def testInitPose(self):
bsp = bsplines.BSplinePose(4,sm.RotationVector())
# Create two random transformations.
T_n_0 = bsp.curveValueToTransformation(numpy.random.random(6))
T_n_1 = bsp.curveValueToTransformation(numpy.random.random(6))
# Initialize the curve.
bsp.initPoseSpline(0.0,1.0,T_n_0, T_n_1)
# Check the values.
self.assertEqual(bsp.t_min(),0.0);
self.assertEqual(bsp.t_max(),1.0);
curve_T_n_0 = bsp.transformation(0.0);
self.assertMatricesEqual(T_n_0, curve_T_n_0, 1e-9,"T_n_0")
curve_T_n_1 = bsp.transformation(1.0);
self.assertMatricesEqual(T_n_1, curve_T_n_1, 1e-9,"T_n_1")
tend = 2.0
# Extend the segment.
T_n_25 = bsp.curveValueToTransformation(numpy.random.random(6))
bsp.addPoseSegment(tend, T_n_25);
# Check the values.
self.assertEqual(bsp.t_min(),0.0);
self.assertEqual(bsp.t_max(),tend);
curve_T_n_0 = bsp.transformation(0.0);
self.assertMatricesEqual(T_n_0, curve_T_n_0, 1e-6, "T_n_0")
curve_T_n_1 = bsp.transformation(1.0);
self.assertMatricesEqual(T_n_1, curve_T_n_1, 1e-4, "T_n_1")
curve_T_n_25 = bsp.transformation(tend);
self.assertMatricesEqual(T_n_25, curve_T_n_25, 1e-4, "T_n_25")
def getUpdatedSpline(self, poseSpline, knots, splineOrder):
"""Get a spline with the new knot sequence build upon the poses of the old spline"""
# linearly sample the old spline
times = np.linspace(poseSpline.t_min(), poseSpline.t_max(), len(knots))
splinePoses = np.zeros((6, len(knots)))
for i, time in enumerate(times):
splinePoses[:, i] = poseSpline.eval(time)
# guarantee that beginning and end times of the spline remain unchanged
oldKnots = poseSpline.knots()
i = 0
while oldKnots[i] < knots[0]:
i += 1
knots = np.insert(knots, 0, oldKnots[0:i])
i = -1
while oldKnots[i] > knots[-1]:
i -= 1
knots = np.append(knots, oldKnots[i:])
newPoseSpline = bsplines.BSplinePose(splineOrder,
poseSpline.rotation())
newPoseSpline.initPoseSplineSparseKnots(times, splinePoses,
np.array(knots), 1e-6)
return newPoseSpline
def __generateInitialSpline(self, splineOrder, timeOffsetPadding, numberOfKnots = None, framerate = None):
poseSpline = bsplines.BSplinePose(splineOrder, sm.RotationVector())
# Get the observation times.
times = np.array([observation.time().toSec() for observation in self.__observations ])
# get the pose values of the initial transformations at observation time
curve = np.matrix([ poseSpline.transformationToCurveValue( observation.T_t_c().T() ) for observation in self.__observations]).T
# make sure all values are well defined
if np.isnan(curve).any():
raise RuntimeError("Nans in curve values")
sys.exit(0)
# Add 2 seconds on either end to allow the spline to slide during optimization
times = np.hstack((times[0] - (timeOffsetPadding * 2.0), times, times[-1] + (timeOffsetPadding * 2.0)))
curve = np.hstack((curve[:,0], curve, curve[:,-1]))
self.__ensureContinuousRotationVectors(curve)
seconds = times[-1] - times[0]
# fixed number of knots
if (numberOfKnots is not None):
knots = numberOfKnots
# otherwise with framerate estimate
else:
knots = int(round(seconds * framerate/3))
print
print "Initializing a pose spline with %d knots (%f knots per second over %f seconds)" % ( knots, 100, seconds)
poseSpline.initPoseSplineSparse(times, curve, knots, 1e-4)
return poseSpline
def testCurveToTransformation(self):
rvs = (sm.RotationVector(), sm.EulerAnglesZYX(), sm.EulerRodriguez())
for r in rvs:
bsp = bsplines.BSplinePose(4,r)
# Build a random, valid transformation.
T1 = bsp.curveValueToTransformation(numpy.random.random(6))
p = bsp.transformationToCurveValue(T1)
T2 = bsp.curveValueToTransformation(p)
self.assertMatricesEqual(T1, T2, 1e-9,"Checking the invertiblity of the transformation to curve values:")
def testAngularVelocity(self):
bsp = bsplines.BSplinePose(4,sm.EulerAnglesZYX())
# Create two
e1 = numpy.array([0,0,0,0,0,0])
T_n_0 = bsp.curveValueToTransformation(e1)
e2 = numpy.array([0,0,0,math.pi*0.5,0,0])
T_n_1 = bsp.curveValueToTransformation(e2)
# Initialize the curve.
bsp.initPoseSpline(0.0,1.0,T_n_0, T_n_1)
def initPoseSplineFromCamera(self,
splineOrder=6,
poseKnotsPerSecond=100,
timeOffsetPadding=0.02):
T_c_b = self.T_extrinsic.T()
pose = bsplines.BSplinePose(splineOrder, sm.RotationVector())
