Image-based control relying on conic curves foliation for passing through a gate

This paper presents a geometric approach to the problem of designing visual feedback control laws to steer a nonholonomic vehicle, equipped with a fixed monocular camera, through a gate. The originality of our approach is to introduce and exploit the natural geometry induced by the presence of a gate in the environment, e.g. bundle of hyperbolae, ellipses and circles, providing stabilizing feedback control laws that steer the vehicle through the middle of the gate. Moreover, using visual servoing we prove that this geometry can be measured directly in the camera image plane. As a consequence, we provide an image-based control scheme, avoiding the use of a state observer. Simulations in a realistic scenario and experiments are provided to show the effectiveness of our feedback control laws.