A Probabilistic Roadmap Planner for Flexible Objects with a Workspace Medial-Axis-Based Sampling Approach Leonidas J. Guibas Department of Computer Science Stanford University Stanford, CA 95305 guibas@cs.stanford.edu Christopher Holleman Lydia E. Kavraki Department of Computer Science Rice University 6100 Main Street, Houston, TX 77005 rusty,kavraki @cs.rice.edu Abstract Probabilistic roadmap planners have been used with success to plan paths for flexible objects such as metallic plates or plastic flexible pipes. This paper improves the performance of these planners by using the medial axis of the workspace to guide the random sampling. At a preprocessing stage, the me- dial axis of the workspace is computed using a recent efficient algorithm. Then the flexible object is fitted at random points along the medial axis. The energy of all generated configura- tions is minimized and the planner proceeds to connect them with low-energy quasi-staticpaths in a roadmap that captures the connectivity of the free space. Given an initial and a final configuration, the planner connects these to the roadmap and searches the roadmap for a path. Our experimental results show that the new sampling scheme is successful in identify- ing critical deformations of the object along solution paths which results in a significant reduction of the computation time. Our work on planning for flexible objects has applica- tions in industrial settings, virtual reality environments, and medicine. 1 Introduction Robot path planning is important in a wide array of applica- tions from industrial automation to computer-aided animation and computational pharmacology [6, 9, 11, 20]. The prob- lem considered in this paper is an extension of the traditional path planning problem of [23]: given a flexible object/robot with known physical characteristics (e.g. an elastic object) and a set of ways that the object can be manipulated (called manipulation constraints or limit conditions hereafter), find a quasi-static path for the object from an initial to a goal con- figuration. The deformations of the object are prescribed by the manipulation constraints in combination with a physical model of the object. Figure 1 offers an illustration. The flexi- ble object is an elastic plate and the manipulation constraints restrict the tangents of two opposite edges of the plate. The snapshot shown is from a path that has been computed by the planner described in this paper. Figure 1: Snapshot along a manipulation path for an elastic plate (Three-quarter view). Several important applications motivate our research on planning for flexible objects: in industrial settings there is a need to manipulate sheets of metal [26], pipes that can bend [30], and cables [25]. In assembly maintainability stud- ies done with virtual prototyping, planning is used to com- pute a removal path for a part from an assembly, given only the CAD model of the assembly [6]. The flexibility of the part needs to be considered as engineers use deformable parts to produce compact assemblies [5]. In medical and surgical procedures, flexible catheters are inserted into human vessels [4, 31]. Accurate planning studies may help in choosing the size and properties of the catheter used. In computer-assisted pharmaceutical drug design, path planning techniques are used to compute paths for drug molecules to their docking sites [29]. In that context the rigorous treatment of the phys- ical properties of the drug molecule is crucial for obtaining sequences that are of low-energy and can thus be encountered in nature. Last but not least, our work may have applications in domains like computer generated animation and virtual en-