Enclosing a moving target with an optimally rotated and scaled multiagent pattern

We propose a novel control method to enclose a moving target in a two-dimensional setting with a team of agents forming a prescribed geometric pattern. The approach optimises a measure of the overall agent motion costs, via the minimisation of a suitably defined cost function encapsulating the pattern rotation and scaling. We propose two control laws which use global information and make the agents exponentially converge to the prescribed formation with an optimal scale that remains constant, while the team's centroid tracks the target. One control law results in a multiagent pattern that keeps a constant orientation in the workspace; for the other, the pattern rotates with constant speed. These behaviours, whose optimality and steadiness are very relevant for the task addressed, occur independently from the target's velocity. Moreover, the methodology does not require distance measurements, common coordinate references, or communications. We also present formal guarantees of collision avoidance for the proposed approach. Illustrative simulation examples are provided