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Path Planning of Mobile Robot Using Optimized ACA

Hao-dong ZHU

1,2,*

and Bao-feng HE

1

1Department of Computer Science, Sias International University, Xinzheng, Henan, 451150, China

2School of Computer and Communication Engineering, Zhengzhou University of Light Industry,

Zhengzhou, Henan, 450002, China

*Corresponding author

Keywords:Mobile robot, Ant colony algorithm, Path planning.

Abstract. In order to solve the problems that the ant colony algorithm easily falls into local optimum and has a slow convergence speed when it is used in path planning for mobile robot, the paper proposed an improved ant colony algorithm which was used in path planning for mobile robot in the static environment. The proposed algorithm improved the transition rule of node state to increase the probability of searching optimal path, designed an improved the heuristic function to improve the searching efficiency of the algorithm, and updated the pheromone avoid falling into local optimum. The simulation results show that the proposed algorithm has faster convergence speed under the condition of the same result of path planning when compared to the traditional algorithm in the same environment. The improved algorithm obtains the optimal path in the environments of different complexity levels and it shows the efficiency and feasibility of the improved algorithm, which has good optimization ability and can be applied to path planning for mobile robot in the environments of different complexity levels.

Introduction

Path planning is one of the core content of mobile robotics research field in recent years, which is to find an optimal and collision free path from the starting point to destination [1].The problem of path planning has the characteristics of complex, more binding, and multi-objective. The traditional path planning algorithms include Dijkstra algorithm and A* algorithm. Dijkstra algorithm is a classic path search algorithm, and it is a kind of greedy algorithm, though it can plan a optimal path, The algorithm will expand from the starting point to outside until find the destination node. Algorithm has high computational and low efficiency because of traversing the node. A* algorithm is a kind of heuristic algorithm, it determines the distance from the current point to the target point through the evaluation function[2]. A non-ideal estimation function may lead to find a bad path in a complex environment. In recent years, the domestic and foreign experts and scholars have put forward to many bionic intelligent optimization algorithms, such as Genetic algorithm[3], artificial fish algorithm[4], leapfrog algorithm[5], neural network algorithm[6] and ant colony algorithm[7], which have been applied to path planning.

In 1992, Marco Dorigo proposed ant colony algorithm in the dissertation. He was inspired by observing the behavior of ants that the ants look for food source. Ant colony algorithm is a new

nature stimulated metaheuristics optimization algorithm which has the advantages

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performance of path planning. Literature [13] put forward to a method of smoothing the path, and effectively improved the quality of the path. At present, many algorithms have the disadvantages of easily trapping into the local optima and having a slow convergence speed in path planning for mobile robot. Because of Genetic algorithm has numerous of evolution algebra, it takes up a lot of storage space, resulting in slower speed. Although artificial fish algorithm has faster convergence speed, it is difficult to get accurate solutions, that is to say, the quality of path is non-ideal. Hybrid leapfrog algorithm easily fall into local optimum and have a slow convergence speed, thus to limiting the application of the algorithm which is used in path planning for mobile robot. Neural network algorithm has a stronger ability to learn, but it is difficult to use mathematical formula to describe it when the environment is complex. Artificial potential field method is widely used in path planning because of its simple mathematical calculations. But it has the disadvantage of a local minimum point and target unreachable. Ant colony algorithm is a kind of bionic algorithm. it has the advantages of self-organization, distributed computing and a strong optimization capability. Therefore, it is very suitable for application to path planning for mobile robot.

The paper puts forward to using the improved ant colony algorithm in path planning for mobile robot. The paper improves the transition rule of node state, improves a heuristic function and the way to update pheromone so that it can get the global optimal path in different complexity of environments, improves the search speed of the algorithm, and accelerates the convergence speed of the algorithm. Through the simulation in matlab software, it shows that the algorithm is effective and feasible.

