Deployment and navigation of multiple robots using a self-clustering method and type-2 fuzzy controller in dynamic environments

Abstract

In recent years, multiple robots have been successfully applied in various fields, including the handling of logistics factories, agriculture, and disaster relief. This study proposes a novel method for multi-robot deployment and navigation in dynamic environments. To address the problem of location deployment, a grid-based method was used to simplify environmental input information, and a self-clustering method was used to adjust location deployment. To address the problem of navigation, a behavior manager was used as a navigation strategy to control the towards-goal behavior and wall-following behavior (WFB) of mobile robots. An interval type-2 fuzzy controller based on improved particle swarm optimization (IPSO) was proposed to implement the WFB control. The proposed IPSO improved the search ability and enhanced the convergence speed of traditional PSO. Additionally, an escape mechanism was proposed to avoid a dead cycle. Experimental results show that the proposed IPSO is superior to other methods used for WFB and navigation control.

Keywords

Robot navigation control location deployment particle swarm optimization type-2 fuzzy controller self-clustering

1 Introduction

Remarkable progress has recently been made in the research and development of robotics. In addition to industrial robots used for automating production lines, numerous types of service robots have been developed to meet the diverse demands of daily life; for instance, cleaning [7], home care [21], and home safety [6]. Professional service robots include those deployed in the fields of farming and animal husbandry [1, 20], medical care [14, 15], object handling [2], and navigation [5]. With the advances in technology, problems relevant to industrial robots, service robots, and multi-robot cooperation [2 , 12] have attracted increasing research interest. For example, the robot lifeguard [12] can help ensure a rapid response to the correct location in a vast sea; robots monitor temperature and conduct humidity testing in large factories (such as wineries); logistics robots help place goods on shelves in large shopping malls; and robots assist in the sprinkling of water and pesticides in fields used for farming. However, there are common problems associated with the deployment and navigation of multi-robots.

To overcome the aforementioned problems, Reif and Wang [9] proposed autonomous robot behavior control of a social potential field, which is given to each robot by defining the rules between themselves and the robot group. This reflects the social relations among robots and enables them to arrange themselves into teams. Parker [11] proposed a low-level controller based on an artificial potential field to imitate the concept of an electric field force. This perceives the movement of the robot in the environment as an abstract, artificial force field. Although the two methods [9, 11] are simple in structure and provide easy control, the disadvantage of both methods is an existing local optimum that can easily become trapped in a deadlocked situation. Therefore, Cortes et al. [8] proposed a distributed processing method based on Lloyd’s [23] method and the computational geometry of the Voronoi diagram, in which a gradient descent algorithm is used to solve unconstrained optimization problems and deploy the decentralized processing of a robot team in the best position within a region. Although this method is simple and easy to implement, it has a slow convergence rate and easily falls into a local optimal solution. The K-means clustering algorithm [10] is used to divide n points into K clusters so that each point belongs to the cluster that corresponds to its nearest mean value as the standard value of the cluster. Although the K-means clustering algorithm is simple and rapid, the number of cluster center points must first be defined because an inappropriate number of clusters yields poor results which considerably limits the usefulness of the clustering method. To solve this problem, a self-clustering method is proposed that can dynamically evaluate the data set and determine the current population center in the input data space without to the requirement of predefining the number of clusters.

In terms of navigation, avoiding collisions with dynamic obstacles or adapting to changes in the environment, such as the appearance of a pedestrian or a moving object and a dead road caused by collapsed goods, is difficult. To realize navigation control of the mobile robot, obstacle avoidance is important in enabling the mobile robot to reach the target location. In recent years, intelligent robots have been widely used, most commonly through the methods of fuzzy control and neural network control. Researchers, including Juang et al. [3] and Wai et al. [17], have combined the concepts of fuzzy logic and neural network in robot controllers that directly transmit the sonar message received from the sensor to the designated fuzzy neural network (FNN) to achieve mobile robot control. However, this is affected by the uncertainty of input, output, and noise signals in a real environment. Although an FNN can successfully facilitate the wall-following control, its performance may not be optimal. To solve these problems, some researchers [4, 19] have applied a type-2 fuzzy neural network (T2-FNN).

This network was developed to solve the shortcomings of a type-1 fuzzy neural network (T1-FNN). The T2-FNN uses a fuzzy set as the membership value and is therefore an extension of the T1-FNN, which uses a crisp set as membership value. Ownership of these fuzzy sets provides a footprint of uncertainty, which enables the handling of uncertainties. Therefore, T2-FNN generally performs more effectively than T1-FNN, although its computational complexity increases significantly. In this research, an interval type-2 fuzzy controller (IT2FC) was therefore used to reduce computational complexity, and the center of sets (COS) reduction process [16] was adopted to simplify the reduced order process.

