Guaranteed Safe Motion of Multiple Lagrangian Systems with Limited Actuation

In this paper we present decentralized, reactive, cooperative collision avoidance strategies for a group of nonlinear Lagrangian vehicles with limited actuation and bounded sensing range. The avoidance control strategies, which are continuous, build on the concept of avoidance functions and are synthesized with a time-varying set-point control law that drives the agents towards their desired final configurations (possibly time-varying) while avoiding deadlocks and unwanted local minima. We show, by using results from packing optimization and Lyapunov-based analysis, that the overall control strategies are bounded, comply with the agents's dynamic constraints (i.e., limited actuation and acceleration), and guarantee collision-free trajectories for all agents. Moreover, we provide a bound on the number of agents that can interact with a single vehicle at any given time and illustrate their performance via a numerical example with a group of twelve vehicles.