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

arXiv: https://arxiv.org/abs/2411.03481 · HTML: https://mlsanity.com/paper/2411.03481/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2024.

## Built on by (most cited first, 2 of 2)

- [Adaptive Time Step Flow Matching for Autonomous Driving Motion Planning](https://mlsanity.com/paper/2602.10285/) (2026)
- [Dynamic Adaptive Legged Locomotion Policy via Decoupling Reaction Force Control and Gait Control](https://mlsanity.com/paper/2509.13737/) (2025)

## Abstract (arXiv)

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/.