# Get the checkerboard times.
times = np.array([
obs.time().toSec() + self.timeshiftCamToImuPrior
for obs in self.targetObservations
])
curve = np.matrix([
pose.transformationToCurveValue(np.dot(obs.T_t_c().T(), T_c_b))
for obs in self.targetObservations
]).T
if np.isnan(curve).any():
raise RuntimeError("Nans in curve values")
sys.exit(0)
# Add 2 seconds on either end to allow the spline to slide during optimization
times = np.hstack((times[0] - (timeOffsetPadding * 2.0), times,
times[-1] + (timeOffsetPadding * 2.0)))
curve = np.hstack((curve[:, 0], curve, curve[:, -1]))
# Make sure the rotation vector doesn't flip
for i in range(1, curve.shape[1]):
previousRotationVector = curve[3:6, i - 1]
r = curve[3:6, i]
angle = np.linalg.norm(r)
axis = r / angle
best_r = r
best_dist = np.linalg.norm(best_r - previousRotationVector)
for s in range(-3, 4):
aa = axis * (angle + math.pi * 2.0 * s)
dist = np.linalg.norm(aa - previousRotationVector)
if dist < best_dist:
best_r = aa
best_dist = dist
curve[3:6, i] = best_r
seconds = times[-1] - times[0]
knots = int(round(seconds * poseKnotsPerSecond))
print
print "Initializing a pose spline with %d knots (%f knots per second over %f seconds)" % (
knots, poseKnotsPerSecond, seconds)
pose.initPoseSplineSparse(times, curve, knots, 1e-4)
return pose
def testInversePose2(self):
rvs = (sm.RotationVector(), sm.EulerAnglesZYX(), sm.EulerRodriguez())
for r in rvs:
bsp = bsplines.BSplinePose(4,r)
# Create two random transformations.
T_n_0 = bsp.curveValueToTransformation(numpy.random.random(6))
T_n_1 = bsp.curveValueToTransformation(numpy.random.random(6))
# Initialize the curve.
bsp.initPoseSpline(0.0,1.0,T_n_0, T_n_1)
for t in numpy.arange(0.0,1.0,0.1):
T = bsp.transformation(t)
invT,J,C = bsp.inverseTransformationAndJacobian(t)
one = numpy.dot(T,invT)
self.assertMatricesEqual(one,numpy.eye(4),1e-14,"T * inv(T)")
def testAngularVelocityBodyFrameJacobian(self):
r = sm.EulerAnglesZYX();
for order in range(2,7):
bsp = bsplines.BSplinePose(order,r)
T_n_0 = bsp.curveValueToTransformation(numpy.random.random(6))
T_n_1 = bsp.curveValueToTransformation(numpy.random.random(6))
# Initialize the curve.
bsp.initPoseSpline(0.0,1.0,T_n_0, T_n_1)
for t in numpy.linspace(bsp.t_min(), bsp.t_max(), 4):
oJI = bsp.angularVelocityBodyFrameAndJacobian(t);
#print "TJI: %s" % (TJI)
je = nd.Jacobian(lambda c: bsp.setLocalCoefficientVector(t,c) or bsp.angularVelocityBodyFrame(t))
estJ = je(bsp.localCoefficientVector(t))
J = oJI[1]
self.assertMatricesEqual(J, estJ, 1e-9,"omega Jacobian")
def __init__(self,
order=4,
target_point=[0., 0, 0],
ctrl_point_num=10,
time=10.,
random_range=[[0, 0, 0.], [1., 1., 1.]]):
self.target_point = np.array(target_point)
self.bsp = bsplines.BSplinePose(4, sm.RotationVector())
self.ctrl_point_num = ctrl_point_num
random_range = np.array(random_range) + self.target_point
self.curve = self.TargetOrientedPose(ctrl_point_num, random_range)
self.time = time
times = np.linspace(0, time, ctrl_point_num)
curve_in = np.array(self.curve)
curve_in[3:] *= -1
self.bsp.initPoseSplineSparse(times, curve_in,
int(ctrl_point_num * 3.), 1e-5)
def testInverseOrientationJacobian(self):
rvs = (sm.RotationVector(), sm.EulerAnglesZYX(), sm.EulerRodriguez())
for r in rvs:
for order in range(2,7):
bsp = bsplines.BSplinePose(order,r)
T_n_0 = bsp.curveValueToTransformation(numpy.random.random(6))
T_n_1 = bsp.curveValueToTransformation(numpy.random.random(6))
# Initialize the curve.
bsp.initPoseSpline(0.0,1.0,T_n_0, T_n_1)
for t in numpy.linspace(bsp.t_min(), bsp.t_max(), 4):
# Create a random homogeneous vector
v = numpy.random.random(3)
CJI = bsp.inverseOrientationAndJacobian(t);
#print "TJI: %s" % (TJI)
je = nd.Jacobian(lambda c: bsp.setLocalCoefficientVector(t,c) or numpy.dot(bsp.inverseOrientation(t), v))
estJ = je(bsp.localCoefficientVector(t))
JT = CJI[1]
J = numpy.dot(sm.crossMx(numpy.dot(CJI[0],v)), JT)
self.assertMatricesEqual(J, estJ, 1e-8,"C_n_0")
import sm
import bsplines
import numpy as np
from scipy.spatial.transform import Rotation as R
if __name__ == "__main__":
bsp = bsplines.BSplinePose(4, sm.RotationVector())
curve = np.array([[0.1, 0.2, 0.3, 0.4, 0.5, 0.6], [0.1, 0, 0, 0, 0, 0.1],
[0.2, 0, 0, 0, 0, 0.1]]).T
bsp.initPoseSplineSparse(np.array([0., 1, 2]), curve, 5, 1e-5)
r0 = R.from_dcm(bsp.orientation(0.0)).as_rotvec()
r0_ = R.from_dcm(bsp.curveValueToTransformation(
curve.T[0])[:3, :3]).as_rotvec()
t0_ = bsp.curveValueToTransformation(curve.T[0])[:3, 3]
print(r0)
print(t0_)
