Hybrid fuzzy response threshold-based distributed task allocation in heterogeneous multi-robot environment

Abstract

Task allocation is a vital challenge in a multi-robot environment. A hybrid fuzzy response threshold-based method is proposed to address the problem of task allocation in a heterogeneous mobile robot environment. The method follows a distributed task allocation approach where every robot chooses its task and performs it, resulting in concurrent execution. The algorithm uses a fuzzy inference system to determine the capability of the robot to carry out a task. Then, the robot employs the response threshold model, utilizing the obtained capability to decide on the task to complete. The objective here is to maximize the tasks completed with the resources available while balancing the affinity with which the task is done. The proposed algorithm is initially applied to the static scenario where there is no failure among the mobile robots. The algorithm is then improved to run in the dynamic scenario to study the effect on the allocation. The proposed algorithm is empirically evaluated in simulation for multiple runs under different environment instances. The results show a good increase in tasks performed successfully across all the instances in static and dynamic scenarios. The proposed algorithms are validated using FireBird V mobile robots in an experimental environment.

Keywords

Multi-robot environment hybrid fuzzy decision-making response threshold model task allocation ambient intelligence

1. Introduction

Multi-robot systems provide better abilities, performance, and reliability than a single robot. When multiple mobile robots collaborate as a team, they can perform large and complex problems that would be impossible for a single robot to accomplish [44,46]. The multi-robot system is deployed widely in applications like exploration, search and rescue, emergency response, logistics, healthcare, package pickup and delivery [7,11,12,35,49]. The core challenges to be addressed in a multi-robot environment are navigation, path planning, task allocation, motion planning, and resource management [10,13,19,48]. Among them, the task allocation problem involves efficiently assigning tasks to robots so that they accomplish the mission. The robots are allocated with the available tasks, which they complete using their resources. The team of robots used can be homogeneous or heterogeneous. All mobile robots in homogeneous teams will have the same capabilities [1,31]. But, in a heterogeneous team, the robots will have varying capabilities based on the available sensors and actuators [12,21,48]. The team shares information about the environment using the radio communication network [9,28,54]. In the network, a base station monitors the performance and assists in the effective operation of the team without controlling their operation [8,23,54]. When the task allocation problem is addressed in a decentralized manner without solely depending on a central entity, it offers a scalable and resilient solution against a single robot failure [44].

This study addresses the task allocation problem in a heterogeneous multi-robot team, with each robot having limited resources. The environment considered has the tasks distributed in the area. Each robot shows varying affinity towards the different tasks to complete. The environment has a base station for communication among the robots. The objective here is to maximize the number of tasks completed with the resources available while balancing the affinity with which the task is done. The task allocation happens in a distributed way through the mission token passed among the robots containing environment information. The environment considered here primarily belongs to the ST-SR-TA class of the multi-robot task allocation taxonomy proposed by Gerkey and Mataric [16]. ST refers to robots being able to carry out a single task at any given moment. SR represents each task needing one robot to perform it. TA means time-extended assignment representing more tasks than the robots available, requiring a separate schedule of tasks for each robot. Since, in the current study, the number of tasks completed depends on the order in which the tasks are performed, it belongs to the sub-category of ID[ST-SR-TA] class as per the iTax taxonomy of multi-robot task allocation by Korsah et al. [26]. ID stands for in-schedule dependencies, where the effective utilization of available resources depends on the sequential arrangement of the tasks in the schedule. The multi-robot task allocation problem, classified as ID[ST-SR-TA], maps to the generalized assignment problem. Hence, the challenge of task allocation in a multi-robot team exhibits strong NP-hard complexity in finding the solution [26,44,48].

In order to handle the challenging task allocation problem in the multi-robot team, a hybrid Fuzzy Response Threshold Allocation (FRTA) algorithm is proposed that maximizes tasks completed by the team. The proposed method combines the response threshold model with the multi-criteria decision-making approach of fuzzy logic, resulting in a balanced strategy for allocating tasks. Then, the algorithm is extended to enable the team to perform tasks in a dynamic environment where robots may get defunct. The simulation experiments of the proposed algorithms under the static and dynamic scenarios are carried out, and the results are analyzed. The real-time assessment is conducted in an experimental environment using FireBird V robots to validate the proposed algorithms.

The subsequent sections are structured in the following order. Section 2 provides the related works to the current study in the literature. Section 3 briefly overviews the response threshold model observed in social insects, along with the problem formulation. Section 4 describes the proposed hybrid fuzzy response threshold algorithm. Then, Section 5 elaborates on the experimental simulation environment in detail. In Section 6, the results are presented with the performance metrics and analyzed. Section 7 discusses the real-time experimental implementation performed with real mobile robots. Section 8 draws the conclusion and suggestions for future directions.

2. Related work

The task allocation problem is primarily addressed through centralized and decentralized approaches [37]. The centralized approach involves a central leader robot or a central node that performs the allocation to other team members. The centralized approaches normally map the problem of task allocation into a combinatorial optimization problem. Then the central planner utilizes heuristic methods [20,30], metaheuristic methods [15,57,58], or integer linear programming methods [17,55] to allocate the tasks. The centralized approaches are good for task allocation in smaller teams. As the team size increases, the complexity increases, requiring improved computation performance in the central node to address the task allocation [37]. Further, each robot requires an exclusive communication link with the central planner. If the quality of communication between the central planner and the robots degrades, the performance worsens [53].

The decentralized approaches to solving the problem of task allocation encompass different methodologies in the literature. They can be broadly grouped as auction-based approaches [3,6,34,51], learning-based approaches [14,40,56], and threshold-based approaches [2,12,24,47,48]. Auction-based approaches mimic the market behaviors where tasks are auctioned, and robots bid for the right to execute these tasks based on individual cost functions and capabilities. Hence, they are also called market-based approaches [44]. As the number of robots and tasks increases in the team, these methods remain scalable. They need multiple rounds of bidding to arrive at a conflict-free allocation. The auction-based methods require reliable communication among the robots during their sophisticated bidding and consensus process for efficient allocation. So, larger teams require more time and increased communication among the team [22]. Also, auction-based approaches see a decline in performance due to lossy communication in the team [38]. A detailed survey of the auction-based approaches is available in [42]. Learning-based approaches have been getting more attention in recent years, utilizing deep learning methods to perform task allocation. Wang and Gombolay [56] combined the graph neural network (GNN) with imitation learning to design a task scheduler for multi-robot teams, which learns scheduling characteristics by modeling the issue as a combinatorial optimization problem. Paul et al. [40] proposed a capture attention-based method utilizing GNN for task allocation considering robot constraints and task deadlines. Gautier et al. [14] developed a multi-agent Branch Duelling Q-network (BDQ) model for task allocation in a multi-robot team distributing the computational load between the robots. The deep neural network approaches face the challenges of the curse of dimensionality, leading to high computational needs, neighborhood explosion, and generalization, which are still evolving in recent works [62].

