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test_pose3d.py
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import numpy.testing as nt
import matplotlib.pyplot as plt
import unittest
import sys
import pytest
"""
we will assume that the primitives rotx,trotx, etc. all work
"""
from math import pi
from spatialmath import SE3, SO3, SE2, UnitQuaternion
import numpy as np
from spatialmath.base import *
from spatialmath.baseposematrix import BasePoseMatrix
from spatialmath.twist import BaseTwist
def array_compare(x, y):
if isinstance(x, BasePoseMatrix):
x = x.A
if isinstance(y, BasePoseMatrix):
y = y.A
if isinstance(x, BaseTwist):
x = x.S
if isinstance(y, BaseTwist):
y = y.S
nt.assert_array_almost_equal(x, y)
class TestSO3(unittest.TestCase):
@classmethod
def tearDownClass(cls):
plt.close("all")
def test_constructor(self):
# null constructor
R = SO3()
nt.assert_equal(len(R), 1)
array_compare(R, np.eye(3))
self.assertIsInstance(R, SO3)
# empty constructor
R = SO3.Empty()
nt.assert_equal(len(R), 0)
self.assertIsInstance(R, SO3)
# construct from matrix
R = SO3(rotx(0.2))
nt.assert_equal(len(R), 1)
array_compare(R, rotx(0.2))
self.assertIsInstance(R, SO3)
# construct from canonic rotation
R = SO3.Rx(0.2)
nt.assert_equal(len(R), 1)
array_compare(R, rotx(0.2))
self.assertIsInstance(R, SO3)
R = SO3.Ry(0.2)
nt.assert_equal(len(R), 1)
array_compare(R, roty(0.2))
self.assertIsInstance(R, SO3)
R = SO3.Rz(0.2)
nt.assert_equal(len(R), 1)
array_compare(R, rotz(0.2))
self.assertIsInstance(R, SO3)
# OA
R = SO3.OA([0, 1, 0], [0, 0, 1])
nt.assert_equal(len(R), 1)
array_compare(R, np.eye(3))
self.assertIsInstance(R, SO3)
np.random.seed(32)
# random
R = SO3.Rand()
nt.assert_equal(len(R), 1)
self.assertIsInstance(R, SO3)
# random constrained
R = SO3.Rand(theta_range=(0.1, 0.7))
self.assertIsInstance(R, SO3)
self.assertEqual(R.A.shape, (3, 3))
self.assertLessEqual(R.angvec()[0], 0.7)
self.assertGreaterEqual(R.angvec()[0], 0.1)
# copy constructor
R = SO3.Rx(pi / 2)
R2 = SO3(R)
R = SO3.Ry(pi / 2)
array_compare(R2, rotx(pi / 2))
def test_constructor_Eul(self):
R = SO3.Eul([0.1, 0.2, 0.3])
nt.assert_equal(len(R), 1)
array_compare(R, eul2r([0.1, 0.2, 0.3]))
self.assertIsInstance(R, SO3)
R = SO3.Eul(0.1, 0.2, 0.3)
nt.assert_equal(len(R), 1)
array_compare(R, eul2r([0.1, 0.2, 0.3]))
self.assertIsInstance(R, SO3)
R = SO3.Eul(np.r_[0.1, 0.2, 0.3])
nt.assert_equal(len(R), 1)
array_compare(R, eul2r([0.1, 0.2, 0.3]))
self.assertIsInstance(R, SO3)
R = SO3.Eul([10, 20, 30], unit="deg")
nt.assert_equal(len(R), 1)
array_compare(R, eul2r([10, 20, 30], unit="deg"))
self.assertIsInstance(R, SO3)
R = SO3.Eul(10, 20, 30, unit="deg")
nt.assert_equal(len(R), 1)
array_compare(R, eul2r([10, 20, 30], unit="deg"))
self.assertIsInstance(R, SO3)
# matrix input
angles = np.array(