Problem Description and Modeling

Robot path planning is one of important issues in environment modeling. Modeling is the process of turning the reality of the physical space into the space which is understood by robot through the extraction and analysis according to the known environment information. It can effectively reduce the trouble in the process of path search. This paper divided the environment of robot into two dimensions by using the grid method, and the grids are numbered from left to right and from top to

[image:2.595.209.388.481.638.2]

bottom. This paper illustrates it with 10  10 grid environment.

Figure 1. Grid coordinate relationship with serial number.

As shown in Figure 1, the origin of coordinates 0 in the lower left corner. It is the level direction

of x axis from left to right, and it is the vertical direction of y axis from bottom to top. The size of

the grid is decided by the size of the mobile robot and its movement step length. A grid of the side length is the robot movement step length, that is to say, it is a unit of length. Serial number corresponds to relationship with the coordinates as shown in formula (1).

mod( , ) 0.5

(N / ) 0.5

i i

i i

x N N

y N ceil N

 

 (1)

(3)

Ceil() is returning the smallest integer which is greater than or equal to specified expression.

Establishing the corresponding matrix represents the state of each grid according to the environment map in order to build environment which can be understood by the robot. In the following matrix, 0 represents feasible grid and 1 represents the obstacle grid. Every obstacle may occupy one or more of the grids. Assume that the obstacle may not take up a grid, we should regard it as a complete grid. The mobile robot is regarded as a dot robot. It will expend the obstacle according to the size of the radius of the mobile robot so that the robots can safely through the obstacle boundaries. Based on grid environment shown in figure 2, the matrix can be expressed as

[image:3.595.235.363.202.325.2]

G.

Figure 2. The matrix G.

Proposed Path Planning

Research shows that the ants can leave behind pheromones on a path, and the ant can senses pheromone within a certain range to guide their own movement. Therefore, the ant colony can exhibit a positive feedback phenomenon, after the more ants pass through one path, the more information will be released on this path. And then at the back of the ants have the greater probability of choosing this path. Ants choose the path through the pheromone communication for each other, and then find a source of food. Ant colony algorithm has the advantages of strong local optimization ability, self-organizing, can effectively apply to the path planning, but the traditional ant colony algorithm has the shortcomings of easing to trapped into local optimal solution and a slow convergence speed. In order to improve the searching efficiency of ant colony algorithm and the quality of path planning, the traditional ant colony algorithm is improved in the paper.

Improved Transition Rule of Node

Ants can choose next feasible node according to the heuristic function of  and the pheromone of

 on the path. Assume that the ants population is m and the current ant k is on node of i, Compare

the size of q and q0, it chooses the next feasible node j according to the formula (2). Where, q is a

random number which is between 0 and 1, q0 is the constant parameter between 0 and 1.

ij ij

0

k ij

arg max (t) (t) q q j

P (t) ootherwise

 

 

 

    

 

 (2)

0 ij

(t) (t)

(t) (t) (t)

0

ij ij k

ij ij j allowed

q q P

otherwise

 

 

 

 

 

   

 

   

 

(3)

where, j is the next node which is chosen by the ant k,ij(t)is pheromone concentration between

(4)

concentration impacts on the degree of probability of selection.  shows that the heuristic

information influence degree of probability of selection. q0 is a threshold. Pijk(t) shows that the

probability of the current ants k from node i to node j, If j is not feasible grid, the probability is zero.

Improved the Heuristic Function

In the traditional ant colony algorithm, heuristic function is reciprocal of the distance between the two nodes. As shown in formula (4). A * algorithm is a kind of heuristic algorithm, it can be

expressed as: f(n)g(n)h(n).g(n) is the real costs which is from the initial node to the current

node. h(n) is the estimated cost which is from the current node to the destination node. Under the

certain conditions of the value of g, the value of h is smaller, in order to the value of f is smaller.

Therefore, it ensures that the search towards the direction of destination. Be inspired by the A*

algorithm, the distance which is between next feasible node j and the destination can be used in the

heuristic function by the heuristic A * algorithm, that is to say, dij and djt are used in heuristic

function. As shown in formula (5).

