An Algorithm for Distributed Computation of Reachable Sets for Multi-Agent Systems

TL;DR

This paper introduces a distributed algorithm for computing reachable sets in multi-agent systems, addressing challenges posed by obscured agent dynamics and ensuring convergence over static and certain time-varying network graphs.

Contribution

It generalizes polytopic reachable set approximation to multi-agent systems and provides a fully distributed algorithm with convergence guarantees.

Findings

Algorithm converges for static MAS graphs.

Algorithm converges for certain time-varying graphs.

Enables distributed reachable set computation in obscured dynamics.

Abstract

In this paper, we consider the problem of distributed reachable set computation for multi-agent systems (MASs) interacting over an undirected, stationary graph. A full state-feedback control input for such MASs depends no only on the current agent's state, but also of its neighbors. However, in most MAS applications, the dynamics are obscured by individual agents. This makes reachable set computation, in a fully distributed manner, a challenging problem. We utilize the ideas of polytopic reachable set approximation and generalize it to a MAS setup. We formulate the resulting sub-problems in a fully distributed manner and provide convergence guarantees for the associated computations. The proposed algorithm's convergence is proved for two cases: static MAS graphs, and time-varying graphs under certain restrictions.