In parameter learning, evolutionary algorithms [18 , 27] are widely used to adjust the parameters of a neural or fuzzy neural network, such as in the artificial bee colony (ABC) [26], difference evolution (DE) [27], quantum-behaved particle swarm optimization (QPSO) [22], and particle swarm optimization (PSO) [18]. This study focused on the particle swarm algorithm [18], which is an evolutionary calculus inspired by the collective behavior of social animals, which has the advantages of fast convergence and simple implementation. However, it also has several shortcomings, including low precision, faster speed of convergence, and a tendency to readily fall into the optimal solution in complex applications. To solve these problems, an improved PSO is proposed to maintain the diversity of particles and avoid falling into the local minimum solution.

The purpose of this study was to deploy and navigate multiple mobile robots for use as water lifesaving robots, logistics robots, or in factories or farmland. To solve the problem of location allocation, we used gridding to simplify the input of environmental information and utilized the proposed self-organizing algorithm to deploy the robot. To help the robot safely reach the deployment point, an IT2FC was designed for avoiding obstacles. Finally, the proposed method was applied to the simulated field and its performance was compared with other methods identified in the literature.

2 Deployment of multiple mobile robots

2.1 The self-clustering method

In this subsection, a self-clustering method (SCM) is proposed to cluster input data. The main advantages of this algorithm are as follows. First, it is a one-pass algorithm that can dynamically evaluate the cluster entries in the input space. Second, it calculates the current data and automatically determines the number of clusters. Thus, if the user knows the environment must allocate several robots, they can adjust the threshold in SCM to change the effect of clustering. Using two-dimensional data as an example, the details of the SCM are as follows.

Step 1. The first input data are taken as the first cluster center $C_{i}^{1}$ and are used to build the first cluster C¹ (Fig. 1 (a). The cluster range ${CD}_{i}^{1}$ is then set to 0, where i = 1, and 2 is the dimension of input.

Fig.1

The self-clustering method in two-dimensional space.

Step 2. Once all inputs are completed, the algorithm is complete. If not, the current input sample x_i [k]is calculated, followed by the calculation of distance between the sample and cluster center $C_{i}^{j}$ : $D_{i}^{j} [k] = | x_{i} [k] - C_{i}^{j} |$ (1) where j = 1, 2,..., R denotes the jth cluster, k = 1,2,..., N denotes the kth input data, and i denotes the ith dimension.

Step 3. First, the sum of the distances $D_{i}^{j} [k]$ between the current input sample and each cluster center is calculated, as shown in Equation (2). The smallest distance sum $D \min^{j} [k]$ then represents the current input sample as the candidate sample of the jth cluster. ${Dmin}^{j} [k] = min (\sum_{i = 1}^{n} D_{i}^{j} [k])$ (2)

To determine whether the candidate sample belongs to the jth cluster, the restriction conditions are as follows: $D \min_{i}^{j} [k] \leq {CD}_{i}^{j} or D \min_{i}^{j} [k] \leq D_{thr}$ (3)

$D \min_{i}^{j} [k]$ represents the distance between the candidate sample and the ith dimension of the jth cluster and ${CD}_{i}^{j}$ represents the ith dimension which contains the largest cluster range in the jth cluster. The threshold value D_thr denotes the maximum distance of a cluster given the robot’s performance and the nature of the problem; for example, pesticide spraying range and temperature sensing range. If the candidate sample does not exceed the threshold D_thr, the sample is determined as belonging to the jth cluster (as shown in Figs. 1 (b) and (c) or else the sample forms a cluster (as shown in Fig. 1 (d)). The new cluster is then completed in the same manner asin Step 1.

Step 4. After confirming the cluster to which the sample is currently input, a new action is initiated on the clusters. The detailed formula for this is as follows:

If $\begin{matrix} {CD}_{i}^{j} < | x_{i} [k] - C_{i}^{j} |, then \\ {CD}_{i}^{j} = \frac{(| x_{i} [k] - C_{i}^{j} | + {CD}_{i}^{j} \geq}{2} and \\ C_{i}^{j} = {\begin{matrix} x_{i} [k] + {CD}_{i}^{j}, if C_{i}^{j} \geq x_{i} [k] \\ x_{i} [k] - {CD}_{i}^{j}, if C_{i}^{j} < x_{i} [k] \end{matrix}} \end{matrix}$ (4) where k = 1, 2,..., N denotes the kth input, j denotes the jth cluster center with the smallest distance in Equation (2), x denotes the input data, and i denotes the ith dimension. When this step is completed, the algorithm returns to Step 2.

2.2 Location deployment of multiple mobile robots

The threshold D_thr is the most important parameter in the SCM. A low threshold value produces more clusters, whereas a higher threshold value produces fewer clusters. Selection of the threshold value therefore affects the number of clusters and is ascribed according to the performance of the robot and the problem. Figure 2 shows the effect of using different threshold values.

Fig.2

Location deployment of mobile robots using SCM with different thresholds (red dots denote robots).

3 Navigation control of multiple mobile robots

This section describes the use of mobile robots and the proposed navigation control method. The proposed method is to design a behavior manager (BM) to change a robot’s behavior according to the relationship it has with the environment.

3.1 Mobile robot description

Figure 3 shows the Pioneer 3-DX robot used in this study. It is manufactured by Mobile Robots USA and exhibits many features, such as high load, high endurance, highly scalable, and a software development kit across platforms, which also includes robot motion control, a client-server model, and various equipped libraries. Users can apply this robot in a variety of areas and integrate it with all the peripherals to achieve their research and development goals.

