Full Self-calibration of a Hand-Mounted Projector Using Structured Light

Abstract

This paper describes two methods to determine the homogeneous transformation of a projector with respect to the robot hand. Since the projector itself has no exteroceptive capabilities, a camera is rigidly attached to the robot base or placed in the environment to detect the projected pattern. The camera’s extrinsic calibration parameters can be simultaneously solved, which is shown by the second method. Self-calibration implies that any kind of calibration tool may be omitted. For calibration, the robot hand has to make at least two movements around nonparallel rotational axes. At each robot configuration, correspondences between the camera and the projector are established to recover the transformation between them, up to an unknown scale factor. The system is described by the common known formulations $\mathbf{AX }=\mathbf{XB }$ and $\mathbf{AX }=\mathbf{ZB }$. Both can be arranged in a linear form with respect to the unknown extrinsic parameters and scale factors, and solved in least square sense. Further optimization allows to refine all intrinsic and extrinsic parameters.