Computing the Minimum-Time Interception of a Moving Target

TL;DR

This paper introduces an algorithmic framework for solving minimum-time interception problems of moving targets, ensuring convergence and applicability to models like the Dubins car, with practical effectiveness demonstrated.

Contribution

The paper develops a convergent algorithmic framework for minimum-time interception problems, including explicit solutions for certain models like the Dubins car.

Findings

The framework guarantees convergence for arbitrary Lipschitz continuous target trajectories.

Explicit distance descriptions are derived for models such as the Dubins car.

The framework is effective for simple motions and Dubins model scenarios.

Abstract

In this study, we propose an algorithmic framework for solving a class of optimal control problems. This class is associated with the minimum-time interception of moving target problems, where a plant with a given state equation must approach a moving target whose trajectory is known a priori. Our framework employs an analytical description of the distance from an arbitrary point to the reachable set of the plant. The proposed algorithm is always convergent and cannot be improved without losing the guarantee of its convergence to the correct solution for arbitrary Lipschitz continuous trajectories of the moving target. In practice, it is difficult to obtain an analytical description of the distance to the reachable set for the sophisticated state equation of the plant. Nevertheless, it was shown that the distance can be obtained for some widely used models, such as the Dubins car, in an explicit form. Finally, we illustrate the generality and effectiveness of the proposed framework for simple motions and the Dubins model.