[[0.1, 0.2, 0.3], [0.2, 0.3, 0.4], [0.3, 0.4, 0.5], [0.4, 0.5, 0.6]]
)
R = SO3.Eul(angles)
self.assertIsInstance(R, SO3)
nt.assert_equal(len(R), 4)
for i in range(4):
array_compare(R[i], eul2r(angles[i, :]))
angles *= 10
R = SO3.Eul(angles, unit="deg")
self.assertIsInstance(R, SO3)
nt.assert_equal(len(R), 4)
for i in range(4):
array_compare(R[i], eul2r(angles[i, :], unit="deg"))
def test_constructor_RPY(self):
R = SO3.RPY(0.1, 0.2, 0.3, order="zyx")
nt.assert_equal(len(R), 1)
array_compare(R, rpy2r([0.1, 0.2, 0.3], order="zyx"))
self.assertIsInstance(R, SO3)
R = SO3.RPY(10, 20, 30, unit="deg", order="zyx")
nt.assert_equal(len(R), 1)
array_compare(R, rpy2r([10, 20, 30], order="zyx", unit="deg"))
self.assertIsInstance(R, SO3)
R = SO3.RPY([0.1, 0.2, 0.3], order="zyx")
nt.assert_equal(len(R), 1)
array_compare(R, rpy2r([0.1, 0.2, 0.3], order="zyx"))
self.assertIsInstance(R, SO3)
R = SO3.RPY(np.r_[0.1, 0.2, 0.3], order="zyx")
nt.assert_equal(len(R), 1)
array_compare(R, rpy2r([0.1, 0.2, 0.3], order="zyx"))
self.assertIsInstance(R, SO3)
# check default
R = SO3.RPY([0.1, 0.2, 0.3])
nt.assert_equal(len(R), 1)
array_compare(R, rpy2r([0.1, 0.2, 0.3], order="zyx"))
self.assertIsInstance(R, SO3)
# XYZ order
R = SO3.RPY(0.1, 0.2, 0.3, order="xyz")
nt.assert_equal(len(R), 1)
array_compare(R, rpy2r([0.1, 0.2, 0.3], order="xyz"))
self.assertIsInstance(R, SO3)
R = SO3.RPY(10, 20, 30, unit="deg", order="xyz")
nt.assert_equal(len(R), 1)
array_compare(R, rpy2r([10, 20, 30], order="xyz", unit="deg"))
self.assertIsInstance(R, SO3)
R = SO3.RPY([0.1, 0.2, 0.3], order="xyz")
nt.assert_equal(len(R), 1)
array_compare(R, rpy2r([0.1, 0.2, 0.3], order="xyz"))
self.assertIsInstance(R, SO3)
R = SO3.RPY(np.r_[0.1, 0.2, 0.3], order="xyz")
nt.assert_equal(len(R), 1)
array_compare(R, rpy2r([0.1, 0.2, 0.3], order="xyz"))
self.assertIsInstance(R, SO3)
# matrix input
angles = np.array(
[[0.1, 0.2, 0.3], [0.2, 0.3, 0.4], [0.3, 0.4, 0.5], [0.4, 0.5, 0.6]]
)
R = SO3.RPY(angles, order="zyx")
self.assertIsInstance(R, SO3)
nt.assert_equal(len(R), 4)
for i in range(4):
array_compare(R[i], rpy2r(angles[i, :], order="zyx"))
angles *= 10
R = SO3.RPY(angles, unit="deg", order="zyx")
self.assertIsInstance(R, SO3)
nt.assert_equal(len(R), 4)
for i in range(4):
array_compare(R[i], rpy2r(angles[i, :], unit="deg", order="zyx"))
def test_constructor_AngVec(self):
# angvec
R = SO3.AngVec(0.2, [1, 0, 0])
nt.assert_equal(len(R), 1)
array_compare(R, rotx(0.2))
self.assertIsInstance(R, SO3)
R = SO3.AngVec(0.3, [0, 1, 0])
nt.assert_equal(len(R), 1)
array_compare(R, roty(0.3))
self.assertIsInstance(R, SO3)
def test_constructor_TwoVec(self):
# Randomly selected vectors
v1 = [1, 73, -42]
v2 = [0, 0.02, 57]
v3 = [-2, 3, 9]
# x and y given
R = SO3.TwoVectors(x=v1, y=v2)
self.assertIsInstance(R, SO3)
nt.assert_almost_equal(R.det(), 1, 5)
