Designing feedback algorithms for controlling the periodic motions of legged robots

A nonlinear feedback control algorithm is developed for repetitive legged robotic locomotion whose global dynamic behavior can be encoded in a Poincare return map. Control synthesis is equivalent to the selection of a nonlinear feedback control law which properly shapes the return map. A method is presented for return map shaping in a neighborhood of a fixed point. In practice, this neighborhood can be quite large. The theory is illustrated with applications to a simplified model of Raibert's hopping machines. An added benefit is accurate control of hopping height above undulating terrain.