Calibration free path planning for visual servoing yielding straight line behaviour both in image and work space

Trajectory planning for eye-in-hand visual servoing is usually performed in the Euclidean work space of the robot or in a two dimensional image space. However, planning in Euclidean space may lead to very inappropriate trajectories in image space and vice versa. These difficulties are due to the perspective transformation of the camera, loss of one dimension due to projection onto the image plane and the fact that only a rough approximation of camera parameters is practically available. Hence, this paper proposes a planning scheme for image trajectories such that straight line behaviour is ensured both in image space and world space, ie. a single but arbitrarily chosen point in the image plane performs straight line behaviour as well as the camera optical center in work space. This way, trajectories become very compact and most of the above mentioned problems are avoided in a natural way. The algorithm requires as a priori information nothing more than matched image points (in pixels) from a current and desired image and a depth set for at least one position.