Abstract-This paper presents a geometric approach to the problem of steering a robot subject to nonholonomic constraints through a door by using only visual measurements coming from a single fixed on-board monocular camera. The door is represented by two landmarks located on its vertical supports. After exploring the geometric structure that naturally emerges from the problem statement, e.g., bundle of hyperbolae, ellipses, and circles, we exploit this planar geometry to provide stabilizing feedback control laws to drive the vehicle through the middle of the door. Using visual servoing, we prove that this geometry can be directly measured in the camera image plane. Hence, 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 the feedback control laws.
Similarly, a geometric approach based on confocal curves (i.e., hyperbolae, ellipses, and circles) for navigating a nonholonomic robot through a door by using only a monocular camera is presented in REF .
The geometry of confocal curves for passing through a door
IEEE Transactions on Robotics
IEEE Transactions on Robotics
Mathematics Computer Science