Finding Narrow Passages with Probabilistic Roadmaps: The Small-Step Retraction Method

Probabilistic Roadmaps (PRM) have been successfully used to plan complex robot motions in configuration spaces of small and large dimensionalities. However, their efficiency decreases dramatically in spaces with narrow passages. This paper presents a new method—small-step retraction—that helps PRM planners find paths through such passages. This method consists of slightly “fattening” robot's free space, constructing a roadmap in fattened free space, and finally repairing portions of this roadmap by retracting them out of collision into actual free space. Fattened free space is not explicitly computed. Instead, the geometric models of workspace objects (robot links and/or obstacles) are “thinned” around their medial axis. A robot configuration lies in fattened free space if the thinned objects do not collide at this configuration. Two repair strategies are proposed. The “optimist” strategy waits until a complete path has been found in fattened free space before repairing it. Instead, the “pessimist” strategy repairs the roadmap as it is being built. The former is usually very fast, but may fail in some pathological cases. The latter is more reliable, but not as fast. A simple combination of the two strategies yields an integrated planner that is both fast and reliable. This planner was implemented as an extension of a pre-existing single-query PRM planner. Comparative tests show that it is significantly faster (sometimes by several orders of magnitude) than the pre-existing planner. Mitul Saha received the B.S. degree from the Indian Institute of Technology, Kanpur, India, in 2001 and the M.S. degree from the Computer Science Department at Stanford University, Stanford, CA, in 2005. He is currently pursuing the Ph.D. degree in mechanical engineering at Stanford University. His research interests include motion planning, computer vision, graphics, and structural biology. Jean-Claude Latombe graduated in electrical and computer engineering from the National Polytechnic Institute of Grenoble, France, in 1970. He received the M.S. degree in electrical engineering from the National Polytechnic Institute of Grenoble in 1972, and the PhD degree in computer science from the University of Grenoble in 1977. He joined the Department of Computer Science at Stanford University in 1987, where he currently is the Kumagai Professor in the School of Engineering. He does research in the general areas of artificial intelligence, robotics, and geometric computing. He is particularly interested in motion planning, computational biology, and computer-assisted surgery. Yu-Chi Chang is a Ph.D. candidate in the Mechanical Engineering at Stanford University. Yu-Chi received the B.Sc. in Mechanical Engineering and the M.Sc. in Material Science from National Taiwan University, Taiwan, and the M.Sc. in Mechanical Engineering from Stanford University, United States. His current research interests include robust design and statistical analysis for manufacturing system. Friedrich Prinz is the Rodney H. Adams Professor of Engineering and Professor of Mechanical Engineering and Materials Science and Engineering, Stanford University. Professor Prinz received his Ph.D. degree in Physics from the University of Vienna in 1975. He has been active in synergistic activities with organizations like the National Research Council Committees, the Japanese Technology Evaluation Center and World Technology Evaluation Center, as well as Portuguese Science and Technology Foundation. He was elected to the Austrian Academy of Science (foreign member), Vienna, Austria in 1996. Dr. Prinz's current research activities address a wide range of problems related to design and rapid prototyping of organic and inorganic devices. His current work focuses on the fabrication and physics of fuel cells as well as the creation of biological cell structures. His group uses atomic force microscopy and impedance spectroscopy to characterize the behavior of electrochemical systems with micro and nano-scale dimensions.