}}(\textit{Id}_{\textit{USVCZ}}$ , $\textit{Energy}_{\textit{capCZ}}$ ) to its $\textit{Leader}_{cz}$ to inform it that its energy is in an average level. After saving this list, $\textit{Leader}_{cz}$ $(\textit{USV}_{cz}\_\textit{discharge})$ sends this $\textit{List}_{\textit{energy\_usv}}$ and $\textit{Parameters}_{\textit{cleaning}}$ $(\textit{PosUSV,Cell}_{cz}$ , $\textit{Id}_{\textit{region}}$ , $\textit{Id}_{\textit{zone}}$ , $\textit{Position}_{\textit{zone}}$ , $\textit{Trajectory}_{\textit{zone}}$ , $\textit{Id}_{\textit{UAVMR}}$ ) to its $\textit{Sup}_{mr}$ . After a deadline of waiting, if $\textit{Sup}_{mr}$ does not receive another message (a detection message of $\textit{USV}_{cz}$ (free) in the same swarm by Leader ${}_{cz}$ $(\textit{USV}_{cz}{\_}\textit{discharge)})$ before exceeding this deadline, then it passes to the second situation (N.b. $\textit{Leader}_{cz}$ plays two roles at the same time in this situation; once $\textit{Leader}_{cz}$ $(\textit{USV}_{cz}{\_}\textit{discharge})$ and once $\textit{Leader}_{cz}$ ( $\textit{USV}_{cz}{\_}\textit{free}$ )). Otherwise, $\textit{Leader}_{cz}$ $(\textit{USV}_{cz}{\_}\textit{discharge})$ sends their $\textit{List}_{\textit{characteristics\_usvs}}$ with their $\textit{List}_{\textit{energy\_usv}}$ to its $\textit{Sup}_{mr}$ . This latter processes the received message and parses these lists. Then, it begins to select the competent USV that has a higher energy capacity. If it does not find any USV that can complete the task of $\textit{USV}_{cz}$ (discharge), then it moves to the second situation. Otherwise, Sup ${}_{mr}$ informs its $\textit{Leader}_{cz}$ $(\textit{USV}_{cz}{\_}\textit{free})$ by the competent USV with the complete cleanup parameters ( $\textit{Sup}_{mr}$ changes the new position of $\textit{USV}_{cz}$ (free), the new cell that $\textit{USV}_{cz}$ (free) will clean it with the same parameters $\textit{Id}_{\textit{region}}$ , $\textit{Id}_{\textit{zone}}$ , $\textit{Position}_{\textit{zone}}$ , $\textit{Path}_{\textit{zone}}$ , $\textit{Id}_{\textit{UAVmr}})$ . Then, $\textit{Leader}_{cz}$ $(\textit{USV}_{cz}{\_}\textit{free})$ returns the received message to the competent USV who presents $\textit{USV}_{cz}$ (free), and $\textit{Leader}_{cz}$ ( $\textit{USV}_{cz}{\_}\textit{discharge}$ ) or $\textit{Leader}_{cz}$ ( $\textit{USV}_{cz}{\_}\textit{free}$ ) waits for the energy capacity message of $\textit{USV}_{cz}$ (discharge) to become low in order to start $\textit{USV}_{cz}$ (free).

Algorithm 5: Situation 1
for all ((int)USV $\in$ swarm) do
if (CleaningTask_USV ! $=$ nul and ErgyCap_USV Threshold_Average) then
send(USV(discharge), Leader(USV_discharge), ‘ErgyCap_USV and Parameters_cleaning’);
save(Leader(USV_discharge), ‘ErgyCap_USV and Parameters_cleaning’);
send(Leader(USV_discharge), Sup(USV_discharge), ‘ErgyCap_USV and Parameters_cleaning’);
save(Sup(USV_discharge), ‘ErgyCap_USV and Parameters_cleaning’);
while (time ! $=$ nul) do
for all ((int)USV DirtyZone) do
if (USV $==$ free) then
inform(USV(free), Leader(USV_discharge $=$ free), ‘CleaningTask_USV $=$ nul’);
save(Leader(USV_discharge), USV(free), ‘List_USV(free)’);
end if
end for
send(Leader(USV_discharge), Sup(USV_discharge), ‘List_USV(free) and ListCharacteristics_usvs’);
analyze(Sup(USVdischarge), ‘List_USV(free) and ListCharacteristics_usvs’);
if (List_USV(free) ! $=$ nul) then
select(Sup(USV_discharge), USV_Competent);
prepare(Sup(USV_discharge), ‘Parameters_cleaning’);
send(Sup(USV_discharge), Leader(USV_discharge), ‘USV_Competent and Parameters_cleaning’);
send(Leader(USV_discharge), USV_Competent, ‘Wait ’);
else
pass(Sup(USV_discharge), Situation2);
end if
end while
pass(Sup(USV_discharge), Situation2);
end if end for

The second situation is illustrated by Algorithm 6. This situation shows the case where there is not a USV ${}_{cz}$ (free) in another dirty zone in the same region (following the first situation).

Algorithm 6: Situation 2
for all ((int)USV $\in$ swarm) do
$\ldots$
while (time ! $=$ nul) do
for all ((int) USV $\in$ AllDirtyZone(same region)) do
if (USV $==$ free) then
inform(USV(free), (int)Leader(USV_free), ‘CleaningTask_USV $=$ nul’);
save(Leader(USV_free), USV(free), ‘List_USV(free)’);
end if
end for
for all ((int) Leader(USVfree) $\in$ AllDirtyZone(same region)) do
send(Leader(USV_free), (int) Sup(USV_discharge), ‘List_USV(free) and ListCharacteristics_usvs’);
save(Sup(USV_discharge), ‘List_USV(free) and ListCharacteristics_usvs’);
end for
analyze(Sup(USV_discharge), ‘List_USV(free) and ListCharacteristics_usvs’);
if (List_USV(free) ! $=$ nul) then
select(Sup(USV_discharge), USV_Competent);
requestFill(Sup(USV_discharge), (int) General ${}_{crd}$ , ‘Parameters_cleaning’);
fill(General ${}_{crd}$ , ‘Parameters_cleaning’);
send(General ${}_{crd}$ , Sup(USV_discharge), ‘Parameters_cleaning’);
send(Sup(USV_discharge), Leader(USV_free), ‘USV_Competent and Parameters_cleaning’);
send(Sup(USV_discharge), Leader(USV_discharge), ‘USV_Competent’);
send(Leader(USV_free), USV_Competent, ‘Wait’);
else
pass(Sup(USV_discharge), Situation3);
end if
end while
pass(Sup(USV_discharge), Situation3);
$\ldots$
end for

