class TestQuaternion(unittest.TestCase):
def setUp(self):
self.q1 = Quaternion(components=[1.0, 2.0, 3.0, 4.0])
self.q2 = Quaternion(components=[-1.0, -2.0, -3.0, -4.0])
self.q3 = Quaternion(axisOfRotation=Vector(1.0, 0.0, 0.0),
angle=pi / 2)
self.q4 = Quaternion(components=[1.0, 0.0, 1.0, 0.0])
self.q5 = Quaternion(components=[1.0, 0.5, 0.5, 0.75])
self.rotQ = Quaternion(axisOfRotation=Vector(2.0, -3.0, 5.0), angle=2)
self.rotQ2 = Quaternion(axisOfRotation=Vector(0.0, 0.0, 1.0),
angle=pi / 2)
self.rotQ3 = Quaternion(axisOfRotation=Vector(0.0, 1.0, 0.0),
angle=pi / 2)
self.rotQ4 = Quaternion(axisOfRotation=Vector(1.0, 0.0, 0.0),
angle=pi / 2)
self.rotQ5 = Quaternion(axisOfRotation=Vector(0.0, 0.0, 1.0), angle=pi)
self.rotQ6 = Quaternion(axisOfRotation=Vector(0.0, 1.0, 0.0), angle=pi)
self.rotQ7 = Quaternion(axisOfRotation=Vector(1.0, 0.0, 0.0), angle=pi)
#Test same method as print statement
def test_str(self):
self.assertEqual(str(self.q1), "<1.0, 2.0, 3.0, 4.0>")
def test_scaleRotation(self):
scaledQuat = self.q3.scaleRotation(0.5)
definedQuat = Quaternion(axisOfRotation=Vector(1, 0, 0), angle=pi / 4)
assertQuaternionsAlmostEqual(self, scaledQuat, definedQuat, 14)
def test_slerp(self):
testQ = self.q1.slerp(self.q3, 0)
assertQuaternionsAlmostEqual(self, (self.q1 * testQ).normalize(),
self.q1.normalize())
testQ = self.q1.slerp(self.q3, 1)
testQ = (self.q1 * testQ).normalize()
assertQuaternionsAlmostEqual(self, testQ, self.q3.normalize())
testQ = self.rotQ2.slerp(self.rotQ5, 0.5)
testQ = (self.rotQ2 * testQ).normalize()
assertQuaternionsAlmostEqual(
self, testQ,
Quaternion(axisOfRotation=Vector(0, 0, 1), angle=3 * pi / 4))
#Test using the quaternion to rotate a vector
#TODO: verify with matlab or other example
def test_rotate(self):
assertVectorsAlmostEqual(self, self.rotQ2.rotate(Vector(1, 1, 1)),
Vector(-1, 1, 1))
assertVectorsAlmostEqual(self, self.rotQ3.rotate(Vector(1, 1, 1)),
Vector(1, 1, -1))
assertVectorsAlmostEqual(self, self.rotQ4.rotate(Vector(1, 1, 1)),
Vector(1, -1, 1))
assertVectorsAlmostEqual(self, self.rotQ5.rotate(Vector(1, 1, 1)),
Vector(-1, -1, 1))
assertVectorsAlmostEqual(self, self.rotQ6.rotate(Vector(1, 1, 1)),
Vector(-1, 1, -1))
assertVectorsAlmostEqual(self, self.rotQ7.rotate(Vector(1, 1, 1)),
Vector(1, -1, -1))
def test_constructor(self):
assertQuaternionsAlmostEqual(
self, self.q1, Quaternion(components=[1.0, 2.0, 3.0, 4.0]))
expectedQ3 = Quaternion(components=[sin(pi / 4), sin(pi / 4), 0, 0])
assertQuaternionsAlmostEqual(self, self.q3, expectedQ3)
#Test ==
def test_equal(self):
self.assertEqual(self.q1, Quaternion(components=[1, 2, 3, 4]))
self.assertNotEqual(self.q1, Quaternion(components=[1, 2, 3, 5]))
#Check that can't compare Quaterion to a scalar
with self.assertRaises(AttributeError):
self.q1 == 33
#Test +
def test_add(self):
self.assertEqual(self.q1 + self.q2,
Quaternion(components=[0, 0, 0, 0]))
self.assertEqual(self.q1 + self.q1,
Quaternion(components=[2, 4, 6, 8]))
#Check that adding a scalar and quaternion is not allowed
with self.assertRaises(AttributeError):
self.q1 + 33
#Test -
def test_subtract(self):
self.assertEqual(self.q1 - self.q1,
Quaternion(components=[0, 0, 0, 0]))
self.assertEqual(self.q1 - self.q2,
Quaternion(components=[2, 4, 6, 8]))
#Check that adding a scalar and quaternion is not allowed
with self.assertRaises(AttributeError):
self.q1 - 33
#Test * scalar
def test_scalarMult(self):
self.assertEqual(self.q1 * 2, Quaternion(components=[2, 4, 6, 8]))
#Test * quaternion
def test_quaternionMult(self):
self.assertEqual(self.q4 * self.q5,
Quaternion(components=[0.5, 1.25, 1.5, 0.25]))
self.assertEqual(self.q4 * self.q4,
Quaternion(components=[0, 0, 2, 0]))
# Check that order of rotations is left to right
rot1 = Quaternion(axisOfRotation=Vector(0, 0, 1), angle=(pi / 2))
rot2 = Quaternion(axisOfRotation=Vector(1, 0, 0), angle=(pi / 2))
totalRotation = rot1 * rot2
initZAxis = Vector(0, 0, 1)
finalZAxis = totalRotation.rotate(initZAxis)
initXAxis = Vector(1, 0, 0)
finalXAxis = totalRotation.rotate(initXAxis)
assertVectorsAlmostEqual(self, finalXAxis, Vector(0, 1, 0))
assertVectorsAlmostEqual(self, finalZAxis, Vector(1, 0, 0))
def test_scalarDivision(self):
