Overview
Using optimal control and learned output tracking to stabilize a 3D hopping robot.
Abstract
We study the design of robust and agile controllers for hybrid underactuated systems. Our approach breaks down the task of creating a stabilizing controller into: 1) learning a mapping that is invariant under optimal control, and 2) driving the actuated coordinates to the output of that mapping. This ap- proach, termed Zero Dynamics Policies, exploits the structure of underactuation by restricting the inputs of the target mapping to the subset of degrees of freedom that cannot be directly actuated, thereby achieving significant dimension reduction. Furthermore, we retain the stability and constraint satisfaction of optimal control while reducing the online computational overhead. We prove that controllers of this type stabilize hybrid underactuated systems and experimentally validate our ap- proach on the 3D hopping platform, ARCHER. Over the course of 3000 hops the proposed framework demonstrates robust agility, maintaining stable hopping while rejecting disturbances on rough terrain.