The third situation is illustrated where if there is not a $\textit{USV}_{cz}$ (free) in the same region, then $\textit{Sup}_{mr}(\textit{USV}_{cz}{\_}\textit{discharge})$ sends a message to the $\textit{General}_{crd}$ to inform it for the need of a USV with cleanup settings. So, $\textit{General}_{crd}$ broadcasts the received message to the neighbors of $\textit{Sup}_{mr}(\textit{USV}_{cz}{\_}\textit{discharge})$ to select the $\textit{USV}_{cz}$ (free) that complete their cleaning tasks. If there is a $\textit{USV}_{cz}$ (free) or more, then each $\textit{Sup}_{mr}$ will emit the message (list of $\textit{USV}_{cz}$ (free) $+$ their features and capabilities of energies) to the $\textit{General}_{crd}$ (and of course through the messages received from their $\textit{Leader}_{cz}(\textit{USV}_{cz}{\_}\textit{free}))$ . Then, $\textit{General}_{crd}$ returns the received message to $\textit{Sup}_{mr}(\textit{USV}_{cz}{\_}\textit{discharge})$ . This latter will process messages received from each $\textit{Sup}_{mr}(\textit{USV}_{cz}{\_}\textit{free})$ , and then if there is not a $\textit{USV}_{cz}$ (free) who is able to finish the task, it passes to the fourth situation. Otherwise, it chooses the competent $\textit{USV}_{cz}$ (free) based on its energy, then it informs the $\textit{General}_{crd}$ by the competent USV and asks it to fill the trajectory box to the new zone in the cleanup parameter. $\textit{General}_{crd}$ processes the received message and fills the trajectory box in the field, then it informs the $\textit{Sup}_{mr}(\textit{USV}_{cz}{\_}\textit{free})$ by its competent USV with the full cleanup parameter. $\textit{Leader}_{cz}(\textit{USV}_{cz}{\_}\textit{free})$ waits for the message to launch $\textit{USV}_{cz}$ (free) and $\textit{Leader}_{cz}$ ( $\textit{USV}_{cz}{\_}\textit{discharge})$ expects the message of the energy capacity of $\textit{USV}_{cz}$ (discharge) becomes low.

The fourth situation is presented where there is not a free and competent USV to complete the task of USV in discharge state. This situation is illustrated by Algorithm 7.

Algorithm 7: Situation 4
for all ((int)USV $\in$ swarm) do
$\ldots$
send(Sup(USV_discharge), GeneralCrd, ‘Need a USV(free) and Parameters_cleaning’);
prepare(General ${}_{crd}$ , USV_competent in BaseofLife);
fill(General ${}_{crd}$ , ‘Parameters_cleaning’);
send(General ${}_{cr}$ , Sup(USV_discharge), ‘Id_USV ${}_{\textit{prepared}}$ and Parameters_cleaning’);
send(Sup(USV_discharge), Leader(USVdischarge), ‘Id_USV ${}_{\textit{prepared}}$ ’);
inform(General ${}_{c}$ , (int) USV(prepared), ‘Wait’);
$\ldots$
end for

Case 3: The cleaning task is not completed and Energy ${}_{\textit{capCZ}}$ is low. This case is realized for all the situations mentioned above (the continuation). It is executed when the energy of $\textit{USV}_{cz}$ (discharge) becomes low, i.e. the energetic capacity ( $\textit{Energy}_{\textit{capCZ}}$ ) of $\textit{USV}_{cz}$ is greater than a $\textit{Threshold}_{\textit{low\_energycap}}$ , so $\textit{USV}_{cz}$ (discharge) sends this information to its supervisor through its leader (all situations except the first situation: $\textit{USV}_{cz}$ (discharge) sends this information right to its leader and the leader informed to return to the base of life). Upon receipt of this information, $\textit{Sup}_{mr}(\textit{USV}_{cz}{\_}\textit{discharge})$ sends a message (Inform launch):

•

Directly to $\textit{Leader}_{cz}(\textit{USV}_{cz}{\_}\textit{free})$ to $\textit{USV}_{cz}$ (free): if this vehicle is owned in another zone in the same region (second situation).

•

$\textit{General}_{crd}$ to another $\textit{Sup}_{mr}(\textit{USV}_{cz}{\_}\textit{free})$ : to run the $\textit{USV}_{cz}$ (free) to prepare it by the parameters of cleaning it, so that it can calculate its trajectory and swim to its new dirty zone and clean it, and $\textit{General}_{crd}$ broadcasts this information to other $\textit{Sup}_{mr}$ (third situation).

•

$\textit{General}_{crd}$ to $\textit{USV}_{cz}$ (prepared): launch the $\textit{USV}_{cz}$ (prepared) which is in the base of life in order to prepare it by Parameters cleaning, and also so that it can calculate its trajectory and swim to its new dirty zone and clean the remaining cells (the fourth situation).

After, $\textit{Sup}_{mr}(\textit{USV}_{cz}{\_}\textit{discharge})$ inform the $\textit{USV}_{cz}$ (discharge) through its $\textit{Leader}_{cz}(\textit{USV}_{cz}{\_}\textit{discharge})$ to return, so that it can swim from its zone to the base of life (and to charge) (all situations except the first situation). $\textit{Leader}_{cz}(\textit{USV}_{cz}{\_}\textit{discharge})$ sends $\textit{List}_{\textit{characteristics\_usvs}}\textit{USV}_{cz}$ (discharge) to its supervisor. This latter sends this list to the $\textit{General}_{crd}$ for the record. Then, $\textit{Sup}_{mr}(\textit{USV}_{cz}{\_}\textit{discharge})$ informs the $\textit{Leader}_{cz}(\textit{USV}_{cz}{\_}\textit{free})$ to modify $\textit{List}_{\textit{characteristics\_usvs}}$ (thesecond and third situations) or prepare it for $\textit{USV}_{cz}$ (prepared) (the fourth situation), and $\textit{Leader}_{cz}(\textit{USV}_{cz}{\_}\textit{free})$ informs its $\textit{USV}_{cz}$ (free) to start the cleanup and modifies the $\textit{List}_{\textit{characteristics\_usvs}}$ of $\textit{USV}_{cz}$ (free) at the same time (first situation).

3.2 Logical formalization for cooperative hybrid approach

3.2.1 Conceptual model for planning

A conceptual model is a simple theoretical device to describe the main elements of a problem [8]. Most of the planning approaches described in [9] relied on a general model, which is common to other areas of computer science, namely the model of state-transition systems (also called discrete-event systems) [2, 3, 8, 9]. The technical words of this formalization (further details in [3]) are given in a general way.

Example 1. This example shows the state transition systems defined for three domains: UAV – Monitoring (or UAV – M domain applied to $\textit{UAV}_{mr}$ ), Swarm (USV) – Cleaning (or SUSV-C domain applied to $\textit{USV}_{cz}$ ) and USV (Substitute) – Cleaning (or USVS-C domain applied to $\textit{USV}_{cz}$ ). These domains are presented by the following Table 4.

