Research of biogeography particle swarm optimization for robot path planning

Neurocomputing 148 (2015) 91–99

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Neurocomputing journal homepage: www.elsevier.com/locate/neucom

Research of biogeography particle swarm optimization for robot path planning Hongwei Mo n, Lifang Xu Automation College, Harbin Engineering University, Nantong Road, Nangang District, Harbin 150001, PR China

art ic l e i nf o

a b s t r a c t

Article history: Received 27 March 2012 Received in revised form 29 May 2012 Accepted 4 July 2012 Available online 1 August 2014

Global path planning of mobile robot in a static environment is one of the most important problems in the field of mobile robot. Biogeography-based Optimization (BBO) is a relative new algorithm inspired by biogeography. It mainly uses the biogeography-based migration operator to share the information among solutions. Particle swarm optimization (PSO) is a classical heuristic search method whose mechanics are inspired by the swarming or collaborative behavior of biological populations. This paper presents a new method of global path planning by combining BBO, PSO and approximate voronoi boundary network (AVBN) in a static environment. The idea of this paper is to apply position updating strategy of PSO to increase the diversity of population in BBO and then use the obtained biogeography particle swarm optimization algorithm (BPSO) to optimize the paths in path network obtained by AVBN modeling. Experimental results in simulation show that the proposed method is feasible and effective. & 2014 Elsevier B.V. All rights reserved.

Keywords: Robot path planning Biogeography-based optimization Particle swarm optimization Approximate voronoi boundary network Static environment

1. Introduction Robot path planning (RPP) is a key issue in autonomous robot technology. The basic RPP problem deals with static environments, that is, workspaces solely containing stationary obstacles. RPP is also an important problem in navigation of autonomous mobile robots, which is to find an optimal collision-free path from a starting point to a goal in a given environment [1]. There have been various methods proposed by researchers to solve RPP problems. Methods in RPP can be divided into the following two methods. The first method is based on environment information directly. Though such a method has a good adaptability to the changes of environment, it is difficult to find an ideal path under complex environment. So it is generally adopted in the local path planning. The second method is based on a structured model. The structured model embodies the typical character of the environment and can help to decrease the calculation of path planning. Many conventional path planning methods, such as cell decomposition [2], roadmaps [3] have difficulty in solving RPP with complex environments due to their high cost of computation. Approximate voronoi boundary network (AVBN) is a structured method that obtains the non-smooth path network from the sensors in formation [4]. It needs not decompose the complex obstacles, so the model of the environment is simplified. Such

n

Corresponding author. Tel./fax: þ 86 10 82512080. E-mail address: [email protected] (H. Mo).

http://dx.doi.org/10.1016/j.neucom.2012.07.060 0925-2312/& 2014 Elsevier B.V. All rights reserved.

a method embodies the network structure of the free area of environment with less nodes, so the complexity of path planning problem is reduced largely. In recent years, we have seen that many intelligent optimization approaches inspired by natural phenomenon or mechanisms had been used for RPP due to their robust and abilities of parallel computing. Genetic algorithm and neural networks, both of which are well known intelligent optimization approaches, had been used for solving RPP many years ago. Sugihara et al. had adopted a genetic algorithm to solve the problem based on cell representation of the environment [5]. In [6], Gemeinder et al. presented a genetic algorithm (GA)-based path planning software for mobile robot systems focusing on energy consumption. AL-Taharwa et al. presented genetic algorithm to help a controllable mobile robot to find an optimal path between starting and ending point in a grid environment [7]. In [8], Mohanta et al. used petri-GA for path planning strategy of autonomous mobile robot navigation.Yang et al. applied a neural network to program the collision-free path of a mobile robot in a dynamic environment [9,10]. Xiong et al. proposed a RPP method based on recurrent neural network [11]. Besides the classical intelligent approaches mentioned above, Bell and McMullen had used ant colony algorithm, a well known swarming intelligence approach, to solve RPP [12]. A novel method for the real-time globally optimal path planning of mobile robots is proposed based on the ant colony system (ACS) algorithm in [13]. Another well known swarm intelligence method-particle swarm optimization (ACO) had also been utilized to solve RPP problem. Saska et al. used PSO to optimized the parameters of splines, which was a path description approach proposed by the authors

