Visual Servoing on the Sphere Using Conformal Geometric Algebra

This paper deals with a visual servoing scheme, which uses a paracatadioptric sensor as visual input. The paracatadioptric sensor provides a wide field of view while maintaining the single center of projection, which is a desirable property of these sensors. The projection induced by this sensor is nonlinear. In this paper a linear model of this projection is presented, the model is developed using the conformal geometric algebra framework which allows to represent nonlinear conformal transformations using a special type of multivectors called versors. With this model we relate the feature time variation with the camera velocity to design a velocity controller used in a visual servoing task.