Using a scale: self-calibration of a robot system with a factor method

A method for the self-calibration of a camera equipped robot manipulator is proposed in this paper. In this method, it is assumed only a scale, which is placed in the field of view of the camera, is known in the world coordinate system. It has been known from the computer vision field that, the extrinsic parameters of the camera along with its intrinsic parameters can be obtained up to a scale factor by using the corresponding points of objects in a natural environment from an image sequence. Now, if the camera is treated as the tool of the robot, one is then able to compute the corresponding robot pose directly from the camera extrinsic parameters once the scale factor is available. This scale factor, which changes from one camera pose to another, can be determined uniquely from the known scale. Another idea is the use of the factor method for pose estimation. The original factor method is sensitive to errors from image quantization, feature extraction, and model simplification. In order to make the factor method robust for robot pose estimation, a nonlinear least-squares algorithm is proposed in the paper. Issues relevant to this algorithm such as formulation of cost functions and selection of initial conditions are addressed. Once a sufficient number of robot poses at various measurement configurations are obtained using the proposed method, the estimation of actual link parameters of the robot becomes possible. Extensive simulations and experiment studies on a PUMA 560 robot reveal the convenience and effectiveness of the proposed self-calibration approach.