A Voronoi-Based Hybrid Motion Planner Mark Foskey Maxim Garber Ming C. Lin Dinesh Manocha Department of Computer Science University of North Carolina at Chapel Hill http://www.cs.unc.edu/ geom/voronoi/vplan Abstract We present a hybrid path planning algorithm for rigid and articulated bodies translating and rotating in a 3D workspace. Our approach generates a Voronoi roadmap in the workspace and combines it with “bridges” computed by a randomized path planner with Voronoi-biased sam- pling. The Voronoi roadmap is computed from a discrete approximation to the generalized Voronoi diagram (GVD) of the workspace, which is generated using graphics hard- ware. By this use of the GVD, portions of the path can be generated without random sampling, substantially re- ducing the number of random samples needed for the full query. The planner has been implemented and tested on a number of benchmarks. Some preliminary comparisons with a randomized motion planner indicate that our plan- ner performs more than an order of magnitude faster in several challenging scenarios. 1 Introduction The problem of automated motion planning has seen impor- tant progress in the past decade. The probabilistic roadmap (PRM) approach has been of particular importance, providing a straightforward method for handling configuration spaces of high dimension with good efficiency [13]. In this paper we use ideas from earlier geometric or “criticality based” methods to improve the performance of a PRM planner on certain classes of problems. In PRM planning, a graph characterizing the topology of the free space is built up by generating robot configurations at ran- dom and, among those for which the robot is not in collision, at- tempting to connect nearby configurations using some very sim- ple, fast planner. The method is probabilistically complete, in the sense that PRM planners can be made arbitrarily likely to find any solution by allowing a sufficient running time. They perform well for a wide variety of problems, but they can be slow when the robot must pass through a narrow passage to reach the goal. The earlier criticality based methods rely on an explicit ge- ometric description of the configuration space to provide a data structure that can be searched for a path. Criticality based algo- rithms are typically complete: They either return a correct path or an indication that none exists. In low dimensions, many workable algorithms of this type have been implemented [16]. For arbitrary dimensions, known algorithms are prohibitively difficult to im- plement and have complexity exponential in the dimension of the C-space. An example of a general algorithm is the roadmap plan- ner based on Whitney’s stratified sets [1]. For our purposes, one benefit of criticality based methods is that they are not hindered by narrow passages. Main Results: We present a hybrid path planning algorithm for free-flying rigid and articulated bodies translating and rotat- ing in a 3D workspace. Our approach utilizes a global geomet- ric analysis of the workspace to generate an approximate path in configuration space. We then identify invalid segments of this estimated path, for which the robot is in collision, and compute linking subpaths or “bridges” [3] to replace the invalid segments. These bridges are generated by a randomized planner with care- fully restricted sampling. Our global geometric analysis uses a discrete approximation of the generalized Voronoi diagram (GVD) of the workspace, computed using graphics hardware [9]. The key distinctive fea- tures of our approach are: We generate an estimated path based on the Voronoi dia- gram of the scene, and only use randomized planning for parts of that path. When we use randomized planning, it is guided by informa- tion in the Voronoi diagram. Our planner has been implemented and applied to a number of benchmarks. We have also compared its performance with a one- shot planner in the general PRM family developed by Hsu et al. at Stanford [12]. Some preliminary results indicate that our hybrid planner for rigid bodies is more than an order of magnitude faster than the PRM planner on many of these benchmarks. The rest of the paper is organized as follows. In Section 2 we discuss related work. In Section 3 we introduce terminology re- lated to the Voronoi diagram, and in Section 4 we explain our al- gorithm. In Section 5 we give implementation details and present performance results. In Section 6 we analyze the performance of the algorithm, and in the final section we conclude and indicate areas of future work. 2 Related Work 2.1 Voronoi Diagrams in Motion Planning Generalized Voronoi diagrams have long been used as a basis for motion planning algorithms [4, 5, 17, 23]. The GVD repre- sents the connectivity of a space but has a dimension lower by one, and (in three dimensions) it is composed of surfaces of max- imal clearance.