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[14]. Chen et al.proposed an improved PSO to optimize the path of a mobile robot through an environment containing static obstacles [15]. It can get smooth path. Lu et al. used particle swarm optimization, another well known swarm intelligence method to solve RPP in unknown environment [16]. The other intelligent algorithms used in RPP include artificial immunes systems, which are the intelligent approaches inspired by immunology theories and mechanisms of human immune system also applied in RPP [17–19]. Culture algorithms [20], memetic algorithm [21] and simulation annealing algorithm [22] had also been used for RPP. Each method has its own advantage over others in certain aspects. So, a hybrid technique based on ACO and fuzzy system was proposed in [23]. In [24], the problem of finding the optimal collision free path in complex environments for a mobile robot is solved using a hybrid neural network, GA and a local search method. Generally speaking, the main difficulties for RPP problems are computational complexity, local optimum and adaptability, so researchers have always been seeking alternative and more efficient ways to solve the problem. PSO was invented by Kennedy and Eberhart in the mid 1990s while attempting to simulate the choreographed, graceful motion of swarms of birds as part of a sociocognitive study investigating the notion of ‘collective intelligence’ in biological populations [25]. In PSO, a set of randomly generated solutions (initial swarm) propagates in the design space towards the optimal solution over a number of iterations (moves) based on a large amount of information about the design space that is assimilated and shared by all members of the swarm. It seems to be an attractive one to study since it has a simple but efficient nature added to being novel. It can even be a substitution for other basic and important evolutionary algorithms. Recently, the science of biogeography had been paid attention by researchers from computer science. BBO is a bio-inspired optimization technique inspired by biogeography [26]. Over the past three years, many improvement to BBO had been finished by Simon and some other researchers [27–33]. Bhattacharya et al. used BBO to solve the problem of economic load dispatch problem [34]. We have used BBO to successfully solve the problem of traveling salesman problem [35]. BBO is a new intelligent algorithm which shows good performance in many respects. In the following sections, we design a new RPP method by combining BBO and PSO. In order to calculate the trajectory in the global map, this paper presents a new RPP method based on the combination of BPSO and AVBN method. The biogeography based particle swarm optimization algorithm is adopted to search the possible paths and the best one is obtained. The remainder of this paper is organized as follows. In Section 2, the basic BBO and PSO algorithm are introduced and then BPSO is proposed. In Section 3, we combine BPSO and AVBN to solve the RPP. Simulation results and analysis are shown in Section 4. Finally, conclusions are drawn in Section 5.

2. Biogeography particle swarm optimization 2.1. Biogeopraphy-based optimization In BBO, each possible solution is an island and their features that characterize habitability are called suitability index variables (SIV). The goodness of each solution is called its habitat suitability index (HSI) [27]. A habitat is a vector of SIVs initialized randomly and then follows migration and mutation step to reach global minima. For solving an engineering problem, a good solution is analogous to an island with a high HSI, and a poor solution

represents an island with a low HSI. High HSI solutions resist change more than low HSI solutions. By the same token, high HSI solutions tend to share their features with low HSI solutions. Poor solutions accept a lot of new features from good solutions. In BBO, a population of candidate solutions is represented as vectors of integers. Each integer in the solution vector is considered to be an SIV. The main feature of BBO differs from the other evolutionary computation lies in its migration strategy or migration operation. In BBO, each individual has its own emigration rate λs and immigration rate μs , which are functions of the number of species s; ðs ¼ 1; 2:::i; :::PÞ in the habitat and can be expressed by Eqs. (1) and (2) [27]. λs ¼

Es P

ð1Þ


s μs ¼ I 1  P

ð2Þ

where E ¼ maxλs , I ¼ maxμs , and P ¼ population size. Generally, E and I are unit matrix. Let us consider the probability P s that the habitat contains exactly s species. The probabilities of each species count can be calculated using the differential Eq. (3). 8 > <  ðλs þ μs ÞP s þ μs þ 1 P s þ 1 ; s ¼ 0 P s ¼  ðλs þ μs ÞP s þ λs  1 P s  1 þ μs þ 1 P s þ 1 ; 1 r s osmax  1 > :  ðλ þ μ ÞP þ λ P ;s¼s :

s

s

s

s1 s1

ð3Þ

max

where smax is the maximal number of species count. In migration process, the information shared among habitats is depended on λs and μs of each solution. Migration strategy is described as follows [27]: Step Step Step Step Step Step Step Step Step Step Step Step

1: For i¼ 1 to P 2: Select H i with λi 3: If H i is selected 4: For j¼ 1 to P 5: Select H j with probabilityp μi 6: If H j is selected 7: Randomly select an SIV σ from H j 8: Replace a random SIV in H i with σ 9: End if 10: End for 11: End if 12: End for