1

ij ij

d

  (4)

1

ij

ij jt

d d

 

 (5)

where, dij is the Euclidean distance between the current node and the next adjacent node. djt is

Euclidean distance between the next adjacent node and destination node.

Updated Pheromone

In the traditional ant colony algorithm, the ants which pass through the worst path release pheromone, the algorithm will trapped in local optimal solution after positive feedback. In order to overcome this shortcoming, the paper uses the wolves rules to update pheromone. It finds the ants which pass through an optimal path and a worst path in a generation. Respectively Increase and reduce pheromone concentration [2]. Every path updates the pheromone concentration according to the formula (6).

ij 1 (t) = ij ij m k ij ij k                

(t +1)=( 1- )

(6)

0

k best ij

Local optimal Q

if Arc i, j L els h e pat         (7)

where, best

L is the length of the best path in a generation. Q is a information number.

Algorithm Flows

Step 1: Initialize each parameter. According to the robot's environment generates raster map what

robot can understand, set the grid number and the number of ant m. The starting point is S and the

destination point is T. Maximum number of iterations is Nmax. Set the effect of pheromone

weightand heuristic information influence weight .

Step 2: All the ants choose the path. Put m ants on starting point. The ant k sets off from the

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formula (2) and (3).If jallowed, Select the next grid j and add the grid j to the tabu table.

Step 3: To judge whether the ants arrival destination point T. If the ant has arrived at the

destination point T, record the grid number and length which has walked through by ants. If it has

not arrived the destination point T, it will continue to search the next node until find destination

point T. If all of ants have searched path in this generation, and return step 4.

Step 4: Update the pheromone. Calculate all the ants getting a viable path length in this generation. Find out the ants which have pass through the best and worst path when all of ants

arrived at the destination T. Update pheromone for each grid according to the formula (6).

Step 5: whether algorithm achieves maximum number of iterations. If algorithm achieves maximum number of iterations, output the shortest path length in current group. Otherwise, empty

the tabu table. For N = N + 1, return step 2 and Continue to search until algorithm achieves the

maximum number of iterations. Output the length of the shortest path in the current group.

Simulation Experiments

Using Matlab software to simulate the optimized ant colony algorithm, and then the simulation results are analyzed and compared to.

(1)The proposed algorithm in this paper compares to the traditional algorithm. The traditional

algorithm was simulated in the 20 20 grid environment. Set the same population of ant colony

[image:5.595.105.279.376.509.2]

number which is 100.Through simulation and experiment, the comparison results are figure 3, figure 4, figure 5 and figure 6:

[image:5.595.316.486.376.508.2]

Figure 3. Simulation results of traditional algorithm. Figure 4. Iterative graph of traditional algorithm.

Figure 5. Simulation results of the optimized algorithm. Figure 6. Iterative graph of the optimized algorithm.

The paper introduces the pseudo-random proportion rule so that the improved algorithm increases the possibility to find the optimal path. The paper introduces the target node into the heuristic function in order to strengthen search direction, which effectively improves the search efficiency of the algorithm. To improve the way of the pheromone line improves the algorithm search efficiency and convergence speed. Through the above simulation results can be seen, in the same complexity

environment (20 20) and the same obstacles, the improved algorithm get the optimal path length

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slightly higher than the traditional algorithm convergence speed. It shows that the improved algorithm has the certain superiority.

(2)To verify the proposed algorithm is effective, the algorithm simulate in the Matlab software by setting different complexity of grid environment. The experimental data set as follows: population

quantity is 50, The largest number of iterations is 100. =1.1, =7.

In the different and complex environment the simulation results are as follows:

a. The algorithm was simulated in the 10  10 grid environment in this paper. The result of path

planning is shown in figure 7 and iteration number is shown in figure 8.

[image:6.595.125.486.200.336.2]

Figure 7. Simulation results of the optimized algorithm Figure 8. Iterative graph of the optimized algorithm.

b. The algorithm was simulated in the 20  20 grid environment. The result of path planning is

shown in figure 9 and Iteration number is shown in figure 10.

