Stabilization of hybrid periodic orbits with application to bipedal walking

This work describes a general computational framework for robust stabilization of periodic orbits for hybrid systems with impact effects. We demonstrate that for such systems dynamics can be decomposed into the transverse and tangential components if a proper orthogonalizing transform is applied before the decomposition. Subsequently, we show that the robust control synthesis problem can be cast as a semi-definite program which implies that computationally efficient linear matrix inequality (LMI) solvers can be used to find the controllers. The methodology is verified through the simulation on a five-link planar under-actuated biped robot, an example often used by other researchers.