一、标定原理
机器人手眼标定分为eye in hand与eye to hand两种。介绍之前进行变量定义说明：
{b}: base基坐标系
{g}: gripper夹具坐标系
{t}: target标定板坐标系
{c}: camera相机坐标系
1、眼在手上(eye in hand)
眼在手上，相机固定在机器人上。
图1. eye in hand示意图
由以上两公式得：
经变换得：
可得：
求解X即标定 ：
2、眼在手外(eye to hand)
眼在在手外，相机固定在机器人外。
图2. eye to hand示意图
由以上两公式可得：
经变换得：
可得：
求解X即标定：
二 、标定步骤
将标定板固定至机械臂末端；
在位置1采集标定板图像，并记录机械臂在位置1下的位置与姿态；
在位置2采集标定板图像，并记录机械臂在位置2下的位置与姿态；
移动机械臂更换不同位置，采集25-40张图像，并记录机械臂在每个位置下的位姿；
相机标定，获取25-40组Tt_c ；
位姿读取，获取25-40组Tb_g ；
根据5,6调用标定接口，获取Tc_b 。
三、标定代码
import osimport cv2import xlrd2from math import *import numpy as npclass Calibration:def __init__(self):self.K = np.array([[2.54565632e+03, 0.00000000e+00, 9.68119560e+02], [0.00000000e+00, 2.54565632e+03, 5.31897821e+02], [0.00000000e+00, 0.00000000e+00, 1.00000000e+00]], dtype=np.float64)self.distortion = np.array([[-0.2557898, 0.81056366, 0.0, 0.0, -8.39153683]])self.target_x_number = 12self.target_y_number = 8self.target_cell_size = 40def angle2rotation(self, x, y, z):Rx = np.array([[1, 0, 0], [0, cos(x), -sin(x)], [0, sin(x), cos(x)]])Ry = np.array([[cos(y), 0, sin(y)], [0, 1, 0], [-sin(y), 0, cos(y)]])Rz = np.array([[cos(z), -sin(z), 0], [sin(z), cos(z), 0], [0, 0, 1]])R = Rz @ Ry @ Rxreturn Rdef gripper2base(self, x, y, z, tx, ty, tz):thetaX = x / 180 * pithetaY = y / 180 * pithetaZ = z / 180 * piR_gripper2base = self.angle2rotation(thetaX, thetaY, thetaZ)T_gripper2base = np.array([[tx], [ty], [tz]])Matrix_gripper2base = np.column_stack([R_gripper2base, T_gripper2base])Matrix_gripper2base = np.row_stack((Matrix_gripper2base, np.array([0, 0, 0, 1])))R_gripper2base = Matrix_gripper2base[:3, :3]T_gripper2base = Matrix_gripper2base[:3, 3].reshape((3, 1))return R_gripper2base, T_gripper2basedef target2camera(self, img):gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)ret, corners = cv2.findChessboardCorners(gray, (self.target_x_number, self.target_y_number), None)corner_points = np.zeros((2, corners.shape[0]), dtype=np.float64)for i in range(corners.shape[0]):corner_points[:, i] = corners[i, 0, :]object_points = np.zeros((3, self.target_x_number * self.target_y_number), dtype=np.float64)count = 0for i in range(self.target_y_number):for j in range(self.target_x_number):object_points[:2, count] = np.array([(self.target_x_number - j - 1) * self.target_cell_size, (self.target_y_number - i - 1) * self.target_cell_size])count += 1retval, rvec, tvec = cv2.solvePnP(object_points.T, corner_points.T, self.K, distCoeffs=distortion)Matrix_target2camera = np.column_stack(((cv2.Rodrigues(rvec))[0], tvec))Matrix_target2camera = np.row_stack((Matrix_target2camera, np.array([0, 0, 0, 1])))R_target2camera = Matrix_target2camera[:3, :3]T_target2camera = Matrix_target2camera[:3, 3].reshape((3, 1))return R_target2camera, T_target2cameradef process(self, img_path, pose_path):image_list = []for root, dirs, files in os.walk(img_path):if files:for file in files:image_name = os.path.join(root, file)image_list.append(image_name)R_target2camera_list = []T_target2camera_list = []for img_path in image_list:img = cv2.imread(img_path)R_target2camera, T_target2camera = self.target2camera(img)R_target2camera_list.append(R_target2camera)T_target2camera_list.append(T_target2camera)R_gripper2base_list = []T_gripper2base_list = []data = xlrd2.open_workbook(pose_path)table = data.sheets()[0]for row in range(table.nrows):x = table.cell_value(row, 0)y = table.cell_value(row, 1)z = table.cell_value(row, 2)tx = table.cell_value(row, 3)ty = table.cell_value(row, 4)tz = table.cell_value(row, 5)R_gripper2base, T_gripper2base = self.gripper2base(x, y, z, tx, ty, tz)R_gripper2base_list.append(R_gripper2base)T_gripper2base_list.append(T_gripper2base)R_camera2base, T_camera2base = cv2.calibrateHandEye(R_gripper2base_list, T_gripper2base_list,R_target2camera_list, T_target2camera_list)return R_camera2base, T_camera2base, R_gripper2base_list, T_gripper2base_list, R_target2camera_list, T_target2camera_listdef check_result(self, R_cb, T_cb, R_gb, T_gb, R_tc, T_tc):for i in range(len(R_gb)):RT_gripper2base = np.column_stack((R_gb[i], T_gb[i]))RT_gripper2base = np.row_stack((RT_gripper2base, np.array([0, 0, 0, 1])))RT_base2gripper = np.linalg.inv(RT_gripper2base)print(RT_base2gripper)RT_camera_to_base = np.column_stack((R_cb, T_cb))RT_camera_to_base = np.row_stack((RT_camera_to_base, np.array([0, 0, 0, 1])))print(RT_camera_to_base)RT_target_to_camera = np.column_stack((R_tc[i], T_tc[i]))RT_target_to_camera = np.row_stack((RT_target_to_camera, np.array([0, 0, 0, 1])))RT_camera2target = np.linalg.inv(RT_target_to_camera)print(RT_camera2target)RT_target_to_gripper = RT_base2gripper @ RT_camera_to_base @ RT_camera2targetprint("第{}次验证结果为:".format(i))print(RT_target_to_gripper)print('')if __name__ == "__main__":image_path = r"D\code\img"pose_path = r"D\code\pose.xlsx"calibrator = Calibration()R_cb, T_cb, R_gb, T_gb, R_tc, T_tc = calibrator.process(image_path, pose_path)calibrator.check_result(R_cb, T_cb, R_gb, T_gb, R_tc, T_tc)