This paper presents a novel approach to enhance Model Predictive Control (MPC) for legged robots through Distributed Optimization. Our method focuses on decomposing the robot dynamics into smaller, parallelizable subsystems, and utilizing the Alternating Direction Method of Multipliers (ADMM) to ensure consensus among them. Each subsystem is managed by its own Optimal Control Problem, with ADMM facilitating consistency between their optimizations. This approach not only decreases the computational time but also allows for effective scaling with more complex robot configurations, facilitating the integration of additional subsystems such as articulated arms on a quadruped robot. We demonstrate, through numerical evaluations, the convergence of our approach on two systems with increasing complexity. In addition, we showcase that our approach converges towards the same solution when compared to a state-of-the-art centralized whole-body MPC implementation. Moreover, we quantitatively compare the computational efficiency of our method to the centralized approach, revealing up to a 75\% reduction in computational time. Overall, our approach offers a promising avenue for accelerating MPC solutions for legged robots, paving the way for more effective utilization of the computational performance of modern hardware.

翻译：本文提出一种通过分布式优化提升腿式机器人模型预测控制（MPC）性能的新方法。该方法将机器人动力学分解为更小且可并行运算的子系统，并利用交替方向乘子法（ADMM）确保各子系统的协同一致性。每个子系统由其自身的最优控制问题管理，ADMM算法则协调各子系统优化过程的一致性。该方法不仅降低了计算时间，还实现了对复杂机器人构型的有效扩展，便于在四足机器人上集成如铰接臂等附加子系统。通过数值评估，我们在两个复杂度递增的系统上验证了该方法的收敛性。此外，与最先进的集中式全身MPC实现相比，该方法展现出收敛至相同解的特性。我们进一步定量对比了本方法与集中式方法的计算效率，结果表明计算时间可减少高达75%。总体而言，本方法为加速腿式机器人MPC求解提供了可行路径，为更高效利用现代硬件计算性能奠定了基础。