Chance-Constrained Convex MPC for Robust Quadruped Locomotion Under Parametric and Additive Uncertainties

TL;DR

This paper introduces a chance-constrained model predictive control framework for quadruped robots that explicitly accounts for uncertainties in payloads and terrain, ensuring safer and more reliable locomotion across diverse environments.

Contribution

The paper presents a novel CCMPC approach that models uncertainties as distributions within the SRBD framework and solves the control problem efficiently via quadratic programming.

Findings

Outperforms benchmarks in stability and slip reduction

Enables robust locomotion with payloads over 50% of robot weight

Successfully tested on hardware across various terrains

Abstract

Recent advances in quadrupedal locomotion have focused on improving stability and performance across diverse environments. However, existing methods often lack adequate safety analysis and struggle to adapt to varying payloads and complex terrains, typically requiring extensive tuning. To overcome these challenges, we propose a Chance-Constrained Model Predictive Control (CCMPC) framework that explicitly models payload and terrain variability as distributions of parametric and additive disturbances within the single rigid body dynamics (SRBD) model. Our approach ensures safe and consistent performance under uncertain dynamics by expressing the model friction cone constraints, which define the feasible set of ground reaction forces, as chance constraints. Moreover, we solve the resulting stochastic control problem using a computationally efficient quadratic programming formulation. Extensive Monte Carlo simulations of quadrupedal locomotion across varying payloads and complex terrains demonstrate that CCMPC significantly outperforms two competitive benchmarks: Linear MPC (LMPC) and MPC with hand-tuned safety margins to maintain stability, reduce foot slippage, and track the center of mass. Hardware experiments on the Unitree Go1 robot show successful locomotion across various indoor and outdoor terrains with unknown loads exceeding 50% of the robot body weight, despite no additional parameter tuning. A video of the results and accompanying code can be found at: https://cc-mpc.github.io/.