Vision-Based Guidance and Control of Robots in Projective Space

In this paper, we address the problem of visually guiding and controlling a robot in projective three-space using stereo vision. As the proposed method is entirely formulated in projective space, metric models of the system have become obsolete and ”easy-to-find” projective models of both, the stereo geometry and the robot’s “projective kinematics”, may be used. More precisely, a given task is decomposed into its elementary parts, a translation and two rotations, based on projective constraints on its mobilityand visibility. These primitives allow trajectories to be defined which are visually and globally feasible, i.e. problems like self-occlusions, local minima, or divergent control vanish. Although robot guidance through tracking the trajectories by image-based visual servoing is now feasible, we investigate a directly computed control which combines feed-forward control with a feed-back error in each component of the task. The method is validated and evaluted on a classical benchmark test in visual robot control – a 180 turn – for which most image-based and stereo-based control laws fail.