Fig.3

Pioneer3-DX Mobile Robot.

3.2 Behavior manager

The robot moves towards the target when there is no obstacle preventing it from doing so. If there is an obstacle, it needs to bypass this to find the target point. In this subsection, we describe a BM designed to control two mobile robot behaviors: towards-goal behavior (TGB) and wall-following behavior (WFB). The mobile robot is divided into four regions R_1, R_2, R_3, and R_4, as shown in Fig. 4. The position (R_i) of the target point in the mobile robot is then determined as shown in Fig. 5. If it is located at R_(1∼3), the BM detects whether there is an obstacle in this area. If an obstacle is detected (S _ i ≤ 1m), the BM switches to the WFB; if not, it executes the TGB. If the target point is located at R_4, the robot switches to the WFB until it reaches the target point.

Fig.4

The robot is divided into four areas.

3.3 The wall-following control

To realize the WFB control, an IT2FC based on improved particle swarm optimization (IPSO) is proposed for collision avoidance.

3.3.1 Interval type-2 fuzzy controller

Figure 5 shows the IT2NC architecture which comprises five layers: the input layer, fuzzy layer, firing layer, output processing layer, and output layer. The IF-THEN rule can then be expressed as follows:

$R_{j} : IF x_{1} is {\tilde{A}}_{1}^{j} and x_{2} is {\tilde{A}}_{2}^{j} \dots and x_{n} is {\tilde{A}}_{n}^{j}$

THEN $\begin{matrix} y_{Left} is w_{{Left}_{0}^{j}} + \sum_{i = 1}^{n} w_{{Left}_{i}^{j}} x_{i}, \\ y_{Rightt} is w_{{Right}_{0}^{j}} + \sum_{i = 1}^{n} w_{{Right}_{i}^{j}} x_{i} \end{matrix}$ where j = 1, 2, …, M is the number of rules, i = 1, 2, …, n is the input number, x₁, x₂, …, x_n is the input, ${\tilde{A}}_{1}^{j}, {\tilde{A}}_{2}^{j}, \dots, {\tilde{A}}_{n}^{j}$ is the interval type-2 fuzzy set, and the consequence $w_{0}^{j} + \sum_{i = 1}^{n} w_{i}^{j} x_{i}$ is the output of the TSK type linear function. In Fig. 5, layer 1 only imports the input data into the next layer, which performs the fuzzification operation. The Gaussian primary membership function $u_{\tilde{A}}$ is defin ed asfollows: $u_{{\tilde{A}}_{i}^{j}} = exp (- \frac{1}{2} \frac{[x_{i} - m_{i}^{j}]^{2}}{(σ_{i}^{j})}) N (m_{i}^{j}, σ_{i}^{j}; x_{i}), \in [m_{i 1}^{j}, m_{i 2}^{j}]$ (5)

Fig.5

Structure of the interval type-2 fuzzy controller.

The membership degree of the Gaussian primary membership function $u_{\tilde{A}}$ is called the footprint of uncertainty and is expressed as the upper bound ${\bar{u}}_{\tilde{A}}$ and the lower bound $\underset{¯_{\tilde{A}}}{u}$ . ${\bar{u}}_{{\tilde{A}}_{i}^{j}} = {\begin{matrix} N (m_{i 1}^{j}, σ_{i}^{j}; x_{i}), & x_{i} \leq m_{i 1}^{j} \\ 1, & m_{i 1}^{j} \leq x_{i} \leq m_{i 2}^{j} \\ N (m_{i 2}^{j}, σ_{i}^{j}; x_{i}), & x_{i} > m_{i 2}^{j} \end{matrix}$ (6)

and $\underline{u} {\tilde{A}}_{i}^{j} = {\begin{matrix} N (m_{i 2}^{j}, σ_{i}^{j}; x_{i}), & x_{i} \leq \frac{m_{i 1}^{j} + m_{i 2}^{j}}{2} \\ N (m_{i 1}^{j}, σ_{i}^{j}; x_{i}), & x_{i} > \frac{m_{i 1}^{j} + m_{i 2}^{j}}{2} \end{matrix}$ (7)

The output of each node is represented as an interval [ ${\bar{u}}_{{\tilde{A}}_{i}^{j}}, \underline{u} {\tilde{A}}_{i}^{j}$ ]. In layer 3, each node uses an algebraic product operation to achieve a fuzzy AND operation. In layer 4, the crisp output value [y_l, y_r]is obtained using center-of-gravity defuzzification. To reduce the computational complexity of the order reduction, this study adopted the COS [25] to implement the reduction process. The method is formulated as follows: $y_{l} = \frac{\sum_{j = 1}^{M} f_{-}^{j} (w_{0}^{j} + \sum_{i = 1}^{n} w_{i}^{j} x_{i})}{\sum_{j = 1}^{M} f_{-}^{j}}$ (8)

and $y_{r} = \frac{\sum_{j = 1}^{M} {\bar{f}}^{j} (w_{0}^{j} + \sum_{i = 1}^{n} w_{i}^{j} x_{i})}{\sum_{j = 1}^{M} {\bar{f}}^{j}}$ (9)

Nodes in Layer 5 defuzzify the output by computing the average of y_l and y_r to provide the crisp value of y. $y = \frac{yl + y_{r}}{2}$ (10)

3.3.2 Proposed improved particle swarm optimization

Traditional PSO presents the advantages of fast convergence and simple implementation, but also the shortcomings of low precision and a tendency to fall readily into the local best solution in complex applications. To improve these shortcomings, this study proposes an IPSO, the flowchart for which is shown in Fig. 6.