# x axis should equal normalized x vector
nt.assert_almost_equal(R.R[:, 0], v1 / np.linalg.norm(v1), 5)
# y and z given
R = SO3.TwoVectors(y=v2, z=v3)
self.assertIsInstance(R, SO3)
nt.assert_almost_equal(R.det(), 1, 5)
# y axis should equal normalized y vector
nt.assert_almost_equal(R.R[:, 1], v2 / np.linalg.norm(v2), 5)
# x and z given
R = SO3.TwoVectors(x=v3, z=v1)
self.assertIsInstance(R, SO3)
nt.assert_almost_equal(R.det(), 1, 5)
# x axis should equal normalized x vector
nt.assert_almost_equal(R.R[:, 0], v3 / np.linalg.norm(v3), 5)
def test_conversion(self):
R = SO3.AngleAxis(0.7, [1,2,3])
q = UnitQuaternion([11,7,3,-6])
R_from_q = SO3(q.R)
q_from_R = UnitQuaternion(R)
nt.assert_array_almost_equal(R.UnitQuaternion(), q_from_R)
nt.assert_array_almost_equal(R.UnitQuaternion().SO3(), R)
nt.assert_array_almost_equal(q.SO3(), R_from_q)
nt.assert_array_almost_equal(q.SO3().UnitQuaternion(), q)
def test_shape(self):
a = SO3()
self.assertEqual(a._A.shape, a.shape)
def test_about(self):
R = SO3()
R.about
def test_str(self):
R = SO3()
s = str(R)
self.assertIsInstance(s, str)
self.assertEqual(s.count("\n"), 3)
s = repr(R)
self.assertIsInstance(s, str)
self.assertEqual(s.count("\n"), 2)
def test_printline(self):
R = SO3.Rx(0.3)
R.printline()
# s = R.printline(file=None)
# self.assertIsInstance(s, str)
R = SO3.Rx([0.3, 0.4, 0.5])
s = R.printline(file=None)
# self.assertIsInstance(s, str)
# self.assertEqual(s.count('\n'), 2)
@pytest.mark.skipif(
sys.platform.startswith("darwin") and sys.version_info < (3, 11),
reason="tkinter bug with mac",
)
def test_plot(self):
plt.close("all")
R = SO3.Rx(0.3)
R.plot(block=False)
R2 = SO3.Rx(0.6)
# R.animate()
# R.animate(start=R.inv())
def test_listpowers(self):
R = SO3()
R1 = SO3.Rx(0.2)
R2 = SO3.Ry(0.3)
R.append(R1)
R.append(R2)
nt.assert_equal(len(R), 3)
self.assertIsInstance(R, SO3)
array_compare(R[0], np.eye(3))
array_compare(R[1], R1)
array_compare(R[2], R2)
R = SO3([rotx(0.1), rotx(0.2), rotx(0.3)])
nt.assert_equal(len(R), 3)
self.assertIsInstance(R, SO3)
array_compare(R[0], rotx(0.1))
array_compare(R[1], rotx(0.2))
array_compare(R[2], rotx(0.3))
R = SO3([SO3.Rx(0.1), SO3.Rx(0.2), SO3.Rx(0.3)])
nt.assert_equal(len(R), 3)
self.assertIsInstance(R, SO3)
array_compare(R[0], rotx(0.1))
array_compare(R[1], rotx(0.2))
array_compare(R[2], rotx(0.3))
def test_tests(self):
R = SO3()
self.assertEqual(R.isrot(), True)
self.assertEqual(R.isrot2(), False)
self.assertEqual(R.ishom(), False)
self.assertEqual(R.ishom2(), False)
def test_properties(self):
R = SO3()
self.assertEqual(R.isSO, True)
self.assertEqual(R.isSE, False)
array_compare(R.n, np.r_[1, 0, 0])
array_compare(R.n, np.r_[1, 0, 0])
array_compare(R.n, np.r_[1, 0, 0])
nt.assert_equal(R.N, 3)
nt.assert_equal(R.shape, (3, 3))
R = SO3.Rx(0.3)
array_compare(R.inv() * R, np.eye(3, 3))