The phenomenon of work division observed in insect societies is the inspiration behind the threshold-based approaches for solving the task allocation problem [52]. Scerri et al. [47] formulated a distributed constraint-based optimization problem for task allocation and utilized the response threshold model to perform decision-making in an extreme team of robots. Their algorithm ensures that agents with a minimum threshold capability towards a task can only complete it in the environment. Swarm-GAP is a threshold-based method proposed for task allocation in a decentralized manner by Ferreira et al. [12]. A probabilistic response threshold-based method effectively addressed the problem of search planning and task distribution in a team of homogeneous robots in [24]. The team is involved in a search operation for targets and destroys them on a battlefield. Schwarzrock et al. [48] presented three response threshold-based algorithms for task allocation in a heterogeneous team. In their approach, individual members complete tasks that provide better rewards. A sigmoid function was utilized by Pang et al. [39] to modify the response threshold model for solving the task allocation problem in a team of homogeneous foraging robots. Amorim et al. [2] assessed the algorithms of Schwarzrock et al. in [48] and extended them to perform task allocation in dynamic scenarios. The task allocation problem for a multi-robot system with deadline constraints is solved using the response threshold model in [21]. The work focussed on effective resource utilization to complete the maximum tasks before their deadlines. Threshold-based approaches utilize the local information available to allocate tasks for individual robots. Hence, lower computation and communication are needed even for larger teams [36].

Fuzzy inference helps to make a human-like decision in complex problems [61]. It helps conflict resolution and better assessment in multi-criteria decision-making where trade-offs are to be considered [25,32,45,50]. Fuzzy systems are applied widely in numerous fields like computer vision, expert systems, robotics, computer networks, communication systems, and CPU scheduling [18,60,63]. Lim and Cho [29] proposed an intelligent fuzzy inference-based CPU process scheduling method with user models. Their work grouped processes as a batch, interactive, or real-time class and assigned the process priority based on the class utilizing the fuzzy inference method. Butt and Akram [5] proposed a fuzzy inference decision system to compute the dynamic priority of tasks for CPU scheduling. The approach used the Mamdani inference method with three triangular membership functions for each input: nice value, CPU usage, and burst time. The method generated the output priority value of a process formulated as a multi-criteria decision system. An intelligent cloud broker to perform service aggregation utilizing the Sugeno fuzzy integral was developed by Nagarajan and Thirunavukarasu [33]. The method selected the suitable cloud service for the cloud user by applying a fuzzy decision tree. An intuitionistic fuzzy-based scheduler for CPU task scheduling was developed by Raheja et al. [43]. The approach made the round-robin scheduler adaptive using fuzzy logic to compute optimal time slices for the tasks. The fuzzy logic is well suited for multi-criteria decision environments as it provides a better solution by balancing the different factors involved. The threshold-based approach is intuitive as it utilizes local information in task allocation. Hence, the fuzzy inference decision-making and the response threshold model are combined together to perform task allocation in a heterogeneous multi-robot environment in this study.

3. Problem formulation

The task allocation problem considered here is such that a message token of the available set of tasks $T = {t_{1}, t_{2}, \dots, t_{q}}$ is circulated to the set of mobile robots $V = {v_{1}, v_{2}, \dots, v_{p}}$ . Each robot is equipped with multiple actuator/sensor combination, which has a varying affinity for different task types. The set of actuator/sensor (represented as AS in short) combinations available in the team be $A = {a_{1}, a_{2}, \dots, a_{x}}$ . Each robot i has a subset of AS combinations as $A_{i} \subseteq A$ . Each task needs one robot to complete it. Each task belongs to one of the task target types $Y = {y_{1}, y_{2}, \dots, y_{z}}$ . Each robot performs only one task at a time. The position $o_{i}$ of each mobile robot i is represented by pair of coordinates as $(x_{i}, y_{i})$ for its position. Hence, each robot $v_{i} \in V$ can be represented by the tuple $V_{i} = (o_{i}, A_{i}, e_{i})$ , where $e_{i}$ is the amount of resources available. Each task $j \in T$ has a corresponding location $c_{j}$ in the region represented by coordinates $(x_{j}, y_{j})$ . The task $j \in T$ can be represented by the tuple of attributes as $T_{j} = (c_{j}, Y_{j}, u_{j})$ .

Theraulaz, Bonabeau, and Denuebourg proposed the response threshold model of social insects in performing tasks [52]. Each insect selects the task to perform utilizing the response threshold model. The task allocation problem can be modeled similarly to an individual robot deciding on its task to complete. Here, the tendency ${TE}_{θ i j}$ determines the likelihood with which a robot will perform a corresponding task. Equation (1) provides the tendency for robot i to perform task j. The response threshold $θ_{i j}$ and the stimulus $s_{j}$ linked with the task are taken for the calculation. The capability $ψ_{i j}$ gives the response threshold $θ_{i j}$ of the robot i to do task j in Eq. (2). $\begin{array}{c} (1) & {TE}_{θ_{i j}} = \frac{s_{j}^{2}}{s_{j}^{2} + θ_{i j}^{2}} \\ (2) & θ_{i j} = 1 - ψ_{i j} \end{array}$

The affinity value of a given AS combination a to perform a target task y is denoted as $ω_{a, y}$ . The affinity value can vary between $ω_{a, y} \in [0, 1]$ . If $ω_{a, y} = 0$ , it indicates that the AS combination a cannot perform that target type y. The affinity of the AS combination is taken as a factor in determining the capability $ψ_{i j}$ of the robot. Hence, the affinity $ω (i, j)$ to do task j by the mobile robot i is provided by Eq. (3). $\begin{matrix} (3) & ω (i, j) = max_{a \in A_{i}} ω_{a, y_{j}} \end{matrix}$

The capability $ψ_{i j}$ also depends on the resource needed to complete task j. $U_{i j}$ represents the amount of resources used for completing task j by robot i, given by Eq. (4). $\begin{matrix} (4) & U_{i j} = E (δ (i, j)) + u_{j} \end{matrix}$

$E (δ (i, j))$ represents the estimated resource required for the robot i to navigate towards task j, which depends on the distance. The resource for performing task j is denoted as $u_{j}$ . The capability $ψ_{i j}$ is obtained using the fuzzy inference system.

