Optimal Time-Invariant Distributed Formation Tracking for Second-Order Multi-Agent Systems

TL;DR

This paper develops a distributed control approach for second-order multi-agent systems that optimizes formation tracking and energy efficiency simultaneously, using a centralized offline solution to inform online control laws.

Contribution

It introduces a novel optimization framework combining trajectory tracking, formation control, and energy minimization, with a practical distributed control law derived from centralized inverse dynamics.

Findings

Successful formation tracking in 3D space demonstrated

Energy-efficient control law validated through simulations

Centralized optimization informs effective distributed control

Abstract

This paper addresses the optimal time-invariant formation tracking problem with the aim of providing a distributed solution for multi-agent systems with second-order integrator dynamics. In the literature, most of the results related to multi-agent formation tracking do not consider energy issues while investigating distributed feedback control laws. In order to account for this crucial design aspect, we contribute by formalizing and proposing a solution to an optimization problem that encapsulates trajectory tracking, distance-based formation control and input energy minimization, through a specific and key choice of potential functions in the optimization cost. To this end, we show how to compute the inverse dynamics in a centralized fashion by means of the Projector-Operator-based Newton's method for Trajectory Optimization (PRONTO) and, more importantly, we exploit such an offline solution as a general reference to devise a stabilizing online distributed control law. Finally, numerical examples involving a cubic formation following a chicane-like path in the 3D space are provided to validate the proposed control strategies.