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

Ananya Trivedi, Sarvesh Prajapati, Mark Zolotas, Michael Everett, Taskin Padir

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/.

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

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/.

Paper Structure

This paper contains 13 sections, 20 equations, 7 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Chance-Constrained Foot Force MPC
  4. Convex QP Reformulation of CCMPC
  5. Uncertainty Propagation
  6. Friction Cone Constraint Adjustment
  7. Reduction to Quadratic Program
  8. Experiments
  9. Implementation Details
  10. Simulation Analysis
  11. Hardware Validation
  12. Conclusion
  13. Acknowledgments

Figures (7)

  • Figure 1: Chance-Constrained MPC (bottom) stabilizes the robot by handling a distribution of inertial uncertainties from 6 kg dumbbells (1) and contact uncertainties, from planks (2). Linear MPC (top) fails under these conditions.
  • Figure 2: The modular control architecture adopted in this work for quadrupedal locomotion.
  • Figure 3: Illustration of friction cone constraint adjustment.
  • Figure 4: Comparison of LMPC (left, fails) and CCMPC (right, succeeds) across various gaits and terrains. Similar failures were also observed with HMPC in these experiments.
  • Figure 5: Simulated height tracking performance with an unmodeled 6 kg payload.
  • ...and 2 more figures