Table 4
A detailed description of domains: UAV-M, SUSV and USVS-C

Domain	System representative	States	Actions	Example ‘state $\to$ action’
UAV – Monitoring (UAV-M) (Fig. 15)	A region involving two locations, a dirty zone, a base of life (a boat for example) and a $\textit{UAV}_{mr}$ .	s0 s1 s2 s3	stayinbase, flaputbase move1 $\wedge$ start-monitor, move2 $\wedge$ end-monitor, discover, undiscover	(s2, s3) $\to$ ‘discover’ (s1, s0) $\to$ ‘stayinbase’
Swarm (USV) – Cleaning (SUSV-C) (Fig. 16)	A region involves three locations, two dirty zones, a base of life, object of the crane type for picking up, putting down and releasing the $\textit{USV}_{cz}$ and $\textit{USV}_{cz}$ swarm.	s0 s1 s2 s3	take, put, start-clean, end-clean, move1, move2	(s0, s1) $\to$ ‘put’ (s3, s2) $\to$ ‘end-clean’
USV (Substitute) – Cleaning (USVS-C) (Fig. 17)	A region involves three locations, two dirty zones, a base of life, object of the crane type for picking up, putting down and releasing the USV ${}_{cz}$ , USVRcz and USVDcz.	s0 s1 s2 s3 s4 s5	takeD $\wedge$ move2, putD $\wedge$ putD, moveD1 $\wedge$ start-clean, moveD2 $\wedge$ end-clean, moveD1 $\wedge$ move2, moveD2 $\wedge$ move1, move1, move2	(s1, s2) $\to$ ‘moveD2 $\wedge$ endclean’ (s3, s4) $\to$ ‘move1’

3.2.2 A running example ‘UAV-Monitoring’, ‘Swarm(USV)-Cleaning’ and ‘USV (Substitute)-Cleaning’

The planning procedures and techniques are illustrated on an example of simple nontrivial execution that include three domains, namely UAV-M, SUSV-C and USVS-C domain. These domains complement each other. An abstract version of these domains can be defined to begin from ten complete sets of constant symbols [3], namely a set of: regions ( $R_{r})$ , locations for each region ( $L_{lr}$ ), base of life ( $B_{br}$ ), dirty zones ( $Z_{zl}$ ), monitoring vehicle ( $\textit{UAV}_{mr}$ ), cleaning vehicle swarm ( $\textit{USV}_{cz}$ ), cleaning vehicle in discharge state ( $\textit{USVD}_{cz}$ ), cleaning vehicle in free state (USVF ${}_{cz})$ , cleaning vehicle in prepared state ( $\textit{USVP}_{cz}$ ) and a set of cranes ( $C_{nb}$ ).

Figure 15.

A state transition system for the UAV – Monitoring (UAV-M) domain.

Figure 16.

A state transition system for the Swarm (USV) – Cleaning (SUSV-C) domain.

Thus, the topology of this domain is noted using the instances of predicates [3]: adjacent(E, E’) where localization $E=\{L_{lr},R_{r}\}$ is adjacent to $E=\{L_{lr}^{\prime},R_{r}^{\prime}\}$ , belong (C, L) where crane $C=C_{nb}$ belongs to location L and belong (B, R) where a base of life $B=\{B_{br}\}$ belongs to region $R=\{R_{r}\}$ . Also, the current configuration of the domains is denoted using instances of the following predicates, which represents the relationships that changes over time [3], namely, at(NAME, E) where, NAME $=$ NAME1{UAV ${}_{mr}$ , USV ${}_{cz}$ } and NAME2 {USVF ${}_{cz}$ , USVP ${}_{cz}$ , USVD ${}_{cz}$ , SUSV ${}_{cz}$ }, occupied (L), start-clean (NAME, Z), end-clean(NAME, Z), start-monitor(NAME, R), endmonitor(NAME, R), replace(NAME, NAME) notreplace (NAME, NAME), discover(NAME, Z), undiscover(NAME, Z), supervise (NAME, NAME), notsupervise(NAME, NAME), holding(C, NAME), stayinbase(NAME, B), flapoutbase(NAME, B). Possible actions for this domains [3] can be: start-clean(NAME, Z), end-clean(NAME, Z), startmonitor(NAME, R), end-monitor (NAME, R), discover(NAME, R, Z), undiscover(NAME, R, Z), stayinbase(NAME, B), flapoutbase(NAME, B), move(NAME, E1, E2), moveD(NAME, E1, E2), take(NAME, C, R), takeD(NAME, C, R). The action ‘moveD’ is executed in parallel with the action ‘start-clean’, ‘end-clean’ and ‘move’. The actions ‘takeD’ and ‘putD’ are executed in parallel with the action ‘move’.

Figure 17.

A state transition system for the USV (Substitute) – Cleaning (USVS-C) domain.

3.2.3 Set theoretic representation

There are three different ways to represent classical planning problems [8], namely: i) Set Theoretic Representation, ii) Classical Representation, iii) State-Variable Representation. This work focuses on the first representation (Set-Theoretic) to apply its planning on the proposed HA-UVC.

Example 2 This example illustrates a classical representation of the scenario ‘UAV-M domain’ and ‘SUSV-C domain combined with USVS-C domain’ which are described in Example 1:

Let $L=\{p_{1},\ldots,p_{n}\}$ be a finite set of proposition symbols:

For the UAV-M domain combined with SUSV-C domain: L $=$ {onbase, inair, onwatersurface, onzone, holding, at1, at2}, where:

inair means that NAME1.UAV ${}_{mr}$ drone is in the air;

onwatersurface means that NAME1.USV ${}_{cz}$ vehicle is on the water surface;

onbase means that NAME1. USV ${}_{cz}$ or NAME1. UAV ${}_{mr}$ or remains on the base of life;

onzone means that NAME1.USV ${}_{cz}$ is found in its dirty zone;

holding means that crane C is holding NAME1.USV ${}_{cz}$ vehicle;

at1means that the vehicle NAME1. USV ${}_{cz}$ or NAME1. UAV ${}_{mr}$ is at location 1; and

at2 means that the vehicle NAME1. USV ${}_{cz}$ or NAME1. UAV ${}_{mr}$ is at location 2.

For the SUSV-C domain combined with USVS-C domain: L $=$ {onbase, onwatersurface, onzone, holding, at1, at2, at3}, where:

onwatersurface means that NAME1.USV ${}_{cz}$ or NAME2 vehicle is on the water surface;

onbase means that NAME1.USV ${}_{cz}$ or NAME2 vehicle remains on the base of life;

onzone means that NAME1.USV ${}_{cz}$ or NAME2 vehicle is found in its dirty zone;

holding means that crane C is holding NAME1.USV ${}_{cz}$ or NAME2 vehicle;

at1 means that the vehicle NAME1.USV ${}_{cz}$ or NAME2 vehicle is at location 1;

at2 means that the vehicle NAME1.USV ${}_{cz}$ or NAME2 vehicle is at location 2; and

at3 means that the vehicle NAME1.USV ${}_{cz}$ or NAME2 vehicle is at location 3.

Each state S is a subset of L,

For the UAV-M domain combined with SUSV-C domain: S $=\{s_{0},\ldots,s_{6}\}$ , where:

$s_{0}=$ {on base, at1}; $s_{1}=$ {inair, at1}; $s_{2}=$ {inair, at2}; $s_{3}=$ { onwatersurface, at1};

$s_{4}=$ {onwatersurface, at2}, $s_{5}=$ {onzone, at2} and $s_{6}=$ {holding, at1}.

For the SUSV-C domain combined with USVS-C domain: S $=$ {s ${}_{0}$ ,…, s ${}_{6}$ }, where:

$s_{0}=$ {onbase, at1}; $s_{1}=$ {onwatersurface, at1}; $s_{2}=$ {onwatersurface, at2};

$s_{3}=$ {onwatersurface, at3}; $s_{4}=$ {onzone, at2}; $s_{5}=$ {onzone, at3} and $s_{6}=$ {holding, at1}.

