A New Algorithm for Optimizing Dubins Paths 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. We introduce an intuitive and efficient mathematical model outlined as an optimal control problem to address this challenge. The proposed model is based on Dubins 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. 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