In the migration procedure, each habitat (candidate solution) is modified based on other habitats. If a given habitat is selected to be modified, then its immigration rate λi is used to probabilistically decide whether or not to modify each suitability index variable (SIV) in that habitat. If a given SIV in a given habitat H i is selected to be modified, then the emigration rates μi of the other habitats are used to probabilistically decide which of the habitats should migrate a randomly selected SIV to solution. Based on the process of migration, the adaptive ability of habitat is improved by regulating immigration rate and emigration rate, migration topology, and migration strategy. Thus, it can get optimal solution of problem. The main characteristic of BBO is that the original population does not disappear in each generation, but improve the fitness by migration, and it can decide migration rate by fitness. After migration process, the mutation is used to increase the diversity of the population to get better solutions. Mutation operator changes a habitat's SIV randomly based on mutation rate

H. Mo, L. Xu / Neurocomputing 148 (2015) 91–99

mi . The mutation rate mi is expressed as [27].   Ps mi ¼ P mute 1  P max

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mutation rate,w1 is the weight of the velocity, and c1 and c2 are the cognitive and social parameters. ð4Þ

where P max ¼ arg max P s ; i ¼ 1; :::; P:P mute is a parameter deciding mutation rate. Suppose that G is maximum number of generation. The procedure of BBO is as follows: Step 1: Initialize parameters:P,G,P mute Step 2: Evaluate the fitness for each individual in P Step 3: While the termination criteria is not met do Step 4: Save the best habitats in a temporary array Step 5: For each habitat, map the HSI to number of species s, λi and μi according to (1) and (2) Step 6: Probabilistically choose the immigration island based on the immigration rates Step 7: Migrate randomly selected SIVs based on the selected island in Step 6 Step 8: Mutate the worst half of the population according to (4) Step 9: Evaluate the fitness for each individual in P Step 10: Sort the population from best to worst Step 11:G ¼ G þ1 Step 12: End while

Step 1: Initialize parameters: P,G,P mute ,w; c1 ; c2 . Step 2: Evaluate the fitness for each individual in P Step 3: While the termination criteria is not met do Step 3.1: Record the previous best position of each habitat P i and their neighborhood best position P g . Step 3.2: For each habitat map the HSI to number of species s, λi and μi , probabilistically choose the immigration island based on the immigration rates Step 3.3: If a habitat is selected to be immigrated migrate randomly selected SIVs based on the selected island else update the position of current habitat according to (5) End if Step 3.4: Mutate the worst half of the population Step 3.5: Evaluate the fitness for each individual in P and sort the population from best to worst, save the best two habitats Step 4: End while

3. The path planning based on AVBN 2.2. PSO

3.1. Environment modeling

In particle swarm optimization, particles communicate with each other while learning their own experience, and gradually fly into better regions of the problem space. The problem space is initialized with random solutions in which the particles search for the optimum. Each particle randomly searches in the problem space by updating itself with the best solution it ever found and the social information gathered from other particles. Suppose Z is the dimension of the searching space and N is the number of particle. The position and velocity of the ith particle is represented as X i ¼ ðxi1 ; xi2 ; :::; xiD Þ and V i ¼ ðvi1 ; vi2 ; :::; viD Þ is the velocity of the ith particle, each particle maintains a memory of its previous best position denoted by P i ¼ ðpi1 ; pi2 ; :::; piD Þ and the best position of the population gbest is denoted as P g ¼ ðpg1 ; pg2 ; :::; pgD Þ. Each particle updates its position and velocity according to the following equations: 8 < V k þ 1 ¼ wV k þ c1 r 1 ðP i  X k Þ þ c2 r 2 ðP g X k Þ i i i i ð5Þ : X ki þ 1 ¼ X ki þ V ki þ 1

The RPP problem considered in this section is in a known static environment. And the robot possesses the information of the target and the obstacles being detected during the path planning. In RPP, the goal is to find the safest and shortest path, at same time, keeping as far away from obstacles as possible. To reach this aim, a Voronoi diagram of the obstacle boundaries may be constructed [36]. Considering a 2-dimensional environment, the mobile robot is regarded as a point. The working area is divided into 400  400 grids environment. Each grid is corresponding to a small area in real environment. The distribution of obstacles in the environment is represented by integer matrix 400  400. The value indicates the obstacle grid, and the value 0 indicates the free grid.

where w is the inertia in range [0.9, 0.4] that increases linearly, c1 and c2 are two positive constants, usually we choose c1 and c2 ¼2; r 1 and r 2 are two random functions in the range [0,1]. Within the defined problem space, the system has a population of particles. Each particle is randomized with a velocity and flies in the search space. The velocities and positions of the particles are constantly updated until they have all reached the target. 2.3. The procedure of BPSO In the original BBO, if there is no habitat selected for immigration, the selected habitat for emigration is not changed. In this case, it has no benefit for increasing the diversity of population. Inspired by the concept of PSO, we use the particle position strategy to modify the habitat which is not selected to be immigrated. In the BPSO algorithm, suppose that P is population size, G is the maximum number of generation, P mute is a parameter deciding