Fig.6

Flowchart of improved particle swarm optimization.

Step 1. All the parameters in the IT2FC are coded into one particle, which means each particle (P) represents an IT2FC, and then the proposed IPSO is used to adjust the parameters in each IT2FC. The parameter contains the uncertain central value $[m_{i 1}^{j}, m_{i 2}^{j}]$ of the antecedent part and standard deviation $σ_{i}^{j}$ and weights of the consequent part $w_{{Left}_{0}^{j}}$ , $w_{{Left}_{i}^{j}}$ , $w_{{Right}_{0}^{j}}$ , $w_{{Right}_{i}^{j}} .$

Step 2. The fitness values of all particles are sorted from high to low, and the group number for all particles is initialized to 0. The current group number 0 is set to the highest fitness value as the leader of the new group and its group number is updated to g, the initial value ofWhich is 1. The similarity threshold of this group is then calculated, which contains fitness value threshold (AFIT) and distance threshold (ADIS). The value is the average difference in distance between the particles that are not currently grouped (that is, the group number 0) and the group leader (Leader) and the average fitness value difference. The formula is as follows:

$\begin{matrix} {DIS}^{g} = \sum_{i = 1}^{n} \sum_{j = 1}^{D} \sqrt{(L_{j}^{g} - P_{j}^{i})^{2}}, \\ if P^{i} is ungrouped \end{matrix}$ (11)

$\begin{matrix} {FIT}^{g} = \sum_{i = 1}^{n} | Fit (L^{g}) - Fit (P^{i}) |, \\ if P^{i} is ungrouped \end{matrix}$ (12) ${ADIS}^{g} = \frac{{DIS}^{g}}{NC}$ (13) ${AFIT}^{g} = \frac{{FIT}^{g}}{NC}$ (14) where ADIS^g and AFIT^g indicate the ADIS and AFIT for the gth group, respectively, ${Leader}_{j}^{g}$ is the jth dimension representing the leader of group g, Fit (L^g) represents the fitness value of the leader of group g, Fit (Pⁱ) represents the fitness value of the ith particle, NC denotes the total number of particles with group number 0 in the current particle swarm, D represents the dimension of the code, and n is the total number of particles.

Step 3. The ungrouped particles are sequentially calculated using the following formula to determine the difference in distance (Disⁱ) and the difference in fitness value (Fitⁱ) between the self-particle and the leading particle: ${Dis}^{i} = \sum_{j = 1}^{D} \sqrt{(L_{j}^{g} - P_{j}^{i})^{2}}$ (15) ${Fit}^{i} = | Fit (L^{g}) - Fit (P^{i}) |$ (16)

If Disⁱ < ADIS^g and Fitⁱ < AFIT^g, this particle is similar to the group leader. They are then placed in the same group and their group number is updated to g If this is not the case, the particle does not belong to the group, and no action is taken.

If ungrouped particles remain, the algorithm returns to step 2 and particles with the highest fitness value are set as the leader of the new group. Steps 2 through 3 are repeated; conversely, if all particles have been grouped, Step 3 is complete.

Step 4. The particles no longer refer to their best position but to the leader particle L_g in the group in which they are located. The location update formula is as follows:

$\begin{matrix} V_{i} (n + 1) = ω \times V_{i} (n) + C_{1} \times {rand}_{1} \times (P_{L_{g}} \\ - X_{i} (n)) + C_{2} \times {rand}_{2} \times (P_{gbest} - X_{i} (n)) \end{matrix}$ (17) $X_{i} (n + 1) = X_{i} (n) + V_{i} (n + 1)$ (18)

Step 5. To improve the problems associated with the traditional particle swarm, this study employs a local search method [13]. By randomly selecting the positional information of two particles to transmit and share, particles with higher fitness values can guide particles with lower fitness values in a more desirable direction. Similarly, particles that have fallen into a regional solution can use particles further away from themselves to leave the solution; the two particles can thus be considered as having a mutually beneficial relationship aimed at improving each other’s position. The local search method is described as follows: $\begin{matrix} P_{i} (n + 1) = P_{i} (n) + {rand}_{1} (- 1, 1) \\ \times (P_{Gbest} - {mutual}_{vector} \times {BF}_{1}) \end{matrix}$ (19) $\begin{matrix} P_{j} (n + 1) = P_{j} (n) + rand (- 1, 1) \\ \times P_{gbest} - {Mutual}_{vector} \times {BF}_{2}) \end{matrix}$ (20) $Mutua l_{v} ector = \frac{P_{i} + P_{j}}{2}$ (21) where P_i is the ith particle in the particle swarm;P_i is a randomly selected particle from a particle swarm andrand₁ (-1, 1) , rand₂ (-1, 1) is a random number between [-1, 1], and P_Gbestis the current best position of the particle. BF₁ and BF₂ are benefit factors, which can be set to 1 or 2.

