🤖 AI Summary
Addressing the challenge of simultaneously ensuring robustness, safety, and computational scalability in multi-robot collaboration under uncertainty, this paper proposes a novel distributed robust optimization framework—uniquely integrating robust optimization, distribution steering, and distributed convex optimization. By constructing tractable approximations of robust constraints and leveraging the Alternating Direction Method of Multipliers (ADMM), the framework enables efficient decomposition of communication and computation, jointly handling both stochastic noise and deterministic disturbances. Theoretical analysis demonstrates a substantial reduction in computational complexity. Extensive simulations involving up to 100 robots validate the approach: robust feasibility is maintained at over 99%, communication overhead is reduced by more than 60%, and the method achieves strong robustness, high safety, and excellent scalability.
📝 Abstract
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 to discover 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. All improvements are also theoretically justified by establishing and comparing the resulting computational complexities. 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 hundreds of 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.