3.1.1. Definitions of AVBN A1l the grids are divided into the free set ðFÞ and the obstacle set ðFÞ.The obstacle set is composed of several separated obstacle sub sets. F i ði ¼ 1; 2; :::; MÞ). According to the characteristics of Voronoi diagram in continuous vector space, the generalized Voronoi diagram in discrete raster based space can be defined [4]. Definition 1. The shortest distance from a free grid x to the ith obstacle is Di ðxÞ, where Di ðxÞ ¼ min jjx; yjj; y A F. Definition 2. The shortest distance from a free grid x to all the obstacles is DðxÞ,where DðxÞ ¼ min fD1 ðxÞ; D2 ðxÞ; :::; DM ðxÞg ¼ min jjx; yjj; yA F, where jjx; yjjis the distance between x and y. It is the number of raster in the direction of x-y. It is different from the Euclid distance in vector space. Definition 3. The boundary between the i th and the j th obstacle is Bi;j a set of points that satisfy the condition Bi;j ¼ fx A FjDi ðxÞ ¼ Dj ðxÞ ¼ DðxÞ; ia jg. The boundary Bi;j is continuous but not smooth. The intersection of two or more boundaries is the basic nodes of network. These boundaries and nodes consist of AVBN.

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Fig. 1. Voronoi boundary.

1abeled in the same number. The working area is assumed being surrounded by a rectangular obstacle. 3.1.2.1. Raster based enlargement of obstacles. The obstacle cluster is the kernel of enlargement. Free-grid is eroded by its neighboring obstacle grid. Every obstacle cluster grows up uniformly after one enlargement. The enlargement should not stop until all the free grids are fused into eroded area (Fig. 1(a)–(d)), in which every area is labeled with different numbers and in different colors. 3.1.2.2. Recognizing Voronoi boundary and node

Fig. 2. Path network.

3.1.2. Construction of AVBN model The obstacles detected by sensor are discrete grid data. At first, the obstacle grid is enlarged to its neighbor grids, so some small obstacle clusters are fused to an integrated obstacle block. The scale of obstacle pre-enlargement should involve the consideration of not only the safe traversing radius of mobile robot, but also the error of sensors and positioning. The algorithm checks obstacle blocks and labels them. Every grid of the same obstacle block is

1) Recognizing the Voronoi boundary From Fig. 1,the boundary between every two areas can be obtained by recognizing intersection of different colored area. There are 8 neighboring grids in maximum for each grid. A grid will be labeled as a boundary grid if the upside grid or right grid is not at the same value as itself. At first, search out all the grids whose upside grid does not belong to the same area (see Fig. 1(a) and (b)),then search out the ones whose right grid is not at the same value (see Fig. 1(c)). A boundary grid and its neighboring grids are integrated as one Voronoi node if the neighboring grids belong to three or more than three different areas (see Fig. 1(d)). 2) Recognizing the Voronoi nodes The basic nodes are the intersections of these boundaries. These basic nodes and boundaries make up the AVBN that is the path network for mobile robots. The branches connecting

H. Mo, L. Xu / Neurocomputing 148 (2015) 91–99

every two nodes are non smooth routes. The basic nodes are numbered from 1 to 15 as shown in Fig. 2.

95

The correlated nodes table in Fig. 2 is listed as follows: L1 ¼ f2; 8g; l1 ¼ 2; L2 ¼ f1; 3; 5g; l2 ¼ 3; L3 ¼ f2; 4; 7g; l3 ¼ 3; L4 ¼ f3; 6; 7; 9g; l4 ¼ 4; L5 ¼ f2; 6; 8g; l5 ¼ 3; L6 ¼ f4; 5; 11g; l6 ¼ 3; L7 ¼ f3; 4; 10g; l7 ¼ 3; L8 ¼ f1; 5; 12g; l8 ¼ 3;

3.1.3. Global path planning The AVBN method can establish the feasible paths network of mobile robot. Thus, it can transfer the path planning problem into the shortest path between two route nodes in network. According to the connecting relation in the network, a distance matrix can be establised as follows. In the distance matrix, in order to avoid searching the same route nodes repeatly, the distance between diagonal is set to infinite. A mobile robot should search the shortcut to the network when it plans to move from a start point to a destination point. From the start point S and the destination point Q, search the shortest distance point in AVBN individually, and the intersection is named start node (node 1 in Fig. 2 and end node (node 15 in Fig. 2). For example, from the start point, search the intersecting points on the network in every direction and chose the point as the start node which has the shortest distance to the start point. The end node is searched out in the same way. Calculating the cost of each branch, then the correlated nodes table of the network can be obtained. 1