def test_arith(self):
R = SO3()
# sum
a = R + R
self.assertNotIsInstance(a, SO3)
array_compare(a, np.array([[2, 0, 0], [0, 2, 0], [0, 0, 2]]))
a = R + 1
self.assertNotIsInstance(a, SO3)
array_compare(a, np.array([[2, 1, 1], [1, 2, 1], [1, 1, 2]]))
# a = 1 + R
# self.assertNotIsInstance(a, SO3)
# array_compare(a, np.array([ [2,1,1], [1,2,1], [1,1,2]]))
a = R + np.eye(3)
self.assertNotIsInstance(a, SO3)
array_compare(a, np.array([[2, 0, 0], [0, 2, 0], [0, 0, 2]]))
# a = np.eye(3) + R
# self.assertNotIsInstance(a, SO3)
# array_compare(a, np.array([ [2,0,0], [0,2,0], [0,0,2]]))
# this invokes the __add__ method for numpy
# difference
R = SO3()
a = R - R
self.assertNotIsInstance(a, SO3)
array_compare(a, np.zeros((3, 3)))
a = R - 1
self.assertNotIsInstance(a, SO3)
array_compare(a, np.array([[0, -1, -1], [-1, 0, -1], [-1, -1, 0]]))
# a = 1 - R
# self.assertNotIsInstance(a, SO3)
# array_compare(a, -np.array([ [0,-1,-1], [-1,0,-1], [-1,-1,0]]))
a = R - np.eye(3)
self.assertNotIsInstance(a, SO3)
array_compare(a, np.zeros((3, 3)))
# a = np.eye(3) - R
# self.assertNotIsInstance(a, SO3)
# array_compare(a, np.zeros((3,3)))
# multiply
R = SO3()
a = R * R
self.assertIsInstance(a, SO3)
array_compare(a, R)
a = R * 2
self.assertNotIsInstance(a, SO3)
array_compare(a, 2 * np.eye(3))
a = 2 * R
self.assertNotIsInstance(a, SO3)
array_compare(a, 2 * np.eye(3))
R = SO3()
R *= SO3.Rx(pi / 2)
self.assertIsInstance(R, SO3)
array_compare(R, rotx(pi / 2))
R = SO3()
R *= 2
self.assertNotIsInstance(R, SO3)
array_compare(R, 2 * np.eye(3))
array_compare(SO3.Rx(pi / 2) * SO3.Ry(pi / 2) * SO3.Rx(-pi / 2), SO3.Rz(pi / 2))
array_compare(SO3.Ry(pi / 2) * [1, 0, 0], np.c_[0, 0, -1].T)
# SO3 x vector
vx = np.r_[1, 0, 0]
vy = np.r_[0, 1, 0]
vz = np.r_[0, 0, 1]
def cv(v):
return np.c_[v]
nt.assert_equal(isinstance(SO3.Rx(pi / 2) * vx, np.ndarray), True)
print(vx)
print(SO3.Rx(pi / 2) * vx)
print(cv(vx))
array_compare(SO3.Rx(pi / 2) * vx, cv(vx))
array_compare(SO3.Rx(pi / 2) * vy, cv(vz))
array_compare(SO3.Rx(pi / 2) * vz, cv(-vy))
array_compare(SO3.Ry(pi / 2) * vx, cv(-vz))
array_compare(SO3.Ry(pi / 2) * vy, cv(vy))
array_compare(SO3.Ry(pi / 2) * vz, cv(vx))
array_compare(SO3.Rz(pi / 2) * vx, cv(vy))
array_compare(SO3.Rz(pi / 2) * vy, cv(-vx))
array_compare(SO3.Rz(pi / 2) * vz, cv(vz))
# divide
R = SO3.Ry(0.3)
a = R / R
self.assertIsInstance(a, SO3)
array_compare(a, np.eye(3))
a = R / 2
self.assertNotIsInstance(a, SO3)
array_compare(a, roty(0.3) / 2)
# power
R = SO3.Rx(pi / 2)
R = R**2
array_compare(R, SO3.Rx(pi))
R = SO3.Rx(pi / 2)
R **= 2
array_compare(R, SO3.Rx(pi))
R = SO3.Rx(pi / 4)
R = R ** (-2)
array_compare(R, SO3.Rx(-pi / 2))
R = SO3.Rx(pi / 4)
R **= -2
array_compare(R, SO3.Rx(-pi / 2))
def test_arith_vect(self):
rx = SO3.Rx(pi / 2)
ry = SO3.Ry(pi / 2)
rz = SO3.Rz(pi / 2)
u = SO3()