self.assertEqual(self.q1.__truediv__(2),
Quaternion(components=[0.5, 1, 1.5, 2]))
def test_quaternionDivision(self):
testQ = self.q4.__truediv__(self.q5)
expectedQ = Quaternion(components=[0.7273, 0.1212, 0.2424, -0.6061])
assertQuaternionsAlmostEqual(self, testQ, expectedQ, 3)
def test_norm(self):
self.assertEqual(self.q1.norm(), sqrt(30))
def test_normalize(self):
testQ = self.q4.normalize()
expectedQ = Quaternion(components=[0.7071, 0.0, 0.7071, 0.0])
assertQuaternionsAlmostEqual(self, testQ, expectedQ, 3)
def test_conjugate(self):
assertQuaternionsAlmostEqual(self, self.q4.conjugate(),
Quaternion(components=[1, 0, -1, 0]))
def test_inverse(self):
assertQuaternionsAlmostEqual(
self, self.q4.inverse(),
Quaternion(components=[0.5, 0.0, -0.5, 0.0]))
def test_rotationAxis(self):
axisResult = self.rotQ.rotationAxis()
axis = Vector(2, -3, 5).normalize()
self.assertAlmostEqual(axisResult.X, axis.X)
self.assertAlmostEqual(axisResult.Y, axis.Y)
self.assertAlmostEqual(axisResult.Z, axis.Z)
def test_rotationAngle(self):
self.assertAlmostEqual(self.rotQ.rotationAngle(), 2)
def test_plot(self):
self.q1.plotRotation(showPlot=False)
class RigidBodyState():
""" Class created to be able to treat rigidBody states like scalars when integrating the movement of a rigid body
Pos/Vel are expected to be Vectors - Defined with reference to the global frame
Orientation is expected to be a Quaternion - Defines the rotation from the global inertial reference frame to the rocket's local frame
(Orientation of the rocket in the global frame)
Angular Velocity is expected to be an Angular Velocity - Defined with reference to the local frame
Adding rigidBodyStates adds the vectors and multiplies the quaternions (which adds the rotations they represent)
Multiplying an rigidBodyState by a scalar scales the vectors and rotation defined by the quaternions
0.5 * = half the vector length, half the rotation size, directions the same
No other operations are defined
"""
def __init__(self,
position=None,
velocity=None,
orientation=None,
angularVelocity=None):
self.position = Vector(0, 0, 0) if (position is None) else position
self.velocity = Vector(0, 0, 0) if (velocity is None) else velocity
self.orientation = Quaternion(
1, 0, 0, 0) if (orientation is None) else orientation
self.angularVelocity = AngularVelocity(
0, 0, 0) if (angularVelocity is None) else angularVelocity
def __add__(self, rigidBodyState2):
''' Used in: initVal {+} (timeStep * slope) '''
newPos = self.position + rigidBodyState2.position
newVel = self.velocity + rigidBodyState2.velocity
newAngVel = self.angularVelocity + rigidBodyState2.angularVelocity
newOrientation = rigidBodyState2.orientation * self.orientation.normalize(
)
return RigidBodyState(newPos, newVel, newOrientation.normalize(),
newAngVel)
def __mul__(self, timeStep):
'''
Used in: initVal + timeStep {*} slope
Expected to always be multiplied by a scalar
'''
timeStep = float(timeStep)
newPos = self.position * timeStep
newVel = self.velocity * timeStep
newAngVel = self.angularVelocity * timeStep
newOrientation = self.orientation.scaleRotation(timeStep)
return RigidBodyState(newPos, newVel, newOrientation, newAngVel)
def __abs__(self):
''' Used to quantify the difference between two RigidBodyStates as a scalar value during error estimation in adaptive time stepping methods '''
positionMag = self.position.length() + self.velocity.length()
orientationMag = abs(
self.orientation.rotationAngle()) + self.angularVelocity.angVel()
return orientationMag * 100 + positionMag
def __eq__(self, iRBS2):
try:
properties = [
self.position, self.velocity, self.orientation,
self.angularVelocity
]
otherProperties = [
iRBS2.position, iRBS2.velocity, iRBS2.orientation,
iRBS2.angularVelocity
]
return all([x == y for (x, y) in zip(properties, otherProperties)])
except AttributeError:
return False
def __str__(self):
''' Called by print function '''
return " {:>10.3f} {:>10.4f} {:>11.7f} {:>9.4f}".format(
self.position, self.velocity, self.orientation,
self.angularVelocity)
### Wrapper/Thin functions ###
def __neg__(self):
return RigidBodyState(self.position * -1, self.velocity * -1,
self.orientation.conjugate(),
self.angularVelocity * -1)