Mobile robot navigation control using recurrent fuzzy cerebellar model articulation controller based on improved dynamic artificial bee colony

Abstract

In this study, an efficient navigation control method of mobile robot is proposed. The proposed navigation control method consists of behavior manager, toward goal behavior, and wall-following behavior. According to the relative position between the mobile robot and the environment, the behavior manager switches to determine toward goal behavior or wall-following behavior of mobile robot. A novel recurrent fuzzy cerebellar model articulation controller based on an improved dynamic artificial bee colony is proposed for performing wall-following control of mobile robot. The proposed improved dynamic artificial bee colony algorithm uses the sharing mechanism and the dynamic identity update to improve the performance of optimization. A reinforcement learning method is adopted to train the wall-following control of mobile robot. Experimental results show that the proposed method obtains a better navigation control than other methods in unknown environment.

Keywords

Evolutionary robots navigation control wall-following control artificial bee colony fuzzy cerebellar model articulation controller

Introduction

In recent years, mobile robot has become one of the popular researches. It is widely used in many applications to assist people solving many problems, such as environmental exploration, suspicious objects removal, object handling, and navigation.^1–3 In order to achieve these objectives, the popular research topics of the mobile robot control include the obstacle avoidance, wall-following, navigation, and target tracking.

Recently, many researchers have successfully used various methods^4,5 on mobile robot control. While keeping a constant distance to the wall, Turennout et al.⁴ solved the WF control problem by moving the mobile robot along a wall in a desired direction. Based on the sensorial information from two infra-red (IR) sensors, Gavrilut and Tiponut⁵ proposed a local navigation method for mobile robot. Together with the advantages of simple and low-cost sensing modalities, the IR sensors successfully resolve navigation tasks in environments with obstacles or WF problems. The external noise interference and sensitivity of sensing module hinder the traditional control methods^4,5 for stable control of mobile robot.

To solve the above-mentioned problems, the fuzzy logic control^6–9 has been successfully applied on mobile robot control. Fuzzy logic is proposed by Zadeh⁶ in 1965, which can be used on processing the situations in imprecision, ambiguity, multiple definitions, or uncertainty. A fuzzy controller consists of four parts: fuzzification, rule base, fuzzy inference engine, and defuzzification. Thongchai et al.⁷ described a sonar-based HelpMate robot using fuzzy control. The proposed fuzzy controller combines different information from all sonar sensors as a sensor mechanism. A novel fuzzy logic-based navigation algorithm was presented to effectively model correct environment and efficiently collect the noisy and uncertain sensory data with low-cost hardware equipment.⁸ Al-Sahib and Ahmed⁹ proposed a fuzzy logic controller by means of fuzzy decision making method. The controller detects obstacles and leads on the mobile robot from the origin to the destination. Although fuzzy control has good performance on WF, the disadvantage is that the rule must be designed by experts. In addition, Alitappeh et al.¹⁰ proposed a multi-objective optimization method to deploy/redeploy robots in the environment by considering two objectives for the deployment. To deal with the deployment problem, a discrete setup of locational optimization framework and Voronoi partitioning technique were employed. Morales et al.¹¹ applied support vector machines (SVM) to the path planning problem. The entire obstacle course is divided into two classes of data sets and a separating class boundary is obtained using SVM. This non-linear class boundary line determines the heading of the robot for a collision-free path. Pandey and Parhi¹² used the minimum rule-based adaptive neuro-fuzzy inference system (ANFIS) controller for the safe navigation of single and multiple mobile robots in the cluttered environment using the sensor-based steering angle control technique.

An evolutionary robotic (ER) becomes popular increasingly.^13–15 A reinforcement ant optimized fuzzy controller (RAOFC) method, proposed by Juang and Hsu,¹³ was designed for controlling mobile robot WF under reinforcement learning environments. A multi-objective, rule-coded, advanced, continuous-ant-colony optimization (MO-RACACO) algorithm¹⁴ was proposed for fuzzy controller (FC) design and was applied on multi-objective WF control for a mobile robot. Based on interval type-2 fuzzy controller (IT2FC), Hsu and Juang proposed an evolutionary WF control for mobile robot and defined a cost function to assess the WF performance of an evolutionary IT2FC.¹⁵ Contreras-Cruz et al.¹⁶ combined the artificial bee colony (ABC) algorithm as a local search procedure and the evolutionary programming algorithm to refine the feasible path found by a set of local procedures for solving the mobile robot path planning problem. According to the above-mentioned methods, these learning approaches avoid the exhaustive collection of supervised input–output training pairs and saves execution time.

