A representation of deformable objects for motion planning with no physical simulation

We propose a new method of representing de-formable objects that allows both physical and qualitative properties to be captured in an efficient representation. We show how to use this representation with two types of motion planners: 1) optimal discrete planners, which are suitable for low-dimensional problems, 2) sampling-based planners that plan in high-dimensional cost spaces. In both cases, our representation allows us to formulate a cost function that directly assesses the cost of deformation without expensive physical simulation or computation of deformed geometry. We show that our methods can generate paths that minimize deformation in both simulated and physical environments with either hard and soft robots in either hard and soft environments. The efficiency of our representation allows these paths to be computed in under 20s for 3-DOF problems. For more complicated 6-DOF problems, low-deformation paths can be computed in under 120s. Additionally, using feedback from simulated and physical test environments, we demonstrate methods for calibrating models based on our representation.