Shortest Trajectory of a Dubins Vehicle with a Controllable Laser

TL;DR

This paper introduces a new motion planning problem for a Dubins vehicle with a controllable laser, characterizing optimal trajectories and providing numerical insights into their properties.

Contribution

It formulates a novel problem combining Dubins vehicle motion with laser control and identifies the structure of optimal trajectories among 16 candidates.

Findings

Optimal trajectories are among 16 specific candidates.

Properties of the optimal paths are characterized mathematically.

Numerical examples illustrate the theoretical properties.

Abstract

We formulate a novel planar motion planning problem for a Dubins-Laser system that consists of a Dubins vehicle with an attached controllable laser. The vehicle moves with unit speed and the laser, having a finite range, can rotate in a clockwise or anti-clockwise direction with a bounded angular rate. From an arbitrary initial position and orientation, the objective is to steer the system so that a given static target is within the range of the laser and the laser is oriented at it in minimum time. We characterize multiple properties of the optimal trajectory and establish that the optimal trajectory for the Dubins-laser system is one out of a total of 16 candidates. Finally, we provide numerical insights that illustrate the properties characterized in this work.