The main purpose of the navigation control is that the mobile robot can effectively explore in unknown environment and reach the designated target successfully. The above-mentioned methods can effectively implement WF control, but some drawbacks exist during the navigation control, such as easily falling into a dead zone. In order to escape the dead zone, the mobile robot needs to rely on other mechanisms. The mobile robot requires at least two control behaviors to switch in the unknown environment. Therefore, this study set the behavior manager (BM) to switch corresponding behaviors according to the relative position between the mobile robot and the environment. Two behavior patterns are proposed as follows: (1) toward goal (TG) behavior and (2) WF behavior. If mobile robot encounters obstacles or wall on the way, it uses the WF behavior to avoid collision. The proposed two behaviors can avoid the dead zone during the mobile robot mining the unknown environment.

This study proposes a recurrent fuzzy cerebellar model articulation controller (RFCMAC) based on the improved dynamic artificial bee colony (IDABC) algorithm to achieve mobile robot WF control. The sensor module of the mobile robot is used to capture environment information as the inputs of the proposed RFCMAC controller. In addition, the proposed IDABC is used to develop the mobile robot autonomous controller. Experimental results show the effectiveness of the proposed navigation control method.

The proposed RFCMAC model

Figure 1 shows the proposed six-layer RFCMAC structure.^17,18 The Takagi–Sugeno–Kang-type (TSK-type) RFCMAC model realizes a similar fuzzy IF–THEN rule (hypercube cell) as follows.

Rule j: IF $x_{i}$ is $A_{1 j}$ and $x_{2}$ is $A_{2 j} \dots$ and $x_{i}$ is $A_{ij} \dots$ and $x_{N_{Dj}}$ is $A_{N_{Dj}}$

Then \hat{y_{j}} = \sum_{j = 1} O_{j}^{(4)} (α_{0 j} + Σ_{i = 1}^{N_{D}} α_{i j} x_{i})

where $x_{i}$ is the input variable, $\hat{y_{j}}$ is the local output variable, and $A_{ij}$ is the linguistic term of the precondition part with Gaussian membership function, i is the number of input variables, $O_{k}^{(4)}$ represents the output of the interaction feedback, $α_{0 j} + \sum_{i = 1}^{N_{D}} α_{ij} x_{i}$ is the basis TSK-type linear function of input variables, and rule j is the jth hypercube cell. The operation functions of the nodes in each layer of the TSK-type RFCMAC model are explained as follows. ( $O^{(l)}$ is the output of a node in the lth layer.)

Layer 1. The inputs are crisp values and any operation is not performed. Each node directly transmits input values to the next layer

O_{i}^{(1)} = u_{i}^{(1)} and u_{i}^{(1)} = x_{i}

(1)

Layer 2. Each fuzzy set $A_{ij}$ in this layer defines a Gaussian membership function and conducts a fuzzification operation for the jth fuzzy set $A_{ij}$ on the input variable $x_{i}$ , i = 1, …, n. Therefore, a Gaussian membership function is computed as follows

O_{i j}^{(2)} = \exp (- \frac{{[u_{i}^{(2)} - m_{i j}]}^{2}}{σ_{i j}^{2}}) and u_{i}^{(2)} = O_{i}^{(1)}

(2)

where $m_{ij}$ and $σ_{ij}$ are the mean and standard deviation (STD) of the Gaussian membership function of the jth term of the ith input variable $x_{i}$ , respectively.

Layer 3. Each node receives one-dimensional membership degree of the related rule from the nodes of a set in layer 2 and executes an algebraic product operation as follows

α_{j} = O_{j}^{(3)} = \prod_{i}^{N_{D}} u_{i j}^{(3)} and u_{i j}^{(3)} = O_{i j}^{(2)}

(3)

where ∏ denotes the product operator, N_D represents the number of the receptive filed functions for each input state, and $α_{j}$ represents the jth element of the association memory selection vector.

