Planning paths for a flexible surface patch

This paper presents a probabilistic planner capable of finding paths for a flexible surface patch. The planner is based on the probabilistic roadmap approach to path planning while the surface patch is modeled as a low degree Bezier surface. We assume that we are dealing with an elastic part and define an approximate energy model for the part. The energy function penalizes excessive shear and bending of the part and we assume that low-energy configurations correspond to reversible elastic deformations of the part. The planner captures the connectivity of a space by building a roadmap, a network of simple paths connecting configurations selected in the space using randomized techniques. We report on the implementation of our planner and show experimental results with examples where the surface patch is required to move through a small hole in its workspace. Our work is a first step towards considering the physical properties of parts when planning paths.