This paper proposes Distributed Model Predictive Covariance Steering (DiMPCS) for multi-agent control under stochastic uncertainty. The scope of our approach is to blend covariance steering theory, distributed optimization and model predictive control (MPC) into a single framework that is safe, scalable and decentralized. Initially, we pose a problem formulation that uses the Wasserstein distance to steer the state distributions of a multi-agent system to desired targets, and probabilistic constraints to ensure safety. We then transform this problem into a finite-dimensional optimization one by utilizing a disturbance feedback policy parametrization for covariance steering and a tractable approximation of the safety constraints. To solve the latter problem, we derive a decentralized consensus-based algorithm using the Alternating Direction Method of Multipliers. This method is then extended to a receding horizon form, which yields the proposed DiMPCS algorithm. Simulation experiments on a variety of multi-robot tasks with up to hundreds of robots demonstrate the effectiveness of DiMPCS. The superior scalability and performance of the proposed method is also highlighted through a comparison against related stochastic MPC approaches. Finally, hardware results on a multi-robot platform also verify the applicability of DiMPCS on real systems. A video with all results is available in https://youtu.be/tzWqOzuj2kQ.

翻译：本文针对随机不确定性下的多智能体控制问题，提出了分布式模型预测协方差控制方法。本方法旨在将协方差控制理论、分布式优化与模型预测控制融合为一个安全、可扩展且去中心化的统一框架。首先，我们构建了一个问题模型，该模型利用Wasserstein距离将多智能体系统的状态分布引导至期望目标，并通过概率约束确保安全性。随后，我们通过采用扰动反馈策略参数化进行协方差控制，并对安全约束进行可处理近似，将原问题转化为有限维优化问题。为求解此优化问题，我们基于交替方向乘子法推导出一种去中心化的共识算法。进一步将该方法扩展至滚动时域形式，从而得到所提出的DiMPCS算法。在多达数百个机器人的多种多机器人任务仿真实验中，DiMPCS的有效性得到了验证。通过与相关随机模型预测控制方法的对比，凸显了所提方法卓越的可扩展性和性能。最后，在多机器人平台上的硬件实验结果也证实了DiMPCS在实际系统中的适用性。所有结果的演示视频可在https://youtu.be/tzWqOzuj2kQ查看。