Layer 4. A recurrent rule node consists of an internal feedback and an external interaction feedback loop in layer 4. A temporal firing strength depends on both the current spatial and the previous temporal firing strengths to represent the output of a recurrent rule node. Equation (4) presents the temporal firing strength as a linear combination function as follows

O_{j}^{(4)} = \sum_{k = 1} (λ_{kj}^{q} \cdot O_{k}^{(4)} (t - 1)) + (1 - γ_{j}^{q}) \cdot u_{j}^{(4)}

(4)

where $u_{j}^{(4)} = O_{j}^{(3)}, γ_{j}^{q} = \sum_{k = 1}^{M} λ_{kj}^{q}, and λ_{kj}^{q} = R_{kj}^{q} / M (0 \leq R_{kj}^{q} \leq 1)$ is the rule and M is the total number of current rules. The compromised ratio between the current and previous inputs to the network outputs is determined by the recurrent weights $λ_{kj}^{q}$ .

Layer 5. A function of linear combination of input variables represents an optional node in layer 5. The value of its corresponding association output of interaction feedback loop was used as matching degree to generate a partial fuzzy output for each linear combination. The formula expressed as

O_{j}^{(5)} = O_{j}^{(4)} (a_{0 j} + \sum_{i = 1}^{N_{D}} a_{ij} x_{i})

(5)

where $a_{0 j}$ and $a_{ij}$ denote the scalar value, N_D the number of the input dimensions, and x_i the ith input dimension.

Layer 6. In order to obtain the actual output y, the centroid of area (COA) is used to convert the fuzzy output into a scalar output

y = \frac{\sum_{j = 1}^{N_{L}} O_{j}^{(4)} (a_{0 j} + \sum_{i = 1}^{N_{L}} a_{ij} x_{i} \sum_{i = 1}^{N_{D}})}{\sum_{j = 1}^{N_{L}} O_{j}^{(4)}}

(6)

where N_L represents the number of the hypercube cells.

Figure 1.

Structure of the RFCMAC model.

Proposed IDABC

In this section, the proposed IDABC is used to adjust the parameters of RFCMAC model effectively. Each bee represents all control parameters of RFCMAC, which is shown in Figure 2. A fuzzy hypercube cell contains the center $m_{ij}$ and width $σ_{ij}$ of Gaussian membership function, the constants $a_{0 j}$ and $a_{ij}$ of the corresponding memory of linear combination of input variables, and hypercube weights $R_{kj}$ of the RFCMAC.

Figure 2.

Encoding of a bee.

The ABC algorithm was proposed for parameter optimization which simulates the foraging behavior of bee colony.¹⁹ It consists of employed bees, onlooker bees, and scout bees. Three kinds of bees cooperate with each other to find the food source. This article proposes the modifications of ABC to enhance the performance of optimization, including best information sharing mechanism and dynamic identity update. Figure 3 shows the flowchart of the proposed IDABC algorithm. The detailed descriptions are introduced as follows:

Initialization phase. Each bee represents a problem solution and is initialized randomly from the solution space.

Fitness evaluation phase. The fitness value of each bee is calculated and represents the corresponding performance.

Employed bees phase. In traditional ABC, employed bees look for new food sources and adopt random search in their neighborhood. To enhance the convergence speed, the information of the best solution is added to the searching direction. Search formula is described as follows

V_{ij} = x_{ij} + \emptyset_{ij} (x_{ij} - Gbes t_{j})

(7)

X_{i} = {\begin{matrix} V_{i}, if f (V_{i}) > f (X_{i}) \\ X_{i}, otherwise \end{matrix}

(8)

Onlooker bees phase. Onlooker bees choose a new food source according to the probability value associated with that fitness value of the employed bee. The roulette wheel is used to ballot the employed bee k. $P_{i}$ and the search rule are defined as follows

P_{i} = \frac{fi t_{i}}{\sum_{n = 1}^{SN} fi t_{n}}

(9)

