Lyapunov-Based Range Identification For Paracatadioptric Systems

Many applications require the interpretation of the Euclidean coordinates of features of a 3-D object through 2-D images. In this paper, the relative range and the Euclidean coordinates of an object or camera undergoing general affine motion are determined for paracatadioptric imaging systems via a nonlinear observer. The nonlinear observer asymptotically determines the range information provided that the motion parameters are known. The observer is developed through a Lyapunov-based design and stability analysis, and simulation results are provided that illustrate the performance of the state estimator. The contributions of this paper are that the developed observer: (1) can be applied to both affine and nonaffine systems; (2) can be used for both the fixed and moving camera configurations; (3) is continuous; and (4) yields an asymptotic result.