Vision guided navigation for a nonholonomic mobile robot

Theoretical and analytical aspects of the visual servoing problem have not received much attention. Furthermore, the problem of estimation from the vision measurements has been considered separately from the design of the control strategies. Instead of addressing the pose estimation and control problems separately, 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 nonholonomic 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 parameters. We present stabilizing control laws for tracking piecewise analytic curves, and propose to track arbitrary curves by approximating them by piecewise "linear" curvature curves. Simulation results are given for these control schemes. Observability of the curve dynamics by using direct measurements from vision sensors as the outputs is studied and an extended Kalman filter is proposed to dynamically estimate the image quantities needed for feedback control from the actual noisy images.