Conformal geometric algebra for visual servoing of nonholonomic mobile robots

This paper presents a new visual servo controller based on geometric algebra (GA). The controller has an angular and translational components that are designed using rotors and translators. The controller does not require additional calculations or jacobian-like matrices. We modify the controller to regulate a mobile robot with three degrees of freedom controllable by two. The proposed controller is applied to a nonholonomic mobile robot with a camera mounted on it. The position of the robot is regulated from its current position to a desired position using current and desired images. We develop a GA-based Lyapunov function to demonstrate the stability of the controller and we present simulations validating the proposed controller.