Fixed-time consensus of multiple double-integrator systems under directed topologies: A motion-planning approach

TL;DR

This paper introduces a novel motion-planning based approach to achieve fixed-time consensus in multi-agent systems with double-integrator dynamics under directed topologies, ensuring convergence within a pre-set time.

Contribution

It is the first to solve the fixed-time consensus problem for double-integrator systems under directed topologies using a motion-planning approach.

Findings

Guarantees fixed-time consensus with directed spanning tree topology.

Achieves fixed-time consensus under switching directed topologies.

Allows pre-assignment of convergence time based on task needs.

Abstract

This paper investigates the fixed-time consensus problem under directed topologies. By using a motion-planning approach, a class of distributed fixed-time algorithms are developed for a multi-agent system with double-integrator dynamics. In the context of the fixed-time consensus, we focus on both directed fixed and switching topologies. Under the directed fixed topology, a novel class of distributed algorithms are designed, which guarantee the consensus of the multi-agent system with a fixed settling time if the topology has a directed spanning tree. Under the directed periodically switching topologies, the fixedtime consensus is solved via the proposed algorithms if the topologies jointly have a directed spanning tree. In particular, the fixed settling time can be off-line pre-assigned according to task requirements. Compared with the existing results, to our best knowledge, it is the first time to solve the fixed-time consensus problem for double-integrator systems under directed topologies. Finally, a numerical example is given to illustrate the effectiveness of the analytical results.