Path Planning of Robot Based on Modified Ant Colony Algorithm

Transcription

1 Boletín Técnico, Vol., Issue, 07, pp.- Path Planning of Robot Based on Modified Ant Colony Algorithm Yuanliang Zhang* School of Mechanical Engineering, Huaihai Institute of Technology, Lianyungang 00, Jiangsu, China *Corresponding author( Yu Zhang School of Mechanical Engineering, Huaihai Institute of Technology, Lianyungang 00, Jiangsu, China Abstract Aiming at the problems in the practical application of the basic ant colony algorithm for the path planning application of the mobile robot, a modified ant colony optimization algorithm is proposed. A short path with lots of turning angles is not a good one. In this paper the proposed modified ant colony algorithm is used to search the optimal path, considering the size of the robot and the turning situation. The modified ant colony algorithm reevaluates the selected path by considering not only the length of the path but also the turning situation of the mobile robot, and can provide an optimal path for the robot to run. Finally, some simulations are done to verify the proposed modified ant colony algorithm. Key words: Path Planning, Ant Colony Algorithm, Turning Situation, Mobile Robot.. INTRODUCTION In the past 0 years, the problem of path planning has been paid more attention with the extensive development of robots. Many scholars have proposed a number of different algorithms to solve the problem of path planning. At present, the methods of solving path planning mainly include artificial potential field method (Triharminto et al., 0), visual graph method (Liu et al., 0), grid method, genetic algorithm (Tuncer and Yildirim, 0), A*(A-star) algorithm (Duchoň et al., 04), and ant colony algorithm (Wang et al., 0). In many algorithms, the ant colony algorithm is a ind of intelligent algorithm which is more mature and effective in solving the path planning problem. So that the ant colony algorithm has been widely developed and used in the path planning of the mobile robot. Ant colony algorithm has the advantages of good searching ability, positive feedbac, distributed computing and so on (Duan et al., 004). But the traditional ant colony algorithm also has some shortcomings, such as slow convergence, easy to fall into the local optimal solution and the phenomenon of stagnation (Zhao, 04). A combination of Cellular Automata and Ant Colony Optimization techniques are provided to create collision-free trajectories for a robot team (Ioannidis et al., 0). The proposded method reacts with obstacle distribution changes and therefore can be used in dynamical or unnown environments, without the need of a priori nowledge of the space. Sudholt and Thyssen analyze the running time of different ant colony algorithm systems for shortest path problems (Sudholt and Thyssen, 0). A robot path planning algorithm for dynamic unnown environments is provided based on an improved ant-based algorithm (Zhu et al., 0). For the path planning application using ant colony algorithm, the optimal path which the ants select is applied directly to the real application of the robot. In this case the robot is regarded as an ant and its own volume is neglected. As well as the big turining angle of the optimal path is also a problem that cannot be ignored. In many cases, the provided optimal path has the shortest length, but it is not the real optimal path for the mobile robot since the mobile robot has to turn many times which maes the mobile spend more time and energy. In this paper, based on the idea of the optimal path of the robot, the grid model of the woring environment is established, firstly. And then the concrete ant search function expression is given. According to the ant colony algorithm, the path is searched. Finally, according to the corners in the path, comprehensive evaluation of an optimal path by considering both the length and the turning situation of the planning path is given. Simulations are done to evaluate the proposed modified ant colony algorithm for the path planning application of the mobile robot.. THE BASIC PRINCIPLE OF ANT COLONY ALGORITHM In reality, the ants search the path through the pheromone on the path. The ants will release pheromone about the length of the path. The following ants will choose the path with a large amount of pheromone, which will form a positive feedbac mechanism. Ants choose the path basing on the amount of pheromone on the path, which is the basic principle of ant colony algorithm.