V_{ij} = x_{ij} + \emptyset_{ij} (x_{ij} - x_{kj})

(10)

Scout bees phase. When employed or onlooker bees are not updated during a specific period of time, the scout bees adopt a random search to find new food source

X_{i}^{j} = X_{\min}^{j} + rand [0, 1] (X_{\max}^{j} - X_{\min}^{j})

(11)

Bees identity update phase. In traditional ABC, the proportions of employed bee and onlooker bee are equal. This property leads the employed bees searching direction to the colony convergence over speed. Therefore, this study adopts the bee identity update method to become employed or onlooker according to the last searching result

Bee {(t + 1)}_{i} = {\begin{matrix} employed, if f (V {(t)}_{i}) < f (X {(t)}_{i}) \\ Onlooker, otherwise \end{matrix}

(12)

Figure 3.

The flowchart of the proposed IDABC algorithm.

Navigation control of a mobile robot

Mobile robot description

The mobile robot of Pioneer 3-DX is shown in Figure 4. The characteristics of the mobile robot are high payload, high endurance, strong extensibility, and support cross-platform Software Development Kit (SDK). The SDK consists of the motion control, the client-server architecture, and the various accessories. Therefore, the mobile robot allows users to integrate all peripheral equipment and fulfill research goals.

Figure 4.

Pioneer 3-DX mobile robot and arrangement of sonar sensors.

The Pioneer 3-DX mobile robot has two-wheel drive with the vehicle of a personal computer (PC) and is fully autonomous intelligence. The Advanced Robot Control and Operations Software (ARCOS)-based robot supports four sonar arrays, each with up to eight sonar sensors that provide obstacle detection and surrounding information for collision avoidance.

WF behavior

First, the training environment is set to 11 m × 8 m and is shown in Figure 5. It consists of the straight line, the bevel-angle, and the right-angle problems. Figure 6 shows the control diagram of the mobile robot using a RFCMAC controller with IDABC learning algorithm.

Figure 5.

Training environment of wall-following control.

Figure 6.

Block diagram of mobile robot wall-following control.

In the training process, the mobile robot WF control includes three terminal conditions. In the evolutionary process, when the terminal condition occurs, the number of evolution counts and the robot returns to the initial point of the training environment and re-runs again. The evolutionary process is not terminated until the mobile robot successfully takes a turn round in an unknown environment. Three terminal conditions are described as follows:

Mobile robot collides with the wall. For example, when the distance from the sonar sensor is less than 0.1 m.

The robot is far away from the wall. For example, when the distance $S_{4}$ is greater than 0.7 m.

The mobile robot can successfully take a turn round in an unknown environment.

The objective function of a mobile robot controller depends on an unknown environment. In this study, the assessment factors consist of four objective functions $C F_{1}, C F_{2}, C F_{3}, and C F_{4}$ and are defined as follows:

(a) Objective function $C F_{1}$ : When a collision occurs, the proportionality of the robot moving distance $(T_{dis})$ and the pre-defined walking maximum distance $(T_{stop})$ is defined as follows

C F_{1} = 1 - \frac{T_{dis}}{T_{stop}}

(13)

If the actual moving distance of mobile robot is larger than the pre-defined walking maximum distance $(T_{stop})$ , set $T_{dis} = T_{stop}$ . In this situation, the robot satisfies the objective function $C F_{1}$ . If the collision-free control occurs, the value of objective function $C F_{1}$ is equal to zero.

(b) Objective function $C F_{2}$ : The objective function describes the distance $RD (t)$ between the right/left wheel of mobile robot and the wall at time t. If the mobile robot keeps a fixed distance to the wall, the $RD (t)$ is equal to zero at time t. $RD (t)$ is defined as follows

RD (t) = | S_{4} (t) - d_{wall} |

(14)

where $d_{wall}$ is the pre-defined fixed distance between robot and wall. $d_{wall}$ is set as 0.4 m in this study. The average distance for taking a turn round is defined as $C F_{2}$

C F_{2} = \frac{\sum_{t = 1}^{T_{total}} RD (t)}{T_{total}}

(15)

