Vision guided navigation for a nonholonomic mobile robot

Visual servoing, i.e., the use of the vision sensor in feedback control, ha s gained recently increased attention from researchers both in vision and c ontrol community. A fair amount of work has been done in applications in au tonomous driving, manipulation, mobile robot navigation and surveillance. H owever, theoretical and analytical aspects of the problem have not received much attention. Furthermore, the problem of estimation from the vision mea surements has been considered separately from the design of the control str ategies. Instead of addressing the pose estimation and control problems sep arately, we attempt to characterize the types of control tasks which can be achieved using only quantities directly measurable in the image, bypassing the pose estimation phase. We consider the task of navigation for a nonhol onomic ground mobile base tracking an arbitrarily shaped continuous ground curve. This tracking problem is formulated as one of controlling the shape of the curve in the image plane. We study the controllability of the system characterizing the dynamics of the image curve, and show that the shape of the image curve is controllable only up to its "linear" curvature paramete rs. We present stabilizing control laws for tracking piecewise analytic cur ves, and propose to track arbitrary curves by approximating them by piecewi se "linear" curvature curves. Simulation results are given for these contro l schemes. Observability of the curve dynamics by using direct measurements from vision sensors as the outputs is studied and an Extended Kalman Filte r is proposed to dynamically estimate the image quantities needed for feedb ack control from the actual noisy images.