Position Control of Cart-Driven Inverted Pendulum by Visual Feedback Controller Using Non-Calibrated Images Taken Through Fisheye Lens

This paper addresses the position control of a cart-driven inverted pendulum, whose position and angle are both calculated from the non-calibrated images taken through a fisheye lens, using a visual feedback controller. Fisheye lenses, which have the ability to obtain 180<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">º</sup>wide or even wider view images, are advantageous to measurement compared to normal lenses; however, large distortion of the images cannot be avoided. In other words, fisheye lenses have a good potential as a measurement apparatus thanks to the wide view angles and the easy implementability as an add-on apparatus, it is necessary to overcome the drawback of the large image distortion to enhance the applicability. When fisheye lenses are used for controlling some systems, one of the possible solutions to overcome the drawback is to make the controllers robust against the image distortion. Along with this approach, we have already designed a visual stabilizing feedback controller for a cart-driven inverted pendulum and have confirmed its robustness against the large image distortion; however, cart position control has not yet been addressed. In this paper, we tackle the cart position control by designing a visual servo feedback controller within the framework of the conventional scaled-H∞ problem, examine control performance by experiments conducted in the laboratory, and confirm the usefulness of fisheye lenses.