Impact Invariant Control with Applications to Bipedal Locomotion

When legged robots impact their environment, they undergo large changes in their velocities in a small amount of time. Measuring and applying feedback to these velocities is challenging, and is further complicated due to uncertainty in the impact model and impact timing. This work proposes a general framework for adapting feedback control during impact by projecting the control objectives to a subspace that is invariant to the impact event. The resultant controller is robust to uncertainties in the impact event while maintaining maximum control authority over the impact invariant subspace. We demonstrate the utility of the projection on a walking controller for a planar five-link-biped and on a jumping controller for a compliant 3D bipedal robot, Cassie. The effectiveness of our method is shown to translate well on hardware.

I. Introduction

Handling the making and breaking of contact lies at the core of controllers for legged robots. Its role becomes increasingly important as the the field demands that our legged robots be capable of more agile motions. However, current controllers for legged robots are incredibly sensitive to these impact events. When a robot’s foot makes contact with the world, the foot is brought instantaneously to a stop by a large contact impulse. The presence of large contact forces and rapidly changing velocities hinders accurate state estimation. Coupled with the poor predictive performance of our contact models [1] [2] [3], this combination of large state uncertainty and poor models makes control especially difficult.