Representation-Free Model Predictive Control for Dynamic Motions in Quadrupeds

TL;DR

This paper introduces a representation-free MPC framework for quadruped robots that directly uses rotation matrices, enabling real-time control of complex dynamic motions like backflips.

Contribution

The novel RF-MPC framework directly models rotational dynamics with rotation matrices, avoiding issues with Euler angles and quaternions, and achieves real-time control at 250 Hz.

Findings

Successfully stabilizes dynamic motions including backflips.

Operates at 250 Hz in real-time.

Validates effectiveness through experimental gaits and maneuvers.

Abstract

This paper presents a novel Representation-Free Model Predictive Control (RF-MPC) framework for controlling various dynamic motions of a quadrupedal robot in three dimensional (3D) 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 (QP) 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 3D maneuvers.