Scaling Robust Optimization for Swarms: A Distributed Perspective

This article introduces a decentralized robust optimization framework for safe multi-agent control under uncertainty. Although stochastic noise has been the primary form of modeling uncertainty in such systems, these formulations might fall short in addressing uncertainties that are deterministic in nature or simply lack probabilistic data. To ensure safety under such scenarios, we employ the concept of robust constraints that must hold for all possible uncertainty realizations lying inside a bounded set. Nevertheless, standard robust optimization approaches become intractable due to the large number or non-convexity of the constraints involved in safe multi-agent control. To address this, we introduce novel robust reformulations that significantly reduce complexity without compromising safety. The applicability of the framework is further broadened to address both deterministic and stochastic uncertainties by incorporating robust chance constraints and distribution steering techniques. To achieve scalability, we derive a distributed approach based on the Alternating Direction Method of Multipliers (ADMM), supported by a convergence study that accounts for the underlying non-convexity. In addition, computational complexity bounds highlighting the efficiency of the proposed frameworks against standard approaches are presented. Finally, the robustness and scalability of the framework is demonstrated through extensive simulation results across diverse scenarios, including environments with nonconvex obstacles and up to 246 agents.