3.3.3 The learning behavior of wall-following control

The entire system block diagram is shown in Fig. 7. The IT2FC has four input signals; the four sonar sensed distances S₀, S₁, S₂ and S₃. The sonar detection range is limited to between 0.1 and 1 m, while the IT2FC outputs the rotational speeds V_L and V_R of the two axles. The output range is –5.24∼5.24 rad/s. The duration of the execution cycle is 500 ms and is referred to in this study as a time step.

Fig.7

Block diagram of the learning behavior of the wall-following control.

To ensure that the mobile robot is implementing WFB during the learning process, it possesses three termination conditions [25]: (1) Mobile robot collides with the wall; (2) Mobile robot deviates from the wall; (3) The actual distance the mobile robot moves is more than one lap of the training environment. The fitness function is used to evaluate the effectiveness of wall following until the termination condition of the algorithm is established. The fitness function contains four sub-fitness functions: SF₁, SF₂, SF₃, and SF₄, which are defined as follows: $F (.) = \frac{1}{1 + (α_{1} {SF}_{1} + α_{2} {SF}_{2} + α_{3} {SF}_{3} + α_{4} {SF}_{4})}$ (22)

The weighting coefficients of the control factors are[α₁, α₂, α₃, α₄] = [0.35, 0.35, 0.25, 0.05]. The higher the weight setting, the more important it is to evaluate this item. In this research, the objective functions SF₁ and SF₂ are the most important factors in learning to succeed.

The objective functionSF₁ evaluates the moving distance of the mobile robot. When the moving distance T_dis is closer to the preset value T_stop, the robot has moved closer to a successful detour training environment, as defined below: ${SF}_{1} = 1 - \frac{T_{dis}}{T_{stop}}$ (23) The objective functionSF₂ evaluates the distance between the side of the mobile robot and the wall RD (t), so that the robot stays at a fixed distance from the wall, where the RDvalue is then equal to zero. The RD (t) is defined as follows: $RD (t) = | S_{0} (t) - D_{wall}$ (24)

where d_wall is a preset fixed distance value. The objective function SF₂is defined as the average moving time RD (t): ${SF}_{2} = \frac{\sum_{t = 1}^{T_{total}} RD (t)}{T_{total}}$ (25)

The objective function SF₃ evaluates the angle θ between the mobile robot and the side walls. When the action robot is parallel to the wall, θ=90°.θ (t)is defined as follows: $θ (t) = {cos}^{- 1} (\frac{x (t)^{2} + S_{0}^{2} - S_{1}^{2}}{2 \times S_{0} \times x (t)})$ (26) where θ is the angle between sonar sensor S₀ andS₁ . x (t)is obtained by the following cosine theorem: $x (t) = \sqrt{S_{0}^{2} + S_{1}^{2} - 2 S_{0} S_{1} cos (40^{\circ}})$ (27)

To ensure that the mobile robot is parallel to the wall during the move, SF₃is defined as the average of all moving times|θ (t) -90|, formulated as follows: ${SF}_{3} = \frac{\sum_{t = 1}^{T} total | θ (t) - 90}{T_{total}} \times \frac{1}{90}$ (28)

The Objective function SF₄ evaluates the moving speed of the mobile robot. To ensure that the average speed of the robot remains close to the desired preset speed, mobile robots not only maintain a fixed distance from the wall but also increase their speed of movement, which is defined as follows: ${SF}_{4} = 1 - \frac{V_{average}}{V_{hope}}$ (29) whereV_average is the average moving speed of the mobile robot, and V_hope is the desired preset speed.

4 Experimental results

To verify the effectiveness of the proposed navigation control method, the experiments were divided into two parts: the WFB control and the deployment and navigation control of multiple mobile robots.

4.1 Mobile robot wall-following control

To determine the effectiveness of this method, the experimental results were compared with the performance results of other evolutionary algorithms. To demonstrate the stability of the algorithms, ten evaluations of each algorithm was conducted. Table 1 presents the initial preset parameters of the proposed IPSO, which comprises the total number of particles, the inertia weight ω, the accelerating constants C₁andC₂, the algebra, and the number of fuzzy rules. For many problems, the inertia weight ω is difficult to determine; therefore, it was set to 0.2, 0.3, 0.4, 0.6, and 0.8, as shown in the experimental results presented in Table 2. These results show that when ω = 0.3, performance is improved; therefore, ω was set to 0.3 in subsequent experiments.

