Distributed consensus on minimum time rendezvous via cyclic alternating projection

TL;DR

This paper introduces a distributed algorithm for multi-vehicle minimum time rendezvous on cyclic graphs, utilizing cyclic alternating projection methods to compute projections onto convex sets in position-time space.

Contribution

The paper develops a novel distributed approach combining cyclic alternating projection and Dykstra's algorithm for multi-vehicle rendezvous with non-uniform velocities.

Findings

Algorithm converges using only neighbor information.

Vehicles can perform asynchronous projections.

Effective in solving minimum time rendezvous problem.

Abstract

In this paper, we propose a distributed algorithm to solve planar minimum time multi-vehicle rendezvous problem with non-identical velocity constraints on cyclic digraph (topology). Motivated by the cyclic alternating projection method that can compute a point's projection on the intersection of some convex sets, we transform the minimum time rendezvous problem into finding the distance between the position plane and the intersection of several second-order cones in position-time space. The distance can be achieved by metric projecting onto the plane and the intersection persistently from any initial point, where the projection onto the intersection is obtained by Dykstra's alternating projection algorithm. It is shown that during the procedure, vehicles use only the information from neighbors and can apply the projection onto the plane asynchronously. Demonstrations are worked out to illustrate the effectiveness of the proposed algorithm.