Game theoretic controller synthesis for multi-robot motion planning Part I : Trajectory based algorithms

TL;DR

This paper introduces a distributed, anytime algorithm for multi-robot motion planning formulated as a differential game, ensuring convergence to Nash equilibria with linear complexity and optimal stability.

Contribution

It proposes a novel distributed algorithm for multi-robot motion planning as a differential game, with proven convergence and efficiency properties.

Findings

Algorithm asymptotically converges to Nash equilibrium

Price of stability equals one for scalar costs

Computational and communication costs are linear in robot number

Abstract

We consider a class of multi-robot motion planning problems where each robot is associated with multiple objectives and decoupled task specifications. The problems are formulated as an open-loop non-cooperative differential game. A distributed anytime algorithm is proposed to compute a Nash equilibrium of the game. The following properties are proven: (i) the algorithm asymptotically converges to the set of Nash equilibrium; (ii) for scalar cost functionals, the price of stability equals one; (iii) for the worst case, the computational complexity and communication cost are linear in the robot number.