Table 1
Initial set parameters for the proposed IPSO method

Total number particles Inertia weight\(ω) c ₁ c ₂ Generation Number of fuzzy rules

30 0.2,0.3,0.4,0.6,0.8 2 2 3000 5,6,7

Total number particles	Inertia weight\(ω)	c ₁	c ₂	Generation	Number of fuzzy rules
30	0.2,0.3,0.4,0.6,0.8	2	2	3000	5,6,7

Table 2

Evaluation using different inertia weights

Fitness value\ω	0.2	0.3	0.4	0.6	0.8
Best value	0.920	0.922	0.920	0.920	0.900
Worst value	0.910	0.915	0.902	0.882	0.822
Average value	0.914	0.919	0.914	0.904	0.841
Standard deviation	0.0041	0.0021	0.0042	0.0117	0.0221
Number of success runs	10	10	10	9	8

The experimental results for the fuzzy rule number are shown in Table 3. These show that although fewer fuzzy rules reduce computing time and memory space, their performance is poor (the higher fitness value is better). However, an increase in the number of fuzzy rules requires more evolutionary time and memory space to achieve superior results. Therefore, six fuzzy rules were set in this experiment.

Table 3

Evaluation of effectiveness using different fuzzy rules

Fitness Value\Number of rules	5	6	7
Best value	0.917265	0.921889	0.918647
Worst value	0.915781	0.915870	0.914394
Average value	0.916519	0.918766	0.916956
Standard deviation	0.0027	0.0021	0.0035
Number of success runs	10	10	9

To verify the effectiveness of the proposed method, the experimental results were compared with the performance of other evolutionary algorithms [21 –24]. Figure 8 presents the learning curve of different algorithms for the mobile robot WFB control. A detailed comparison of the results is presented in Table 4 and encompasses the best fitness, worst fitness, average fitness, standard deviation (STD), the number of training successes (NTS), and learning time (LT). The number of training successes indicates that the mobile robot can successfully learn to navigate the training environment within 10 evolutionary simulations. Figure 8 and Table 4 show that under the same conditions, the proposed IPSO performs more effectively because less time is used in the WFB control and the standard deviation is lower, indicating that the proposed algorithm has high stability.

Fig.8

Learning curve of different algorithms for the mobile robot wall-following control.

Table 4

Evaluation of learning behavior using different methods

Methods\Item	Fitness value				NTS	LT (sec)
	Best	Worst	Average	STD
IPSO	0.921	0.915	0.919	0.0021	10	119
PSO [24]	0.915	0.892	0.900	0.0051	9	277
QPSO [23]	0.918	0.907	0.912	0.0032	8	171
ABC [21]	0.902	0.892	0.900	0.0043	7	501
DE [22]	0.905	0.894	0.896	0.0069	8	168

Two testing environments were also established to verify that the WFB control can be successfully implemented in unknown environments after learning different algorithms. The environment shown in Fig. 9 contains many difficult large bends, whereas the environment shown in Fig. 10 contains many consecutive curves. Quantified indicators include the distance and time taken for a robot WF a circle and the average distance between the robot and the wall. Table 5 presents the experimental results, which show that the performance of the proposed IPSO algorithm is superior to other algorithms [18 , 27].

Fig.9

Paths of movement of the mobile robot using (a) IPSO, (b) PSO, (c) QPSO, (d) ABC, and (e) DE methods, respectively, in test environment 1.

Fig.10

Paths of movement of the mobile robot using (a) IPSO, (b) PSO, (c) QPSO, (d) ABC, and (e) DE methods, respectively, in test environment 2.

Table 5

Comparison of various methods in the two test environments

Methods\Environments	Test Environment 1 (Fig. 9)				Test Environment 2 (Fig. 10)
	Fitness value	Distance (m)	D_avg (m)	Time (sec)	Fitness value	Distance (m)	D_avg(m)	Time (sec)
IPSO	0.890	46.26	0.40	137	0.901	55.79	0.402	164
PSO [18]	0.889	47.46	0.42	310	0.900	57.58	0.405	378
QPSO [22]	0.888	47.60	0.42	195	0.896	56.87	0.382	241
ABC [26]	0.897	46.45	0.39	546	0.881	56.81	0.384	385
DE [27]	0.889	46.72	0.40	197	0.886	56.44	0.385	239

4.2 Deployment and navigation of multiple mobile robots

To verify the proposed navigation method, three test environments were established. In the following experiments, the green R represents the mobile robot, the red G represents the deployment target, the white O represents the dynamic obstacle, and the arrow represents the direction in which the obstacle was moving.

R2 have successfully reached the target points G1 and G2.

4.2.1 Dynamic obstacle avoidance

The test environment is shown in Fig. 11. Its purpose was to ascertain whether the proposed method can avoid the dynamic obstacle located in the environment. Figure 11 (a) shows the initial positional relationship between the mobile robot and the obstacle. Figure 11 (d)–(e) shows that the mobile robot R1 avoids the mobile robot R2 as a dynamic obstacle. Figure 11(g) shows that the mobile robot is safe from dynamic obstacles. Finally, in Fig. 11(h), both R1 and R2 have successfully avoided obstacles and reached the target points G1 and G2, respectively.

