A Path Planning Model for Intercepting a Moving Target with Finite Obstacle Avoidance

Abstract This paper investigates the problem of computing a two-dimensional curvature-constrained shortest path for an unmanned aerial vehicle (UAV) to intercept a moving target, with both the UAV (pursuer) and the target travelling at constant speeds. We formulate an optimal control problem that integrates two critical objectives: avoiding static obstacles and successfully intercepting the target. The formulation integrates curvature constraints, geometric obstacle-avoidance conditions, and time-consistent interception constraints within a constrained optimal control framework. A geometric framework is developed, along with sufficient conditions for path optimality under the imposed constraints. The problem is initially examined in the presence of a single obstacle and later extended to scenarios involving a finite number of obstacles. Numerical experiments are carried out to evaluate the performance and efficiency of the proposed model using illustrative examples. Finally, we present a realistic case study using actual geographic data, including obstacle placement, target trajectory, and heading angles, to demonstrate the practical applicability and effectiveness of the proposed method in real-world scenarios. AMSsubject classifications: 34K35 49M37, 90C30, 90C39.