Nonlinear Model Predictive Control of a 3D Hopping Robot: Leveraging Lie Group Integrators for Dynamically Stable Behaviors

TL;DR

This paper presents a novel nonlinear model predictive control framework using Lie group integrators to achieve stable 3D hopping and complex maneuvers on a robot, addressing challenges of underactuation and rapid ground interactions.

Contribution

It introduces a geometrically consistent control approach leveraging Lie group integrators for stable 3D hopping and dynamic behaviors in legged robots.

Findings

Successful experimental demonstration of stable 3D hopping

Trajectory tracking and flipping achieved in simulation

Effective control of complex maneuvers on a hopping robot

Abstract

Achieving stable hopping has been a hallmark challenge in the field of dynamic legged locomotion. Controlled hopping is notably difficult due to extended periods of underactuation combined with very short ground phases wherein ground interactions must be modulated to regulate global state. In this work, we explore the use of hybrid nonlinear model predictive control paired with a low-level feedback controller in a multi-rate hierarchy to achieve dynamically stable motions on a 3D hopping robot. In order to demonstrate richer behaviors on the manifold of rotations, both the planning and feedback layers must be designed in a geometrically consistent fashion; therefore, we develop the necessary tools to employ Lie group integrators and appropriate feedback controllers. We experimentally demonstrate stable 3D hopping, as well as trajectory tracking and flipping in simulation.