LIMIT-CYCLES IN A PASSIVE COMPASS GAIT BIPED AND PASSIVITY-MIMICKING CONTROL LAWS

It is well-known that a suitably designed unpowered mechanical biped r obot can ''walk'' down an inclined plane with a steady periodic gait. The energy required to maintain the motion comes from the conversion o f the biped's gravitational potential energy as it descends. Investiga tion of such passive natural motions may potentially lead us to strate gies useful for controlling active walking machines as well as to unde rstand human locomotion. In this paper we demonstrate the existence an d the stability of symmetric and asymmetric passive gaits using a simp le nonlinear biped model. Kinematically the robot is identical to a do uble pendulum (similar to the Acrobot and the Pendubot) and is able to walk with the so-called compass gait. Using the passive behavior as a reference we also investigate the performance of several active contr ol schemes. Active control can enlarge the basin of attraction of pass ive limit cycles and can create new gaits.