Navigation functions in Conformal Geometric Algebra

Abstract

Conformal Geometric Algebra (CGA) can greatly improve controllers by simplifying the necessary equations and by its ability to apply geometric operations to more complicated geometric entities. In this paper we extend a singularity free CGA-based angular and linear velocity controller with navigation functions. The first navigation function ensures that the object being tracked is always within the camera's field of view. The second navigation function is the ability of the controller to avoid collisions with other objects. These navigation functions can be easily added to the CGA-based controller, experimentally ensured the desired goals and proven stable by Lyapunov.