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/.

翻译：四足机器人运动控制领域的最新进展主要集中于提升其在多样化环境中的稳定性和性能。然而，现有方法往往缺乏充分的安全性分析，难以适应变化的负载与复杂地形，通常需要大量参数调整。为克服这些挑战，我们提出一种机会约束模型预测控制框架，该框架将负载与地形变化显式建模为单刚体动力学模型中的参数扰动与加性扰动的概率分布。通过将定义地面反作用力可行集的模型摩擦锥约束表达为机会约束，本方法能在不确定动力学条件下确保安全稳定的性能表现。此外，我们采用计算高效的二次规划形式求解所得随机控制问题。针对不同负载与复杂地形条件下的四足机器人运动，大量蒙特卡洛仿真实验表明，CCMPC在维持稳定性、减少足部滑移及跟踪质心轨迹方面显著优于两种基准方法：线性模型预测控制与采用人工调整安全裕度的模型预测控制。在Unitree Go1机器人上进行的硬件实验表明，即使负载超过机器人自重50%且未进行额外参数调整，系统仍能成功在多种未知室内外地形环境中实现稳定运动。实验结果视频及相关代码可见：https://cc-mpc.github.io/。