Occasional stabilisation of limit cycle walking and control of chaos in the passive dynamics of the compass-gait biped model

It is known that the compass-gait biped model exhibits cyclic walking patterns and attractive complex phenomena, namely chaos and bifurcations. This work is concerned with the stabilisation of limit cycles and then the control of chaos. A new stabilisation process of the limit cycle walking is developed based on self-detection of the fixed point of the (un)stable limit cycle and on energy-shaping-based trajectory-tracking controller. The control process is applied in the beginning of the swing stage during a desired short time interval making hence the compass-gait biped robot to be completely passive on the remaining swing phase. We demonstrate that such occasional stabilisation of the limit cycles considerably increases the energetic efficiency of the bipedal locomotion. We show also that the proposed control method allows the compass-gait biped to walk efficiently and with a periodic gait down sloped surfaces of different angles.