bindings_SE3.py

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import unittest
import pinocchio as pin
import numpy as np
from pinocchio.utils import eye, zero, rand
from copy import deepcopy, copy
 
ones = lambda n: np.ones([n, 1] if isinstance(n, int) else n)
 
 
class TestSE3Bindings(unittest.TestCase):
    def test_identity(self):
        transform = pin.SE3.Identity()
        self.assertTrue(np.allclose(zero(3), transform.translation))
        self.assertTrue(np.allclose(eye(3), transform.rotation))
        self.assertTrue(np.allclose(eye(4), transform.homogeneous))
        self.assertTrue(np.allclose(eye(6), transform.action))
        transform.setRandom()
        transform.setIdentity()
        self.assertTrue(np.allclose(eye(4), transform.homogeneous))
 
    def test_constructor(self):
        M = pin.SE3.Random()
        quat = pin.Quaternion(M.rotation)
        M_from_quat = pin.SE3(quat, M.translation)
        self.assertTrue(M_from_quat.isApprox(M))
 
    def test_get_translation(self):
        transform = pin.SE3.Identity()
        self.assertTrue(np.allclose(transform.translation, zero(3)))
 
    def test_get_rotation(self):
        transform = pin.SE3.Identity()
        self.assertTrue(np.allclose(transform.rotation, eye(3)))
 
    def test_set_translation(self):
        transform = pin.SE3.Identity()
        transform.translation = ones(3)
        self.assertFalse(np.allclose(transform.translation, zero(3)))
        self.assertTrue(np.allclose(transform.translation, ones(3)))
 
    def test_set_rotation(self):
        transform = pin.SE3.Identity()
        transform.rotation = zero([3, 3])
        self.assertFalse(np.allclose(transform.rotation, eye(3)))
        self.assertTrue(np.allclose(transform.rotation, zero([3, 3])))
 
    def test_homogeneous(self):
        amb = pin.SE3.Random()
        H = amb.homogeneous
        self.assertTrue(
            np.allclose(H[0:3, 0:3], amb.rotation)
        )  # top left 33 corner = rotation of amb
        self.assertTrue(
            np.allclose(H[0:3, 3], amb.translation)
        )  # top 3 of last column = translation of amb
        self.assertTrue(
            np.allclose(H[3, :], [0.0, 0.0, 0.0, 1.0])
        )  # last row = 0 0 0 1
 
        amb_from_H = pin.SE3(H)
        self.assertTrue(amb_from_H.isApprox(amb))
 
    def test_action_matrix(self):
        amb = pin.SE3.Random()
        aXb = amb.action
        self.assertTrue(
            np.allclose(aXb[:3, :3], amb.rotation)
        )  # top left 33 corner = rotation of amb
        self.assertTrue(
            np.allclose(aXb[3:, 3:], amb.rotation)
        )  # bottom right 33 corner = rotation of amb
        tblock = pin.skew(amb.translation).dot(amb.rotation)
        self.assertTrue(
            np.allclose(aXb[:3, 3:], tblock)
        )  # top right 33 corner = translation + rotation
        self.assertTrue(
            np.allclose(aXb[3:, :3], zero([3, 3]))
        )  # bottom left 33 corner = 0
 
    def test_inverse(self):
        amb = pin.SE3.Random()
        aMb = amb.homogeneous
        bma = amb.inverse()
        self.assertTrue(np.allclose(np.linalg.inv(aMb), bma.homogeneous))
 
    def test_internal_product_vs_homogeneous(self):
        amb = pin.SE3.Random()
        bmc = pin.SE3.Random()
        amc = amb * bmc
        cma = amc.inverse()
 
        aMb = amb.homogeneous
        bMc = bmc.homogeneous
        aMc = amc.homogeneous
        cMa = np.linalg.inv(aMc)
 
        self.assertTrue(np.allclose(aMb.dot(bMc), aMc))
        self.assertTrue(np.allclose(cma.homogeneous, cMa))
 
    def test_internal_product_vs_action(self):
        amb = pin.SE3.Random()
        bmc = pin.SE3.Random()
        amc = amb * bmc
        cma = amc.inverse()
 
        aXb = amb.action
        bXc = bmc.action
        aXc = amc.action
        cXa = np.linalg.inv(aXc)
 
        self.assertTrue(np.allclose(aXb.dot(bXc), aXc))
        self.assertTrue(np.allclose(cma.action, cXa))
 
    def test_point_action(self):
        amb = pin.SE3.Random()
        aMb = amb.homogeneous
        p_homogeneous = rand(4)
        p_homogeneous[3] = 1
        p = p_homogeneous[0:3].copy()
 
        # act
        self.assertTrue(np.allclose(amb.act(p), (aMb.dot(p_homogeneous))[0:3]))
 
        # actinv
        bMa = np.linalg.inv(aMb)
        bma = amb.inverse()
        self.assertTrue(np.allclose(bma.act(p), (bMa.dot(p_homogeneous))[0:3]))
 
    def test_member(self):
        M = pin.SE3.Random()
        trans = M.translation
        M.translation[2] = 1.0
 
        self.assertTrue(trans[2] == M.translation[2])
 
    def test_conversions(self):
        def compute(m):
            tq_vec = pin.SE3ToXYZQUAT(m)
            tq_tup = pin.SE3ToXYZQUATtuple(m)
            mm_vec = pin.XYZQUATToSE3(tq_vec)
            mm_tup = pin.XYZQUATToSE3(tq_tup)
            mm_lis = pin.XYZQUATToSE3(list(tq_tup))
            return tq_vec, tq_tup, mm_vec, mm_tup, mm_lis
 
        m = pin.SE3.Identity()
        tq_vec, tq_tup, mm_vec, mm_tup, mm_lis = compute(m)
        self.assertTrue(np.allclose(m.homogeneous, mm_tup.homogeneous))
        self.assertTrue(np.allclose(m.homogeneous, mm_vec.homogeneous))
        self.assertTrue(np.allclose(m.homogeneous, mm_lis.homogeneous))
        for i in range(6):
            self.assertTrue(tq_vec[i] == 0 and tq_tup[i] == 0)
        self.assertTrue(tq_vec[6] == 1 and tq_tup[6] == 1)
 
        m = pin.SE3.Random()
        tq_vec, tq_tup, mm_vec, mm_tup, mm_lis = compute(m)
        self.assertTrue(len(tq_vec) == 7)
        self.assertTrue(len(tq_tup) == 7)
        for a, b in zip(tq_vec, tq_tup):
            self.assertTrue(a == b)
        self.assertTrue(np.allclose(m.homogeneous, mm_tup.homogeneous))
        self.assertTrue(mm_vec == mm_tup)
        self.assertTrue(mm_vec == mm_lis)
 
        M = pin.SE3.Random()
        h = np.array(M)
 
        M_from_h = pin.SE3(h)
        self.assertTrue(M == M_from_h)
 
    def test_several_init(self):
        for _ in range(100000):
            r = pin.SE3.Random() * pin.SE3.Random()
            s = r.__str__()
            self.assertTrue(s != "")
 
    def test_copy(self):
        M = pin.SE3.Random()
        Mc = copy(M)
        Mdc = deepcopy(M)
        self.assertTrue(M == Mc)
        self.assertTrue(M == Mdc)
 
        Mc.setRandom()
        self.assertFalse(M == Mc)
        Mdc.setRandom()
        self.assertFalse(M == Mc)
 
 
if __name__ == "__main__":
    unittest.main()