[image:6.595.130.479.392.516.2]

Figure 9. Simulation results of the optimized algorithm. Figure 10.Iterative graph of the optimized algorithm.

c. The algorithm was simulated in the 30  30 grid environment. The result of path planning is

shown in figure 11and Iteration number is shown in figure 12.

Figure 11. Simulation results of the optimized algorithm. Figure 12. Iterative graph of the optimized algorithm.

[image:6.595.197.475.581.708.2] [image:6.595.126.287.583.701.2]
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Conclusions

Traditional ant colony algorithm has the shortcomings of slow convergence speed and easily trapped into the local optimum. To overcome these problems, the paper improves the transition rule of node state, improves the heuristic function and the way to update pheromone. The algorithm was simulated in the different complexity of grid environments and can always find the ideal path. It shows the efficiency and feasibility of the improved algorithm. In addition, comparing to the traditional ant colony algorithm, the improved algorithm in this paper can find the optimal path by a fewer iterations in the complex environments. It shows that the improved algorithm has the feasibility and superiority. The paper mainly researches global path planning for mobile robot in a static environment without considering the existence of a finite number of dynamic obstacles. This is the shortage of the paper and the focus of future research.

Acknowledgement

This work was supported in part by the Science and Technology Plan Projects of Henan Province of China under grant No. 152102210357 and No. 152102210149.

References

[1] C. B. Li, R. X. Guo, M. Li, Application of improved ant colony algorithm in travelling salesman problem, Journal of Computer Applications. 34 (2014) 131-132.

[2] P. Raja, S. Pugazhenthi, Optimal path planning of mobile robots: A review, International Journal of Physical Sciences. 7 (2012) 1314-1320.

[3] G. B. Pan, F. Pan, G. D. Liu, Path planning for mobile robots based on improved shuffled frog leaping algorithm, Journal of Computer Applications. 34 (2014) 2850-2853.

[4] J. H. Duan, X. A. Li, Robot Path Planning Based on Improved Genetic Algorithm, Microelectronics & Computer. 22 (2005) 70-72.

[5] L. M. Nie, Y. Q. Zhou, Path planning of robot based on artificial fish-swarm algorithm, Computer Engineering and Applications. 44 (2008) 48-50.

[6] A. M. Wang, Q. G Shi, C. L. Lv, Path Planning and Optimizing Algorithm of Robot Based Neural Network, Journal of Hebei University of Technology. 28 (1999) 13-16.

[7] C. A. Liu, X. H. Yan, C. Y. Liu , H. Wu,Dynamic Path Planning for Mobile Robot Based on Improved Ant Colony Optimization Algorithm,Acta Electronica Sinica. 39 (2011) 1220-1223. [8] Y. Zhang, Y. Q. Gao, X. J. Niu, Simulation Research With An Improved Ant Colony Algorithm, Journal of Wuhan University of Technology (Transportation Science & Engineering). 37 (2013) 1330-1332.

[9] C. Z. Sun, G. S. Gui, D. Han, L. Zhang, Algorithm for mobile robot path planning based on the ant colony algorithm and its application, Journal of Hefei University of Technology. 29 (2006) 1208-1211.

[10] X. F. Wan, W. Hu, W. Y. Fang, B. J. Zhang, Research on path planning of robot based on improved ant colony algorithm, Computer Engineering and Applications. 50 (2014) 63-66.

[11] D. H. Liu, Y. Xiong, W. H. Li, X. Y. Li, Ant colony optimization with self-adaptive parameter adjusting, Application Research of Computers. 28 (2011) 905-908.

[12] Y. Lu, X. Y. Yi, J. L. Cheng, A new potential field method for mobile robot path planning in the dynamic environments, Asian Journal of Control. 11 (2009) 214-225.

Figure

Figure 1. Grid coordinate relationship with serial number.
Figure 2. The matrix G.
figure 4, figure 5 and figure 6:
Figure 7. Simulation results of the optimized algorithm    Figure 8. Iterative graph of the optimized algorithm

References

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