# multiply
R = SO3([rx, ry, rz])
a = R * rx
self.assertIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx * rx)
array_compare(a[1], ry * rx)
array_compare(a[2], rz * rx)
a = rx * R
self.assertIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx * rx)
array_compare(a[1], rx * ry)
array_compare(a[2], rx * rz)
a = R * R
self.assertIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx * rx)
array_compare(a[1], ry * ry)
array_compare(a[2], rz * rz)
a = R * 2
self.assertNotIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx * 2)
array_compare(a[1], ry * 2)
array_compare(a[2], rz * 2)
a = 2 * R
self.assertNotIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx * 2)
array_compare(a[1], ry * 2)
array_compare(a[2], rz * 2)
a = R
a *= rx
self.assertIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx * rx)
array_compare(a[1], ry * rx)
array_compare(a[2], rz * rx)
a = rx
a *= R
self.assertIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx * rx)
array_compare(a[1], rx * ry)
array_compare(a[2], rx * rz)
a = R
a *= R
self.assertIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx * rx)
array_compare(a[1], ry * ry)
array_compare(a[2], rz * rz)
a = R
a *= 2
self.assertNotIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx * 2)
array_compare(a[1], ry * 2)
array_compare(a[2], rz * 2)
# SO3 x vector
vx = np.r_[1, 0, 0]
vy = np.r_[0, 1, 0]
vz = np.r_[0, 0, 1]
a = R * vx
array_compare(a[:, 0], (rx * vx).flatten())
array_compare(a[:, 1], (ry * vx).flatten())
array_compare(a[:, 2], (rz * vx).flatten())
a = rx * np.vstack((vx, vy, vz)).T
array_compare(a[:, 0], (rx * vx).flatten())
array_compare(a[:, 1], (rx * vy).flatten())
array_compare(a[:, 2], (rx * vz).flatten())
# divide
R = SO3([rx, ry, rz])
a = R / rx
self.assertIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx / rx)
array_compare(a[1], ry / rx)
array_compare(a[2], rz / rx)
a = rx / R
self.assertIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx / rx)
array_compare(a[1], rx / ry)
array_compare(a[2], rx / rz)
a = R / R
self.assertIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], np.eye(3))
array_compare(a[1], np.eye(3))
array_compare(a[2], np.eye(3))
a = R / 2
self.assertNotIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx / 2)
array_compare(a[1], ry / 2)
array_compare(a[2], rz / 2)
a = R
a /= rx
self.assertIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx / rx)
array_compare(a[1], ry / rx)
array_compare(a[2], rz / rx)
a = rx
a /= R
self.assertIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx / rx)
array_compare(a[1], rx / ry)
array_compare(a[2], rx / rz)
a = R
a /= R
self.assertIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], np.eye(3))
array_compare(a[1], np.eye(3))
array_compare(a[2], np.eye(3))
a = R
a /= 2
self.assertNotIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx / 2)
