怎样进行机器人手眼标定？

　　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   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   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 os import cv2 import xlrd2 from math import * import numpy as np   class 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 = 12         self.target_y_number = 8         self.target_cell_size = 40      def 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 @ Rx         return R      def gripper2base(self, x, y, z, tx, ty, tz):         thetaX = x / 180 * pi         thetaY = y / 180 * pi         thetaZ = z / 180 * pi         R_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_gripper2base      def 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 = 0         for 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 += 1         retval, 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_target2camera      def 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_list      def 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_camera2target             print(＂第{}次验证结果为:＂.format(i))             print(RT_target_to_gripper)             print(＂＂)   if __name__ == ＂__main__＂:     image_path = r＂Dcodeimg＂     pose_path = r＂Dcodepose.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)
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