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

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