Virtual Constraint Generation for Stable Acrobot Gaits

Abstract

This thesis presents a method of designing virtual holonomic constraints (VHCs) which induce stable walking gaits for the simplest biped robot, an acrobot without fixed pivot. Developing a stable walking gait corresponds to designing a VHC such that the constrained dynamics possess a hybrid limit cycle associated with repetitive walking. Our methodology relies on the virtual constraint generator, a control system whose orbits are all possible enforceable VHCs. We map the stable gait problem into a motion planning problem with endpoint control constraints for the constraint generator. We present a core theoretical result concerning constraint generator motion planning via constant controls, and build an algorithm around it producing stable walking gaits. We apply this algorithm to two gaits: a traditional “compass” gait and a novel “walkover” gait. The ideas behind this methodology are amenable to generalization and provide an avenue for future research in walking gait design for underactuated robots.