Each action a $\in$ A is a triple of subsets of L, which a $=$ (precond(a), effects ${}^{-}$ (a), effects ${}^{+}$ (a)). The set precond (a) is called the preconditions of a, and the sets effects ${}^{+}$ (a) and effects ${}^{-}$ (a) are called the effects of a.

For the UAV-M domain combined with SUSV-C domain: A $=$ {flapoutbase, stayinbase, take, put, start-monitor, fin-monitor, discover, undiscover, start-clean, end-clean, supervise, notsupervise, move1, move2}, where:

stayintbase $=$ ({inair, at1}, {inair}, {onbase, at1});

take $=$ ({onwatersurface, at1}, {onwatersurface}, {holding, at1});

flapoutbase $=$ ({onbase}, {onbase}, {outbase});

put $=$ ({onbase, at1}, {holding}, {onwatersurface, at1});

move1start-monitor $=$ [({at1}, {at1}, {at2}) ({outbase, at1},{at1}, {outbase, at2})];

move2end-monitor $=$ [({at2},{at2}, {at1}) ({outbase, at2}, {outbase}, {onbase, at1})];

discover $=$ ({outbase, at2}, {outbase}, {at2});

undiscover $=$ ({outbase, at2}, {at2}, {outbase});

supervise $=$ ({outbase}, {outbase}, {at2});

notsupervise $=$ ({outbase, at2}, {outbase, at1}, {onbase});

start-clean $=$ ({underwater, atl}, {underwater}, {onzone, at2});

end-clean $=$ ({onzone, at2}, {onzone},{underwater, at2});

move1 $=$ ({at1}, {at1}, {at2}); and

move2 $=$ ({at2}, {at2}, {at1}).

For the UAV-M domain combined with SUSV-C domain: A $=$ {take, takeD, put,putD, start-clean, end-clean, replace, notreplace, move1, move2, moveD1, moveD2}, where:

take $=$ ({onwatersurface, at1}, {onwatersurface}, {holding, at1});

put $=$ ({onbase, at1}, {holding}, {onwatersurface, at1});

moveD1start-clean $=$ [({at1}, {at1}, {at2}) ({underwater, at1}, {underwater}, {onzone, at3})].

MoveD2end-clean $=$ [({at2}, {at2}, {at1}) ({onzone, at3}, {onzone}, {underwater, at3}).

replace $=$ ({underwater, at2}, {underwater}, {onzone, at3});

notreplace $=$ ({underwater, at2}, {at2}, {underwater});

moveD1move2 $=$ [({at2}, {at2}, {at3}) ({at3}, {at3}, {at2}) ].

moveD2move1 $=$ [({at3}, {at3}, {at2}) ({at2}, {at2}, {at3})].

takeDmove2 $=$ [({onwatersurface, at1}, {onwatersurface}, {holding, at1}), ({at3}, {at3}, {at2})].

move1putD $=$ [({at2}, {at2}, {at3}) ({holding, at1}, {holding}, {onwatersurface, at1});.

move1 $=$ ({at1}, {at1}, {at2}); and

move2 $=$ ({at2}, {at2}, {at1}).

4. Simulation

An illustrative example with two scenarios for dirty zones (with a strong degree of dirt and a low degree of dirt) is provided to simulate the functioning of the proposed approach. Two trajectory planning solutions are given for $\textit{USV}_{cz}$ swarm, namely the modified- GA and the proposed CCA. The following measures allow to highlight the contributions of the proposed HA-UVC: displacement energy consumption between the base of life and dirty zone, displacement-cleaning energy consumption in the dirty zone and total energy consumption of $\textit{USV}_{cz}$ swarm. Before starting the experiments, the virtual environment and its discretization are described.

4.1 Discretization of the virtual environment

Figure 18 illustrates a simplistic example of the virtual environment of the Oran Coast (Fig. 2). The maritime space of a region ‘Maritime Region’ is assumed to includes two polluted zones ‘Z1 and Z2’, three obstacles ‘O1, O2 and O3’ and a central unit which consists of a base of life. These dirty zones are proposed according to the degrees of dirt in this region, namely: Z1 and Z2 that respectively represent the low and strong degrees of dirt. After defining the degrees of dirt randomly for this environment with two different zones, the discretization step is activated. A matrix is obtained, where the black cells represent the dirty zones. While the obstacles are illustrated by grey cells (see Fig. 19).

Figure 18.

Example of a simplistic virtual environment.

Figure 19.

Matrix of discretization of region.

4.2 Results

Before starting the simulations of the proposed scenarios, the assumptions and parameters are presented in this section that are used in this work with the two solutions for trajectory planning. These solutions were implemented by using a modified GA and a proposed CCA. These two algorithms are programmed via an open source Java. The simulations were run on a PC with a Core (TM) i5-5200U @ 2.20 GHz running the Windows 7 Professional Operating System.

The proposed HA-UVC was implemented for a maritime region, where containing strong (hard) obstacles. This region includes a surveillance vehicle ( $\textit{UAV}_{mr})$ , a cleaning vehicle swarm ( $\textit{USV}_{cz}$ ), two dirty zones and three obstacles. Based on a metric map (Grid) of 29 $\times$ 10 cells, the $\textit{UAV}_{mr}$ captures data from its region. These data are measured against a color metric. These colors are partitioned on four intervals [0, 25], [25, 50], [50, 75], [75, 100] which they involve a white cell (weak dirt), light brown (average dirt), dark brown (medium-strong dirt), and black (strong dirt). $\textit{UAV}_{mr}$ classify this data (degrees) of the cells by comparing the predefined threshold value (equal to 25% of the degree of dirt) with the $\textit{Degree}_{cel}$ of each cell. The number of $\textit{USV}_{cz}$ containing the swarm used in the simulations is varied from 3 $\textit{USV}_{cz}$ to 7 $\textit{USV}_{cz}$ . Each $\textit{USV}_{cz}$ swarm planned its movement based on optimal trajectories to reach its dirty zone and clean it. These trajectories are built based on a modified GA, or a proposed CCA. The modified GA was executed by each leader of swarm $\textit{USV}_{cz}$ or $\textit{Leader}_{cz}$ starts with a $\textit{Pos}_{\textit{start}}=$ 0 and the fourth end position in $\textit{List}_{\textit{PosE}}$ . The population was composed of four individuals and the maximum number of generations equaled to four because the obtained solution from the third generation was identical to that of the fourth generation compared at a tolerated threshold. Moreover, the initial population was randomly generated where each individual (trajectory) has a start and end position. Besides, the tournament selection has been applied to find the individual (trajectory) who has a weak fitness. This fitness function uses two balancing parameters: A $=$ 0.02, B $=$ 0.01. The cross was used on this individual (the description cited above). The mutation was not applied in this work because it was noticed that the two new children (trajectories) are 100% correct at the end of each generation. When the $\textit{Leader}_{cz}$ finds a position, it shares this one with its followers. In addition, the proposed CCA algorithm was used to find the best trajectory where each leader of a $\textit{USV}_{cz}$ swarm can find a trajectory from a fixed starting position equal to 0 to a search for an end position (arrival at the dirty zone). Thus, these traversed positions are shared with the $\textit{USV}_{cz}$ of each swarm.

