Robotic control with partial visual information

We consider a robotic setting and a class of control tasks that rely on par tial visual information. These tasks are difficult in the sense that at eve ry given moment, the available information is insufficient for the control task. This implies that the image Jacobian, which relates the image space a nd the control space, is no longer of full rank. However, the amount of inf ormation collected throughout the control process is still large and thus s eems sufficient for carrying out the task. Such situations commonly arise w hen the object is frequently occluded from one of the camera in a stereo pa ir or when only one moving camera is available. We propose a generic contro l for such tasks and characterize the conditions required for the success o f the task. The analysis is based on the observation that mathematically th e behavior of such systems is related to a class of row-action optimization algorithms which are special cases of POCS (Projection On Convex Sets) alg orithms. In the second part of the paper we focus on one particular task fr om this class: position and orientation control with a single rotating came ra. We show that this task can be carried out, in principle, for any camera rotation and suggest efficient control and camera moving strategies. We su bstantiate our claims by simulations and experiments. Interestingly, it see ms that the advisable control law is not consistent with simple intuition.