Multi-agent system for target tracking on a sphere and its asymptotic behavior

TL;DR

This paper introduces a second-order multi-agent system on a sphere for target tracking, utilizing a novel regularized rotation operator to analyze asymptotic rendezvous behavior under various information conditions.

Contribution

It develops a new velocity alignment operator based on a regularized rotation, enabling detailed phase decomposition and convergence analysis for multi-agent target tracking on a sphere.

Findings

Complete rendezvous when target acceleration is known.

Practical rendezvous achievable with large enough coefficients.

Decomposition of agent phase into translational and structural parts.

Abstract

We propose a second-order multi-agent system for target tracking on a sphere. The model contains a centripetal force, a bonding force, a velocity alignment operator to the target, and cooperative control between flocking agents. We propose an appropriate regularized rotation operator instead of Rodrigues' rotation operator to derive the velocity alignment operator for target tracking. By the regularized rotation operator, we can decompose the phase of agents into translational and structural parts. By analyzing the translational part of this reference frame decomposition, we can obtain rendezvous results to the given target. If the multi-agent system can obtain the target's position, velocity, and acceleration vectors, then the complete rendezvous occurs. Even in the absence of the target's acceleration information, if the coefficients are sufficiently large enough, then the practical rendezvous occurs.