Limit Cycles in a Passive Compass Gait Biped and Passivity-Mimicking Control Laws

It is well-known that a suitably designed unpowered mechanical bipedrobot can “walk” down an inclined plane with a steady periodicgait. The energy required to maintain the motion comes from theconversion of the biped's gravitational potential energy as itdescends. Investigation of such passive natural motions maypotentially lead us to strategies useful for controlling activewalking machines as well as to understand human locomotion.In this paper we demonstrate the existence and the stability ofsymmetric and asymmetric passive gaits using a simple nonlinear bipedmodel. Kinematically the robot is identical to a double pendulum(similar to the Acrobot and the Pendubot) and is able to walk withthe so-called compass gait. Using the passivebehavior as a reference we also investigate the performance ofseveral active control schemes. Active control can enlarge the basinof attraction of passive limit cycles and can create new gaits.

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