Figure 20.

Displacement energy consumption (DEC) in a zone with a low degree of dirt.

The cost value between the cells in the grid is randomly generated between 5 and 10. The energy required for the $\textit{USV}_{cz}$ of swarm to turn left/right from its position to another position is 0.2% and 0.05% to continue directly. When the $\textit{USV}_{cz}$ swarm arrives at its zone, it starts cleaning dirty cells based on the proposed Algorithm 4. Also, the proposed energy required to clean a black cell is 0.9%, for a medium-high dirt cell of 0.5% and for an average dirt cell of 0.2%. A formula was developed to calculate the total energy consumption (TEC) of each $\textit{USV}_{cz}$ swarm: TEC $=$ DEC $+$ D-CEC. This formula groups the displacement energy consumption of the base of life to the dirty zone (DEC), the displacement and cleaning energy consumption in the dirty zone (D-CEC).

4.2.1 Scenario 1: Zone (1) with a low degree of dirt

This scenario presents the simulations results for a dirty zone with low degrees of dirt. These results give the curves of displacement energy consumption (DEC), displacement plus cleaning energy consumption in the zone (D-CEC) and total energy consumption (TEC) of $\textit{USV}_{cz}$ swarm for the two proposed solutions.

Result of displacement energy consumption (DEC): Figure 20 shows the results of DEC of each $\textit{USV}_{cz}$ swarm from the base of life to its dirty zone. The modified GA was compared with the proposed CCA with in terms of DEC. It can be noted that the DEC curve of proposed CCA is less than the DEC curve of the modified GA. Therefore, the $\textit{USV}_{cz}$ swarm consumes less energy to plan its trajectory through using the proposed CCA algorithm compared to the modified GA.

Figure 21.

Displacement plus cleaning energy consumption (D-CEC) in a zone with a low degree of dirt.

Result of displacement-cleaning energy consumption (D-CEC): Figure 21 shows a simulation to evaluate the $\textit{USV}_{cz}$ swarm behavior by its D-CEC in its dirty zone. It can be noted that the proposed CCA D-CEC decreases when the swarm is composed of 3 and 4 $\textit{USV}_{cz}$ comparing to the second curve. On the other hand, it increases, when the swarm contains 4 to 6 $\textit{USV}_{cz}$ , and modified GA increases in a fast way when the swarm includes 7 $\textit{USV}_{cz}$ . Thus, the modified GA is generally better than the proposed CCA regarding the moving and cleaning for the $\textit{USV}_{cz}$ swarm in an zone with low degrees of dirt.

Result of total energy consumption (TEC): the two previous results were combined to calculate the TEC based on the two proposed algorithms. Figure 22 shows that the TEC curve of proposed CCA is below the TEC curve of modified GA. Therefore, the proposed CCA proposal consumes less energy in comparison to the modified GA with an average gain of 3.74% in a zone of low degrees of dirt.

Figure 22.

Total energy consumption (TEC) with in a zone with a low degree of dirt.

Figure 23.

Displacement energy consumption (DEC) in a zone with a strong degree of dirt.

4.2.2 Scenario 2: Zone (2) with a strong degree of dirt

The second scenario shows the simulations results for a dirty zone with strong degrees of dirt. These results give the curves of displacement energy consumption (DEC), displacement plus cleaning energy consumption (D-CEC), and total energy consumption (TEC) of $\textit{USV}_{cz}$ swarm for the two proposed solutions.

Result of displacement energy consumption (DEC): Figure 23 shows the results of the displacement energy consumption of each $\textit{USV}_{cz}$ swarm from the base of life to its dirty zone. The modified GA was compared with proposed CCA with respect to this DEC. It can be noted that the DEC curve of proposed CCA is less than the DEC curve of the modified GA. Therefore that the $\textit{USV}_{cz}$ consumes less energy in its displacement by using the proposed CCA algorithm compared to the modified GA.

Result of displacement-cleaning energy consumption (D-CEC): Figure 24 presents a simulation that evaluates the $\textit{USV}_{cz}$ swarm behavior in the D-CEC in a dirty zone with strong dirty degrees. It can be noted that the D-CEC curve of proposed CCA and the D-CEC curve of modified GA are almost equiva-

Table 5
Comparison between several related works

Criteria /work	System type	Main objective	Used type of method	Gear type	Environment	Algorithm /Functions	Metrics to measure	Simu-lator	Robu-stness	Feasi-bility	Scala-bility	Stabi-lity	Effecti-veness
[16]	Online real-time path planning	Plan and predict a collision-free trajectory of moving obstacles	Path planning based on polar coordinates space	One mobile robot	Uncertain dynamic (2D navigational Space)	Real-time path planning, obstacle avoidance strategy, reachability and security	Determine the desirable direction of robot movement	Auto-regre-ssive (AR) model	–	$\surd$	–	$\surd$	$\surd$
[5]	Backs-tepping approach	Control to follow both the curve and the straight line trajectory	Trajectory tracking based on underactuated control	One USV	–	Lyapunov theory and Barbalat’s Lemma	Tracking velocities errors, control USV input, tracking errors of position (shapes)	FLUENT software	–	–	–	$\surd$	$\surd$
[4]	Exploratory path planning System	Find a path goal	GA	One robot	–	C, A, GA	Distance traveled by Robots	P-S Tools	–	–	–	–	–
[7]	UAV-Assisted Disaster Management	Identifies main applications and open research issues of UAV networks and UAV-assisted disaster management	–	UAV	–	WSN, cellular network	–	Framework of the project “IMATISS” (Inundation Monitoring, Alarm Technology In a System of SystEms)	–	–	$\surd$	–	–

Table 5, continued
Criteria /work	System type	Main objective	Used type of method	Gear type	Environment	Algorithm /Functions	Metrics to measure	Simu-lator	Robu-stness	Feasi-bility	Scala-bility	Stabi-lity	Effecti-veness
[15]	Evolutionary approach to coverage region planning	Find a path avoiding obstacles	GA based-path planning	Vacuum cleaner robot	Dynamic	GA, ORD, SCD	Length of the trajectory, the number of turns, the cells revisited	Imple-mented in C #	$\surd$	–	$\surd$	–	$\surd$
[2]	Centralized autonomous cooperation system	Reduce the pollution level, manage the fault tolerance problem of vehicles	UAV-based monitoring, USV-based cleaning	UAV, USV	Maritime/Atmosphere space	Checking the existence of vehicles, recovery phase, collect analyze the zones, calculate the number (USV)	TEC, average of ECC, number of cleaned cells by selected USV	Imple-mented in java	$\surd$	–	$\surd$	–	–
[11]	Studies of optimal approaches to trajectory planning	Find an optimal path planning of unmanned surface vehicles	Optimal trajectory planning approaches for a USV, a USV swarm	USV	Static, dynamic	ROA, DOA, SLAM techniques	–	–	$\surd$	$\surd$	–	–	–

