Confinement Control of Double Integrators using Partially Periodic Leader Trajectories

TL;DR

This paper presents a method for controlling multiple agents with double-integrator dynamics using a single leader with partially periodic trajectories, ensuring followers stay confined around a moving target.

Contribution

It introduces a novel confinement control strategy using decomposed periodic leader trajectories and provides conditions for guaranteed follower confinement based on averaging theory.

Findings

Followers can be confined around a moving trajectory with arbitrarily small error.

The method is validated through simulations and experiments with mobile robots.

Conditions for confinement depend on the frequency of leader's periodic control components.

Abstract

We consider a multi-agent confinement control problem in which a single leader has a purely repulsive effect on follower agents with double-integrator dynamics. By decomposing the leader's control inputs into periodic and aperiodic components, we show that the leader can be driven so as to guarantee confinement of the followers about a time-dependent trajectory in the plane. We use tools from averaging theory and an input-to-state stability type argument to derive conditions on the model parameters that guarantee confinement of the followers about the trajectory. For the case of a single follower, we show that if the follower starts at the origin, then the error in trajectory tracking can be made arbitrarily small depending on the frequency of the periodic control components and the rate of change of the trajectory. We validate our approach using simulations and experiments with a small mobile robot.