Path Planning for Elastic Plates Under Manipulation Constraints

This paper addresses the problem of path planning for a thin elastic metal plate under fairly general manipulation constraints. The underlying geometric model for the plate is provided by a B ezier representation. The geometric model is augmented by a realistic mechanical model. We assume that the plate is manipulated in accordance with a set of user-deened grasping constraints that specify the position and orientation of two opposite edges. Our mechanical model permits the computation of the shape of the plate with respect to the grasping constraints by minimizing the energy function of the deformation of the plate. Paths are computed by a planner that is based on the principle of probabilistic roadmaps. The planner builds a roadmap in the connguration space. The nodes of the roadmap are equilibrium conngurations of the plate under the grasping constraints, while its edges correspond to quasi-static equilibrium paths. Paths are found by searching the roadmap. Several experimental results illustrate our approach.