Hand-projector self-calibration using structured light

This paper describes two methods for determining the extrinsic calibration parameters of a projector with respect to the robot hand. One of them simultaneously solves the transformation between a camera with respect to the robot base. Self-calibration means that no sort of calibration rig like a chessboard is needed. Since the projector has no exteroceptive capabilities, a camera is placed in the environment or rigidly attached to the robot base to detect the projected pattern. At different robot configurations correspondences between the camera and projector are established to recover the transformation between them up to an unknown scale factor. The common known formulations AX = XB and AX = ZB can be arranged in a linear form with respect to the unknown extrinsic parameters and scale factors, and solved in least square sense.