Three-Dimensional Kneed Bipedal Walking: A Hybrid Geometric Approach

A 3D biped with knees and a hip is naturally modeled as a nontrivial hybrid system; impacts occur when the knee strikes and when the foot impacts the ground causing a switch in the dynamics governing the system. Through a variant of geometric reduction—termed functional Routhian reduction—we can reduce the dynamics on each domain of this hybrid system to obtain a planar equivalent biped. Using preexisting techniques for obtaining walking gaits for 2D bipeds, and utilizing the decoupling effect afforded by the reduction process, we design control strategies that result in stable walking gaits for the 3D biped. That is, the main result of this paper is a control law that results in 3D bipedal walking obtained through stable walking gaits for the equivalent 2D biped.