An Intuitional Method for Mobile Robot Path-planning in a Dynamic Environment

Transcription

1 An Intuitional Method for Mobile Robot Path-planning in a Dynamic Environment Ching-Chang Wong, Hung-Ren Lai, and Hui-Chieh Hou Department of Electrical Engineering, Tamkang University Tamshui, Taipei Hsien, Taiwan, Republic of China Abstract: - An intuitional path-planning method is addressed for a mobile robot moving through a field of obstacles to a goal. Such as the robot soccer game, the locations of the mobile robot, obstacles, and goal are known via a real time global vision system and all objects are movable in a bounded environment. In order to efficiently avoid obstacles in dynamic environment, seven exploratory points locate in a semicircle that is oriented toward goal are found first. After that, according to the surroundings of the mobile robot, a temporary destination is selected between seven exploratory points to avoid collisions with obstacles and approach to goal. Next, a fuzzy controller is designed to determine a suitable action of mobile robot to approach the select temporary destination. Since the temporary destination determination refers to both obstacle avoidance and goal approach, the mobile robot will reach goal as fast as possible in a collision-free path. Some simulation results are illustrated the effectiveness of the proposed method. Key-Words: - Path planning, Obstacle avoidance, Fuzzy logic controller. 1 Introduction Path planning issue for robots has received much attention over the last decades. The general problem is to find collision-free paths for a robot in an environment containing obstacles. In the former researches of path-planning issue, the problem can be roughly categorized into two types: offline planner and online planner. In the most of offline path planning issues [1-4], a complete known environment is provided for planner, and an optimal path with collision-free can lead mobile robot reach goal based on some criteria (e.g. the shortest path or the minimum cost). Online planner usually cannot plan an optimal path for the robot such as offline planner does, but it can provide an immediate react to response to the rapid changing environment [5-10]. Furthermore, many familiar techniques are applied in this issue. In [1, 2], the numerical potential field techniques are addressed to plan the best global and local path for mobile robot. Han etc. [3], Xiao etc. [6] and Juidette [8] using genetic algorithms or evolutionary computation concepts as a search and optimization tool for path planning and navigation. In [4, 5, 9, 10], the path planners based on grid or small area decomposition are presented and involve the network simplex method to solve a minimum cost flow problem. In this paper, the path planning based on a simple and intuitional concept is proposed. The global path is decomposed into lots of local paths that are generated according to the surroundings of mobile robot to achieve the capability of obstacle avoidance. A real time global vision system is provided, than mobile robot can react the environment changing immediately. The rest of this paper is organized as follows: In Section II, the proposed path planning is

2 presented. In Section III, some simulations are considered to illustrate the effectiveness of the proposed algorithm, and finally, we conclude this paper. 2 Path-planning method In this paper, a global vision system provides the necessary overall environment information in real time, and the locations of all objects and goal are completely known when the path planning method are proceeding. In order to deal with obstacles avoidance at once, the mobile robot has to react to avoid collision with obstacles or boundaries in a short period. A fast exploratory method is addressed according to the immediate vision information. The proposed method includes three parts: (i) the generation of exploratory points, (ii) the determination of optimal temporary destination, and (iii) fuzzy logic controller design. All of them are described as follows: mobile robot. d is the secure distance that ensures successful obstacle avoidance. The detailed description of generation of seven exploratory points is shown as below. First, the coordinate of central candidate point x, ) can be evaluated by following equation: ( 4 y4 ( xg xr, yg yr ) ( x 4, y4 ) = d + ( xr, yr ) (1) d _ gr where d_gr is the distance from goal ( x g, y g ) to robot ( x r, yr ). The coordinates of other six exploratory points can be obtained by solving the equation: r r d 4 di cosθ 2 i = d, i = 1, 2, L, 7 (2) d = ( xi xr ) + ( yi yr ) d r i is the vector from robot to the i-th exploratory point, and θ i is the included angle between d v 4 and d v, where θ = = 90, θ = = 60, and i 1 θ 7 2 θ 6 θ 3 = θ 5 = 30. After seven exploratory points is found, in next step, a temporary destination of mobile robot is going to be select between seven points to avoid obstacles and approach goal. 2.1 The generation of exploratory points In order to avoid obstacles successfully at once and lead the mobile robot to reach goal, seven exploratory points around the mobile robot are determined according to the real time locations of obstacles and the orientation of goal. At first, a point in the orientation forward to goal and is d apart from mobile robot is found. Next, other six exploratory points that evenly distributed on both sides of the first point on a semicircle with radius d from mobile robot are determined by some simple geometry formulas, like the diagram shows in Fig.1. Since the range of steering of mobile robot is limited, an enough distance d is necessary for obstacle avoidance when an obstacle is located in front of 2.2 The determination of optimal temporary destination In this step, an optimal temporary destination is determined. An optimal temporary destination is the closest point to goal and can avoid collision with obstacles. In general, the 4th exploratory point is the best choice to approach goal if no obstacles around that point. In the contrary, if there are obstacles located around that point, a collision will happen when the mobile robot move toward goal. Therefore, a variable td i is used to determine whether collision will happen if robot moves toward i-th exploratory point.

