A computational approach to dynamic bipedal walking

The main contribution of this work is a general method for stabilization of periodic orbits for hybrid systems with impact effects. Our primary motivation is controller synthesis for walking robots, but the method can be also applied to problems such as flight control or automotive control. Limit cycles of hybrid systems are characterized by the fact that they span different dynamic regimes. For smooth systems, dynamics of the system along the limit cycle can be decomposed into the transverse and tangential components. We demonstrate that this decomposition can be adapted to hybrid systems. Furthermore, we show that when the transverse dynamics is linearized and discretized, the resulting robust control synthesis problem can be cast as a semidefinite program and thus efficiently solved. We demonstrate our results through the simulation on a simple planar biped robot.