Let $l_{i j}$ represent the allocation of robot i with task j. $l_{i j} = 1$ , if robot i is assigned with task j; $l_{i j} = 0$ otherwise. The allocation is subject to the following constraints: $\begin{array}{c} (5) & l_{i j} = 1, iff ω (i, j) > 0 \forall i \in V, j \in T \\ (6) & \sum_{i \in V} l_{i j} ⩽ 1, \forall j \in T \\ (7) & \sum_{j \in J} l_{i j} \times U_{i j} ⩽ e_{i}, \forall i \in V \end{array}$

Equation (5) confirms that task j is assigned to robot i only if it has an AS combination with a non-zero affinity value to perform the task. The constraint in Eq. (6) ensures that each task is allotted to a single robot in the multi-robot environment. Equation (7) satisfies the condition that the tasks are to be allocated if the robot has the resources. Here, $e_{i}$ represents the total amount of resources available with robot i.

In a dynamic scenario, the failure of the robots is considered in the task allocation problem. It is naturally possible that the chance of robot failure is very small at the start of the mission, and the probability increases as the mission proceeds. Hence, in the proposed dynamic scenario, the failure of the robots is induced, utilizing Eq. (8). $\begin{matrix} (8) & τ_{h} = \frac{τ}{3} + \frac{(h * \frac{2}{3} * τ)}{(p / 2)} where 1 ⩽ h < p / 2 \end{matrix}$

Here, p is the total number of mobile robots, and h is an integer value. At each time instant $τ_{h}$ , one of the active robots is selected randomly and put to failure. Here, τ is the total mission time. So, the tasks assigned to the defunct robot are transmitted to the remaining active robots via a mission token. The remaining robots then reallocate the unfinished tasks to maximize their overall task completion using the available resources.

4. Proposed solution

Each robot gets the mission token and executes the proposed hybrid Fuzzy Response Threshold Allocation (FRTA) algorithm to determine which tasks to perform. In the proposed solution, the Fuzzy Inference System (FIS) generates the capability $ψ_{i j}$ value used in the response threshold allocation process. The model of the Mamdani fuzzy inference system proposed is shown in Fig. 1. The capability $ψ_{i j}$ value depends on the resource spent on performing the task and the affinity value of the AS combination utilized to complete the task. The resource spent on a task is based on the distance traveled and the resource utilized to do the task. All the tasks require the same amount of resources to complete [12,48]. Hence, the resource spent on traveling the distance to the task is the influencing factor in finding the capability $ψ_{i j}$ . As the distances and affinity values on the tasks span a wide range for each robot, the values are normalized. Equation (9) represents the normalization method used for both input factors. The normalized crisp inputs are then passed to the fuzzifier. $\begin{matrix} (9) & Normalized F (j) = \frac{F (j) - min (F)}{max (F) - min (F)} \end{matrix}$

Fig. 1.

Structure of Mamdani fuzzy inference system.

The fuzzifier performs the fuzzification utilizing the triangular membership function. Equation (10) gives the membership function $μ_{A} (z)$ of triangular fuzzy number A for a crisp value z. $\begin{matrix} (10) & μ_{A} (z) = \{\begin{array}{ll} 0, & 0 < z ⩽ a \\ \frac{z - a}{b - a}, & a < z ⩽ b \\ \frac{c - z}{c - b}, & b < z ⩽ c \\ 0, & z > c \end{array} \end{matrix}$

In the proposed FIS, the normalized distance input has five fuzzy membership rating values: very low, low, medium, high, and very high. The three fuzzy membership rating values that comprise the normalized affinity value are low, medium, and high. The number of fuzzy memberships for normalized distance is five; for normalized affinity, it is three. Hence, the number of rules is $5 \times 3 = 15$ rules. The rules used in the system are given in Table 1.

Table 1

Fuzzy knowledge-base rules in the proposed fuzzy inference system

Rules	IF		THEN

	Normalized distance	Normalized affinity	Capability
1	Very low	High	Very high
2	Very low	Medium	High
3	Very low	Low	Medium
4	Low	High	High
5	Low	Medium	Medium
6	Low	Low	Low
7	Medium	High	High
8	Medium	Medium	Medium
9	Medium	Low	Low
10	High	High	Medium
11	High	Medium	Low
12	High	Low	Very low
13	Very high	High	Medium
14	Very high	Medium	Low
15	Very high	Low	Very Low

Fig. 2.

Membership functions of input and output fuzzy set values: (a) input value – normalized distance (b) input value – normalized affinity and (c) output value – capability.

Figure 2 depicts the membership functions of the fuzzy sets for the two inputs and single output, along with their membership rating names. The fuzzy knowledge base contains “IF (condition) and THEN (assessment)” rules. The fuzzy inference engine utilizes the knowledge base to generate the fuzzified output capability. The inference engine uses the min-max aggregation method to arrive at the rule assessment based on the fuzzified input factors [18,41]. Finally, the defuzzifier converts the fuzzy capability output to the crisp value for each task utilizing the center of gravity (COG) method [18,27].