3 1 d _ obi > r tdi = (3) 0 o. w where d _ obi is the shortest distance between i-th exploratory point and all obstacles, and r is a given safe distance that determine by the size of obstacles and mobile robot. When d _ obi > r, the variable td i will equal to 1, and it means robot can through the field without collision toward the orientation of i-th exploratory point. When d _ obi r, and td i is equal to 0. That means the orientation is not under consideration. Besides, the distance between exploratory point and goal is another important factor we have to think over. An evaluation function is therefore given as follows to reflect the obstacle avoidance and goal approach measurement when i-th exploratory point is selected to be the temporary destination. f i = t di dgi (4) where dg i is the distance from the i-th t exploratory point to goal. When td i = 1, the evaluation value is an inverse proportion to the distance dg i. In conclusion, the largest evaluation value is the optimal temporary destination td _ best, and can be determined by td _ best = arg(max( fi )) (5) The determination of optimal temporary destination process will keep on until the distance from robot to goal is shorter than d _ gr. When goal appears within the distance d away from robot (i.e. d _ cb < d ), the temporary destination point p _ best transfers to goal. Finally, the mobile robot will reach the goal. 2.3 Fuzzy logic controller design When the temporary destination point p _ best is determined, a fuzzy logic controller is designed to lead robot approaching the point. Two inputs of the fuzzy controller are the distance between goal and robot d _ gr and the angle between robot orientation and the direction of point p _ best, called turn_ang that are illustrated in Fig.2. The output of the fuzzy controller is the rotational velocity of mobile robot w. The input-output relationship of the fuzzy controller is shown in Fig.3. The universe of discourse of d_gr, turn_ang and w are [0, 100], [-150, 150], and [-30, 30], respectively. For the angle and rotational velocity in this research, we define right hand side as positive. When the turn_ang is positive, mobile robot should turn right to approach the destination, and the rotational velocity w is positive. In our consideration, the distance between goal and robot d_gr will influence the rotational velocity w. When mobile robot is far away from goal, a large rotational velocity is not necessary. A large rotational velocity will result in a swinging path. But when mobile robot gets close to goal, a large rotational velocity will help robot reach goal as soon as possible. The fuzzy rules are established as the list in Table 1, where N, P, ZO, S, M, and B stand for negative, positive, zero, small, medium and big, respectively. According the output of the fuzzy controller, the rotational velocity of mobile robot can be determined to approach the destination. The dynamic model of the mobile robot can be expressed by [6]. x( t + 1) = x( t) + v cos(( φ( t) /180) π y( t + 1) = y( t) + vsin(( φ( t) /180) π φ( t + 1) = φ( t) + w (6) where (x(t), y(t)) is the location of mobile robot in the present step, (x(t+1), y(t+1)) is the location in the next step, φ is the angle between mobile robot orientation and the horizontal axis, w is the rotational velocity of mobile robot, and v is the forward velocity of mobile robot. When all the above parameters are given, the explicit location of mobile