Table 5, continued
Criteria /work	System type	Main objective	Used type of method	Gear type	Environment	Algorithm /Functions	Metrics to measure	Simu-lator	Robu-stness	Feasi-bility	Scala-bility	Stabi-lity	Effecti-veness
[3]	Cooperative hybrid architecture	Reduce the level of pollution, manage the problem of trajectory planning, fault tolerance	UAV-based monitoring, USV swarm-based cleaning, trajectory planning based on a P-GA	Semi autono-mous UAV, USV Swarm	Maritime/Atmosphere space	Calculate the needed number of USVcz, proposed GA, USVs placement to clean an zone, nodirty function	Average of TEC of USVcz swarm, average of TEC of USVcz selected	Imple-mented in java	$\surd$	–	$\surd$	–	–
[1]	Evaluating system performance in a post-disaster application	Monitor, map an affected area during a disaster by avoiding	Flight plan based on HITL	Multi-rotor, fixed-wing UAV	La ville de Sendai au Japon	Artificial intelligence algorithms	Relations among number of flight strips, area, flight height, photographs investigated by different interpolation	HITL	–	$\surd$	–	–	–
[6]	Development of Surface Cleaning Robot	Real-time monitoring of water cleanliness	Surface cleaning, purification process, water quality control	Waste Hunter Surface Robot	Three shallow water locations	Several functions on the mobile app	Distance, time, movement speed et connectivity of robot	Waste Hunter Surface Robot model	–	–	–	–	–

Table 5, continued
Criteria /work	System type	Main objective	Used type of method	Gear type	Environment	Algorithm /Functions	Metrics to measure	Simu-lator	Robu-stness	Feasi-bility	Scala-bility	Stabi-lity	Effecti-veness
[14]	A multi-domain inversion strategy based on CGA	Improve local search capability, with an excellent individuals for a path	An Improved Genetic Algorithm for Path-Planning	USV	Real maritime	CGA, SDGA, MDIGA, DDGA	Length of the path, the cost in time, the speed of convergence of a path	Monte-Carlo	$\surd$	$\surd$	–	–	$\surd$
[17]	New coordinate system for path planner	UAV Offline 3D path planner	EDA- based path planner using a new coordinate system	UAV	Real space of uncertain mission (using Air Defense Units (ADUs))	EDA, Cartesian coordinate system, polar coordinate system	Efficiency, improvement of a new coordinate system compared to other Cartesian, polar systems	Framework of EDAs based path planners	$\surd$	–	$\surd$	$\surd$	$\surd$
[21]	Prototype of a USV	Navi-gation, locali-zation the gas source of an oil spill	Research the road to get to the gas source (navigation)	One USV	Sea	Gas sensors (concentration), fuzzy logic controller	USV speed, gas sensing on the USV, error rate in the direction of the goal	USV Prototype	–	–	–	–	$\surd$

Table 5, continued
Criteria /work	System type	Main objective	Used type of method	Gear type	Environment	Algorithm /Functions	Metrics to measure	Simu-lator	Robu-stness	Feasi-bility	Scala-bility	Stabi-lity	Effecti-veness
[22]	New robotic System swarm	Oil Spill Cleaning Up	Sensing, localization, navigation, collection an oil spill	Swarm of ship robots	Sea	Navigation operation of the swarm, Cleaning method	Consum-ption of money, time	Robot design(GPS module, communication, etc.)	$\surd$	–	–	–	$\surd$
HA-UVC	Cooperative hybrid approach	UAV-based monitor region, swarm based-cleaning dirty zone, plan trajectory, static obstacle avoidance, fault tolerance	Modified- GA, proposed CCA	Semi autono-mous UAV, USV swarm	Atmosphere/ Maritime space (zone with strong, low dirt )	Calculate the needed number of USV, modified GA, proposed CCA, cleaning algorithms	DEC, D-CEC, TEC of USV swarm	Imple-mented in java	$\surd$	–	$\surd$	–	–

Figure 24.

Displacement plus cleaning energy consumption (D-CEC) in a zone with a strong degree of dirt.

Figure 25.

Total energy consumption (TEC) with in a zone with a strong degree of dirt.

lent in D-CEC consumption. In addition, the amount of energy consumed by a swarm of 5 and 6 $\textit{USV}_{cz}$ using the modified GA increases rapidly than the D-CEC curve of proposed CCA. Thus, the modified GA is generally better than the proposed CCA in the moving and cleaning of the $\textit{USV}_{cz}$ swarms in a zone with strong degrees of dirt.

Result of total energy consumption (TEC): the two previous results were used to calculate the TEC based on the two proposed algorithms. Figure 25 shows that the TEC curve of proposed CCA is below the TEC curve of modified GA. Therefore, the proposed CCA proposal consumes less energy than the modified GA with an average gain of 5.52% in a zone of strong degrees of dirt.

5. Critical evaluation

This section positions a HA-UVC in relation to the literature review cited above (Section 2). Each mentioned study has its own characteristics/parameters that differentiate it from others. Table 5 presents a comparative study of these studies and the benefits of the proposed HA-UVC.

In this proposed hybrid, a method of cooperation and coordination between a general coordinator, a semi-autonomous unmanned ariel vehicle (UAV ${}_{mr})$ and a semi-autonomous surface vehicle swarm ( $\textit{USV}_{cz}$ ) was proposed to accomplish the task of cleaning dirty ocean zones contrary to the work of [2]. The authors of [2] propose a centralized decision-making approach for air-sea cooperation and coordination, which consists of a $\textit{UAV}_{mr}$ to monitor an ocean region and a $\textit{USV}_{cz}$ to clean a dirty zone. In addition, the article of [1] proposed a two model system of (multirotor and fixed-wing) common with different camera specifications to map an affected area during a disaster in Japan. This system is feasible compared to the proposed HA-UVC system but it is robust in fault management like the HA-UVC system and the other systems of [2, 3, 11, 14, 15, 17, 22]. Thus, a Waste Hunter Surface robot cleaning of rivers was developed by the authors of [6] which allowed a real-time monitoring of the cleanliness of the water. It has a flexible design that is built by several functions on the mobile application as the wireless controllers with WIFI have been used to communicate between the user and the robot.

The communication link of IEEE.802.11a standard is used between the UAV and the general coordinator, and another of IEEE.802.11b standard to connect the UAV with the USV swarm with respect to network cited in the paper of [7]. During the test, the Waste Hunter Surface is examined with four motion conditions, namely: forward, backward, left and right motion like the $\textit{USV}_{cz}$ of HA-UVC and robot of [4] except it does not have a motion backward.

The design of UAV flight plans used in HA-UVC is based on a map (square-shaped 2D grid), onboard sensory sensors and two movements, namely: rectilinear and sweeping. With a sweeping motion, it prepares a maritime space map of its region (lower level) with its captured data. On one hand, the flight plan proposed in [1] is based on the information recorded after the disaster and the mapping capabilities of UAVs. The color was chosen as a degree of dirt from the dirty zones, so that UAV could detect them and start the cleaning as it is mentioned in [2]. Thus, the robot of [6] has a function to control the data quality (PH value) of the water. On the other hand, the developed USV [21] locates the gas source in the sea by two on-board gas sensors. The latter system is effective in performing its tasks like the system of [5, 14, 15, 16, 17, 21, 22] compared to HA-UVC.

