Controlled Reduction with Unactuated Cyclic Variables: Application to 3D Bipedal Walking with Passive Yaw Rotation

IEEE Trans Automat Contr. 2013 Oct;58(10):2679-2685. doi: 10.1109/TAC.2013.2256011.

Abstract

This paper shows that viscous damping can shape momentum conservation laws in a manner that stabilizes yaw rotation and enables steering for underactuated 3D walking. We first show that unactuated cyclic variables can be controlled by passively shaped conservation laws given a stabilizing controller in the actuated coordinates. We then exploit this result to realize controlled geometric reduction with multiple unactuated cyclic variables. We apply this underactuated control strategy to a five-link 3D biped to produce exponentially stable straight-ahead walking and steering in the presence of passive yawing.