Unified Cooperative Control of Multiple Agents on a Sphere for Different Spherical Patterns

In this technical note, we consider the cooperative control of multiple agents on a sphere, provide the appropriate attraction-repulsion interactions between agents with introduction of the state-dependent repulsive coefficients, and design the unified control laws for agents to achieve three fundamental spherical configurations or patterns: rendezvous, uniform deployment, and formation, using both the first- and second-order models. We present the analysis of the stability, scaling and geometric patterns of the models on the sphere under different attraction-repulsion parameters, with illustration of the geometrical patterns and the geometrical isomerism by simulations. The closed-loop dynamics of agents are invariant with respect to group rotation actions on the sphere.