Distributed Online Aggregative Optimization for Dynamic Multi-Robot Coordination

This paper focuses on an online version of the emerging distributed constrained aggregative optimization framework, which is particularly suited for applications arising in cooperative robotics. Agents in a network want to minimize the sum of local cost functions, each one depending both on a local optimization variable, subject to a local constraint, and on an aggregated version of all the variables (e.g., the mean). We focus on a challenging online scenario in which the cost, the aggregation functions and the constraints can all change over time, thus enlarging the class of captured applications. Inspired by an existing scheme, we propose a distributed algorithm with constant step size, named Projected Aggregative Tracking, to solve the online optimization problem. We prove that the dynamic regret is bounded by a constant term and a term related to time variations. Moreover, in the static case (i.e., with constant cost and constraints), the solution estimates are proved to converge with a linear rate to the optimal solution. Finally, numerical examples show the efficacy of the proposed approach on a robotic surveillance scenario.