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 \gls{ocp}, 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：本文提出了一种新颖方法，通过分布式优化增强腿式机器人的模型预测控制（MPC）。该方法将机器人动力学分解为更小、可并行化的子系统，并利用交替方向乘子法（ADMM）确保子系统间的一致性。每个子系统由其自身的优化控制问题（OCP）管理，ADMM促进其优化过程的一致性。该方法不仅缩短了计算时间，还能有效扩展至更复杂的机器人构型，例如在四足机器人上集成诸如关节臂等额外子系统。通过数值评估，我们证明了该方法在两个复杂度递增的系统上的收敛性；同时，对比最先进的集中式全身MPC实现，展示了该方法能收敛至相同解。此外，我们定量比较了该方法与集中式方法的计算效率，结果显示计算时间最高可降低75%。总体而言，本研究为加速腿式机器人MPC求解提供了有前景的途径，为更高效利用现代硬件的计算性能奠定了基础。