Momentum-Aware Trajectory Optimization and Control for Agile Quadrupedal Locomotion

In this letter, we present a versatile hierarchical offline planning algorithm, along with an online control pipeline for agile quadrupedal locomotion. Our offline planner alternates between optimizing centroidal dynamics for a reduced-order model and whole-body trajectory optimization, with the aim of achieving dynamics consensus. Our novel momentum-inertia-aware centroidal optimization, which uses an equimomental ellipsoid parameterization, is able to generate highly acrobatic motions via “inertia shaping”. Our whole-body optimization approach significantly improves upon the quality of standard DDP-based approaches by iteratively exploiting feedback from the centroidal level. For online control, we have developed a novel convex model predictive control scheme through a linear transformation of the full centroidal dynamics. Our controller can efficiently optimize for both contact forces and joint accelerations in single optimization, enabling more straightforward tracking for momentum-rich motions compared to existing quadrupedal MPC controllers. We demonstrate the capability and generality of our trajectory planner on four different dynamic maneuvers. We then present one hardware experiment on the MIT Mini Cheetah platform to demonstrate the performance of the entire planning and control pipeline on a twisting jump maneuver.

I. Introduction

With the recent rapid increase in capabilities of legged robots, the demand for more sophisticated approaches to trajectory optimization and online control has motivated a plethora of optimization-based motion planning strategies. Broadly speaking, these can be divided into methods that solve a single trajectory optimization (TO) problem, and those that decompose the overall problem into a set of decoupled subproblems. Single-optimization methods can be further subdivided into those that use reduced order models and those that optimize over the full-order dynamics.