The task allocation using the proposed FRTA approach is described in Algorithm 1. The robot receives the mission token and decides on tasks it wishes to perform (lines 2 to 13). The robot i calculates the capability $ψ_{i j}$ to perform task j for all unallocated tasks using the FIS. The tendency for each task j is obtained using Eq. (1). Then, the robot computes the amount of resources required $U_{i j}$ for the completion of task j based on Eq. (4). The allocable tasks for the robot i are sorted based on the tendency obtained for each task in descending order. Then, the response threshold-based decision-making on task allocation happens on the list (lines 8 to 12) utilizing tendency and available resources. Task j is allocated only if the affinity constraint in Eq. (5) is satisfied. Task j is marked as allotted in the mission token if it is successfully assigned. The position coordinates of the robot i are updated to reflect the current task allocation so that it assists in estimating resource requirements in the next iteration (line 11). Also, the available resource with robot i is updated based on the current allocation. The iteration is repeated k times to perform a maximum of k allocations.

Algorithm 1:

Fuzzy response threshold allocation (FRTA)

Algorithm 2:

Dynamic scenario mission token update

The response threshold-based decision-making ensures that the robot will not always make a greedy decision, as in a multi-robot environment, the greedy decision may not always result in the best outcome for the team. The robot is moved to the list of visited robots (line 14) for the current token passing round. The mission token is updated in the FRTA algorithm from lines 15 to 22. The mission token consists of three lists of robots: the visited list, the unvisited list, the unavailable list, and the list of unallocated tasks. The current robot i checks if it has the resources to do any unallocated tasks. If it cannot perform any of the remaining tasks, it enrolls itself to the unavailable robot list for the next token passing round. Then, it checks if there is any robot available in the unvisited list to pass the mission token. An empty unvisited list indicates that all the robots have completed their allocation in the current round. Then, the robot i clears the visited list of robots. The members in the unavailable robots list are not visited in the new token passing round. The remaining robots are moved to the unvisited robots list. Then, a new robot in the unvisited robots list is identified. The current robot i hands over the mission token to it, and a new token passing round begins.

Under real-world conditions, the robots can malfunction due to various reasons. The performance of the proposed algorithm is portrayed in such situations through the dynamic scenario. Using Eq. (8), the dynamic scenario is created by the failure of an active robot at time $τ_{h}$ . In case of a robot failure, its unfinished tasks already assigned to it are available for allocation. The other active robots are allowed to assess their existing allocation of tasks along with the uncompleted tasks of the failed robot to decide on better tasks for completion with their available resources. When a robot i becomes defunct, its uncompleted tasks are updated to the token and passed on to active robots. Algorithm 2 is used to update the mission token for task reallocation during the dynamic scenario. Robot i is cleared from the active robots list and updated to the failed robots list (lines 1 & 2). The uncompleted tasks of the failed robot are updated in the token to be passed (line 3). Next, the list of unvisited robots is updated with the list of active robots in the token (line 4). Then, the token is passed to the active robots (line 5). The base station performs this operation and sends the mission token. If a robot fails, it sends a signal to the base station before it goes down. Then, the mission token is updated by the base station and passed on to the active robots. The active robots look into their current allocation and check if their allotment can be reshuffled to maximize the total tasks completed utilizing Algorithm 1. The allocation update happens at each active robot without disturbing the existing allocation of other active robots. There may be situations where the active robot cannot find a better set of tasks to perform than its existing allocation. In such a case, the robot will make itself unavailable for further token rounds.

5. Simulation framework

The proposed method is evaluated using simulations in the Java-based NetLogo simulator. It is a multi-robot simulation environment [59]. The platform employed for the experiment is a desktop computer running on a 64-bit Windows 10 operating system, with an i7 Intel processor operating at 3.4 GHz. The tasks are scattered across multiple locations within the environment. The environment is represented in pixels (px) in the simulation. It has an associated simulation time increment unit called a tick. At each tick, mobile robots move one pixel in the simulation environment. Four different environment instances are created in the NetLogo simulator, varying the number of robots, the number of tasks, mission time, and the environment size. Each robot is allocated resources for functioning within the mission time. The following are the instances:

6 mobile robots; 64 tasks; 300 ticks as mission time; 200 × 160 px area,

9 mobile robots; 96 tasks; 300 ticks as mission time; 300 × 240 px area,

50 mobile robots; 500 tasks; 500 ticks as mission time; 750 × 750 px area,

100 mobile robots; 500 tasks; 500 ticks as mission time; 750 × 750 px area.

The simulation incorporates four task target types, each depicted with a unique color for visualization. The task target types are denoted as $y_{0}$ , $y_{1}$ , $y_{2}$ , $y_{3}$ . Four AS combinations are available named $a_{0}$ , $a_{1}$ , $a_{2}$ , $a_{3}$ . Every mobile robot has a set of one or two AS combinations. The simulation with mobile robots and tasks in the NetLogo environment is shown in Fig. 3. Each task is displayed with its target type denoted by an ‘x’ symbol. Each mobile robot with its AS combinations is displayed.

Fig. 3.

Initial placement of tasks and robots in the environment with 6 mobile robots (depicted in square shape) and 64 tasks (other colors in the x shape) in NetLogo environment.

The affinity values of AS combination associated with tasks are taken from the work by Schwarzrock et al. [48] for better comparison. Table 2 provides the AS combination affinity values used in the simulation. For the AS combination $a_{0}$ , the target type $y_{0}$ is the most preferred to perform with affinity value 1.0, and the next preferred target is type $y_{3}$ . The target type $y_{2}$ is the next preferred one with a value of 0.3 for $a_{0}$ , as given in Table 2. However, a robot with AS combination $a_{0}$ will not select target type $y_{1}$ to perform as its affinity value is 0. The tasks have a stimulus value of 0.6 in Eq. (1), as it is found to yield superior results. The resource to complete a task u in Eq. (4) is considered in terms of the task execution time. The task execution time is taken as ten ticks for all tasks. The simulation experiments revealed that the value of $k = 2$ for the number of tasks selected during each run of the FRTA algorithm provided better results. The instances were subjected to 100 simulation runs in both static and dynamic scenarios. The simulation ends when all the tasks are done or when the robots in the system lack the resources to execute the remaining tasks in the scenario.

