def test_getOrientationErrorAndGetTargetOrientation(self): # Basic spin case pos = Vector(0,0,0) vel = Vector(0,0,0) orientation = Quaternion(axisOfRotation=Vector(0,0,1), angle=0.12) angularVelocity = AngularVelocity(axisOfRotation=Vector(0,0,1), angularVel=0) rigidBodyState = RigidBodyState(pos, vel, orientation, angularVelocity) # targetDir = Vector(0,0,1) # targetSpin = 0 targetState = [ 0,0,1,0 ] ExpectedResult = ( 0, 0, -0.12 ) targetOrientation = self.stabilizer.getTargetOrientation(rigidBodyState, targetState, 0) result = self.momentController._getOrientationError(rigidBodyState, targetOrientation) for i in range(3): self.assertAlmostEqual(result[i], ExpectedResult[i]) # Longitudinal 1 orientation = Quaternion(axisOfRotation=Vector(0,1,0), angle=0.12) rigidBodyState = RigidBodyState(pos, vel, orientation, angularVelocity) # targetDir = Vector(0,0,1) # targetSpin = 0 targetState = [ 0,0,1,0 ] ExpectedResult = ( 0, -0.12, 0 ) targetOrientation = self.stabilizer.getTargetOrientation(rigidBodyState, targetState, 0) result = self.momentController._getOrientationError(rigidBodyState, targetOrientation) for i in range(3): self.assertAlmostEqual(result[i], ExpectedResult[i]) # Longitudinal 2 orientation = Quaternion(axisOfRotation=Vector(1,0,0), angle=0.12) rigidBodyState = RigidBodyState(pos, vel, orientation, angularVelocity) # targetDir = Vector(0,0,1) # targetSpin = 0 targetState = [ 0,0,1,0 ] ExpectedResult = ( -0.12, 0, 0 ) targetOrientation = self.stabilizer.getTargetOrientation(rigidBodyState, targetState, 0) result = self.momentController._getOrientationError(rigidBodyState, targetOrientation) for i in range(3): self.assertAlmostEqual(result[i], ExpectedResult[i]) # Pre-rotated longitudinal rot1 = Quaternion(axisOfRotation=Vector(1,0,0), angle=0.12) rot2 = Quaternion(axisOfRotation=Vector(0,0,1), angle=pi/4) orientation = rot2*rot1 rigidBodyState = RigidBodyState(pos, vel, orientation, angularVelocity) # targetDir = Vector(0,0,1) # targetSpin = 0 targetState = [ 0,0,1,0 ] ExpectedResult = orientation.conjugate().toRotationVector() targetOrientation = self.stabilizer.getTargetOrientation(rigidBodyState, targetState, 0) result = self.momentController._getOrientationError(rigidBodyState, targetOrientation) for i in range(3): self.assertAlmostEqual(result[i], ExpectedResult[i]) # Post-rotated longitudinal 2 orientation = Quaternion(axisOfRotation=Vector(1,1,0), angle=0.12) rigidBodyState = RigidBodyState(pos, vel, orientation, angularVelocity) # targetDir = Vector(0,0,1) # targetSpin = 0 targetState = [ 0,0,1,0 ] ExpectedResult = orientation.conjugate().toRotationVector() #Zerror here assumed correct - not calculated analytically targetOrientation = self.stabilizer.getTargetOrientation(rigidBodyState, targetState, 0) result = self.momentController._getOrientationError(rigidBodyState, targetOrientation) for i in range(3): self.assertAlmostEqual(result[i], ExpectedResult[i])
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)