hand_eye_calibration.md

1. Hand Eye Calibration

1.1 Eye-in-Hand

From robot kinematic we have the position of griper in robot base at time i,j:

From the camera we have the position of target in camera at time i,j:

Now

and:

Now if we solve a set of equation in the from of:

since the relative position of griper and camera is always fixed at time i and j we can drop them.

Refs: 1, 2, 3

1.2 Eye-to-Hand

1.3 OpenCV Eye-in-Hand API

The following API computes Hand-Eye calibration:

calibrateHandEye	(	InputArrayOfArrays 	R_gripper2base,
InputArrayOfArrays 	t_gripper2base,
InputArrayOfArrays 	R_target2cam,
InputArrayOfArrays 	t_target2cam,
OutputArray 	R_cam2gripper,
OutputArray 	t_cam2gripper,
HandEyeCalibrationMethod 	method = CALIB_HAND_EYE_TSAI 
)	

2. Robot-World/Hand-Eye Calibration

This API computes Robot-World/Hand-Eye calibration:

1.3 OpenCV Robot-World/Hand-Eye API

cv::calibrateRobotWorldHandEye	(	InputArrayOfArrays 	R_world2cam,
InputArrayOfArrays 	t_world2cam,
InputArrayOfArrays 	R_base2gripper,
InputArrayOfArrays 	t_base2gripper,
OutputArray 	R_base2world,
OutputArray 	t_base2world,
OutputArray 	R_gripper2cam,
OutputArray 	t_gripper2cam,
RobotWorldHandEyeCalibrationMethod 	method = CALIB_ROBOT_WORLD_HAND_EYE_SHAH 
)	

Refs: 1, 2, 3