2 Boletín Técnico, Vol., Issue, 07, pp.- The basic mathematical model of ant colony algorithm is as follows. m is the number of the ants, bi ( t ) is the number of ants in the node i at t moment, and ( t) is the amount of pheromone from the node i to the node j at t moment. So the Eq.() can be obtained. n m b ( t) () i i In order to satisfy the constraint that each ant must go through n different nodes, a data structure for each ant is produced. A set called tabu (,,...m) which records the nodes that have been gone through at t moment is built. It can forbid the ants to go through these nodes in this data structure again. The translation probability from node i to node j at t moment for the ant is defined as: ( t) ( t), j allowed P ( t) ( t) ( t) () is is 0, otherwise where allowed is the set which includes the nodes that can be chosen by ant next step is the factor of heuristic pheromone is the expected factor of heuristic pheromone and is a reflection of the heuristic function, which can be expressed as follows. () where d is the distance between node i to node j. When an iteration cycle is completed, the pheromone update is performed on each path. The update formula is as shown in Eqs. (4)-(). d ( t n) ( ) ( t) (0,) (4) m () where (0,) is the volatile coefficient of pheromone. is the total amount of the increased pheromone on the edge ( i, j ), and is the amount of the increased pheromone on the edge ( i, j ) by the th ant between time t and t n. There are three updated models about the pheromone, which are the antcycle system, the ant-quantity system and the ant-density system. For path planning application, the ant-cycle system has a better performance. Its formula is as shown in Eq. (). Q th, If ant uses path in tour L () 0, otherwise. ALGORITHM DESIGN.. The Problem of Ant Colony Algorithm When the path chosen by the ant colony algorithm is applied directly to the path planning of the robot, the traditional algorithm ignores the two problems. () The size of the mobile robot itself In the traditional ant colony algorithm, before the use of ant colony algorithm into the simulation, it is necessary to establish the environment by using the grid map. In the grid map the physical obstacles in the environment is generally mared as the barrier grid. But in this case the environment model does not tae into account the size of the mobile robot itself. So there is a problem with this definition. As shown in Fig., in the simulation the ant in the node g can choose to move to the node g9 even if the nodes g 8 are the obstacle nodes. But in practical applications, it is necessary to consider the size of mobile robots. When the

3 Boletín Técnico, Vol., Issue, 07, pp.- nodes g 8 are the obstacle nodes, the mobile robot cannot move directly from the node g to the node g 9 in order to avoid the collision because of the size of the mobile robot. In fact the mobile robot has to detour a long way. In this paper the size of the robot is taen into account and the barrier grid and the free grid are redefined. As shown in Figure, the node g is considered. For the node g the statuses of the four diagonal nodes g, g, g 7 9 are not only decided by themselves but also their neighbours. For instance, only when the nodes g, g are all free nodes the node g can be set as free node. g g g g 4 g g g 7 g 8 g 9 Figure. Grid environment model () Mobile robot turning angle In the actual woring environment, it is better for the mobile robot to move straight and avoid turning big angles. This is because that when the mobile robot turns, especially big angles, the robot has to slow down, turn and reaccelerate. In the turning process, the mobile robot has to spend more time and more energy. In this case the planned shortest path may not be the optimal one because of the existence of the lots of big turning angles. As shown in Figure, assuming that the ant moves from the node g 4 to the node g at the beginning, and then transfers to the node g or g 9. In this case the robot needs to turn the angle of degrees. If the robot transfers from node g to the node g or g 8 it needs to transfer the angle of 90 degrees. In the same way, if the robot transfers from node g to the node g or g 7 it needs to transfer the angle of 4 degrees. In the actual operation environment of the mobile robot, the degrees angle transferring is easy to realize for the robot due to the inertia during the process of the robot s movement. But if the rotation angle is 90 degrees it will be difficult for the robot. Especially, when the rotation angle is 4 degrees, it will be much more difficult to realize. To sum up, in the path planning process, it is not only needed to consider the length, but also needed to tae care of the turning angles in the whole path so that the robot does not need to turn too small angle. g g g g 4 g g g 7 g 8 g 9 Figure. Angle relationship between travel routes.. Modified Ant Colony Algorithm Through the analysis of the above problems in the practical application, the basic ant colony algorithm is modified in this paper. It is necessary to improve the evaluation standard of the optimal path. That is, not only the length of the path but also the turing angles should be considered during the path planning process. Here a borad length is defined using Eq. (7). L L N N N (7) r where L is the broad length of the path, L r is the length of the path, N is the number of the degrees angles in the path, N is the number of the 90 degrees angles in the path, and N is the number of the 4 degrees angles in the path. The parameters are the gain of the turning angles. In general, smaller turning angle means more difficult to realize for the robot. So is bigger than and is bigger than.

4 Boletín Técnico, Vol., Issue, 07, pp.- 4. SIMULATION In this paper simulation using the modified ant colony algorithm to the path planning is done to verify the proposed method. The *, 0*0, and 0*0 grid maps are used in this simulation. And the basic ant colony algorithm and the modified ant colony algorithm are applied, respectively. In the simulation m is set as 0, the maximum number of iterations N c is set as 00, and the angle gain factors are set as,, and respectively. The pheromone volatilization coefficient is 0.4 is, and is 4. () * grid map environment Figure shows the simulation results using the basic ant colony algorithm. Figure (a) shows the obtained optimal path, and Figure (b) shows all feasible paths. The length of the obtained optimal path is.40. If only consider the length factor, the obtained path is the optimal one. In this case the robot needs to turn three degrees angles. The broad length of the obtained path calculated using Eq.(7) is L (a) (b) Figure. Simulation results using the basic ant colony algorithm (case ) Figure 4 shows the simulation results using the modified ant colony algorithm. In this case the obtained optimal path includes two degrees angles. The broad length of the obtained optimal path is L From Figures and 4 it can be seen that the modified ant colony algorithm can provide better path with less turning angles. Figure 4. Modified ant colony algorithm simulation results (case ) () 0 * 0 grid environment Figure shows the simulation results using the basic ant colony algorithm in this case. Figure 4(a) shows the obtained optimal path, and Figure 4(b) shows all feasible paths. The length of the obtained optimal path is In this case the robot needs to turn seven degrees angles. The broad length of the obtained path calculated using Eq.(7) is L And since the size of the robot is ignored when doing the path planning the obtained optimal path is not feasible as shown in Figure (a) using the circle mar. 4