array_compare(a[1], ry / 2)
array_compare(a[2], rz / 2)
# add
R = SO3([rx, ry, rz])
a = R + rx
self.assertNotIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx + rx)
array_compare(a[1], ry + rx)
array_compare(a[2], rz + rx)
a = rx + R
self.assertNotIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx + rx)
array_compare(a[1], rx + ry)
array_compare(a[2], rx + rz)
a = R + R
self.assertNotIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx + rx)
array_compare(a[1], ry + ry)
array_compare(a[2], rz + rz)
a = R + 1
self.assertNotIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx + 1)
array_compare(a[1], ry + 1)
array_compare(a[2], rz + 1)
# subtract
R = SO3([rx, ry, rz])
a = R - rx
self.assertNotIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx - rx)
array_compare(a[1], ry - rx)
array_compare(a[2], rz - rx)
a = rx - R
self.assertNotIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx - rx)
array_compare(a[1], rx - ry)
array_compare(a[2], rx - rz)
a = R - R
self.assertNotIsInstance(a, SO3)
nt.assert_equal(len(a), 3)
array_compare(a[0], rx - rx)
array_compare(a[1], ry - ry)
array_compare(a[2], rz - rz)
def test_functions(self):
# inv
# .T
# conversion to SE2
poseSE3 = SE3.Tx(3.3) * SE3.Rz(1.5)
poseSE2 = poseSE3.yaw_SE2()
nt.assert_almost_equal(poseSE3.R[0:2, 0:2], poseSE2.R[0:2, 0:2])
nt.assert_equal(poseSE3.x, poseSE2.x)
nt.assert_equal(poseSE3.y, poseSE2.y)
posesSE3 = SE3([poseSE3, poseSE3])
posesSE2 = posesSE3.yaw_SE2()
nt.assert_equal(len(posesSE2), 2)
def test_functions_vect(self):
# inv
# .T
pass
def test_functions_lie(self):
R = SO3.EulerVec([0.42, 0.73, -1.17])
# Check log and exponential map
nt.assert_equal(R, SO3.Exp(R.log()))
np.testing.assert_equal((R.inv() * R).log(), np.zeros([3, 3]))
# Check euler vector map
nt.assert_equal(R, SO3.EulerVec(R.eulervec()))
np.testing.assert_equal((R.inv() * R).eulervec(), np.zeros(3))
def test_rotatedvector(self):
v1 = [1, 2, 3]
R = SO3.Eul(0.3, 0.4, 0.5)
v2 = R * v1
Re = SO3.RotatedVector(v1, v2)
np.testing.assert_almost_equal(v2, Re * v1)
Re = SO3.RotatedVector(v1, v1)
np.testing.assert_almost_equal(Re, np.eye(3))
R = SO3() # identity matrix case
# Check log and exponential map
nt.assert_equal(R, SO3.Exp(R.log()))
np.testing.assert_equal((R.inv() * R).log(), np.zeros([3, 3]))
# Check euler vector map
nt.assert_equal(R, SO3.EulerVec(R.eulervec()))
np.testing.assert_equal((R.inv() * R).eulervec(), np.zeros(3))
def test_mean(self):
rpy = np.ones((100, 1)) @ np.c_[0.1, 0.2, 0.3]
R = SO3.RPY(rpy)
self.assertEqual(len(R), 100)
m = R.mean()
self.assertIsInstance(m, SO3)
array_compare(m, R[0])
# range of angles, mean should be the middle one, index=25
R = SO3.Rz(np.linspace(start=0.3, stop=0.7, num=51))
m = R.mean()
self.assertIsInstance(m, SO3)
array_compare(m, R[25])