Table 2

Affinity value of AS combination with respect to different target types

AS Combination / target type	$y_{0}$	$y_{1}$	$y_{2}$	$y_{3}$
$a_{0}$	1.0	0	0.3	0.5
$a_{1}$	0	0	1.0	0
$a_{2}$	0.2	0	0	1.0
$a_{3}$	0	1.0	0	0.3

6. Results and discussion

The performance metrics considered for evaluating the proposed approach are the percentage of completed tasks, affinity value of completed tasks, total reward sum, resource utilization, number of exchanged messages, and total runtime of the algorithm. Tables 3 and 4 provide the achieved mean results in the static and dynamic scenarios. The performance is assessed by comparing the proposed method with five other methods. The response threshold model is utilized in conjunction with the widely known First Come First Served (FCFS) algorithm as a baseline for the comparison. Then, the response threshold-based Sorting and Allocation Loop (SAL) algorithm, the Limit and Allocation Loop (LAL) algorithm proposed by Schwarzrock et al. [48] and assessed in dynamic environments by Amorim et al. [2] are taken for comparison.

Table 3
Performance metrics in instances (1) and (2) under the static & dynamic scenarios for 100 runs

Completed tasks (%) Reward sum Resource utilization Affinity value Exchanged message Total runtime

Mobile robots: 6; Tasks: 64; Mission time: 300 ticks; Area: 200 × 160 px

Static scenario FCFS 31.09 11.2944 0.9778 0.7221 6 2.28

SAL 53.63 28.679 0.9653 0.9526 6.66 2.51

FIA 61.08 31.1183 0.9626 0.8281 21.24 12.71

LAL 67.55 38.5218 0.9539 0.9701 43.67 12.92

IFIS 68.88 39.8815 0.9534 0.9556 24.03 13.15

FRTA 73.31 42.7291 0.9507 0.8446 25.92 13.85

Dynamic scenario FCFS 26.06 9.2438 0.9811 0.7018 15 6.05

SAL 38.21 21.4303 0.8884 0.9702 15.66 7.21

FIA 43.05 24.1999 0.8674 0.8368 29.31 13.62

LAL 48.69 28.2369 0.8186 0.9924 52.61 14.51

IFIS 48.96 29.0255 0.8491 0.9862 32.44 15.36

FRTA 54.01 33.8123 0.8047 0.8538 32.77 17.12

Mobile robots: 9; Tasks: 96; Mission time: 300 ticks; Area: 300 × 240 px

Static scenario FCFS 25.89 13.9731 0.9839 0.7265 9 3.76

SAL 45.84 37.2574 0.9709 0.9672 9.86 4.08

FIA 50.99 42.4319 0.9698 0.8345 26.98 20.27

LAL 52.06 44.4454 0.9637 0.9721 50.99 18.71

IFIS 53.11 45.3715 0.9661 0.9469 28.21 21.24

FRTA 55.83 49.4053 0.9627 0.8931 29.39 23.64

Dynamic scenario FCFS 18.94 10.4203 0.9825 0.73 30 14.15

SAL 32.58 28.0699 0.9183 0.9923 33.92 17.44

FIA 34.96 27.1556 0.9361 0.8538 48.45 32.76

LAL 36.51 32.2199 0.9078 0.9925 76.84 30.21

IFIS 37.08 33.1654 0.9219 0.9573 50.58 33.08

FRTA 39.06 35.8107 0.9087 0.9072 50.59 36.56

		Completed tasks (%)	Reward sum	Resource utilization	Affinity value	Exchanged message	Total runtime
Mobile robots: 6; Tasks: 64; Mission time: 300 ticks; Area: 200 × 160 px
Static scenario	FCFS	31.09	11.2944	0.9778	0.7221	6	2.28
SAL	53.63	28.679	0.9653	0.9526	6.66	2.51
FIA	61.08	31.1183	0.9626	0.8281	21.24	12.71
LAL	67.55	38.5218	0.9539	0.9701	43.67	12.92
IFIS	68.88	39.8815	0.9534	0.9556	24.03	13.15
FRTA	73.31	42.7291	0.9507	0.8446	25.92	13.85
Dynamic scenario	FCFS	26.06	9.2438	0.9811	0.7018	15	6.05
SAL	38.21	21.4303	0.8884	0.9702	15.66	7.21
FIA	43.05	24.1999	0.8674	0.8368	29.31	13.62
LAL	48.69	28.2369	0.8186	0.9924	52.61	14.51
IFIS	48.96	29.0255	0.8491	0.9862	32.44	15.36
FRTA	54.01	33.8123	0.8047	0.8538	32.77	17.12
Mobile robots: 9; Tasks: 96; Mission time: 300 ticks; Area: 300 × 240 px
Static scenario	FCFS	25.89	13.9731	0.9839	0.7265	9	3.76
SAL	45.84	37.2574	0.9709	0.9672	9.86	4.08
FIA	50.99	42.4319	0.9698	0.8345	26.98	20.27
LAL	52.06	44.4454	0.9637	0.9721	50.99	18.71
IFIS	53.11	45.3715	0.9661	0.9469	28.21	21.24
FRTA	55.83	49.4053	0.9627	0.8931	29.39	23.64
Dynamic scenario	FCFS	18.94	10.4203	0.9825	0.73	30	14.15
SAL	32.58	28.0699	0.9183	0.9923	33.92	17.44
FIA	34.96	27.1556	0.9361	0.8538	48.45	32.76
LAL	36.51	32.2199	0.9078	0.9925	76.84	30.21
IFIS	37.08	33.1654	0.9219	0.9573	50.58	33.08
FRTA	39.06	35.8107	0.9087	0.9072	50.59	36.56

The proposed algorithm is also compared with two fuzzy-based methods. They are the Fuzzy Inference Allocation (FIA) algorithm proposed by Butt and Akram [5] and the Intuitionistic Fuzzy Inference System (IFIS) allocation based on the intuitionistic fuzzy-based inference system in the work by Raheja et al. [43]. The FIA algorithm uses three triangular membership functions for the two inputs, namely, distance and affinity value. Instances (1) and (2) are used to analyze the performance metrics in detail with fewer mobile robots and tasks on a medium scale. The remaining instances (3) and (4) are implemented to study the performance on a large scale. In all instances, the robots are provided with limited resources. Hence, the robots work aiming to finish the maximum number of tasks possible. Following Eq. (8), the dynamic scenario generates robot failure in the instances. For the dynamic scenario, the proposed update method is applied, and the performances of the algorithms are compared.

