Rune Harlyk
183 lines
5.0 KiB
Python
183 lines
5.0 KiB
Python
#!/usr/bin/env python
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import numpy as np
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# NOTE: Code snippets from Modern Robotics at Northwestern University:
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# See https://github.com/NxRLab/ModernRobotics
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def RpToTrans(R, p):
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"""
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Converts a rotation matrix and a position vector into homogeneous
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transformation matrix
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:param R: A 3x3 rotation matrix
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:param p: A 3-vector
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:return: A homogeneous transformation matrix corresponding to the inputs
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Example Input:
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R = np.array([[1, 0, 0],
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[0, 0, -1],
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[0, 1, 0]])
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p = np.array([1, 2, 5])
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Output:
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np.array([[1, 0, 0, 1],
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[0, 0, -1, 2],
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[0, 1, 0, 5],
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[0, 0, 0, 1]])
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"""
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return np.r_[np.c_[R, p], [[0, 0, 0, 1]]]
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def TransToRp(T):
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"""
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Converts a homogeneous transformation matrix into a rotation matrix
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and position vector
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:param T: A homogeneous transformation matrix
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:return R: The corresponding rotation matrix,
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:return p: The corresponding position vector.
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Example Input:
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T = np.array([[1, 0, 0, 0],
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[0, 0, -1, 0],
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[0, 1, 0, 3],
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[0, 0, 0, 1]])
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Output:
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(np.array([[1, 0, 0],
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[0, 0, -1],
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[0, 1, 0]]),
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np.array([0, 0, 3]))
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"""
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T = np.array(T)
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return T[0:3, 0:3], T[0:3, 3]
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def TransInv(T):
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"""
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Inverts a homogeneous transformation matrix
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:param T: A homogeneous transformation matrix
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:return: The inverse of T
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Uses the structure of transformation matrices to avoid taking a matrix
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inverse, for efficiency.
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Example input:
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T = np.array([[1, 0, 0, 0],
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[0, 0, -1, 0],
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[0, 1, 0, 3],
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[0, 0, 0, 1]])
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Output:
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np.array([[1, 0, 0, 0],
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[0, 0, 1, -3],
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[0, -1, 0, 0],
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[0, 0, 0, 1]])
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"""
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R, p = TransToRp(T)
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Rt = np.array(R).T
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return np.r_[np.c_[Rt, -np.dot(Rt, p)], [[0, 0, 0, 1]]]
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def Adjoint(T):
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"""
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Computes the adjoint representation of a homogeneous transformation
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matrix
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:param T: A homogeneous transformation matrix
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:return: The 6x6 adjoint representation [AdT] of T
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Example Input:
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T = np.array([[1, 0, 0, 0],
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[0, 0, -1, 0],
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[0, 1, 0, 3],
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[0, 0, 0, 1]])
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Output:
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np.array([[1, 0, 0, 0, 0, 0],
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[0, 0, -1, 0, 0, 0],
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[0, 1, 0, 0, 0, 0],
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[0, 0, 3, 1, 0, 0],
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[3, 0, 0, 0, 0, -1],
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[0, 0, 0, 0, 1, 0]])
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"""
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R, p = TransToRp(T)
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return np.r_[np.c_[R, np.zeros((3, 3))], np.c_[np.dot(VecToso3(p), R), R]]
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def VecToso3(omg):
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"""
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Converts a 3-vector to an so(3) representation
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:param omg: A 3-vector
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:return: The skew symmetric representation of omg
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Example Input:
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omg = np.array([1, 2, 3])
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Output:
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np.array([[ 0, -3, 2],
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[ 3, 0, -1],
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[-2, 1, 0]])
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"""
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return np.array([[0, -omg[2], omg[1]], [omg[2], 0, -omg[0]],
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[-omg[1], omg[0], 0]])
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def RPY(roll, pitch, yaw):
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"""
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Creates a Roll, Pitch, Yaw Transformation Matrix
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:param roll: roll component of matrix
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:param pitch: pitch component of matrix
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:param yaw: yaw component of matrix
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:return: The transformation matrix
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Example Input:
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roll = 0.0
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pitch = 0.0
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yaw = 0.0
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Output:
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np.array([[1, 0, 0, 0],
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[0, 1, 0, 0],
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[0, 0, 1, 0],
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[0, 0, 0, 1]])
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"""
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Roll = np.array([[1, 0, 0, 0], [0, np.cos(roll), -np.sin(roll), 0],
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[0, np.sin(roll), np.cos(roll), 0], [0, 0, 0, 1]])
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Pitch = np.array([[np.cos(pitch), 0, np.sin(pitch), 0], [0, 1, 0, 0],
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[-np.sin(pitch), 0, np.cos(pitch), 0], [0, 0, 0, 1]])
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Yaw = np.array([[np.cos(yaw), -np.sin(yaw), 0, 0],
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[np.sin(yaw), np.cos(yaw), 0, 0], [0, 0, 1, 0],
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[0, 0, 0, 1]])
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return np.matmul(np.matmul(Roll, Pitch), Yaw)
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def RotateTranslate(rotation, position):
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"""
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Creates a Transformation Matrix from a Rotation, THEN, a Translation
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:param rotation: pure rotation matrix
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:param translation: pure translation matrix
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:return: The transformation matrix
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"""
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trans = np.eye(4)
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trans[0, 3] = position[0]
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trans[1, 3] = position[1]
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trans[2, 3] = position[2]
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return np.dot(rotation, trans)
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def TransformVector(xyz_coord, rotation, translation):
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"""
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Transforms a vector by a specified Rotation THEN Translation Matrix
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:param xyz_coord: the vector to transform
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:param rotation: pure rotation matrix
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:param translation: pure translation matrix
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:return: The transformed vector
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"""
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xyz_vec = np.append(xyz_coord, 1.0)
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Transformed = np.dot(RotateTranslate(rotation, translation), xyz_vec)
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return Transformed[:3]
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