Dynamic Locomotion in the MIT Cheetah 3 Through Convex Model-Predictive Control

TLDR

This paper implements model predictive control to compute ground reaction forces for a torque‑controlled quadruped robot. The authors simplify the robot dynamics into a convex optimization problem, enabling ground‑reaction‑force planning over 0.5‑second horizons solved in under 1 ms at 20–30 Hz. The resulting controller enables robust locomotion across a wide range of gaits and speeds, achieving up to 3 m/s forward, 1 m/s lateral, and 180 deg/s angular velocities with a single set of gains and weights.

Abstract

This paper presents an implementation of model predictive control (MPC) to determine ground reaction forces for a torque-controlled quadruped robot. The robot dynamics are simplified to formulate the problem as convex optimization while still capturing the full 3D nature of the system. With the simplified model, ground reaction force planning problems are formulated for prediction horizons of up to 0.5 seconds, and are solved to optimality in under 1 ms at a rate of 20-30 Hz. Despite using a simplified model, the robot is capable of robust locomotion at a variety of speeds. Experimental results demonstrate control of gaits including stand, trot, flying-trot, pronk, bound, pace, a 3-legged gait, and a full 3D gallop. The robot achieved forward speeds of up to 3 m/s, lateral speeds up to 1 m/s, and angular speeds up to 180 deg/sec. Our approach is general enough to perform all these behaviors with the same set of gains and weights.