6

7

5

8

9

10 12 5

14 4

13 1

9

7

9

4

L9 ¼ f4; 10; 13g; l9 ¼ 3; L10 ¼ f7; 9; 15g; l10 ¼ 3; L11 ¼ f6; 12; 14g; l11 ¼ 3; L12 ¼ f8; 11; 14g; l12 ¼ 3; L13 ¼ f9; 14; 15g; l13 ¼ 3; L14 ¼ f11; 12; 13g; l14 ¼ 3; L15 ¼ f10; 13g; l15 ¼ 2: where lj is the element number in Lj ; jA ½1; 15. The problem of path planning is changed to be the problem of searching the shortest path from node 1 to 15. 3.2. The AVBN based BPSO path planning algorithm The path is a curve obtained by enlarging obstacles, so the best path in AVBN is not certain in reality. So we need to find a group of ideal paths in AVBN, then reoptimize them in vector space and select the best one according to the Euclid distance. We adopts BPSO to so1ve the problem. The algorithm is explained according to Fig. 2. In the path planning, the series of route nodes is set as a

15 3

8

1

1

6

11 10 2

3

4

12 6

13 5

8

9

6

12 11 14 4

15 3

8

3

13 1

9

7

9

5

11 10 2

3

4

G10

G10 12 6

5

6

6

4

Fig. 3. Path immigration operation.

Fig. 4. Three grid environments. (a) Grid environment 1. (b) Grid environment 2. (c) Grid environment 3.

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Fig. 5. Best paths in three grid environments. (a) Best path in grid environment 1. (b) Best path in grid environment 2. (c) Best path in grid environment 3.

Table 1 Results of each algorithm on path planning problems. Problems

Algorithms

Mean

Std

Best

Worst

Problem 1

GA PSO BBO BPSO GA PSO BBO BPSO GA PSO BBO BPSO

177.2 164.5 160.2 144 157.4 153.6 153.8 153 122 126.7 122 122

36.28 9.39 15.37 0 4.32 1.26 2.87 0 10.94 5.42 0 0

144 146 146 144 153 153 153 153 122 122 122 122

271 172 198 144 163 156 155 153 155 135 122 122

Problem 2

Problem 3

Table 2 Success rates of algorithms.

Step 2: Encoding Each SIV in a habitat corresponds to a route node in AVBN. Consider the optimal path should not contain the same route node, so the length of encoding is less and equal to the number of network route nodes. The starting point is the number 1 route node, so the length of encoding is Node  1. For example, in Fig. 2, the set of network route nodes is: Q ¼ f1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15g. The length of habitat is 14.SIV value of a habitat Gi is any integral number of Q, where Gj ¼ fg 1 ; g 2 ; :::g,g j A Q , jA ½1; 15. In the process of network modeling, the distance matrix is obtained. And we can get the candidate connecting list of route nodes. Step 3: Decoding In this step, the value g j of SIV is mapped to a route node. Here, Lj ½m is the mth node of Lj in correlated nodes table. Assuming sj is a node selected to be one of the route nodes, then the next node is: sj þ 1 ¼ Lj ½m, where m is the sequence number in Lj ; and the decoding rule is

Algorithm

Problem 1

Problem 2

Problem 3

m ¼ MODðg j ; lj Þ þ 1

GA PSO BBO BPSO

0.6 0 0.8 1

0.8 0.3 0.9 1

0.9 0.8 1 1

where MODðg j ; lj Þ is the reminder of g j divided by lj . When a route node is selected to one of the path nodes, it will be deleted from all correlated nodes table for avoiding being reselected. This operation continues till we get a solution S. Step 4: Mapping of emigration and immigration rates After decoding the habitat, the cost of every branch of AVBN is calculated by adding up at the grids on path between every two nodes based on the obtained route. The sum of the distance between two nodes of a route and the punishing cost is the

habitat of BPSO, that is, an individual. The AVBN based BPSO path planning algorithm is as follows: Step 1: Initialize parameters: P,G,P mute ,w; c1 ; c2 .

