Speed Consensus and Reference Tracking for a Swarm of Second-order Agents

In this paper a second-order model for a swarm of agents is proposed to face the team reference tracking problem. The described model is a double integrator where each agent dynamic is ruled by a control input formed by attractive parts to the reference position and speed, and by a repulsive part that rules the interactions among agents. It will be proved that following the proposed model, the swarm centroid will asymptotically reach the reference trajectory and the agents’ speeds will reach a consensus on the reference speed while their positions will be fixed in a reference frame that moves according to the reference trajectory. The main novelty of the proposed work is the interaction term among agents, the effect of which can be easily tuned by modifying an interaction matrix that modulates the effect of agents interactions on their various components. Properly choosing this matrix, aggregation properties can be modified to ensure that all the agents enter and remain in a defined zone around the reference trajectory, moving according to it.