Synthesis of a Calibration-Free Visual Feedback Controller for an Inverted Pendulum Using a Fisheye Lens

This article considers the synthesis of feedback controllers for a class in which strong robust stability is required against sensing errors. The motivation dealing with this class arises from the stabilization problem of a cart-driven inverted pendulum by visual feedback control using a fisheye lens. While fisheye lenses guarantee a wide-angle of view, a large image distortion at off-center area is inevitable. Therefore this study first derives a geometric measurement model of a pendulum angle using a general fisheye lens model. A new design method for robust controllers for our problem is then proposed. Finally, a robust feedback controller that allows lens distortion is designed. The effectiveness of the controller based on the proposed model and the proposed design method is verified through numerical simulations and experiments.