Structure of Motion under Constraints and non-Holonomic Path-Following on $R^3$

TL;DR

This paper investigates non-holonomic path-following in three-dimensional space, analyzing the geometric structure of velocity constraints and developing guiding vector fields for effective path tracking.

Contribution

It introduces a novel approach to construct guiding vector fields for non-holonomic systems in R^3, enabling global coordinate design and path-following.

Findings

Guiding vector fields are constructed to fulfill path-following requirements.

The geometric structure of velocity constraints is characterized.

Principles for global coordinate vector field design are established.

Abstract

In this paper we study a path-following problem on $R^3$ with a non-holonomic constraint. The geometric structure associated to the velocity constraint is explored, and general principles for constructing guiding vector fields are obtained, fulfilling the path-following requirements on a neighborhood of the desired path while allowing the design of vector fields to be conducted in global coordinates.