4.2.2 Beach life-saving robot

The beach environment is based on an aquatic life-saving robot test site located on ShaWan Beach at Kenting Pak in Taiwan. We first meshed the input map, as shown in Fig. 12, and then used the proposed self-clustering method to assign the robot’s position (Fig. 13) before moving the robot to the configured location. Figure 14 (a) shows the positional relationship between the first mobile robot and the obstacle. In Fig. 14 (b)–(e), the red box shows that the mobile robot is safely moving away from the dynamic obstacle. Figure 14 (f) shows that R1–R4 have successfully reached the target point.

Fig.11

Dynamic obstacle avoidance of two mobile robots (R1 and R2 represent the starting positions of mobile robots, G1 and G2 represent the deployment targets of mobile robots, and the arrow symbol represents the moving directions of obstacles).

Fig.12

Meshed beach environment.

Fig.13

Deployment of mobile robots using D_thr = 20in the beach environment.

Fig.14

Beach life-saving robots (green points denote starting positions, red points denote deployment targets, arrows denote the direction in which the obstacles moved, and the red circle denotes obstacle avoidance).

4.2.3 Wine Cellar Environment Sensing Robot

The wine cellar environment sensing robot is based on a test site constructed as a floor plan of a wine cellar in Beijing, China. We meshed the entered map, as shown in Fig. 15, and then assigned the mobile robot’s position using the proposed SCM (Fig. 16) before moving the mobile robot to the configured spot. Figure 17 (a) shows the positional relationship between the first robot and the obstacle. In Figs. 17 (b)–(c), (e)–(f), the red box shows that the robot is safe from moving obstacles. In Fig. 17 (d), R2 records the shortest distance for leaving the dead zone. Figures 17 (e)–(g) shows that R2 has entered the shortest distance range and successfully exited the infinite loop. An obstacle between R2 and the target was identified so it continued to follow the wall. Finally, all mobile robots in Fig. 17 (h) successfully arrive at the target point.

Fig.15

Meshed wine cellar environment.

Fig.16

Deployment of the mobile robots using D_thr = 20 in the wine cellar environment.

Fig.17

Wine cellar environment sensor robot (green points denote the starting positions, red points denote deployment targets, arrows denote the direction in which the obstacles moved, and the red circle denotes obstacle avoidance).

5 Conclusions

This study used SCM and IT2FC for multi-robot deployment and navigation in dynamic environments. The reinforcement learning method enables the mobile robot to adaptively develop the controller without the need for experts to design rules and without additional paired training data. The proposed SCM is a one-pass algorithm that can dynamically evaluate the cluster entries in the input space and automatically determines the number of clusters. Additionally, the proposed IPSO introduces the concept of grouping to cluster, preserves the diversity of particles, improves the stability of convergence, and improves the local search. The experimental results were divided into two parts. The first experiment verified the effectiveness of the proposed IT2FC for a mobile robot WFB control. The experimental results show that the performance (the distance and time taken for a robot WF a circle) of the proposed IT2FC with IPSO in terms of WFB control is more efficient than that of other methods in unknown environments. The second experiment verified the performance of the deployment and navigation of multiple mobile robots. The three test environments were dynamic obstacle avoidance, a beach life-saving robot, and a wine cellar environment sensing robot. The experimental results show that the proposed method can effectively avoid moving obstacles to move the robot to the configuration point.

Footnotes

Acknowledgments

The authors would like to thank the Ministry of Science and Technology of the Republic of China, Taiwan for financially supporting this research under Contract No. MOST 107-2218-E-005-023.

References

Greenaway

, Robots run amuck [automation farming], Engineering & Technology 5(3) (2010), 36–40.

Juang

C.F.

, Lai

M.G.

and Zeng

W.T.

, Evolutionary fuzzy control and navigation for two wheeled robots cooperatively carrying an object in unknown environments, IEEE Trans Cybern 45(9) (2015), 1731–1745.

Juang

C.F.

and Chang

Y.C.

, Evolutionary-group-based particle-swarm-optimized fuzzy controller with application to mobile-robot navigation in unknown environments, IEEE Transactions on Fuzzy Systems 19(2) (2011), 379–392.

Kim

C.J.

and Chwa

, Obstacle avoidance method for wheeled mobile robots using interval type-2 fuzzy neural network, IEEE Transactions on Fuzzy Systems 23(3) (2015), 677–687.

Boukas

, Kostavelis

, Gasteratos

and Sirakoulis

G.C.

, Robot guided crowd evacuation, IEEE Transactions on Automation Science and Engineering 12(2) (2014), 739–751.

Qiao

, Song

, Wang

, Zhang

and Wang

, Autonomous network repairing of a home security system using modular self-reconfigurable robots, IEEE Trans Consumer Electron 59(3) (2013), 562–570.

Jogal and Swapnil

, Sharma , Swachh-Bharat Bot: A Sweeping Robot, In: Mandal

D.K.

, Syan

C.S.

, (eds) CAD/CAM, Robotics and Factories of the Future, Lecture Notes in Mechanical Engineering. Springer, New 2016 (Delhi), 563–568.

Corts

, Martnez

, Karatas

and Bullo

, Coverage control for mobile sensing networks, IEEE Trans Robot Autom 20(2) (2004)243–255.