6.1. Percentage of completed tasks

The completed tasks percentage metric indicates the number of completed tasks out of the available tasks in the instance by the team. It is the primary indicator of the effectiveness of the team. Under the static scenario, FRTA shows more than a 7% increase in task completion in all instances than the LAL algorithm. FRTA exhibits a minimum of 4%, 9%, and 21% increase when compared with the IFIS, FIA and SAL algorithms, respectively, in the instances (1), (2), and (3). In the instance (4), FRTA provides a 1.01%, 1.51%, and 1.55% increase over IFIS, FIA and SAL algorithms, respectively.

Table 4
Performance metrics in instances (3) and (4) under the static & dynamic scenarios for 100 runs

Completed tasks (%) Reward sum Resource utilization Affinity value Exchanged message Total runtime

Mobile robots: 50; Tasks: 500; Mission time: 500 ticks; Area: 750 × 750 px

Static scenario FCFS 26.41 87.7086 0.9964 0.7167 50 228.8

SAL 62.9 294.4399 0.9836 0.9802 52.14 355.06

FIA 72.55 347.9634 0.9915 0.9307 195.88 1172.54

LAL 73.81 352.6162 0.9857 0.9777 375.16 1142.74

IFIS 76.45 358.0142 0.9867 0.9716 214.33 1298.65

FRTA 79.64 362.4682 0.9812 0.9672 215.69 1313.89

Dynamic scenario FCFS 17.21 58.0981 1 0.7126 365 700.11

SAL 42.02 203.857 1 0.9982 373.03 824.02

FIA 46.79 220.4398 1 0.9581 500 1364.48

LAL 46.43 225.1771 1 0.9901 500 1316.39

IFIS 50.62 230.3525 1 0.9865 500 1526.11

FRTA 52.75 233.1266 1 0.9825 500 1585.61

Mobile robots: 100; Tasks: 500; Mission time: 500 ticks; Area: 750 × 750 px

Static scenario FCFS 50.41 173.0393 0.9972 0.7322 100 427.47

SAL 97.89 442.6176 0.9894 0.9668 107.75 490.53

FIA 97.93 436.6369 0.9931 0.9178 295.88 1401.65

LAL 84.63 401.731 0.9945 0.9673 459.4 1373.85

IFIS 98.42 447.1243 0.9911 0.9472 306.13 1485.36

FRTA 99.41 452.618 0.9882 0.9493 307.94 1505.24

Dynamic scenario FCFS 34.26 119.865 1 0.7395 427 823.64

SAL 67.75 325.0935 1 0.9865 434.87 897.86

FIA 73.31 332.9708 1 0.9515 500 1532.64

LAL 58.22 281.7493 1 0.9858 500 1457.74

IFIS 75.29 345.5843 1 0.9673 500 1601.12

FRTA 77.23 351.6932 1 0.9751 500 1660.78

		Completed tasks (%)	Reward sum	Resource utilization	Affinity value	Exchanged message	Total runtime
Mobile robots: 50; Tasks: 500; Mission time: 500 ticks; Area: 750 × 750 px
Static scenario	FCFS	26.41	87.7086	0.9964	0.7167	50	228.8
SAL	62.9	294.4399	0.9836	0.9802	52.14	355.06
FIA	72.55	347.9634	0.9915	0.9307	195.88	1172.54
LAL	73.81	352.6162	0.9857	0.9777	375.16	1142.74
IFIS	76.45	358.0142	0.9867	0.9716	214.33	1298.65
FRTA	79.64	362.4682	0.9812	0.9672	215.69	1313.89
Dynamic scenario	FCFS	17.21	58.0981	1	0.7126	365	700.11
SAL	42.02	203.857	1	0.9982	373.03	824.02
FIA	46.79	220.4398	1	0.9581	500	1364.48
LAL	46.43	225.1771	1	0.9901	500	1316.39
IFIS	50.62	230.3525	1	0.9865	500	1526.11
FRTA	52.75	233.1266	1	0.9825	500	1585.61
Mobile robots: 100; Tasks: 500; Mission time: 500 ticks; Area: 750 × 750 px
Static scenario	FCFS	50.41	173.0393	0.9972	0.7322	100	427.47
SAL	97.89	442.6176	0.9894	0.9668	107.75	490.53
FIA	97.93	436.6369	0.9931	0.9178	295.88	1401.65
LAL	84.63	401.731	0.9945	0.9673	459.4	1373.85
IFIS	98.42	447.1243	0.9911	0.9472	306.13	1485.36
FRTA	99.41	452.618	0.9882	0.9493	307.94	1505.24
Dynamic scenario	FCFS	34.26	119.865	1	0.7395	427	823.64
SAL	67.75	325.0935	1	0.9865	434.87	897.86
FIA	73.31	332.9708	1	0.9515	500	1532.64
LAL	58.22	281.7493	1	0.9858	500	1457.74
IFIS	75.29	345.5843	1	0.9673	500	1601.12
FRTA	77.23	351.6932	1	0.9751	500	1660.78

As the FCFS algorithm completes the task blindly in the order of arrival in the mission token, it is not utilizing the resources efficiently. Hence, it achieves lesser completion than all other algorithms. Figure 4 depicts the percentage of tasks completed in static and dynamic scenarios. Under the dynamic scenario, FRTA shows more than 2.57%, 5.34%, 6.98%, and 13.99% increase in task completion in all instances compared with the IFIS, FIA, LAL, and SAL algorithms, respectively.

6.2. Affinity value of completed tasks

Fig. 4.

Percentage of completed tasks in different instances for tasks: (a) static and (b) dynamic scenario.

The next performance metric considered is the affinity value. It shows the competitiveness of the robot which performs the chosen task. It is a metric illustrating the perfection in completing the task. The plot of the normalized affinity values in the static and dynamic scenario is shown in Fig. 5. The affinity values used for doing the completed tasks are summed up and normalized by the total number of completed tasks. Under the static scenario, FRTA shows a 12.93%, 8.12%, 1.07%, and 1.92% decrease in normalized affinity value than the LAL algorithm across the instances (1), (2), (3), and (4), respectively. Compared with the SAL algorithm, the normalized affinity value obtained with the FRTA algorithm is 11.33%, 7.66%, 1.32%, and 1.81% less in the instances (1), (2), (3), and (4), respectively. FRTA shows an 11.62%, 5.68%, and 0.45% lesser affinity value than the IFIS algorithm in the instances (1), (2), and (3), respectively. In the instance (4), FRTA gives a 0.22% increase in affinity value than the IFIS algorithm. FRTA algorithm provides better values of normalized affinity than FIA and FCFS algorithms across all instances. The outcomes in the dynamic scenario indicate a similar trend in the normalized affinity value among the algorithms.

