2020/12/22 by Yuan Zheng, Xueming Shao, Zheng, Yuan +5 · 1 citation
Computer Science · Engineering · #Control and Dynamics of Mobile Robots #FOS: Mathematics #Guidance and Control Systems #Optimization and Control (math.OC) #Robotic Path Planning Algorithms
paper · pdf · doi:10.48550/arxiv.2012.11855
openalex publication_date 2020/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with a Minimum-Time Intercept Problem (MTIP), for which a Dubins vehicle is guided from a position with a prescribed initial orientation angle to intercept a moving target in minimum time. Some geometric properties for the solution of the MTIP are presented, showing that the solution path must lie in a sufficient family of 4 candidates. In addition, necessary and sufficient conditions for optimality of each candidate are established. When the target's velocity is constant, by employing the geometric properties, those 4 candidates are transformed to a class of sufficiently smooth real-valued functions. In order to compute all the 4 candidates, an efficient and robust algorithm to find all the zeros of sufficiently smooth real-valued functions is developed. Since the MTIP with a constant target's velocity is equivalent to the path planning problem of Dubins vehicle in a constant drift field, developing such an algorithm also enables efficiently finding the shortest Dubins path in a constant drift field. Finally, some numerical examples are presented, demonstrating and verifying the developments of the paper.