(c) Objective function $C F_{3}$ : The objective function describes the angle $(θ)$ between the side of mobile robot and the wall, as shown in Figure 7. If the mobile robot moves parallel to the wall, the angle $θ$ is 90°. The angle $θ (t)$ is defined as follows

θ (t) = co s^{- 1} \frac{x {(t)}^{2} + S_{4}^{2} - S_{3}^{2}}{2 \times S_{4} \times x (t)}

(16)

where θ is an angle between $S_{3}$ and $S_{4}$ of sonar sensing distances. The $C F_{3}$ defines the average angle $θ (t)$ at all time steps $T_{total}$ as follows

C F_{3} = \frac{\sum_{t = 1}^{T_{total}} | \emptyset (t) - 90 |}{T_{total}}

(17)

(d) Objective function $C F_{4}$ : The objective function describes the proportionality between an average moving speed $(V_{average})$ of mobile robot and the pre-defined speed $V_{hope}$ (set at 0.6 m/s in this study)

C F_{4} = 1 - \frac{V_{average}}{V_{hope}}

(18)

Figure 7.

Illustration of the $d_{wall}$ and $θ$ .

If the average moving speed is greater than the pre-defined speed, set $V_{hope} = V_{average}$ . This indicates that the mobile robot satisfies the conditions and moves at high speed.

The fitness function $f (\cdot)$ is based on the control factor of four objective functions $C F_{1}, \dots, C F_{4}$ , which combine the weighting coefficients $α_{1}$ , $α_{2}, α_{3}$ , and $α_{4}$ to form a total objective function

f (\cdot) = \frac{1}{1 + (α_{1} C F_{1} + α_{2} C F_{2} + α_{3} C F_{3} + α_{4} C F_{4})}

(19)

In the training process, the goal is the mobile robot can keep a fixed distance to the wall and take a turn round in an unknown environment. Thus, CF₁ and CF₂ are more important than CF₃ and CF₄ for performing the mobile robot WF control. Therefore, the weighting coefficients of control factors are set as $[α_{1}, α_{2}, α_{3}, α_{4}] = [0.45, 0.45, 0.05, 0.05]$ in this study.

TG behavior

In TG behavior, the mobile robot needs to compute the angle with the mobile robot and the goal $θ_{TG}$ defined as follows

θ_{TG} = θ_{Robot} - θ_{Goal}

(20)

where $θ_{Robot}$ is the angle between robot’s orientation and x axis. $θ_{Goal}$ is the angle between goal and x axis (Figure 8).

Figure 8.

Illustration of the goal angle $θ_{Goal}$ and the robot orientation $θ_{Robot}$ .

BM

The BM switches TG behavior and WF behavior according to the relative position between the mobile robot and environment. First, we divide the mobile robot into four regions ( $R_{1}$ , $R_{2}$ , $R_{3}$ , $R_{4}$ ). The four regions are shown in Figure 9. Thereafter, locate which region the orientation of the goal is.

Figure 9.

Division of the mobile robot into four regions.

If the mobile robot detects obstacles $(S_{n} < 1 m)$ in these regions, BM will execute mobile robot the WF mode. Otherwise, execute the TG mode until reach the goal.

Experimental results

In this section, a RFCMAC based on an IDABC is proposed for controlling the mobile robot WF in an unknown environment. Four testing environments are generated to verify the proposed method for navigation control.

WF learning

The proposed IDABC algorithm is used to train the mobile robot WF control. Table 1 shows the initial parameters of the proposed algorithm. Figure 10 presents the moving path of mobile robot by the proposed RFCMAC model with IDABC learning algorithm.

Table 1.

Initial parameters of the proposed algorithm.

SN	Limit	Generation	Number of fuzzy hypercube
30	100	3000	6

Figure 10.

The moving path of mobile robot using the proposed algorithm in training environment.

