Optimal Time-Invariant Formation Tracking for a Second-Order Multi-Agent System

TL;DR

This paper introduces a trajectory optimization approach for multi-agent systems that combines formation control, trajectory tracking, and energy minimization using a novel numerical method and potential functions.

Contribution

It presents a new trajectory optimization framework with a projection operator Newton's method for multi-task formation control in second-order systems.

Findings

Successfully stabilizes formations with desired geometries.

Achieves trajectory tracking with minimized energy consumption.

Provides a numerical method for multi-task trajectory optimization.

Abstract

Given a multi-agent linear system, we formalize and solve a trajectory optimization problem that encapsulates trajectory tracking, distance-based formation control and input energy minimization. To this end, a numerical projection operator Newton's method is developed to find a solution by the minimization of a cost functional able to capture all these different tasks. To stabilize the formation, a particular potential function has been designed, allowing to obtain specified geometrical configurations while the barycenter position and velocity of the system follows a desired trajectory.