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.

翻译：本文提出了一种完全去中心化的模型预测控制（MPC）框架，该框架引入控制障碍函数（CBF）约束，用于多机器人腿足系统的安全关键轨迹规划。CBF约束的引入导致了显式的智能体间耦合，阻碍了最优控制问题的直接分解。针对这一挑战，我们基于交替方向乘子法（ADMM），采用结构化分布式优化框架重新构建了集中式安全关键MPC问题。通过引入一种新颖的节点-边分裂公式（含一致性约束），所提方法将全局问题分解为可独立并行求解的节点局部与边局部二次规划问题，且仅需邻居间通信。这使得在保持安全性和动态可行性的同时，能够实现计算负载在各智能体间对称分配的完全去中心化轨迹优化。该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、中层基于非线性MPC（施加单刚体动力学约束）以及低层全身控制（施加全阶机器人动力学约束）。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崎岖地形和外部扰动的不确定环境中导航的数值模拟，验证了所提方法的有效性。结果表明，所提分布式公式在四智能体场景下实现了与集中式MPC相当的性能，同时将平均单周期规划时间降低了高达51%，从而支持高效的实时去中心化实现。