We also compare the proposed IDABC algorithm with particle swarm optimization (PSO),²⁰ quantum-behaved particle swarm optimization (QPSO),²¹ differential evolution (DE),²² adaptive DE with optional external archive (JADE),²³ and traditional ABC.¹⁹ In all, 10 replications are run in this experiment. The performance measurements include the best fitness value, the worst fitness value, the average fitness value, the STD of fitness value, and the number of success runs. The STD of fitness value represents the square root of the average of the squared deviations of each fitness values from the mean fitness value. The number of success runs represents how many times mobile robot can detour around the training environment successfully in 10 replications. Comparison results are shown in Table 2. The proposed IDABC has a better fitness value than other methods^19–23 under the same conditions. Moreover, the STD of the proposed IDABC is the smallest, which represents that the proposed algorithm is more stable during learning process.

Table 2.

Comparison results of various evolutionary methods for the mobile robot wall-following control.

Fitness	Algorithm
Fitness	PSO²⁰	QPSO²¹	DE²²	JADE²³	ABC¹⁹	Proposed
Best	0.895	0.907	0.888	0.900	0.874	0.903
Worst	0.743	0.765	0.746	0.828	0.796	0.886
Average	0.823	0.871	0.797	0.869	0.856	0.894
STD	0.054	0.028	0.046	0.016	0.018	0.004
Number of success runs	4	7	3	8	6	10

PSO: particle swarm optimization; QPSO: quantum-behaved particle swarm optimization; DE: differential evolution; ABC: artificial bee colony; STD: standard deviation.

Navigation control of mobile robot

The navigation control of mobile robot uses the BM to determine TG behavior or WF behavior of mobile robot according to the relative position between the mobile robot and the environment. Four different environments are used for testing the proposed navigation control method. Figure 11 shows the trajectory of a mobile robot in four different unknown environments. In Figure 11(a), the path of blue arrow represents the mobile robot executing the TG behavior, whereas the others represent the mobile robot executing the WF behavior. Experimental results demonstrate that the proposed method successfully implements the mobile robot navigation control in unknown environments.

Figure 11.

Navigation control results using the proposed approach in four testing environments.

In order to verify the performance of the proposed navigation control method, two evaluation indices are used. One index is the total moving distance of mobile robot. If the mobile robot has a better WF behavior, the total moving distance is reduced effectively. The other index is the time spending of mobile robot for completing the navigation control. That is to evaluate the moving speed of the mobile robot in an unknown environment. The detailed best performance analysis is shown in Table 3. In this table, the proposed navigation control method is better than other methods^19–23 in the total moving distance and the time spending.

Table 3.

The best performance analysis of various evolutionary methods in navigation control.

Algorithm	Environment
	Figure 11(a)		Figure 11(b)		Figure 11(c)		Figure 11(d)
	Distance (m)	Time (s)	Distance (m)	Time (s)	Distance (m)	Time (s)	Distance (m)	Time (s)
Proposed	35.24	134.5	58.53	220.5	28.67	110	56.38	215.5
ABC¹⁹	35.32	143.5	58.19	230.5	28.91	111	56.94	229
PSO²⁰	35.84	608	58.91	818	28.80	370	57.87	963.5
QPSO²¹	35.51	376.5	58.41	520	28.82	273.5	57.1	605
DE²²	35.76	423.1	58.95	592	28.97	332	57.68	698
JADE²³	35.28	410.5	58.65	585	28.77	325	57.44	691

PSO: particle swarm optimization; QPSO: quantum-behaved particle swarm optimization; DE: differential evolution; ABC: artificial bee colony; STD: standard deviation; JADE: adaptive DE with optional external archive.

Conclusion

This study proposes a novel RFCMAC based on IDABC learning algorithm for the mobile robot navigation control. The proposed navigation control method consists of BM, TG behavior, and WF behavior. According to the relative position between the mobile robot and the environment, the BM switches to determine TG behavior or WF behavior of mobile robot. The proposed IDABC algorithm uses the sharing mechanism and the dynamic identity update to improve the performance of optimization. The advantages of the proposed method include the global search ability, the convergent speed, and the solution accuracy. Thus, the proposed method prevents falling into a local solution. Experiment results show the effectiveness and stability of the proposed navigation control method.

Footnotes

Academic Editor: Stephen D Prior

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This paper was sponsored by the Program of Tianjin Science and Technology Commissioner of China (no.16JCTPJC50700).

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