Underactuated dynamic three-dimensional bipedal walking

The main contribution of this work is a method for robust stabilization of three-dimensional bipedal walking robots with more than one degree of under-actuation. The general framework we previously developed for stabilization of periodic orbits for hybrid systems with impact effects is shown to be applicable to three-dimensional under-actuated bipedal robots. It is shown how periodic solutions for the hybrid dynamical equations describing three-dimensional under-actuated bipedal robots can be found and that these periodic solutions (walking gaits) can be robustly stabilized if a certain semi-definite program can be solved. The fact that the robust control synthesis problem can be cast as a semi-definite program implies that computationally efficient linear matrix inequality (LMI) solvers can be used to find the controllers. We demonstrate the methodology through the simulations on a five-link spatial biped with two degrees of under-actuation