Mathematical Model for Optimal Dubins Path to Intercept a Stationary Target

Abstract

This paper presents a comprehensive mathematical model designed to determine the most efficient trajectory for intercepting a stationary target, with a primary focus on minimizing interception time and resource utilization. The proposed model incorporates key parameters such as target location, interception speed, and environmental constraints to formulate a set of differential equations that describe the motion dynamics of both the pursuer and the target. The objective function is defined to optimize the interception path. The study employs advanced mathematical techniques, including optimal control theory and numerical optimization algorithms, to solve the formulated equations and derive the optimal path. The model is adaptable to various scenarios, accounting for different pursuit vehicle dynamics and target characteristics. Simulation results are presented to validate the effectiveness of the proposed mathematical model in practical applications.

GANIT J. Bangladesh Math. Soc. 43.1 (2023) 049- 064