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/.
Learning Quadrupedal Locomotion over Challenging Terrain
Robotic Systems Lab, ETH Zurich（苏黎世联邦理工学院机器人系统实验室）；Robotics and Artificial Intelligence Lab, KAIST（韩国科学技术院机器人与人工智能实验室）；Intelligent Systems Lab, Intel（英特尔智能系统实验室）
MASQ: Multi-Agent Reinforcement Learning for Single Quadruped Robot Locomotion
Harbin Institute of Technology Shenzhen（哈尔滨工业大学（深圳））；School of Mechanical Engineering and Automation（机械工程与自动化学院）；Guangdong Key Laboratory of Intelligent Morphing Mechanisms and Adaptive Robotics（广东省智能变胞机构与自适应机器人重点实验室）
Dynamic Quadrupedal Legged and Aerial Locomotion via Structure Repurposing
Department of Electrical and Computer Engineering, Northeastern University（电气与计算机工程系，东北大学）；Department of Aerospace Engineering, California Institute of Technology（航空航天工程系，加州理工学院）
Towards An Adaptive Locomotion Strategy For Quadruped Rovers: Quantifying When To Slide Or Walk On Planetary Slopes
Dynamic Legged Systems Lab, Istituto Italiano di Tecnologia (IIT)（动态腿系统实验室，意大利技术研究院）；Dipartimento di Ingegneria Elettrica Elettronica e Informatica, Università di Catania（电气电子与信息工程系，卡塔尼亚大学）
Physics-informed Neural Network Predictive Control for Quadruped Locomotion
School of Intelligent Systems Engineering, Shenzhen Campus of Sun Yat-sen University（中山大学深圳校区智能系统工程学院）；General Embodied AI Center of Sun Yat-sen University（中山大学通用具身人工智能中心）；Guangdong Provincial Key Laboratory of Fire Science and Intelligent Emergency Technology（广东省火灾科学与智能应急技术重点实验室）；College of Engineering, Peking University（北京大学工学院）；Robotics and Autonomous Systems Thrust, The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州）机器人与自主系统部）；George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology（佐治亚理工学院乔治·W. 伍德拉夫机械工程学院）
Momentum-Aware Trajectory Optimization and Control for Agile Quadrupedal Locomotion
Institute for Robotics and Intelligent Machines, Georgia Institute of Technology（佐治亚理工学院机器人与智能机器研究所）；MIT Biomimetic Robotics Lab（麻省理工学院仿生机器人实验室）；NAVER LABS（NAVER实验室）
End-to-End Multi-Task Policy Learning from NMPC for Quadruped Locomotion
Institute for Artificial Intelligence and Autonomous Systems (A2S)（人工智能与自主系统研究所）；Bonn-Rhein-Sieg University of Applied Sciences（波恩-莱茵-锡格应用科学大学）；Humanoid Robots Lab（人形机器人实验室）；University of Bonn（波恩大学）；Lamarr Institute for Machine Learning and Artificial Intelligence（Lamarr机器学习与人工智能研究所）；Center for Robotics（机器人中心）；Fraunhofer Institute for Intelligent Analysis and Information Systems（弗劳恩霍夫智能分析与信息系统研究所）
Load-bearing Assessment for Safe Locomotion of Quadruped Robots on Collapsing Terrain
Dynamic Legged Systems Lab, Istituto Italiano di Tecnologia (IIT)（动态腿系统实验室，意大利技术研究院）；Department of Mechanical Engineering, São Carlos School of Engineering (EESC), University of São Paulo (USP)（机械工程系，圣卡洛斯工程学院（EESC），圣保罗大学）
Dynamic Modeling and MPC for Locomotion of Tendon-Driven Soft Quadruped
Department of Electrical Engineering, IIT Gandhinagar（电子工程系，印度加尔各直辖区理工学院）；Department of Electronics and Computer Engineering, Sreenidhi Institute of Science and Technology（电子与计算机工程系，斯里尼迪学院科学与技术研究所）；Department of Mechanical Engineering, IIT Gandhinagar（机械工程系，印度加尔各直辖区理工学院）
Versatile, Robust, and Explosive Locomotion with Rigid and Articulated Compliant Quadrupeds
Cognitive Robotics, Delft University of Technology（代尔夫特理工大学认知机器人学系）；University of Trento（特伦托大学）；University of Manchester（曼彻斯特大学）；Institute of Robotics and Mechatronics, German Aerospace Center (DLR)（德国航空航天中心机器人与机电一体化研究所）
Vision-based Navigation for a Small-scale Quadruped Robot Pegasus-Mini
Institute of Robotics and Intelligent Manufacturing (IRIM), The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）机器人与智能制造研究院（IRIM））；Shenzhen Institute of Artificial Intelligence and Robotics for Society (AIRS), The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）深圳人工智能与机器人研究院（AIRS））
Zero-Shot Retargeting of Learned Quadruped Locomotion Policies Using Hybrid Kinodynamic Model Predictive Control
University of Notre Dame（圣母大学）；Robotics at Google（谷歌机器人部门）
强化学习（RL）在四足动物运动方面取得了长足的进步，并在策略的可靠仿真到现实迁移方面取得了持续的进展。然而，在另一个机器人上重用策略仍然是一个挑战，这可以节省重新训练的时间。在这项工作中，我们提出了一个框架zero-shot政策重定向，其中不同的运动技能可以在不同形状和大小的机器人之间转移。新的框架集中在一个规划和控制管道，系统地集成RL和模型预测控制（MPC）。规划阶段采用RL生成动态似然轨迹以及接触时间表，避免了接触序列优化的组合复杂性。然后，这些信息被用于播种MPC，以通过一个新的混合Kinodynamic（HKD）模型来稳定和鲁棒化政策推出，该模型隐式优化了立足点位置。硬件结果表明，能够将策略从A1和Laikago机器人传输到MIT Mini Cheetah机器人，而无需任何策略重新调整。