6.3. Reward sum

The capability of the robot determines the selection of a task to perform (as discussed in Section 3). It represents the combined factor of the resource needed for a task with the affinity value utilized to complete it. Hence, the reward of the robot is taken as the capability factor with which a task is done [48]. The better reward values indicate that the robot has made a good decision in selecting the tasks. The reward sum is computed by summing the reward values accumulated for the tasks completed by all robots. In the static scenario, FRTA provides a greater reward than the other compared algorithms in all the instances. In the instance (4), FRTA provides 2.26%, 3.66%, and 12.67% more rewards than SAL, FIA, and LAL algorithms, respectively. In other instances, FRTA shows significantly increased rewards compared to the SAL, FIA, and LAL algorithms. FRTA shows a 7.14%, 8.89%, 1.24%, and 1.22% increase compared to the IFIS algorithm in the instances (1), (2), (3), and (4), respectively. The reward sum obtained under different instances in the static and dynamic scenarios is plotted in Fig. 6.

Fig. 5.

Normalized affinity value in different instances for tasks: (a) static scenario and (b) dynamic scenario.

Fig. 6.

Reward sum obtained in different instances for tasks: (a) static scenario and (b) dynamic scenario.

The dynamic scenario shows a reduction in the number of tasks completed. Hence, the reward received is less than the static scenario for all algorithms. FRTA outdoes the other algorithms in gaining rewards across all the instances in the dynamic scenario. The rise in rewards by 1.2% for FRTA against the IFIS algorithm in the experimental instance (3) is the smallest compared to other algorithms in all instances. Since the FCFS algorithm does not factor in the capability while deciding on tasks, it generates a lower reward sum than other algorithms.

6.4. Resource utilization

The simulation ends when the robots in the team are unable to complete any more tasks in the instance. The resource utilized so far is taken as a measure of performance. The resource spent is normalized by the total resource allocated for the robots to get the resource utilization factor. The total resource allocated for each robot is equal to the mission ticks in the simulation. The normalized resource utilization of the instances under the static and dynamic scenarios is plotted in Fig. 7. Under the static scenario, the FRTA shows a marginally lesser normalized resource utilization value than other algorithms in all instances. Under the dynamic scenario in instances (1) and (2), FRTA has reduced resource utilization than other algorithms. In the remaining instances, all algorithms utilize the entire resource allocated. As the number of tasks is more than the mission time in these instances, the active robots exhaust all their resources, searching for any unfinished tasks to complete.

Fig. 7.

Normalized resource utilization in different instances for tasks: (a) static scenario and (b) dynamic scenario.

6.5. Exchanged messages

The exchanged messages parameter gives the number of times the mission token is passed among the robots. This metric depends on the algorithm. The FRTA, FIA and IFIS algorithms select a maximum of two tasks every time the robot receives the token. Hence, under the static scenario, it is nearly half the number of completed tasks for the FIA, IFIS and FRTA algorithms in every instance. For the FCFS and SAL algorithms, it is proportional to the number of mobile robots available in the instance, as a robot receives the token once and allocates its tasks to complete. As the LAL algorithm limits the tasks allotted in each run to a maximum value of one, the number of exchanged messages nearly equals the number of tasks completed. In the dynamic scenario, the active robots exchange tokens to improve their allocation during robot failure. Hence, the number of exchanged messages is increased in the dynamic scenario for all algorithms.

6.6. Total runtime

The runtime of the algorithm is calculated using the NetLogo Profiler extension. It is observed that the runtime varies based on the operating system and hardware platform in which the simulation runs. Table 3 and Table 4 show the runtime of the algorithms in the hardware platform. The mean total runtime is the average of 100 runs. Every time a robot receives the mission token, it invokes the algorithm for task allocation. The total runtime of the FIA, LAL, IFIS, and FRTA algorithms exceeds the total runtime of the FCFS and SAL in all the instances. The runtime is greater because the exchanged messages are lesser in the FCFS and SAL algorithms. On the other hand, in the FIA, LAL, IFIS, and FRTA algorithms, the mission token is exchanged more times. Hence, they show an increase in the runtime across all instances.

6.7. Analysis

The proposed FRTA algorithm shows improvement in the percentage of completed tasks in all the instances. It exhibits a slight decrease in the normalized affinity value compared with the SAL, LAL and IFIS algorithms. As the team has robots with varying affinity values, it is not always possible to complete a task with a robot having the best affinity value towards the task. Allocating a task to a robot with the best affinity value may lead the robot to travel a longer distance, resulting in increased resources spent to complete the task. Hence, always mapping the robot with the best affinity value towards each task may lead to poor overall task completion. This situation is managed well in the FRTA algorithm using the FIS as it balances between the resource needed and the affinity value while selecting the task. The results show that the fuzzy response threshold model in the FRTA algorithm does not always force the robot to do a task with the best affinity value of the AS combination. The FIS helps in calculating capability such that, wherever possible, it maps the best affinity value towards the task; otherwise, it settles with a relatively lower affinity value for the task with fewer resources spent. Thus, it leads to more tasks being completed successfully. As the decrease in the normalized affinity value is marginal in the instances (3) and (4), it shows that the FRTA algorithm does not always allow robots to perform tasks with very poor affinity value of AS combination. Though the decrease in normalized affinity value causes a decrease in the rewards, it is compensated by utilizing the saved resources in doing more tasks that increase the rewards. Thus, the total reward sum achieved with the FRTA algorithm is greater than the other algorithms. The instance (4) has 100 mobile robots to perform the same number of tasks (500 tasks) as in the instance (3). The additional robots improve the performance of all the algorithms. In this case, FRTA gives the percentage of completed tasks as 99.41%. It shows that when more robots are allocated to a given instance, FRTA is quicker to complete the tasks in such a case.