4 robot in the next step will be obtained by substituting the parameters to (6). In order to instantly response the rapid changing of the objects in the environment, we have to update a new temporary destination after few steps. The determination of the temporary destination update period depends on how fast the environment changes. When you update after more steps, a smoother path might be obtained, but the performance to response the environmental change will be decreased. On the contrary, if you update in fewer steps, the path will be not so smooth, but it will response the environmental change well. 3 Simulation Results and conclusions In this section, two examples are illustrated the effectiveness of the proposed method. Two and four movable obstacles are considered in two simulations respectively, those are shown in Fig. 4 and Fig. 5, where the big circles are movable obstacles and the small one is the goal. There are seven path points (small circles) around the robot. The black point is the selected optimal point p _ best (temporary destination). We can see the path from mobile robot approaches to goal step by step. After a temporary destination is determined, mobile robot approaches this target for a period and then searches the next optimal temporary destination to continuous this strategy until the robot reaches the goal. According to the simulation results, we know that the robot can through movable obstacles in a dynamic environment without collision and finally reach the goal. Therefore, the proposed method with a good performance is proved. In this research, a simple and intuitional path planning method is proposed such that mobile robot can through a dynamic field with movable obstacles to reach goal. The temporary destination leads mobile robot to avoid obstacles immediately, and the rapid update of local path target can response the change of environment at once. Next, the fuzzy logic controller is successfully provided the suitable rotational velocity to mobile robot, and a smoother local path is obtained. According to the simulations, we can prove that the proposed simple method can successfully plan a collision-free path for mobile robot to reach goal. References: [1] J. Barraquand, B. Langlois, and J. Latombe, Numerical potential field techniques for robot path planning, IEEE Transactions on Systems, Man, Cybernetics, Vol.22, No.2, 1992, pp [2] Y. K. Hwang, and H. Ahuja, A potential field approach to path planning, IEEE Transactions on Robotics and Automation, Vol. 8, No.1, 1992, pp [3] W. G. Han, S. M. Beak and T. Y. Kuc, Genetic algorithm based planning and dynamic obstacle avoidance of mobile robots, IEEE International Conference on System, Man, and Cybernetics, Vol.3, 1997, pp [4] R. Bohlin, Path planning in practice; lazy evaluation on a multi-resolution grid, International Conference on Intelligent Robots and Systems, Vol.1, 2001, pp [5] A. Stentz, Optimal and efficient path planning for partially-known environments, IEEE International Conference on Robotics and Automation, Vol.4, 1994, pp [6] J. Xiao, Z. Michalewicz, L. Zhang, and K. Trojanowski, Adaptive evolutionary planner /navigator for mobile robots, IEEE Transactions on Evolutionary Computation, Vol.1, No.1, 1997, pp

5 [7] J. T. Cho, and B. H. Nam, A study on the fuzzy control navigation and the obstacle avoidance of mobile robot using camera, IEEE International Conference on Systems, Man, and Cybernetics, Vol.4, 2000, pp [8] H. Juidette, and H. Youlal, Fuzzy dynamic path planning using genetic algorithms, Electronics Letters, Vol.36, No.4, 2000, pp [9] T. H. Lee, H. K. Lam, F. H. F. Leung, and P.K.S. Tam, A path planning method for micro robot soccer game, IEEE Annual Conference on Industrial Electronics Society, Vol.1, 2001, pp [10] T. Ersson, and X. Hu, Path planning and navigation of mobile robots in unknown environments, International Conference on Intelligent Robots and Systems, Vol.2, 2001, pp [11] J. M. Yang, and J. H. Kim, Sliding mode control for trajectory tracking of nonholonomic wheeled mobile robots, IEEE Transactions on Robots and Automation, Vol.15, 1999, pp Fig.1 Diagram of seven path exploratory points and the notation in (2). Fig.2 The illustration of fuzzy controller inputs. Fig.3 The block diagram of fuzzy logic controller. Table 1. The fuzzy rule base of fuzzy logic controller. d _ gr Turn _ ang ZO S M B NB NB NB NB NB NM NM NB NB NM NS NS NM NM NS ZO ZO ZO ZO ZO PS PS PM PM PS PM PM PB PB PM PB PB PB PB PB

6 (a) (b) (c) (d) (e) (f) (g) (h) (i) Fig.4 Path planning of the proposed method for two movable obstacles. (a) (b) (c) (d) (e) (f) (g) (h) (i) Fig.5 Path planning of the proposed method for four movable obstacles.