The geometry of confocal curves for passing through a door


This paper presents a geometric approach to the matter of steering a robot subject to nonholonomic constraints through a door by using only visual measurements returning from a single fastened on-board monocular camera. The door is represented by two landmarks located on its vertical supports. Once exploring the geometric structure that naturally emerges from the matter statement, e.g., bundle of hyperbolae, ellipses, and circles, we have a tendency to exploit this planar geometry to supply stabilizing feedback control laws to drive the vehicle through the middle of the door. Using visual servoing, we have a tendency to prove that this geometry will be directly measured within the camera image plane. Hence, we give an image-based control theme, avoiding the utilization of a state observer. Simulations in a very realistic situation and experiments are provided to point out the effectiveness of the feedback management laws.

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