Abstract—The F 2 (Force Field) method is a novel approach for multi-robot motion planning and collision avoidance. The setting of parameters is however vital to its performance. This paper presents an approach using Particle Swarm Optimization (PSO) to properly determine the control parameters for the F 2 method. The goal of the optimization is to minimize the resultant path lengths. The approach presented in this paper can be used as a tool to obtain optimal parameters for various tasks before their execution. Simulations are carried out in various environments to show the feasibility of this approach. I. INTRODUCTION HIS paper addresses the problem of motion planning for multiple robots. Although many algorithms have been proven to be feasible and efficient for single-robot motion planning and collision avoidance, they cannot be transferred directly to multi-robot systems. The existing methods are often categorized into centralized and decentralized approaches [1]. Centralized approaches consider all robots together as if they are forming a high degree of freedom system and are capable of providing complete and optimal solutions. However, as the number of robots and obstacles in the working environment increases, such approaches will suffer from the exponentially increasing computational complexity. Decentralized approaches generate each path for individual robot independently and avoid collisions locally. Decentralized approaches are not affected by the number of robots but are usually incomplete, i.e., they may fail to find a solution even if it exists. Priority planning is an efficient approach for multi-robot motion planning [2-7]. Techniques of this class assign priorities to each robot and compute paths in order of decreasing priority. A robot with higher priority is treated as an obstacle in the planning of a robot with lower priority. This reduces the multi-robot motion planning problem into several single-robot motion planning problems. The configuration-space-time method was first introduced in [2]. By introducing time as an additional dimension, this approach discretizes the configuration space to a sequence of slices of the configuration space at successive time intervals. Manuscript received March 23, 2007. This work is supported in part by the ARC Centre of Excellence programme, funded by the Australian Research Council (ARC) and the New South Wales State Government, Australia. All Authors are with the ARC Centre of Excellence for Autonomous Systems (CAS), Faculty of Engineering, University of Technology, Sydney, (UTS), NSW 2007, Australia. (e-mail: {Da-Long.Wang, ngai.kwok, dkliu, hlau, gdissa}@ eng.uts.edu.au). Some approaches decomposed the motion planning problem into two smaller sub-problems: path planning and velocity planning [8-10]. Under these approaches, robots are kept on their preplanned paths and speed changing strategies are applied to avoid collisions. The F 2 method is a force field based method for multi- robot path planning and collaboration [11]. Instead of generating potential fields or force fields based on obstacles, a virtual force field is constructed for each robot based on its status, including traveling speed, dimension, priority, location and environmental factors, etc. The force field of a robot is different from those of other robots due to its different status and varies with the robot during its movement. A robot with larger volume, traveling with higher speed, or with higher task priority than other robots will have priority in collision avoidance. The interaction among the robots’ force fields and obstacles provides a feasible and efficient way for multi-robot motion planning and collaboration. This paper builds upon the F 2 method proposed in our previous work [11], which operates using a number of parameters. The setting of these parameters can noticeably affect its performance. Accordingly, this paper analyses the effect of parameters in the F 2 method. Since the problem is highly coupled, non-linear and incomplete, closed-form solutions are not always available. An emerging algorithm in the evolutionary computation family, the Particle Swarm Optimization (PSO), is then utilized to obtain appropriate parameters in single-robot and multi-robot cases. PSO was proposed by Kennedy and Eberhart in 1995, motivated by social behavior of organisms such as bird flocking [12]. Due to its simple mechanism and high performance of global optimization, PSO has been applied for many optimization problems successfully, including motion planning problems [13, 14]. This paper is organized as follows. In Section II, we give the detailed description of the F 2 method. Then a simple case is studied to show how the selections of parameters affect its performance. Section III introduces the concept of PSO and describes how to use PSO for parameter optimization. The feasibility of the presented approach is supported by simulations in Section IV. Conclusion and future work are given in Section V. II. F 2 METHOD In the F 2 method, a robot is assumed to travel in a 2-D environment and its location can be precisely known. Each robot is aware of the updated information of all other robots, PSO-Tuned F 2 Method for Multi-Robot Navigation D. Wang, N. M. Kwok, D. K. Liu, H. Lau, G. Dissanayake T Proceedings of the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems San Diego, CA, USA, Oct 29 - Nov 2, 2007 ThC9.2 1-4244-0912-8/07/$25.00 ©2007 IEEE. 3765