Collision-Free Trajectory Design for 2-D Persistent Monitoring Using Second-Order Agents

This article considers a 2-D persistent monitoring problem by controlling movements of second-order agents to minimize some uncertainty metric associated with targets in a dynamic environment. In contrast to common sensing models depending only on the distance from a target, we introduce an active sensing model, which considers the distance between an agent and a target, as well as the agent's velocity. We propose an objective function, which can achieve a collision-free agent trajectory by penalizing all possible collisions. Applying structural properties of the optimal control derived from the Hamiltonian analysis, we limit agent trajectories to a simpler parametric form under a family of 2-D curves depending on the problem setting, e.g., ellipses and Fourier trajectories. Our collision-free trajectories are optimized through an event-driven infinitesimal perturbation analysis and gradient descent method. Although the solution is generally locally optimal, this method is computationally efficient and offers an alternative to other traditional time-driven methods. Finally, simulation examples are provided to demonstrate our proposed results.