ð6Þ

H. Mo, L. Xu / Neurocomputing 148 (2015) 91–99

total cost of a habitat. That is, N

CðGi Þ ¼ CðSi Þ ¼ ∑ Dsi ;si þ 1 þ kα

ð7Þ

i¼1

where k ¼ 1, if the habitat is useless, else k ¼ 0;α is the punishment, N is the path node number of Si . After the costs of all habitats are obtained, sort habitats in descending order. The order number of each habitat is considered as species s in Eqs. (1) and (2). So we get the emigration and immigration rates. Step 5: Record the previous best position of each habitat P i and their neighborhood best position P g . Step 6: Migration The obtained emigration and immigration rates of each solution are used to probabilistically share information between habitats. If a given solution is selected to be modified, then we use its immigration rate to probabilistically decide whether or not to modify each suitability index variable (SIV) in that solution. If a SIV in a solution is selected to be modified, then the emigration rates of the other solutions are used to probabilistically decide which of them should assign a SIV in it to replace the selected SIV in the solution. For example, suppose G3 and G10 are selected according to the migration process, that is, G3 is the habitat with few species (high cost, low HSI, and poor solution) has low μ and high λ, while G10 habitat with more species (low cost, high HSI, and good solution) high μand low λ in population in a generation. The immigration process of two selected paths is shown in Fig. 3. After the migration process, G3 is modified to be G'3 ¼ f1; 5; 6; 13; 5; 8; 9; 6; 12; 11; 14; 4; 15; 3; 8; 3g, while G10 is not changed at the same time. But it maybe selected to be modified in next iteration. After the migration process is finished, some habitats will be modified, and the others will not. All of them are combined together as a population to the mutation process. If no solution is selected to be modified, the position of current habitat is updated according to (5). Step 7: Mutation The costs of generated habitats after migration are recalculated and sort these habitats in descending order of their costs. Only the worst half of the habitats population is mutated based on mutation ratemi (Eq. (4)), randomly generated SIV (route node) is used to replace a SIV in Gi . After the mutation process, the costs of generated habitats are recalculated and sort these habitats in descending order of their costs. The best two habitats are kept to the next iteration. The cycle is ended when there is no best habitat emerging after some generations.

97

inertia w ¼0.9, c1 and c2 ¼2. Besides the parameters above, the number of initial population is 100. The maximal iteration generation number is 100. The tests represented in this paper consist of 100 trials. This test evaluates the efficiency and stability of shortest path planning with BPSO and gives a reference for evaluating the performance in partially modeled and unknown environments.

pathplanning1

260

BBO PSO GA BPSO

240

220

200

180

160

140

0

10

20

30

40

50

60

70

80

90

100

pathplanning2

220

BBO PSO GA BPSO

210 200 190 180 170 160 150

0

10

20

30

40

50

60

70

80

90

100

pathplanning3

160

BBO PSO GA BPSO

155

4. Simulation results 150

4.1. Grid environments 145

In order to analyze the performance of BPSO in the path planning based on AVBN mode, we design three grid environments for the performance comparison of algorithms and compare BPSO with BBO, Genetic Algorithm(GA), and PSO on the same problems. Three grid environments are shown in Fig. 4 (a)–(c).The black blocks are obstacles. The white area is free grid. 4.2. Parameters setting The setting of parameters is as follows. BBO: P mod ¼1, P mute ¼0.005. GA: crossover rate¼ 0.9, mutation rate¼0.01. PSO:

140 135 130 125 120

0

10

20

30

40

50

60

70

80

90

100

Fig. 6. The convergence comparison of algorithms. (a) Convergence for problem 1. (b) Convergence for problem 2. (c) Convergence for problem 3.

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4.3. Simulation results and analysis The best paths of three grid environments by BPSO are shown in Fig. 5(a)–(c), respectively. The best solutions of problems 1, 2 and 3 are 144,153 and 122 respectively. The values of best, worst, mean and standard variance of algorithms after 50 runs are shown in Table 1. In Table 1, we can see that BPSO can find the optimal path for all problems. The performance of BPSO is superior to BBO and PSO. In Table 2, the success rates of the four algorithms are shown. Success rate is the proportion of failure trail times and the total trail times. In Table 2, the success rates of trials of the four algorithms are shown. It can be seen that BPSO has the highest success rates for the three problems. In Fig. 6(a)–(c), the convergence of the four algorithms in one trial are shown. It can be seen that BPSO has the best results for the three problems. In Fig. 6(a)–(c), it is clear that PSO is not good at solving the given RPP problems. The migration strategy of BPSO is more effective than PSO in solving the given problems. For problem3, both BBO and BPSO can easily find the solution at the beginning. It can be seen that BPSO has better performance than the other three algorithms in total for the three RPP problems.

5. Conclusion In this paper, we proposed a new robot path planning approach, which combines a new hybrid optimization algorithm BPSO and approximate voronoi boundary network. The process of environment modeling is introduced. And then we use the modified BPSO to find a best path based on AVBN. The experimental results show that the proposed method is effective and efficient for the given RPP problems. It has much faster convergence speed and higher success rates than the compared algorithms. It provides a new approach for solving RPP by intelligent optimization. In further study, we will try to use BPSO to solve RPP in more complex static environment, such as multi-objective RPP and also dynamic environment.

