This paper presents a novel distributed robust optimization scheme for steering distributions of multi-agent systems under stochastic and deterministic uncertainty. Robust optimization is a subfield of optimization which aims in discovering an optimal solution that remains robustly feasible for all possible realizations of the problem parameters within a given uncertainty set. Such approaches would naturally constitute an ideal candidate for multi-robot control, where in addition to stochastic noise, there might be exogenous deterministic disturbances. Nevertheless, as these methods are usually associated with significantly high computational demands, their application to multi-agent robotics has remained limited. The scope of this work is to propose a scalable robust optimization framework that effectively addresses both types of uncertainties, while retaining computational efficiency and scalability. In this direction, we provide tractable approximations for robust constraints that are relevant in multi-robot settings. Subsequently, we demonstrate how computations can be distributed through an Alternating Direction Method of Multipliers (ADMM) approach towards achieving scalability and communication efficiency. Simulation results highlight the performance of the proposed algorithm in effectively handling both stochastic and deterministic uncertainty in multi-robot systems. The scalability of the method is also emphasized by showcasing tasks with up to 100 agents. The results of this work indicate the promise of blending robust optimization, distribution steering and distributed optimization towards achieving scalable, safe and robust multi-robot control.

翻译：本文提出了一种新颖的分布式鲁棒优化方案，用于在随机和确定性不确定性条件下引导多智能体系统的分布。鲁棒优化是优化领域的一个分支，旨在发现一个最优解，该解对于给定不确定集内问题参数的所有可能实现均保持鲁棒可行性。这类方法自然成为多机器人控制的理想候选，因为在多机器人场景中，除了随机噪声外，还可能存在外源性确定性扰动。然而，由于这些方法通常伴随极高的计算需求，其在多智能体机器人领域的应用仍十分有限。本研究的目标是提出一个可扩展的鲁棒优化框架，既能有效处理这两种不确定性，又能保持计算效率和可扩展性。为此，我们为多机器人环境中相关的鲁棒约束提供了易于处理的近似形式。随后，我们展示了如何通过交替方向乘子法（ADMM）实现计算分布化，以达成可扩展性和通信效率。仿真结果突出了所提算法在处理多机器人系统中随机和确定性不确定性方面的性能。通过展示多达100个智能体的任务，该方法在可扩展性方面的优势也得到了强调。本研究成果表明，融合鲁棒优化、分布引导与分布式优化，有望实现可扩展、安全且鲁棒的多机器人控制。