5 Boletín Técnico, Vol., Issue, 07, pp.- (a) (b) Figure. Simulation results of basic ant colony algorithm (case ) Figure shows the simulation results using the modified ant colony algorithm. In this case the obtained optimal path includes two degrees angles. The broad length of the obtained optimal path is L 7.9. From Figures and it can be seen that the modified ant colony algorithm can provide better path by considering the turing angles of the robot and the size of the robot. In this case the planned path avoids the narrow channel between two obstacle grids. Figure. Modified ant colony algorithm simulation results (case ) () 0 * 0 grid map environment Figure 7 shows the simulation results using the basic ant colony algorithm in this case. In this case the map is bigger and more complex. The planned path provided by the basic ant colony algorithm provide contains much more turning angles which maes the robot spend much more time and energy to run. The length of the obtained optimal path is.790. The broad length of the obtained path calculated using Eq.(7) is L.790. Figure 7. Simulation results of basic ant colony algorithm (case )

6 Boletín Técnico, Vol., Issue, 07, pp.- Figure 8 shows the simulation results using the modified ant colony algorithm. In this case the obtained optimal path includes two degrees angles. The broad length of the obtained optimal path is L CONCLUSIONS Figure 8. Modified ant colony algorithm simulation results (case ) In this paper, a modified ant colony algorithm is proposed to do the path planning for mobile robots. When do the path planning using the basic ant colony algorithm the size of the mobile robot and the turning angles are ignored. In this case the robot may collide to the obtacles when go through the narrow channel between two obstacle grids and the planned path may contain much more turning angles. When the robot turns, especially the big turning angle, it has to slow down, turns and reaccelerate. During the turning process the robot will spend more time and energy. In the modified ant colony algorithm these two factors are considered. In the planned path the collision is avoided and the turning angles are less which can improve the efficiency of the robot. Several simulations using different size map are done to verify the proposed modified algorithm. The results show that the modified algorithm can provide better path. ACKNOWLEDGEMENTS This wor is supported by National Natural Science Foundation of China (70), Science and Technology Planning Project of Jiangsu Province (BY00-0, BY00-08) and Science and Technology Planning Project of Lianyungang City (CG7). REFERENCES Duan, H. B., Wang, D. B., Zhu, J. Q. (004) Development on Ant Colony Algorithm Theory and its Application, Control and Decision, 9(), pp.-. Duchoň, F., Babinec, A., Kajan, M., Beňo, P., Flore, M., Fico, T., Jurišica, L. (04) Path Planning with Modified A Star Algorithm for a Mobile Robot, Procedia Engineering, 9, pp Ioannidis, K., Siraoulis, G. C., Andreadis, I. (0) Cellular Ants: a Method to Create Collision Free Trajectories for a Cooperative Robot Team, Robotics and Autonomous Systems, 9(), pp. -7. Liu, G., Liu, Y. B., Zhao, J., Zhu, L. (0) Path Planning for a New Mine Rescue Robot Base on Visual Tangent Graphs, Journal of Jilin University, 4(4), pp Sudholt, D., Thyssen, C. (0) Running Time Analysis of Ant Colony Optimization for Shortest Path Problems, Journal of Discrete Algorithms, 0(), pp Triharminto, H. H., Wahyunggoro, O., Adji, T. B., Cahyadi, A. I. (0) An Integrated Artificial Potential Field Path Planning with Kinematic Control for Nonholonomic Mobile Robot, International Journal on Advanced Science, Engineering and Information Technology, (4), pp Tuncer, A., Yildirim, M. (0) Dynamic Path Planning o Mobile Robots with Improved Genetic Algorithm, Computers & Electrical Engineering, 8, pp Wang, X., Zhang, Y. Y., Wu, D., Gao, S. D. (0) Collision-Free Path Planning for Mobile Cranes Based on Ant Colony Algorithm, Key Engineering Materials, 47-49, pp Zhao, J. D. (04) Ant Colony Algorithm Improvement Strategies, Computer nowledge and technology in Chinese, 0(8), pp Zhu, Q. B., Jun, H., Cai, W. B., Henschen, L. (0) A New Robot Navigation Algorithm for Dynamic Unnown Environments Based on Dynamic Path Re-Computation and an Improved Scout Ant Algorithm, Applied Soft Computing, (8), pp