Self-Calibration of Camera-Equipped Robot Manipulators

Abstract

A new approach to self-calibrate a camera-equipped robot manipulator is proposed in this paper. Self-calibration here means that the camera-robot system is capable of determining its geometric parameters without any external measurements and/or ground truth calibration data. With the proposed approach, one is able to identify all the rotational parameters and, up to a scale factor, all the translational parameters of a robotic system without any ground truth data. It is known from the computer vision literature that the extrinsic and intrinsic parameters of the camera can be obtained up to a scale factor by using the corresponding points of objects in a natural environment from an image sequence without knowing the positions of these object points. It is also well known that if the camera is treated as the tool of the robot, one is able to compute the corresponding robot pose directly from the camera-extrinsic parameters. An important question is how to determine the scale factors, which vary from one robot pose to another. It is discovered in this paper that if the robot pose measurement configurations follow a specially planned optimal trajectory, a unique scale factor can be used for all the poses measured along the trajectory. Thus, one is able to identify all the independent parameters of the robot with the poses measured in this manner with an inherently undetermined scale factor. One question remains: how do we obtain this unknown scale factor? Actually, the problem can be solved in a separate process. By two views of, say, a yardstick with the known length, the scale factor can be computed. If more than one measurement of the scale or measurements of multiple scales are provided from different viewing angles, the scale factor can be estimated with better accuracy in a least squares sense. Extensive simulation and experiment studies on a PUMA 560 robot reveal the convenience and effectiveness of the proposed approach.