Collision-free and crossing-free trajectory design for second-order agents persistent monitoring

Abstract

In this paper, we utilize second-order agents to address a one-dimensional persistent monitoring problem with potential agent collision and boundary-crossing problems. The objective is to minimize a sum of accumulated performance metric associated with targets over a finite time horizon by controlling the movements of agents. Different from the existing work where a collision avoidance algorithm is designed for avoiding collisions and boundary crossings, we consider these problems at the beginning of the problem formulation and further utilize Exterior Point Method (EPM) to propose a novel combinatorial objective function which guarantees a collision-free and crossing-free solution by penalizing all possible agents collisions and boundary crossings. According to Pontryagin Minimum Principle (PMP), we show that the optimal agent trajectories can be fully described by some parameters. Based on Infinitesimal Perturbation Analysis (IPA), a standard gradient descent method is proposed to obtain the optimal parameters. Our collision-free and crossing-free approach is computationally efficient as compared to the existing algorithm. Numerical examples are included to demonstrate the effectiveness of the proposed methods.