Using projected dynamics to plan dynamic contact manipulation

This paper addresses the planning and control of dynamic contact manipulation. In an earlier paper (Srinivasa et al., 2005), we derived a constraint on the robot joint accelerations that needed to be satisfied to obtain a desired contact mode and a desired dynamic motion of the object. We proposed a technique for trajectory planning which involved planning a path in the system configuration space followed by time-scaling the path to satisfy dynamic constraints. This paper tackles a problem where only a small set of paths can be time-scaled to satisfy the constraints. We note that the dynamic constraints depend only on a subspace of the system state space. Projecting the dynamics and the constraints onto the subspace allows us to compute an analytical solution for the trajectory generation problem. We generate controllable simulations by allowing the user to control the system in the space orthogonal to the projection. We also demonstrate the construction of feedback controllers using dynamic programming.