Estimation of angular velocity using a single fixed camera
Visual systems provide a rich representation of the observed environment and are frequently utilized in navigation and tracking across a broad class of engineering endeavors. This report explores the application of a single camera, fixed in position and orientation, towards the estimation of the angular velocity of an observed rigid object undergoing general motion in three dimensions. A summary is provided for historically significant methods in motion estimation using vision, and the underlying dynamics of the problem are discussed. A particular solution is examined in which the angular velocity is estimated asymptotically via a robust integral of the sign of the error (RISE)-based observer. The observer exploits homography techniques in image processing along with nonlinear systems theory to achieve its goal. Convergence proofs are summarized, and the observer is numerically simulated for a few simple example cases for demonstration. A key advantage of this solution is that it does not require supplementary information in the form of knowledge of a subset of linear velocity components or a true Euclidean length between two identifiable features on the object. This trait is not shared in estimation of linear velocity where some additional knowledge is necessary to resolve scale factor ambiguities.