Representation-Free Model Predictive Control for Dynamic Motions in Quadrupeds

This article presents a novel representation-free model predictive control (RF-MPC) framework for controlling various dynamic motions of a quadrupedal robot in three-dimensional (3-D) space. Our formulation directly represents the rotational dynamics using the rotation matrix, which liberates us from the issues associated with the use of Euler angles and quaternion as the orientation representations. With a variation-based linearization scheme and a carefully constructed cost function, the MPC control law is transcribed to the standard quadratic program form. The MPC controller can operate at real-time rates of 250 Hz on a quadruped robot. Experimental results including periodic quadrupedal gaits and a controlled backflip validate that our control strategy could stabilize dynamic motions that involve singularity in 3-D maneuvers.

I. Introduction

The quadrupedal animals possess extraordinary competence of navigating harsh terrains by executing agile yet well-coordinated movements. For example, mountain goats demonstrate their extraordinary mobility on traversing steep cliffs [2]. Domesticated canine animals could be trained to execute a variety of acrobatic Parkour maneuvers [3]. These remarkable abilities of quadrupedal animals motivated the development of many quadrupedal robots. Minitaur [4] realized various dynamic running gaits: ANYmal [5] and HyQ [6] could navigate challenging terrains autonomously; MIT Cheetah robots achieved galloping [7], high speed bounding [8], and dynamic yet robust locomotion [9]. As the capabilities of quadrupedal robot rapidly grow, related researches have geared toward motions beyond locomotion on flat terrains. For example, ANYmal demonstrated the stair climbing capability [10]; MIT Cheetah 2 overcame obstacles by planning jumping trajectories online [11]; MIT Cheetah 3 achieved leaping onto high platforms [12]; MIT Mini Cheetah could execute 360 backflips [13]. In general, the ability of quadrupedal robots is being developed toward applications that involve more dynamic maneuvers in increasingly complex scenarios.