Hybrid Differential Dynamic Programming for Planar Manipulation Primitives

We present a hybrid differential dynamic programming (DDP) 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 developing hybrid DDP both to plan finite horizon trajectories with a few contact switches and to create linear stabilizing controllers. We evaluate the performance and computational cost of our framework in ablations studies for two primitives: planar pushing and planar pivoting. We find that generating pose-to-pose closed-loop trajectories from most configurations requires only a couple (one to two) hybrid switches and can be done 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 our work can be found at https://youtu.be/YGSe4cUfq6Q.