3D-Algorithms of Composed Pursuit Navigation

TL;DR

This paper introduces a new family of pursuit algorithms in 3D space by combining existing Pure Pursuit and Pure Rendezvous methods, demonstrating their properties and advantages through real examples and geometric analysis.

Contribution

It presents a novel family of pursuit algorithms called Composed Pursuit Navigation, integrating two known methods and analyzing their properties in 3D space.

Findings

Trajectories benefit from combined advantages of two methods

Algorithms are characterized by Matsumoto metrics

Demonstrated effectiveness through real-world examples

Abstract

The problem of pursuing a moving target is always one of the main topics in navigation. In the literatures, there are two well-known algorithms called Pure Pursuit and Pure Rendezvous navigation in the 3-dimensional space $\mathbb{R}^3$. In this paper, these two methods are combined to introduce a novel family of pursuing algorithms called Composed Pursuit Navigation. The Kinematic and geometric properties of this navigation is studied. The trajectories of this new family of algorithms benefit the advantages of two known methods and its prominence is demonstrated in two real examples. Moreover, it is shown that the metric related to the algorithms are given by Matsumoto metrics.