Consensus for double-integrator dynamics with velocity constraints

The problem of consensus for double-integrator dynamics with velocity constraints and a constant group reference velocity is addressed such that: (i) the control law of an agent does not depend on the local neighbors’ velocities or accelerations, but only on the neighbors’ positions and on the own agent velocity; (ii) the constraints are non-symmetric; (iii) the class of nonlinear functions used to account for the velocity constraints is more general than the ones that are normally considered in the literature. We propose a decentralized control strategy with the neighboring topology described by an undirected interaction graph that is connected. Mathematical guarantees of convergence without violating the constraints are given. A numerical experiment is provided to illustrate the effectiveness of our approach.