Vector Field-based Guidance in Space Based on Implicitization of Parametric Curves Using Approximate Orthogonal Surfaces

Abstract

This paper presents a methodology for implementing a vector field-based guidance algorithm for path following in three-dimensional space. The study focuses on converting the path given as a parametric function of a three-dimensional space curve into an implicit form. The paper explores how to compute vector fields in the space surrounding the reference curve by conducting implicitization on the parametric curve. The efficiency of computing the vector field using the implicit form curve is compared to the efficiency of computing the vector field using generalized cylinders. The results indicate that the coefficient area for the basis vectors becomes wider when using the approximate orthogonal surface compared to generalized cylinders.