Distributed MPC of Uncertain Multi-Agent Systems Considering Formations and Obstacles

Abstract

This paper proposes a method to control a class of multi-agent systems with uncertainties modeled as stochastic processes with arbitrary probability distributions. The considered control problem is to lead a formation of agents through a space which is partially obstructed by obstacles. The proposed solution is to use a hierarchically structured approach of distributed stochastic model predictive control (DSMPC). The approach combines elements of formation reference structures, leader-follower concepts, and successive convexification (SC) for collision avoidance. To consider the stochastic uncertainties, over-approximated probabilistic reachable sets (PRS) are computed based on Chebyshev's inequality. The nominal (expected) agent behavior is optimized within the DSMPC such that (probabilistic) constraints are satisfied in a distributed way. For the overall approach, closed-loop stability of the distributed control concept is investigated and an illustrating example is provided.