Multi-Robot Realization Based on Goal Adjacency Constraints

This paper considers the problem of multi-robot realization. A realization is a set of robot positions where pairwise distances are either bounded from above or from below by a given adjacency threshold - depending on whether the respective robot pairs are to be adjacent or not. In the realization problem, unlike the related coordinated navigation or formation control problems, exact goal positions or relative distances need not be specified. Rather, only pairwise adjacency constraints are given and the robots' positions are required to satisfy these constraints. Applications of realization problem include multi-robots involved in team games (playing soccer, etc), patrolling and area coverage. We present a novel solution to this problem in which the robots simultaneously navigate to find a realization of a given adjacency matrix without colliding with each other along the way. In this solution, complete information about pairwise distances and free configuration space are encoded using an artificial potential function over the cross product space of the robots' simultaneous positions and proximity variables. The closed-loop dynamics governing the motion of each velocity-controlled robot take the form of the appropriate projection of the gradient of this function while pairwise distances are adjusted accordingly. Our extensive simulations demonstrate that the proposed approach has considerably higher realization percentage and shorter movement distances in comparison to a standard 2-stage approach.