A Two-Point Boundary-Value Approach for Planning Manipulation Tasks

We consider the problem of planning manipulation tasks in which rigid body dynamics are significant and the rigid bodies undergo frictional contacts. We develop a dynamic model with frictional compliant contacts, and a time-stepping algorithm that lends itself to finding trajectories with constraints on the starting and goal conditions. Because we explicitly model the local compliance at the contact points, we can incorporate impacts without resetting the states and reinitializing the dynamic models. The problem of solving for the frictional forces with the Coulomb friction cone law reduces to a convex quadratic program. We show how this formulation can be used to solve boundary value problems that are relevant to process design, design optimization and trajectory planning with practical examples. To our knowledge, this paper is the first time boundary value problems involving changes in contact conditions have been solved in a systematic way.