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Keep twist poles invariant under angular speed scaling #249

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Keep twist poles invariant under angular speed scaling #249

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4 changes: 2 additions & 2 deletions spatialmath/twist.py
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Original file line number Diff line number Diff line change
Expand Up @@ -986,7 +986,7 @@ def pole(self):
>>> S = Twist3(T)
>>> S.pole
"""
return np.cross(self.w, self.v) / self.theta
return np.cross(self.w, self.v) / np.dot(self.w, self.w)

def SE3(self, theta=1, unit="rad"):
"""
Expand Down Expand Up @@ -1500,7 +1500,7 @@ def pole(self):
>>> S.pole()

"""
p = np.cross(np.r_[0, 0, self.w], np.r_[self.v, 0]) / self.theta
p = np.cross(np.r_[0, 0, self.w], np.r_[self.v, 0]) / self.w**2
return p[:2]

# ------------------------- methods -------------------------------#
Expand Down
35 changes: 35 additions & 0 deletions tests/test_twist_pole.py
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Original file line number Diff line number Diff line change
@@ -0,0 +1,35 @@
import numpy as np
import pytest
from scipy.linalg import expm

from spatialmath import Twist2, Twist3


@pytest.mark.parametrize("speed", [-2.0, -0.3, 0.3, 1.0, 2.0])
def test_twist2_pole_is_rotation_center(speed):
"""A change in angular speed must not move the center of rotation."""
center = np.array([3.0, -2.0])
twist = Twist2(speed * np.r_[center[1], -center[0], 1])
np.testing.assert_allclose(twist.pole, center)
transform = expm(twist.skewa() * 0.7)
np.testing.assert_allclose(
transform @ np.r_[twist.pole, 1], np.r_[center, 1], atol=1e-14
)


@pytest.mark.parametrize("speed", [-2.0, -0.3, 0.3, 1.0, 2.0])
@pytest.mark.parametrize("pitch", [0, 0.4])
def test_twist3_pole_is_on_screw_axis(speed, pitch):
"""The closest axis point is fixed except for translation along the axis."""
axis = np.array([1.0, 2.0, -2.0]) / 3
center = np.array([3.0, -2.0, 1.0])
center -= (center @ axis) * axis
angular = speed * axis
linear = -np.cross(angular, center) + pitch * angular
twist = Twist3(linear, angular)
np.testing.assert_allclose(twist.pole, center)
transform = expm(twist.skewa() * 0.7)
expected = center + pitch * angular * 0.7
np.testing.assert_allclose(
(transform @ np.r_[twist.pole, 1])[:3], expected, atol=1e-14
)