Control of camera state based on perspective observation

This paper describes a control law of the camera movement to track the object in such a way that it keeps the projected image of the object at a desired place on the image plane. The camera state which is composed of the position and the attitude is regarded as a point in the manifold S=SO(₃)×R³. For measuring the difference between the two points in S, A distance is introduced. The set of all the desired position of camera states which satisfy the purpose of control for an object on the camera is a submanifold S_d of S. The minimum distance ρ*(F, S_d) from a point F∈S to S_d is explicitly calculated and is regarded as the distance between a point F and a set S_d. A control strategy for the camera movement to reduce p*(F, S_d) is given based on the measurement of the projected image of the object. A controller for this strategy is given and its convergence is proven