Subsequently, UAV sends its environment card to its $\textit{General}_{crd}$ after the discretization. After an analysis of the data collected, the $\textit{General}_{crd}$ assigns the scanned map to the USV swarm to clean each dirty zone. This swarm plans its movement through a proposed solutions for trajectory planning from the base of life to the dirty zone. The first solution is based on a modified GA compared to the genetic algorithms proposed in [2, 4, 11]. While the second proposed solution was based on Cartesian coordinates in contrast to the coordinates proposed in the work of [5, 16, 17] which allows stability in its system and not in HA-UVC. The coordinates of [16] are used in 2D path planning in the presence of an obstacle as coordinates of the global environment by positions of the starting point, goal point, and the real-time location of the mobile robot, so that global information can be considered in every-time planning window. Thus, a rotation of the Cartesian coordinate system [17] is applied in a new coordinate system to build a new route planner and facilitate local modification by the UAV. Moreover, the Cartesian coordinate of [5] is applied to know the centre of mass of a USV to follow the trajectory. The swarm is moved in a square grid (space 2 D) discretized by the supervisor of the UAV. This grid is built by $\textit{USV}_{cz}$ positions or cities according to the applied solution (modified GA/proposed CCA). Alternatively, the work of [15] uses a grid is modelled on a disk shape to represent the robot position.

In addition, the swarm applies both solutions to find an effective trajectory from its initial position to its objective with less distance and minimum obstacles as the effective global path with a short distance, a minimum of turns, and repeated clean positions cited in [15]. Another MDIGA algorithm presented in [14], in order to find a shorter optimal path, a faster convergence speed, and a better robustness than the other algorithms (CGA, SDGA, DDGA). The fitness function of the modified GA is calculated in relation to the energy consumed between the travelled positions and the consumed energy by all the performed actions (turn left/right or continue directly) by the USV. In contrast, the fitness function of [4] is based on the distance travelled and the Euclidean distance from the goal. The tournament selection method [20] and the one-point cross have been applied in the modified GA and GA of [2, 4, 14]. The tournament is not mentioned in the work [14]. However, the crossover has been presented with different techniques. The mutation was not applied in this work compared to other work [4, 2, 14] because it was noticed that the two new children (trajectories) are 100% correct at the end of each generation (after the crossover step).

Furthermore, The static obstacle avoidance method of $\textit{USV}_{cz}$ swarm is proposed in this work where the positions obstacles are known by the $\textit{USV}_{cz}$ via the map discretized by $\textit{UAV}_{mr}$ . On other hand, the positions of moving obstacles are sampled by the robot’s sensor system, and the sampling position information on dynamic obstacles are treated as instantly static in [16]. With these current sampling positions, an autoregressive (AR) model predicts the future positions of the obstacles in the next sampling period. Then, the trajectory of the robot is planned with such predicted positions. The second solution is based on Cartesian coordinates to plan a trajectory and to find the new direction contrary to the polar coordinates used in the approach [16]. Additionally, a new state feedback based on back stepping control algorithm of an under actuated unmanned surface ship was proposed in [5]. This algorithm allows a controller to track both the curve path and the straight line trajectory with great accuracy. The controller for $\textit{USV}_{cz}$ trajectory tracking is proven by Lyapunov’s Theory and Barbalat’s Lemma. For this purpose, a dirty zone cleaning algorithm (Algorithm 4) was applied to the $\textit{USV}_{cz}$ swarm where each swarm can at the same time move and clean its dirty cells without specifying how to remove the dirt (the oil spill). On the other hand, the swarms of labor robots [22] can place the barge with oil suction equipment and move it to another location to remove the oil more safely.

The two proposed solutions for trajectory planning were also compared with respect to the two different scenarios, namely zone with a strong degree of dirt and a zone with a low degree of dirt. Each swarm of $\textit{USV}_{cz}$ measures its amount of energy by an energy threshold unlike $\textit{USV}_{cz}$ of [2], which uses its own LEDs, then sends its information to its leader. Thus, the scenarios of HA-UVC were simulated according to three metrics: energy consumption of displacement of the base of life towards the dirty zone, energy consumption of displacement and cleaning in the dirty zone and total energy consumption. On the other hand, the metrics measured in [2, 3] are the average of the total energy consumption of USV swarm and the average of total energy consumption of the $\textit{USV}_{cz}$ selected [2], and the total energy consumption of $\textit{USV}_{cz}$ selected, the average of cleaning energy consumption and the number of cells cleaned by the $\textit{USV}_{cz}$ selected [3].

To this end, the simulation results obtained confirmed the choice to use both solutions of planning trajectory, and the proposed HA-UVC allows the scalability of its system like the other systems mentioned in [2, 3, 7, 15, 17]. Thus, the proposed CCA algorithm has tremendously given encouraging and boosting results compared to the modified GA.

6. Conclusion

This article presented a hierarchical decision system for a HA-UVC. This HA-UVC represents the cooperation of several semi-autonomous unmanned vehicles (a $\textit{UAV}_{mr}$ and a $\textit{USV}_{cz}$ swarm) and their coordination by a general coordinator. It also helps to manage the problem trajectory of $\textit{USV}_{cz}$ swarm and fault-tolerance planning in performing their tasks. The proposed HA-UVC uses a $\textit{UAV}_{mr}$ for each maritime region and a $\textit{USV}_{cz}$ swarm to clean dirty zones. A method has been proposed for the displacement of $\textit{UAV}_{mr}$ in its region in order to detect the data (degrees of dirtiness). These data are processed based on the color of the water. Then, two solutions were proposed: ‘modified GA’ and ‘proposed CCA’ for $\textit{USV}_{cz}$ swarm to plan the trajectory from the base of life to its dirty zone. When this swarm arrives at the dirty zone, it begins to move and clean dirty cells based on a proposed Algorithm 4. $\textit{USV}_{cz}$ swarm measures its amount of energy according to an energy threshold, and then sends its information to its leader $\textit{Leader}_{cz}$ . $\textit{Leader}_{cz}$ returns its data to its $\textit{Sup}_{mr}$ to find a competent $\textit{USV}_{cz}$ . $\textit{Sup}_{mr}$ launches the competent $\textit{USV}_{cz}$ that will replace the $\textit{USV}_{cz}$ in a discharge state when the amount of energy of the latter becomes low. The proposition is formalized by means of a set theoretic representation.

Two scenarios were proposed to simulate this proposal, namely a zone with strong degrees of dirt and a zone with low degrees of dirt. The measurements measured are the displacement energy consumption (DEC), the displacement-cleaning energy consumption (D-CEC), and the total energy consumption (TEC) of each $\textit{USV}_{cz}$ swarm. The situation in which $\textit{USV}_{cz}$ breaks down was not simulated in this article (a simulation was performed in [2, 3]). The realized HA-UVC shows that the proposal method applied with the proposed CCA makes it possible to find an optimal trajectory avoiding static obstacles and gives encouraging results compared to the modified GA.

