Vision-based robot control with omnidirectional cameras and conformal geometric algebra

Traditional cameras have a narrow field of view, to enlarge the field of view omnidirectional cameras can be used. In this work, we propose, a simple an elegant solution to the image formation model for omnidirectional cameras with parabolic mirrors. We propose the use of conformal geometric algebra (CGA), since the involved transformation operations in the model can be represented as an special group of multivectors. This representation is advantageous since the inversions are linearized, furthermore the transformation can be applied to all the geometric objects of the CGA. In consequence, the paracatadioptric image formation can be simplified, since the procedure is the same for points, point-pairs, lines, or circles. As an application example the control of a nonholonomic mobile robot using paracatadioptric line images and the proposed framework is described.