The dynamic scenario better helps understand the conditions when the robot failure happens. The mission token update algorithm for the dynamic scenario aids in performing the maximum number of tasks possible by actively reshuffling the task allocation. As the FRTA algorithm selects a maximum of two tasks when the mission token is received, they show a reduction in the total number of exchanged messages compared to the LAL algorithm. The FIA, IFIS, and FRTA algorithms show a nearly equal number of exchanged messages. However, the runtimes of these three algorithms are increased. The performance improvement of FRTA outweighs the increase in runtime. Also, with improved computational resources, the runtime can be minimized. The robots spend their resources on moving toward the task and performing the task. Hence, when the algorithm reduces the resources spent on the travel of the robot, it improves resource utilization. The primary objective of the FRTA algorithm is to maximize the number of tasks completed by the team. The obtained results indicate that FRTA is capable of completing more tasks with the allocated resources. It achieves the goal by striking a balance between the resource utilized and the affinity value chosen for performing the tasks.

7. Real-time experimental implementation

The proposed algorithms are evaluated using the FireBird V mobile robot platform. The specifications of the robot platform are given in Table 5. The FireBird V robot is equipped with a NodeMCU WiFi module to form the network and pass the mission token in the environment. The experimental evaluation takes place in a grid environment. The robots utilize the modified path-planning algorithm proposed by Buschmann, Müller, and Fischer [4], running in the ATMEGA2560 microcontroller, to move across the grids. The dimensions of each grid measures 20 cm × 20 cm. The environment consists of 12 × 12 grids. The NodeMCU module runs the proposed algorithm to perform the task allocation. The allocated task is communicated to the ATMEGA2560 microcontroller through the UART communication. The robot then starts moving towards the task to complete it. Figure 8 depicts the initial state of the environment. Three mobile robots are used in the experiment, with 12 tasks to be performed. The types of tasks are highlighted with different colors, namely red, blue, green, and pink. The three mobile robots are named MR1, MR2, and MR3. MR1 is capable of doing tasks in red, pink, and green colors. MR2 can perform blue and pink tasks. MR3 can complete red and green tasks.

Table 5
Technical specifications of FireBird V robot

Specification Details

Microcontroller ATMEGA2560 microcontroller

Wireless communication NodeMCU WiFi Module

Weight 1250 gm

Max speed 0.24 m/s

Locomotion 2 geared motors

Power supply 9.6 V Battery

Control mode Automated / wireless control

Dimensions Diameter: 16 cm, Height: 10 cm

Specification	Details
Microcontroller	ATMEGA2560 microcontroller
Wireless communication	NodeMCU WiFi Module
Weight	1250 gm
Max speed	0.24 m/s
Locomotion	2 geared motors
Power supply	9.6 V Battery
Control mode	Automated / wireless control
Dimensions	Diameter: 16 cm, Height: 10 cm

The resource needed to complete a task is taken in terms of the task execution time by the robot. The mobile robot goes to the location of a task and stays there to complete the task. In this experimental study, the task execution time to do a task has been taken as 10 seconds in Eq. (4). For simplicity, the robot imitates doing an activity by staying in the task location for 10 seconds. After completing the task, the robot moves to the next task to perform. The speed of the robot is set as one grid in 2 seconds to maintain its localization in the environment. The experiment is first performed under the static scenario. Upon obtaining the mission token and running the FRTA algorithm, MR1 starts with performing task R1, MR2 with B3, and MR3 with R3. After multiple rounds of mission token passing, the final allocation is as in Table 6.

Fig. 8.

Initial state (top view) of the mobile robot experiment.

Table 6

Final task allocation in the real-time experiment

Mobile robot	Tasks
MR1	R1 → P1 → G1 → P2
MR2	B3 → B2 → B1 → P3
MR3	R3 → G3 → G2 → R2

Figure 9 illustrates the intermediate state of the experiment when the mobile robots are doing their assigned tasks. It also highlights the task allocation for each mobile robot. In this state, MR1 can be seen performing task P1, MR2 is doing task B2, and MR3 is completing task G3.

Fig. 9.

Intermediate state of the experiment where mobile robots perform tasks under the FRTA algorithm.

The final state at the end of completing all the tasks is seen in Fig. 10. The mission time of the experiment is 300 seconds. As a result, the mobile robots can perform all the tasks within the mission time in the static scenario. Under the dynamic scenario, MR3 is made to fail after 15 seconds. This results in MR3 completing task R3 and going to the defunct state. Nevertheless, as the mission time is sufficient for other robots to complete the remaining tasks, MR1 and MR2 complete the tasks initially allocated to the defunct robot MR3. When the mission time is reduced, it has resulted in a few tasks left unfinished in the environment.

Fig. 10.

Final state of the experiment after all the tasks are completed.

8. Conclusion

This work addresses the task allocation problem in a heterogeneous multi-robot environment. The proposed hybrid fuzzy response threshold-based distributed method allocates tasks, maximizing the tasks completed while balancing the affinity with which the task is done. The robots utilize the algorithm to choose the tasks for execution. The capability to perform a task is found using the fuzzy inference system. The fuzzy logic helps to balance the influence of the two factors, namely, distance and affinity value, in obtaining the capability. The response threshold model is then applied with the obtained capability to choose the tasks. Both static and dynamic scenarios are considered in the simulation environment. The empirical results showed an improvement in task completion than existing methods across all instances. The robots better adapt to the dynamic scenario utilizing the proposed token update with task reshuffling. The real-time experimental evaluation is carried out with the FireBird V mobile robot platform, and the usefulness of the proposed algorithm is verified successfully. In the future, the algorithm can be extended to a mixed team of mobile robots with aerial or underwater vehicles. Other aspects for improvement are addressing situations with each task requiring multiple robots to do it and sequential completion of tasks in order. Also, the work can be enhanced to support multiple regions, with separate teams working in each region, allowing inter-team cooperation for task completion. Further, metaheuristic algorithms, like the genetic algorithm, can be used to evolve the optimal fuzzy membership functions and rule sets.

Footnotes

Acknowledgements

The authors would like to thank the Management and Principal of Mepco Schlenk Engineering College, Sivakasi for providing the necessary facilities and support to carry out this research.

Conflict of interest

None to report.

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