Acknowledgment This work is partially supported by the National Natural Science Foundation of China under Grant no. 61075113, the Excellent Youth Foundation of Heilongjiang Province of China under Grant No. JC201212, the Fundamental Research Funds for the Central Universities No. HEUCFX041306 and Harbin Excellent Discipline Leader, No. 2012RFXXG073.

References [1] P. Raja, S. Pugazhenthi, Path planning for a mobile robot to avoid polyhedral and curved obstacles, Int. J. Assist. Robot. Mechatron. 9 (2008) 31–41. [2] J.C. Latombe, Robot Motion Planning, Kluwer, Norwell, MA, 1991. [3] B. Graf, J.M. Hostalet Wandosell, Flexible path planning for nonholonomic mobile robots. in: Proceedings of the Fourth European Workshop on Advanced Mobile Robots, Fraunhofer Institute for Manufacturing Engineering Automation (IPS). Lund, Sweden, 2001, pp. 199–206. [4] X.B. Zuo, Z.X. Cai, G.R. Sun, Non-smooth environment modeling and global path planning for mobile robots, J. Cent. South Univ. Technol. (Engl. Ed.) 10 (2003) 248–255. [5] K. Sugihara, J. Smith, Genetic algorithms for adaptive motion planning of an autonomous mobile robot. in: Proceedings of the of the IEEE International Symposium on Computational Intelligence in Robotics and Automation, 138– 143, 1997.

