Hybrid Differential Dynamic Programming for Planar Manipulation Primitives

We present a hybrid differential dynamic programming algorithm for closed-loop execution of manipulation primitives with frictional contact switches. Planning and control of these primitives is challenging as they are hybrid, under-actuated, and stochastic. We address this by planning a trajectory over a finite horizon, considering a small number of contact switches, and generating a stabilizing controller. We evaluate the performance and computational cost of our framework in ablations studies for two primitives: planar pushing and planar pivoting. We can plan pose-to-pose trajectories from most configurations with only a couple (one to two) hybrid switches and in reasonable time (one to five seconds). We further demonstrate that our controller stabilizes these hybrid trajectories on a real pushing system. A video describing out work can be found at https://youtu.be/YGSe4cUfq6Q.