UMAPRM: Uniformly Sampling the Medial Axis Hsin-Yi (Cindy) Yeh, Jory Denny, Aaron Lindsey, Shawna Thomas, and Nancy M. Amato Abstract— Maintaining clearance, or distance from obstacles, is a vital component of successful motion planning algorithms. Maintaining high clearance often creates safer paths for robots. Contemporary sampling-based planning algorithms that utilize the medial axis, or the set of all points equidistant to two or more obstacles, produce higher clearance paths. However, they are biased heavily toward certain portions of the medial axis, sometimes ignoring parts critical to planning, e.g., specific types of narrow passages. We introduce Uniform Medial Axis Probabilistic RoadMap (UMAPRM), a novel planning variant that generates samples uniformly on the medial axis of the free portion of Cspace. We theoretically analyze the distribution generated by UMAPRM and show its uniformity. Our results show that UMAPRM’s distribution of samples along the medial axis is not only uniform but also preferable to other medial axis samplers in certain planning problems. We demonstrate that UMAPRM has negligible computational overhead over other sampling techniques and can solve problems the others could not, e.g., a bug trap. Finally, we demonstrate UMAPRM successfully generates higher clearance paths in the examples. I. INTRODUCTION Planning valid (e.g., collision-free) motions for a movable object (robot) is challenging. Motion planning has been extensively studied and has applications not only in robotics but also in augmented reality [11], computer-aided design [2], and bioinformatics [15]. One method of computing motions is sampling-based planning [8]. A major breakthrough, sampling-based plan- ners solved many previously intractable problems, especially for high-dimensional robotic systems. While many of these methods are probabilistically complete, i.e., they guarantee finding a solution, if one exists, as they sample ad infinitum. They may compute low clearance paths, making the extracted paths high-risk and undesirable for certain applications. Generally, most methods aim to simply generate feasible paths instead of paths with certain characteristics, e.g., high clearance. One method of computing high clearance paths, Medial Axis Probabilistic RoadMap (MAPRM) [17], generates mile- stones along the medial axis of the planning space, or the set of points equidistant to two or more obstacles. Lien et. al. extended this to high dimensional spaces by allowing This research supported in part by NSF awards CNS-0551685, CCF- 0833199, CCF-0830753, IIS-0916053, IIS-0917266, EFRI-1240483, RI- 1217991, by NIH NCI R25 CA090301-11, by Chevron, IBM, Intel, Ora- cle/Sun and by Award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). J. Denny supported in part by an NSF Graduate Research Fellowship. Hsin-Yi (Cindy) Yeh, Jory Denny, Aaron Lindsey, Shawna Thomas, and Nancy M. Amato are with the Parasol Lab, Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA, {hyeh, jdenny, alindsey, sthomas, amato}@cse.tamu.edu. for approximate clearance and penetration computations [12]. This approach computes higher clearance paths and biases samples to segments of the medial axis with large Voronoi regions. Moreover, in MAPRM the probability of sampling a configuration in a narrow passage depends on both its volume and its surrounding obstacle volume. Therefore, MAPRM can efficiently solve problems with narrow passages that have large surrounding obstacle volume. However, MAPRM does not provide any guarantee regarding the distribution of samples along the medial axis. In this paper, we propose a new planning variant, Uniform Medial Axis PRM (UMAPRM), which uniformly samples the medial axis of the planning space. Briefly, UMAPRM samples fixed length line segments from the planning space and analyzes adjacent configurations along the segment with a simple test determining if the medial axis has been crossed. The test essentially analyzes changes in the nearest obstacles of successive configurations. It retains samples of maximal clearance when medial axis crossings are detected. Our specific contributions are as follows: • We present a novel sampling technique, UMAPRM, that uniformly samples the medial axis of the planning space. • We theoretically prove that UMAPRM samples are uniformly distributed along the medial axis. • We experimentally show how UMAPRM uniformly samples the medial axis and how this uniformity can yield efficiency improvements in planning compared to MAPRM and uniform random sampling. UMAPRM is inspired by both MAPRM and the recently proposed UOBPRM (Uniform Obstacle-Based PRM) [19]. UOBPRM guarantees uniformly distributed samples along the boundary of obstacle space; it works by analyzing random line segments for changes in validity and retains intersections between line segments and obstacles. II. PRELIMINARIES AND RELATED WORK In this section, we discuss motion planning preliminaries and the basics of sampling-based planning. We discuss methods focused on planning in the presence of narrow passages and methods which generate solutions biased to the medial axis of the space. A. Motion Planning A robot is a movable object whose position and orientation can be described by n parameters, or degrees of freedom (DOFs), each corresponding to an object component (e.g., object positions, object orientations, link angles, and/or link displacements). Hence, a robot’s placement, or configuration, can be uniquely described by a point 〈x 1 ,x 2 , ..., x n 〉 in 2014 IEEE International Conference on Robotics & Automation (ICRA) Hong Kong Convention and Exhibition Center May 31 - June 7, 2014. Hong Kong, China U.S. Government work not protected by U.S. copyright 5798