Measurement and Storage of a Network of Jacobians as a Method for the Visual Positioning of a Robot Arm

The goal of this paper is to describe a method to position a robot arm at any visible point of a given workspace without an explicit on line use of the analytical form of the transformations between real space and camera coordinates (camera calibration) or between cartesian and joint coordinates (direct or inverse kinematics of the robot arm). The formulation uses a discrete network of points distributed all over the workspace in which a procedure is given to measure certain Jacobian matrices which represent a good local linear approximation to the unknown compound transformation between camera and joint coordinates. This approach is inspired by the biological observation of the vestibulo-ocular reflex in humans (VOR). We show that little space is needed to store the transformation at a given scale, as feedback on the visual coordinates is used to improve precision up to the limit of the visual system. This characteristic also allows the plant to cope with disturbances in camera positioning or robot parameters. Furthermore, if the dimension of the visual space is equal or bigger than the motor space dimension, the transformation can be inverted, resulting in a realistic model of the plant able to be used to train other methods for the determination of visuo-motor mapping. As a test of the method an experiment to position a real robot arm is presented, together with another experiment showing the robot executing a simple task (building a tower of blocks).