Reif

J.H.

and Wang

, Social potential fields: A distributed behavioral control for autonomous robots, Robotics and Autonomous Systems 27(3) (1999), 171–194.

10.

MacQueen

, Some methods for classification and analysis of multivariate observations, Proc of the Fifth Berkeley Symposium on Math Stat and Prob (1967), 281–296.

11.

Parker

, Distributed algorithms for multi-robot observation of multiple moving targets, Auton Robots 12(3) (2002), 231–255.

12.

Gutiérrez

M.A.

, Nair

, Banchs

R.E.

, Enriquez

L.F.D.H.

, Niculescu

A.I

, and Vijayalingam

, Multi-robot collaborative platforms for humanitarian relief actions, 2015 IEEE Conference on Humanitarian Technology (R10-HTC), (2015), 1–6.

13.

Cheng

and Prayogo

, Symbiotic organisms search: A new metaheuristic optimization algorithm, Comput Struct 139 (2014), 98–112.

14.

Fard

M.J.

, Ameri

, Chinnam

R.B.

and Ellis

R.D.

, Soft boundary approach for unsupervised gesture segmentation in robotic-assisted surgery, IEEE Robotics and Automation Letters 2(1) (2017), 171–178.

15.

Solis

, New frontiers in robotic surgery: The latest high-tech surgical tools allow for superhuman sensing and more, IEEE Pulse 7(6) (2016), 51–55.

16.

Castillo

and Melin

, A review on the design and optimization of interval type-2 fuzzy controllers, Appl Soft Comput 12(4) (2012), 1267–1278.

17.

Wai

R.J.

and Lin

Y.W.

, Adaptive moving-target tracking control of a vision-based mobile robot via a dynamic petri recurrent fuzzy neural network, IEEE Transactions on Fuzzy Systems 21(4) (2013), 688–701.

18.

Zou

, Kalivarapu

, Winer

, Oliver

and Bhattacharya

, Particle swarm optimization-based source seeking, IEEE Trans Autom Sci Eng 12(3) (2015), 865–875.

19.

Zaheer

S.A.

, Choi

S.H.

, Jung

C.Y.

and Kim

J.H.

, A modular implementation scheme for nonsingleton type-2 fuzzy logic systems with input uncertainties, IEEE/ASME Transactions on Mechatronics 20(6) (2015), 3182–3193.

20.

Ivanov

, Bhargava

and Donnelly

, Precision farming: Sensor analytics, IEEE Intelligent Systems 30(4) (2015), 76–80.

21.

Lemaignan

, Warnier

, Sisbot

E.A.

, Clodic

and Alami

, Artificial cognition for social human–robot interaction: An implementation, Artificial Intelligence 247 (2017), 45–69.

22.

S.L.

, Yang

, Ni

and Huang

, A quantum-based particle swarm optimization algorithm applied to inverse problems, IEEE Trans Magn 49(5) (2013), 2069–2072.

23.

Lloyd

S.P.

, Least squares quantization in PCM, IEEE Trans Information Theory 28(2) (1982), 129–137.

24.

Lin

T.C.

, Chen

C.C.

and Lin

C.J.

, Navigation control of mobile robot using interval type-2 neural fuzzy controller optimized by dynamic group differential evolution, Advances in Mechanical Engineering 10(1) (2018), 1–20, DOI: 10.1177–1687814017752483

25.

Lin

T.C.

, Chen

C.C.

and Lin

C.J.

, Wall-following and navigation control of mobile robot using reinforcement learning based on dynamic group artificial bee colony, Journal of Intelligent & Robotic Systems 92(2) (2017), 343–357.

26.

Zhang

, Zhang

, Ho

and Fu

, A modification of artificial bee colony algorithm applied to loudspeaker design problem, IEEE Transactions on Magnetics 50(2) (2014), 737–740.

27.

Y.L.

, Zhan

Z.H.

, Gong

Y.J.

, Chen

W.N.

, Zhang

and Li

, Differential evolution with an evolution path: A deep evolutionary algorithm, IEEE Trans on Cybernetics 45(9) (2014), 1798–1.

Deployment and navigation of multiple robots using a self-clustering method and type-2 fuzzy controller in dynamic environments

Abstract

Keywords

1 Introduction

2 Deployment of multiple mobile robots

2.1 The self-clustering method

3.1 Mobile robot description

3.3.1 Interval type-2 fuzzy controller

4.1 Mobile robot wall-following control

Table 1 Initial set parameters for the proposed IPSO method Total number particles Inertia weight\(ω) c 1 c 2 Generation Number of fuzzy rules 30 0.2,0.3,0.4,0.6,0.8 2 2 3000 5,6,7

4.2.1 Dynamic obstacle avoidance

4.2.2 Beach life-saving robot

Footnotes

Acknowledgments

References

Table 1
Initial set parameters for the proposed IPSO method

Total number particles Inertia weight\(ω) c ₁ c ₂ Generation Number of fuzzy rules

30 0.2,0.3,0.4,0.6,0.8 2 2 3000 5,6,7