Energy-Optimal Motion Planning for Agents: Barycentric Motion and Collision Avoidance Constraints

Abstract

As robotic swarm systems emerge, it is increasingly important to provide strong guarantees on energy consumption and safety to maximize system performance. One approach to achieve these guarantees is through constraint-driven control, where agents seek to minimize energy consumption subject to a set of safety and task constraints. In this paper, we provide an equivalent sufficient and necessary optimality condition for an energy-minimizing agent with integrator dynamics that only depends on the state and control actions of the agent. In particular, we show that the agent must have a continuous control input at the transition between unconstrained and constrained trajectories. In addition, we present and analyze barycentric motion and collision avoidance constraints to be used in constraint-driven control of swarms.