基于ADMM的分布式MPC与控制屏障函数用于安全多机器人四足运动
ADMM-Based Distributed MPC with Control Barrier Functions for Safe Multi-Robot Quadrupedal Locomotion
AI总结：
本文提出基于ADMM的去中心化MPC框架，结合控制屏障函数约束，用于多机器人腿部系统的安全轨迹规划。通过节点-边分割公式与共识约束，将全局问题分解为独立二次规划问题，实现高效去中心化优化，提升实时性与安全性。
摘要：
本文提出了一种完全去中心化的模型预测控制（MPC）框架，结合控制屏障函数（CBF）约束，用于多机器人腿部系统的安全关键轨迹规划。CBF约束的引入引入了显式的跨代理耦合，从而防止直接分解由此产生的最优控制问题。为解决这一挑战，本文采用基于交替方向乘子法（ADMM）的结构化分布式优化框架，将集中式安全关键MPC问题重新表述。通过引入一种新的节点-边分割公式与共识约束，所提出的方法将全局问题分解为独立的节点局部和边局部二次规划问题，这些问题可以通过仅使用邻居到邻居的通信进行并行求解。这使得在保持安全性和动态可行性的同时，实现了完全去中心化的轨迹优化，各代理具有对称的计算负载。所提出的框架被集成到四足机器人的分层运动控制架构中，结合了高层分布式轨迹规划、中层非线性MPC强制单刚体动力学，以及底层整体控制强制完整机器人动力学。通过在两个Unitree Go2四足机器人上的硬件实验以及涉及多达四个机器人在不确定环境中导航的数值模拟，验证了所提出方法的有效性。结果表明，所提出的分布式方法在性能上与集中式MPC相当，同时在四代理情况下将平均每个周期的规划时间减少了高达51%，从而实现了高效的实时去中心化实现。
英文摘要：
This paper proposes a fully decentralized model predictive control (MPC) framework with control barrier function (CBF) constraints for safety-critical trajectory planning in multi-robot legged systems. The incorporation of CBF constraints introduces explicit inter-agent coupling, which prevents direct decomposition of the resulting optimal control problems. To address this challenge, we reformulate the centralized safety-critical MPC problem using a structured distributed optimization framework based on the alternating direction method of multipliers (ADMM). By introducing a novel node-edge splitting formulation with consensus constraints, the proposed approach decomposes the global problem into independent node-local and edge-local quadratic programs that can be solved in parallel using only neighbor-to-neighbor communication. This enables fully decentralized trajectory optimization with symmetric computational load across agents while preserving safety and dynamic feasibility. The proposed framework is integrated into a hierarchical locomotion control architecture for quadrupedal robots, combining high-level distributed trajectory planning, mid-level nonlinear MPC enforcing single rigid body dynamics, and low-level whole-body control enforcing full-order robot dynamics. The effectiveness of the proposed approach is demonstrated through hardware experiments on two Unitree Go2 quadrupedal robots and numerical simulations involving up to four robots navigating uncertain environments with rough terrain and external disturbances. The results show that the proposed distributed formulation achieves performance comparable to centralized MPC while reducing the average per-cycle planning time by up to 51% in the four-agent case, enabling efficient real-time decentralized implementation.
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