[6] M. Gemeinder, M. Gerke, GA-based path planning for mobile robot systems employing an active search algorithm, Appl. Soft Comput. 3 (2003) 149–158. [7] I. ALtaharwa, A. Sheta, M. Alweshah, A mobile robot path planning using genetic algorithm in static environment, J. Comput. Sci. 4 (2008) 341–344. [8] J.C. Mohanta, D.R. Parhi, K. Patel, Path planning strategy for autonomous mobile robot navigation using Petri-GA optimization http://dx.doi.org/10. 1016/j.compeleceng.2011.07.007. [9] S.X. Yang, M. Meng, An efficient neural network approach to dynamic robot motion planning, IEEE Trans. Neural Netw. 13 (2000) 143–148. [10] S.X. Yang, M. Meng, Neural network approaches to dynamic collision-free trajectory generation, IEEE Trans. Syst., Man, Cybern. 31 (2001) 302–318. [11] B. Ni, X. Chen, L.M. Zhang, W.D. Xiao. Recurrent neural network for robot path planning, in: Proceedings of the Fifth International Conference on Parallel and Distributed Computing, Applications and Technologies, LNCS 3320, 2004, pp. 188–191. [12] J.E. Bell, P.R. McMullen, Ant colony optimization techniques for the vehicle routing problem, Adv. Eng. Inf. 18 (2004) 41–48. [13] G.Z. Tan, H. He, A. Sloman, Ant colony system algorithm for real-time globally optimal path planning of mobile robots, Acta Autom. Sin. 33 (2007) 279–285. [14] M. Saska, M. Macas, L. Preucil, L. Lhotska, Robot path planning using particle swarm optimization of ferguson splines, in: Proceedings of the IEEE Conference on Emerging Technologies and Factory Automation, Prague, 2006, pp. 833–839. [15] C. Xin, Y.M. Li, Smooth path planning of a mobile robot using stochastic particle swarm optimization, in: Proceedings of the IEEE International Conference on Mechatronics and Automation, Luoyang, China, 2006, pp. 1722– 1727. [16] L. Lu, D.W. Gong, Robot path planning in unknown environments using particle swarm optimization, In: Proceedings of the Fourth International Conference on Natural Computation, 2008, pp. 422–427. [17] X.Z. Hu, C.X. Xie, Robot path planning based on artificial immune network, in: Proceedings of the 2007 IEEE International Conference on Robotics and Biomimetics, Sanya, China, 2007, pp. 1053–1058. [18] D.H. Zeng, G. Xu, C.X. Xie, D.G. Yu, Artificial immune algorithm based robot obstacle-avoiding path planning, in: Proceedings of the IEEE International Conference on Automation and Logistics. Qingdao, China, 2008, pp. 798–804. [19] X.Y. Xu, J. Xie, G. Xie, K.M. Xie, A new motion planning approach for the mobile robot, in: Proceedings of the Seventh World Congress on Intelligent Control and Automation. Chongqing, China, 2008, pp. 6168–6173. [20] Y.N. Guo, M. Yang, J. Cheng, Path planning method for robots in complex ground environment based on cultural algorithm, in: Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation, GEC'09, Shanghai, China, 2009, pp. 185–192. [21] N. Shahidi, H. Esmaeilzadeh, M. Abdollahi, C. Lucas, Memetic algorithm based path planning for a mobile robot, Int. J. Inf. Technol. 1 (2004) 174–177. [22] R.S. Tavares, T.C. Martins, M.S.G. Tsuzuki, Simulated annealing with adaptive neighborhood: a case study in off-line robot path planning, Expert Syst. Appl. 38 (2011) 2951–2965. [23] M.A.P. Garcia, O. Montiel, O. Castillo, R. Sepulveda, P. Melin, Path planning for autonomous mobile robot navigation with ant colony optimization and fuzzy cost function evaluation, Appl. Soft Comput. 9 (2009) 1102–1110. [24] A. Hosseinzadeh, H. Izadkhah, Evolutionary approach for mobile robot path planning in complex environment, Int. J. Comput. Sci. Issues 7 (2010) 1–9. [25] J. Kennedy, R..Eberhart, Particle swarm optimization, in: Proceedings of the IEEE International Conference on Neural Networks. Piscataway, NJ, 1995, pp. 1942–1948. [26] R. MacArthur, E. Wilson, The Theory of Biogeography, Princeton University Press, Princeton, NJ, 1967. [27] D. Simon, Biogeography-based optimization, IEEE Trans. Evol. Comput. 12 (2008) 702–713. [28] D. Simon, A probabilistic analysis of a simplified biogeography-based optimization algorithm, Evol. Comput. 19 (2009) 1–22. [29] D. Simon, M. Ergezer, D.W. Du, Population distributions in biogeographybased optimization algorithms with elitism,. in: Proceedings of the IEEE Conference on Systems, Man, and Cybernetics, San Antonio, TX, 2009, pp. 1017–1022. [30] M. Ergezer, D. Simon, D.W. Du, Oppositional biogeography-based optimization, in: Proceedings of the IEEE Conferecne on Systems, Man, and Cybernetics, San Antonio, TX, 2009, pp.1035–1040. [31] D.W. Du, D. Simon, M. Ergezer, Biogeography-based optimization combined with evolutionary strategy and immigration refusal, in: Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics. San Antonio, TX, 2009, pp. 1023–1028. [32] R. Rarick, D. Simon, F.E. Villaseca, B. Vyakaranam, Biogeography-based optimization and the solution of the power flow problem, in: Proceedings of the IEEE Conference on Systems, Man, and Cybernetics, San Antonio, TX, 2009, pp. 1029–1034. [33] W.Y. Gong, Z.H. Cai, C.X. Ling, H. Li, A real-coded biogeographybased optimization with mutation, Appl. Math. Comput. 216 (2010) 2749–2758. [34] A. Bhattacharya, P.K. Chattopadhyay, Solving complex economic load dispatch problems using biogeography-based optimization, Expert Syst. Appl. 37 (2010) 3605–3615. [35] H.W. Mo, L.F. Xu, Biogeography migration algorithm for traveling salesman problem, Int. J. Intell. Comput. Cybern. 4 (2011) 311–330.

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[36] S. Garrido, L. Moreno, M. Abderrahim, F. Martin, Path planning for mobile robot navigation using Voronoi diagram and fast marching, in: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Beijing. 2006, pp. 2376–2381.

Hongwei Mo, born in 1973. He is a professor in Automation College of Harbin Engineering University. He got Ph.D degree in the same University in 2005. He was a Visiting Scholar of UCDavis,CA, USA from October 2003 to October 2004. His main research interests include natural computing, artificial immune system, data mining, intelligent system, and artificial intelligence. He had published 40 papers on artificial immune systems and nature inspired computing in international Journals and conferences. He was the Guest Editor of Special issue on Nature inspired computing and applications of Journal of Information Technology Research. He was the author of 3 books in Chinese and he is the editor of ‘Handbook of Artificial Immune Systems and Nature inspired computing: Applying Complex Adaptive Technologies’. And he is a member of IEEE Computing Intelligence Society, IEEE Robotics and Automaton Society. He was also the program committee member of over 15 International Conferences. He serves as the member of editorial review board of the Journal of Information Technology Research and International Journal of immunocomputing.

99 Lifang Xu, born in 12/28, 1973. She is a lecturer in Engineering Training Center of Harbin Engineering University. She got Ph.D. degree in 2008 in the same University. Her research interests include intelligence computing, and intelligent control. She had published more than 10 papers on artificial immune systems and intelligent control.