Receding horizon control and coordination of multi-agent systems using polynomial expansion

The present paper proposes a flexible and efficient methodology for constructing norm-bounded optimal receding horizon control laws for a group of agents, each one of which is described as a repeated integrator of an arbitrary order and with a common input delay. The goal of each agent is to track the given target, while simultaneously avoiding other agents in the group. Polynomial expansion, together with appropriate subspace projection, is utilized in order to derive receding control law in the closed form. Properties of this control law have been investigated, and its link to a well-known control strategy based on avoidance functions, which ensures collision avoidance in the case of first-order integrator agents, has been derived.