# now add noise
rng = np.random.default_rng(0) # reproducible random numbers
rpy += rng.normal(scale=0.00001, size=(100, 3))
R = SO3.RPY(rpy)
m = R.mean()
array_compare(m, SO3.RPY(0.1, 0.2, 0.3))
# ============================== SE3 =====================================#
class TestSE3(unittest.TestCase):
@classmethod
def tearDownClass(cls):
plt.close("all")
def test_constructor(self):
# null constructor
R = SE3()
nt.assert_equal(len(R), 1)
array_compare(R, np.eye(4))
self.assertIsInstance(R, SE3)
# construct from matrix
R = SE3(trotx(0.2))
nt.assert_equal(len(R), 1)
array_compare(R, trotx(0.2))
self.assertIsInstance(R, SE3)
# construct from canonic rotation
R = SE3.Rx(0.2)
nt.assert_equal(len(R), 1)
array_compare(R, trotx(0.2))
self.assertIsInstance(R, SE3)
R = SE3.Ry(0.2)
nt.assert_equal(len(R), 1)
array_compare(R, troty(0.2))
self.assertIsInstance(R, SE3)
R = SE3.Rz(0.2)
nt.assert_equal(len(R), 1)
array_compare(R, trotz(0.2))
self.assertIsInstance(R, SE3)
# construct from canonic translation
R = SE3.Tx(0.2)
nt.assert_equal(len(R), 1)
array_compare(R, transl(0.2, 0, 0))
self.assertIsInstance(R, SE3)
R = SE3.Ty(0.2)
nt.assert_equal(len(R), 1)
array_compare(R, transl(0, 0.2, 0))
self.assertIsInstance(R, SE3)
R = SE3.Tz(0.2)
nt.assert_equal(len(R), 1)
array_compare(R, transl(0, 0, 0.2))
self.assertIsInstance(R, SE3)
# triple angle
R = SE3.Eul([0.1, 0.2, 0.3])
nt.assert_equal(len(R), 1)
array_compare(R, eul2tr([0.1, 0.2, 0.3]))
self.assertIsInstance(R, SE3)
R = SE3.Eul(np.r_[0.1, 0.2, 0.3])
nt.assert_equal(len(R), 1)
array_compare(R, eul2tr([0.1, 0.2, 0.3]))
self.assertIsInstance(R, SE3)
R = SE3.Eul([10, 20, 30], unit="deg")
nt.assert_equal(len(R), 1)
array_compare(R, eul2tr([10, 20, 30], unit="deg"))
self.assertIsInstance(R, SE3)
R = SE3.RPY([0.1, 0.2, 0.3])
nt.assert_equal(len(R), 1)
array_compare(R, rpy2tr([0.1, 0.2, 0.3]))
self.assertIsInstance(R, SE3)
R = SE3.RPY(np.r_[0.1, 0.2, 0.3])
nt.assert_equal(len(R), 1)
array_compare(R, rpy2tr([0.1, 0.2, 0.3]))
self.assertIsInstance(R, SE3)
R = SE3.RPY([10, 20, 30], unit="deg")
nt.assert_equal(len(R), 1)
array_compare(R, rpy2tr([10, 20, 30], unit="deg"))
self.assertIsInstance(R, SE3)
R = SE3.RPY([0.1, 0.2, 0.3], order="xyz")
nt.assert_equal(len(R), 1)
array_compare(R, rpy2tr([0.1, 0.2, 0.3], order="xyz"))
self.assertIsInstance(R, SE3)
# angvec
R = SE3.AngVec(0.2, [1, 0, 0])
nt.assert_equal(len(R), 1)
array_compare(R, trotx(0.2))
self.assertIsInstance(R, SE3)
R = SE3.AngVec(0.3, [0, 1, 0])
nt.assert_equal(len(R), 1)
array_compare(R, troty(0.3))
self.assertIsInstance(R, SE3)
# OA
R = SE3.OA([0, 1, 0], [0, 0, 1])
nt.assert_equal(len(R), 1)
array_compare(R, np.eye(4))
self.assertIsInstance(R, SE3)
np.random.seed(65)
# random
R = SE3.Rand()
nt.assert_equal(len(R), 1)
self.assertIsInstance(R, SE3)
# random
T = SE3.Rand()
