A new mathematical model and algorithm for the optimal path to intercept a moving target

Abstract: This paper is concerned with determining the shortest path for a pursuer aiming to intercept a moving target travelling at a constant speed. To address this challenge, we introduce an efficient mathematical model outlined as an optimal control problem. The proposed model is based on Dubin's path, where we concatenate two possible paths: a left-circular curve or a right-circular curve followed by a straight line. We develop and explore this model, providing a comprehensive geometric interpretation, and design an algorithm tailored to implement the proposed mathematical approach efficiently. Extensive numerical experiments involving diverse target positions highlight the strength of the model. The method exhibits a remarkably high convergence rate in finding solutions. We compare the proposed model and demonstrate its advantages through examples. For experiment purposes, we utilized the modelling software AMPL, employing a range of solvers to solve the problem. Subsequently, we simulated the obtained solutions using MATLAB, demonstrating the efficiency of the model in intercepting a moving target. The proposed model distinguishes itself by employing fewer parameters and making fewer assumptions, setting the model simplifies the complexities, and thus, makes it easier for experts to design optimal path plans.