用python书写一个眼在手外的手眼标定代码

在视觉引导机器人等领域，手眼标定是一个非常重要的问题。以下是一个使用Python编写的手眼标定代码示例：

import numpy as np
from scipy.spatial.transform import Rotation

# 机器人末端执行器位姿
robot_poses = [
    np.array([
        [ 0.70710678,  0.        , -0.70710678, -0.5       ],
        [ 0.        ,  1.        ,  0.        ,  0.        ],
        [ 0.70710678,  0.        ,  0.70710678,  0.5       ],
        [ 0.        ,  0.        ,  0.        ,  1.        ]
    ]),
    np.array([
        [ 1.        ,  0.        ,  0.        , -0.5       ],
        [ 0.        ,  1.        ,  0.        ,  0.        ],
        [ 0.        ,  0.        ,  1.        ,  0.5       ],
        [ 0.        ,  0.        ,  0.        ,  1.        ]
    ]),
    np.array([
        [-0.70710678,  0.        ,  0.70710678, -0.5       ],
        [ 0.        ,  1.        ,  0.        ,  0.        ],
        [-0.70710678,  0.        , -0.70710678,  0.5       ],
        [ 0.        ,  0.        ,  0.        ,  1.        ]
    ])
]

# 标定物体姿态
object_poses = [
    np.array([
        [ 0.99947886, -0.01862355, -0.02571654, -0.015     ],
        [ 0.01857627,  0.99981949,  0.00412505,  0.135     ],
        [ 0.02579311, -0.00360933,  0.99966261,  0.19      ],
        [ 0.        ,  0.        ,  0.        ,  1.        ]
    ]),
    np.array([
        [ 0.99960435, -0.02716068, -0.00160679,  0.055     ],
        [ 0.02714492,  0.99896677,  0.03634583, -0.105     ],
        [ 0.00196778, -0.03633688,  0.99934018,  0.18      ],
        [ 0.        ,  0.        ,  0.        ,  1.        ]
    ]),
    np.array([
        [ 0.99912269, -0.04122606,  0.00295757,  0.12      ],
        [ 0.04121315,  0.99863852, -0.03104084, -0.13      ],
        [-0.00376669,  0.03103051,  0.99951025,  0.2       ],
        [ 0.        ,  0.        ,  0.        ,  1.        ]
    ])
]

# 手眼标定
def hand_eye_calibration(robot_poses, object_poses):
    A = np.empty((0, 4))
    B = np.empty((0, 4))

    for i in range(len(robot_poses)):
        for j in range(i+1, len(robot_poses)):
            A = np.vstack((A, np.dot(np.linalg.inv(robot_poses[i]), robot_poses[j])))
            B = np.vstack((B, np.dot(np.linalg.inv(object_poses[i]), object_poses[j])))

    X = np.dot(np.linalg.pinv(A), B)
    r = Rotation.from_matrix(X[:3, :3])
    t = X[:3, 3]

    return r, t

# 输出结果
r, t = hand_eye_calibration(robot_poses, object_poses)
print('旋转矩阵：')
print(r.as_matrix())
print('平移向量：')
print(t)

这个示例代码中，我们假设机器人末端执行器和标定物体都在视野范围内，分别记录它们的位姿，然后使用手眼标定算法计算出机器人基坐标系相对于标定物体的旋转矩阵和平移向量。