| import copy |
|
|
| import numpy as np |
|
|
| from liegroups.numpy import SE3 |
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|
| def test_identity(): |
| T = SE3.identity() |
| assert isinstance(T, SE3) |
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|
|
| def test_dot(): |
| T = np.array([[0, 0, -1, 0.1], |
| [0, 1, 0, 0.5], |
| [1, 0, 0, -0.5], |
| [0, 0, 0, 1]]) |
| T2 = T.dot(T) |
| assert np.allclose( |
| (SE3.from_matrix(T).dot(SE3.from_matrix(T))).as_matrix(), T2) |
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|
|
| def test_wedge_vee(): |
| xi = [1, 2, 3, 4, 5, 6] |
| Xi = SE3.wedge(xi) |
| xis = np.array([[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12]]) |
| Xis = SE3.wedge(xis) |
| assert np.array_equal(xi, SE3.vee(Xi)) |
| assert np.array_equal(xis, SE3.vee(Xis)) |
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|
|
| def test_curlywedge_curlyvee(): |
| xi = [1, 2, 3, 4, 5, 6] |
| Psi = SE3.curlywedge(xi) |
| xis = np.array([[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12]]) |
| Psis = SE3.curlywedge(xis) |
| assert np.array_equal(xi, SE3.curlyvee(Psi)) |
| assert np.array_equal(xis, SE3.curlyvee(Psis)) |
|
|
|
|
| def test_odot(): |
| p1 = [1, 2, 3] |
| p2 = [1, 2, 3, 1] |
| p3 = [1, 2, 3, 0] |
|
|
| odot12 = np.vstack([SE3.odot(p1), np.zeros([1, 6])]) |
| odot13 = np.vstack([SE3.odot(p1, directional=True), np.zeros([1, 6])]) |
| odot2 = SE3.odot(p2) |
| odot3 = SE3.odot(p3) |
|
|
| assert np.array_equal(odot12, odot2) |
| assert np.array_equal(odot13, odot3) |
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|
|
|
| def test_odot_vectorized(): |
| p1 = [1, 2, 3] |
| p2 = [2, 3, 4] |
| ps = np.array([p1, p2]) |
|
|
| odot1 = SE3.odot(p1) |
| odot2 = SE3.odot(p2) |
| odots = SE3.odot(ps) |
|
|
| assert np.array_equal(odot1, odots[0, :, :]) |
| assert np.array_equal(odot2, odots[1, :, :]) |
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|
|
| def test_exp_log(): |
| T = SE3.exp([1, 2, 3, 4, 5, 6]) |
| assert np.allclose(SE3.exp(SE3.log(T)).as_matrix(), T.as_matrix()) |
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|
|
| def test_left_jacobian(): |
| xi1 = [1, 2, 3, 4, 5, 6] |
| assert np.allclose( |
| SE3.left_jacobian(xi1).dot(SE3.inv_left_jacobian(xi1)), |
| np.identity(6) |
| ) |
|
|
| xi2 = [0, 0, 0, 0, 0, 0] |
| assert np.allclose( |
| SE3.left_jacobian(xi2).dot(SE3.inv_left_jacobian(xi2)), |
| np.identity(6) |
| ) |
|
|
|
|
| def test_perturb(): |
| T = SE3.exp([1, 2, 3, 4, 5, 6]) |
| T_copy = copy.deepcopy(T) |
| xi = [0.6, 0.5, 0.4, 0.3, 0.2, 0.1] |
| T.perturb(xi) |
| assert np.allclose(T.as_matrix(), (SE3.exp(xi).dot(T_copy)).as_matrix()) |
|
|
|
|
| def test_normalize(): |
| T = SE3.exp([1, 2, 3, 4, 5, 6]) |
| T.rot.mat += 0.1 |
| T.normalize() |
| assert SE3.is_valid_matrix(T.as_matrix()) |
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|
|
|
| def test_inv(): |
| T = SE3.exp([1, 2, 3, 4, 5, 6]) |
| assert np.allclose((T.dot(T.inv())).as_matrix(), np.identity(4)) |
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|
|
| def test_adjoint(): |
| T = SE3.exp([1, 2, 3, 4, 5, 6]) |
| assert T.adjoint().shape == (6, 6) |
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|
|
| def test_transform_vectorized(): |
| T = SE3.exp([1, 2, 3, 4, 5, 6]) |
| pt1 = np.array([1, 2, 3]) |
| pt2 = np.array([4, 5, 6]) |
| pt3 = np.array([1, 2, 3, 1]) |
| pt4 = np.array([4, 5, 6, 1]) |
| pts12 = np.array([pt1, pt2]) |
| pts34 = np.array([pt3, pt4]) |
| Tpt1 = T.dot(pt1) |
| Tpt2 = T.dot(pt2) |
| Tpt3 = T.dot(pt3) |
| Tpt4 = T.dot(pt4) |
| Tpts12 = T.dot(pts12) |
| Tpts34 = T.dot(pts34) |
| assert np.allclose(Tpt1, Tpts12[0]) |
| assert np.allclose(Tpt2, Tpts12[1]) |
| assert np.allclose(Tpt3, Tpts34[0]) |
| assert np.allclose(Tpt4, Tpts34[1]) |
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|
