Collective Circular Motion with Trajectory and Turn-Rate Constraints

This paper stabilizes the collective motion of a group of agents, with second-order unicycle model, about a desired circular orbit, while constraining their trajectories and turn-rates within predefined limits. Additionally, we achieve synchronization, balancing and splay patterns in their heading angles. To solve this problem, the stabilizing control laws are derived by combining the concept of the barrier Lyapunov function with phase-potential functions. Imposing these constraints have advantages in terms of the following: i) the agents do not transgress the given workspace and hence, this ensures safety from territorial attacks ii) maintain a proximity to the desired circular motion iii) the applied lateral force does not exceed the desired limit of a vehicle, imposed by its physical constraints. Simulations are provided to illustrate the theoretical findings.