This work did not address the failure problem of central unit (i.e. the $\textit{General}_{crd}$ ) and the $\textit{UAV}_{mr}$ . Accordingly, as future work, the authors intend to develop a approach HA-UVC to address this problem. In addition, the authors aim to study the influence of speed variations in the monitoring, cleaning, and trajectory planning step. Furthermore, the authors would intend to build a decentralized architecture with a task planner and compare hybrid and centralized approaches. Besides, the authors would to propose to assign a cluster of drones for each region in a complex environment through solid obstacles to carry out experiments on real data. Then, the authors would like to improve the data processing part (processing of recovered images) of the ocean region captured by the $\textit{UAV}_{mr}$ supervisor by basing, for example, on unsupervised classification methods such as: the Kmeans method, ClusteringLARgeApplication (CLARA), AGglomrativeNESting (AGNES), DIvisiveANAlysing (DIANA), etc. To this end, the authors will consider the use of other criteria to determine if an area is dirty, such as chemical criteria and other indicators of water pollution (temperature and dissolved oxygen, suspended sediments, and hydrogen potential, etc.) [13].

Footnotes

Authors’ Bios

Salima Bella is a PhD candidate in the Department of Computer Science, Faculty of Exact and Applied Sciences, University Oran1 in Algeria. She received her M.S. degree in 2015 from the University Oran1. Her current research interests are distributed system, cloud computing, multi-agent systems, robotics mobile, decision support.

Assia Belbachir received a BEng in Computer Engineering (Algeria, 2006), a MSc in Computer Science from UCBL (France, 2007), and a PhD in AI from INPT, LAAS-CNRS (France, 2011). She worked as a postdoc at IFSTTAR (Paris, France) on the evaluation of advanced assistance driving systems. Then, she worked as a postdoc at ESIGELEC (Rouen, 2012) on the multi-robots cooperation. She is actually working at IPSA as a researcher on cooperative drones and also an associate professor at LIP6, team SMA. Her research interests lie in autonomous robots, cooperative systems, task planning and machine learning.

Ghalem Belalem Graduated from Department of computer science, Faculty of exact and applied sciences, University of Oran1 Ahmed Ben Bella, Algeria, where he received PhD degree in computer science in 2007. His current research interests are distributed system; grid computing, cloud computing, replication, consistency, fault tolerance, resource management, economic models, energy consumption, Big data, IoT, mobile environment, images processing, Supply chain optimization, Decision support systems, High Performance Computing.

References

Aljehani

and Inoue

, Performance evaluation of multi-UAV system in post-disaster application: validated by HITL simulator, IEEE Access 7 (2019), 64386–64400.

Bella

Belbachir

and Belalem

, A centralized autonomous system of cooperation for uavs- monitoring and usvs-cleaning, International Journal of Software Innovation (IJSI) 6(2) (2018), 50–76.

Bella

Belbachir

and Belalem

, A hybrid architecture for cooperative UAV and USV swarm vehicles, in: International Conference on Machine Learning for Networking (MLN’2018), Paris, France, 2018.

de Carvalho Santos

Toledo

C.F.M.

and Osório

F.S.

, An exploratory path planning method based on genetic algorithm for autonomous mobile robots, in: IEEE Congress on Evolutionary Computation (CEC), Sendai, Japan, 2015, pp. 62–69.

Dong

Wan

Liu

and Zhang

, Trajectory tracking control of underactuated USV based on modified backstepping approach, International Journal of Naval Architecture and Ocean Engineering 7(5) (2015), 817–832.

Dahlan

M.Q.

Kadir

H.A.

Isa

Ambar

Arshad

M.R

and Noh

M.M.

, Development of surface cleaning robot for shallow water, in: Proceedings of the 10th National Technical Seminar on Underwater System Technology 2018, Springer, Singapore, 538 (2019), 45–54.

Erdelj

and Natalizio

, UAV-assisted disaster management: Applications and open issues, in: IEEEInternational Conference on Computing, Networking and Communications (ICNC), Kauai, HI, USA, 2016, pp. 1–5.

Ghallab

Nau

and Traverso

, Automated planning: theory & practice, Edition Elsevier, 2004.

Ghallab

Nau

and Traverso

, Automated planning and acting, Cambridge University Press, 2016.

10.

Oil tanker spill statistics 2018, https://www.itopf.org/knowledge-resources/data-statistics/statistics, Accessed 1 June 2019.

11.

Singh

Sharma

Hatton

and Sutton

, Optimal path planning of unmanned surface vehicles, Indian Journal of Geo-Marine Sciences (IJMS) 47 (2018), 1325–1334.

12.

Roomba-Like robots dropped by helicopter could clean up oil spills, https://www.treehugger.com/clean-technology/floating-drone-cleans-oil-oceans.html, Accessed 25 January 2017.

13.

Water quality indicators, http://www.ramp-alberta.org/river/water+sediment+quality/chemical.aspx, Accessed 20 November 2017.

14.

Xin

Zhong

Yang

Cui

and Sheng

, An improved genetic algorithm for path-planning of unmanned surface vehicle, Sensors 19(11) (2019), 2640.

15.

Yakoubi

M.A.

and Laskri

M.T.

, The path planning of cleaner robot for coverage region using genetic algorithms, Journal of Innovation in Digital Ecosystems 3(1) (2016), 37–43.

16.

Zhuang

H.Z.

S.X.

and Wu

T.J.

, On-line real-time path planning of mobile robots in dynamic uncertain environment, Journal of Zhejiang University-SCIENCE A 7(4) (2006), 516–524.

17.

Yang

Tang

and Lozano

J.A.

, Estimation of distribution algorithms based unmanned aerial vehicle path planner using a new coordinate system, in: IEEE Congress on Evolutionary Computation (CEC), Beijing, China, 2014, pp. 1469–1476.

18.

Moujahed

Simonin

and Koukam

, Location problems optimization by a self-organizing multiagent approach, Multiagent and Grid Systems 5(1) (2009), 59–74.

19.

Bella

Belbachir

and Belalem

, A hybrid air-sea cooperative approach combined with a swarm trajectory planning method, Paladyn, Journal of Behavioral Robotics 11(1) (2020).

20.

Amédée

, Algorithmes génétiques, Master’s thesis, University of Nice, France, 2004 (In French).

21.

Putra

M.L.R.

Rivai

and Irfansyah

A.N.

, unmanned surface vehicle navigation based on gas sensors and fuzzy logic control to localize gas source, Journal of Physics: Conference Series 1201(1) (2019), 012001.

22.

Zahugi

E.M.H.

Shanta

M.M.

and Prasad

T.V.

, Oil spill cleaning up using swarm of robots, in Advances in Computing and Information Technology, Springer, Berlin, Heidelberg, 2013, pp. 215–224.

HA-UVC: Hybrid approach for unmanned vehicles cooperation

Abstract

Keywords

1. Introduction

3. Proposed cooperative hybrid approach and formulation

3.1 Proposed cooperative hybrid approach

3.1.1 Architecture of the system

Table 1 Descriptive table of the different vehicles

Table 2 Descriptive table of defined agents

3.2.1 Conceptual model for planning

Table 4 A detailed description of domains: UAV-M, SUSV and USVS-C

4. Simulation

4.1 Discretization of the virtual environment

Table 5 Comparison between several related works

6. Conclusion

Footnotes

Authors’ Bios

References

Table 1
Descriptive table of the different vehicles

Table 2
Descriptive table of defined agents

Table 4
A detailed description of domains: UAV-M, SUSV and USVS-C

Table 5
Comparison between several related works