R = T.R
t = T.t
T = SE3.Rt(R, t)
self.assertIsInstance(T, SE3)
self.assertEqual(T.A.shape, (4, 4))
nt.assert_equal(T.R, R)
nt.assert_equal(T.t, t)
nt.assert_equal(T.x, t[0])
nt.assert_equal(T.y, t[1])
nt.assert_equal(T.z, t[2])
TT = SE3([T, T, T])
desired_shape = (3,)
nt.assert_equal(TT.x.shape, desired_shape)
nt.assert_equal(TT.y.shape, desired_shape)
nt.assert_equal(TT.z.shape, desired_shape)
ones = np.ones(desired_shape)
nt.assert_equal(TT.x, ones * t[0])
nt.assert_equal(TT.y, ones * t[1])
nt.assert_equal(TT.z, ones * t[2])
# random constrained
T = SE3.Rand(theta_range=(0.1, 0.7))
self.assertIsInstance(T, SE3)
self.assertEqual(T.A.shape, (4, 4))
self.assertLessEqual(T.angvec()[0], 0.7)
self.assertGreaterEqual(T.angvec()[0], 0.1)
# copy constructor
R = SE3.Rx(pi / 2)
R2 = SE3(R)
R = SE3.Ry(pi / 2)
array_compare(R2, trotx(pi / 2))
# SO3
T = SE3(SO3())
nt.assert_equal(len(T), 1)
self.assertIsInstance(T, SE3)
nt.assert_equal(T.A, np.eye(4))
# SE2
T = SE3(SE2(1, 2, 0.4))
nt.assert_equal(len(T), 1)
self.assertIsInstance(T, SE3)
self.assertEqual(T.A.shape, (4, 4))
nt.assert_equal(T.t, [1, 2, 0])
# Bad number of arguments
with self.assertRaises(ValueError):
T = SE3(1.0, 0.0)
with self.assertRaises(TypeError):
T = SE3(1.0, 0.0, 0.0, 0.0)
def test_shape(self):
a = SE3()
self.assertEqual(a._A.shape, a.shape)
def test_listpowers(self):
R = SE3()
R1 = SE3.Rx(0.2)
R2 = SE3.Ry(0.3)
R.append(R1)
R.append(R2)
nt.assert_equal(len(R), 3)
self.assertIsInstance(R, SE3)
array_compare(R[0], np.eye(4))
array_compare(R[1], R1)
array_compare(R[2], R2)
R = SE3([trotx(0.1), trotx(0.2), trotx(0.3)])
nt.assert_equal(len(R), 3)
self.assertIsInstance(R, SE3)
array_compare(R[0], trotx(0.1))
array_compare(R[1], trotx(0.2))
array_compare(R[2], trotx(0.3))
R = SE3([SE3.Rx(0.1), SE3.Rx(0.2), SE3.Rx(0.3)])
nt.assert_equal(len(R), 3)
self.assertIsInstance(R, SE3)
array_compare(R[0], trotx(0.1))
array_compare(R[1], trotx(0.2))
array_compare(R[2], trotx(0.3))
def test_tests(self):
R = SE3()
self.assertEqual(R.isrot(), False)
self.assertEqual(R.isrot2(), False)
self.assertEqual(R.ishom(), True)
self.assertEqual(R.ishom2(), False)
def test_properties(self):
R = SE3()
self.assertEqual(R.isSO, False)
self.assertEqual(R.isSE, True)
array_compare(R.n, np.r_[1, 0, 0])
array_compare(R.n, np.r_[1, 0, 0])
array_compare(R.n, np.r_[1, 0, 0])
nt.assert_equal(R.N, 3)
nt.assert_equal(R.shape, (4, 4))
# Testing the CopyFrom function
mutable_array = np.eye(4)
pass_by_ref = SE3(mutable_array)
pass_by_val = SE3.CopyFrom(mutable_array)
mutable_array[0, 3] = 5.0
nt.assert_allclose(pass_by_val.data[0], np.eye(4))
nt.assert_allclose(pass_by_ref.data[0], mutable_array)
nt.assert_raises(
AssertionError, nt.assert_allclose, pass_by_val.data[0], pass_by_ref.data[0]
)
def test_arith(self):
T = SE3(1, 2, 3)
# sum