def test_left_jacobian_batch():
xis = torch.Tensor([[1, 2, 3, 4, 5, 6],
[0, 0, 0, 0, 0, 0]])
assert utils.allclose(
SE3.left_jacobian(xis).bmm(SE3.inv_left_jacobian(xis)),
torch.eye(6).unsqueeze_(dim=0).expand(2, 6, 6)
)
def calculate_log_se3_delta(predicted_position, target_position):
predicted_matrix = predicted_position.matrix
target_matrix = target_position.matrix
delta_matrix = torch.bmm(inverse_pose_matrix(predicted_matrix),
target_matrix)
delta_log = SE3.log(
SE3.from_matrix(delta_matrix, normalize=False, check=False))
if delta_log.dim() < 2:
delta_log = delta_log[None]
return delta_log
def test_from_matrix():
T_good = SE3.from_matrix(torch.eye(4))
assert isinstance(T_good, SE3) \
and isinstance(T_good.rot, SO3) \
and T_good.trans.shape == (3,) \
and SE3.is_valid_matrix(T_good.as_matrix()).all()
T_bad = SE3.from_matrix(torch.eye(4).add_(1e-3), normalize=True)
assert isinstance(T_bad, SE3) \
and isinstance(T_bad.rot, SO3) \
and T_bad.trans.shape == (3,) \
and SE3.is_valid_matrix(T_bad.as_matrix()).all()
def test_odot_batch():
p1 = torch.Tensor([1, 2, 3])
p2 = torch.Tensor([4, 5, 6])
ps = torch.cat([p1.unsqueeze(dim=0),
p2.unsqueeze(dim=0)], dim=0)
odot1 = SE3.odot(p1)
odot2 = SE3.odot(p2)
odots = SE3.odot(ps)
assert (odot1 == odots[0, :, :]).all()
assert (odot2 == odots[1, :, :]).all()
def test_from_matrix_batch():
T_good = SE3.from_matrix(torch.eye(4).repeat(5, 1, 1))
assert isinstance(T_good, SE3) \
and T_good.trans.shape == (5, 3) \
and SE3.is_valid_matrix(T_good.as_matrix()).all()
T_bad = T_good.as_matrix()
T_bad[3, :, :].add_(0.1)
T_bad = SE3.from_matrix(T_bad, normalize=True)
assert isinstance(T_bad, SE3) \
and T_bad.trans.shape == (5, 3) \
and SE3.is_valid_matrix(T_bad.as_matrix()).all()
def test_left_jacobian():
xi1 = torch.Tensor([1, 2, 3, 4, 5, 6])
assert utils.allclose(
torch.mm(SE3.left_jacobian(xi1), SE3.inv_left_jacobian(xi1)),
torch.eye(6)
)
xi2 = torch.Tensor([0, 0, 0, 0, 0, 0])
assert utils.allclose(
torch.mm(SE3.left_jacobian(xi2), SE3.inv_left_jacobian(xi2)),
torch.eye(6)
)
def test_odot():
p1 = torch.Tensor([1, 2, 3])
p2 = torch.Tensor([1, 2, 3, 1])
p3 = torch.Tensor([1, 2, 3, 0])
odot12 = torch.cat([SE3.odot(p1), torch.zeros(6).unsqueeze_(dim=0)], dim=0)
odot13 = torch.cat([SE3.odot(p1, directional=True),
torch.zeros(6).unsqueeze_(dim=0)], dim=0)
odot2 = SE3.odot(p2)
odot3 = SE3.odot(p3)
assert (odot12 == odot2).all()
assert (odot13 == odot3).all()
def compute_mate(self, t, x, chi, dataset_name):
chi_est = torch.zeros(x.shape[0], 4, 4)
chi_est[:, :3, :3] = SO3.from_rpy(x[:, 3:6]).as_matrix()
chi_est[:, :3, 3] = x[:, :3]
chi_est[:, 3, 3] = 1
chi_est = SE3.from_matrix(chi_est)
chi = SE3.from_matrix(chi)
error = (chi.inv().dot(chi_est)).log()
mate_translation = error[:, :3].abs().mean()
mate_rotation = error[:, 3:].abs().mean()
return mate_translation, mate_rotation
def log_prob(self, value_matrix, mean_matrix, logvar):
if logvar.dim() < 2:
logvar = logvar[None].expand(mean_matrix.shape[0], logvar.shape[0])
delta_matrix = torch.bmm(inverse_pose_matrix(mean_matrix), value_matrix)
delta_log = SE3.log(SE3.from_matrix(delta_matrix, normalize=False, check=False))
if delta_log.dim() < 2:
delta_log = delta_log[None]
inverse_sigma_matrix = self.get_inverse_sigma_matrix(logvar).expand(delta_log.shape[0], delta_log.shape[1],
delta_log.shape[1])
delta_log = torch.bmm(inverse_sigma_matrix, delta_log[:, :, None])[:, :, 0]
log_determinant = self.get_logvar_determinant(logvar)
log_prob = torch.sum(delta_log ** 2 / 2., dim=1) + 0.5 * log_determinant
return torch.mean(log_prob)
def test_normalize_batch():
T = SE3.exp(0.1 * torch.Tensor([[1, 2, 3, 4, 5, 6],
[7, 8, 9, 10, 11, 12],
[13, 14, 15, 16, 17, 18]]))
assert SE3.is_valid_matrix(T.as_matrix()).all()
T.rot.mat.add_(0.1)
assert (SE3.is_valid_matrix(T.as_matrix())
== torch.ByteTensor([0, 0, 0])).all()
T.normalize(inds=[0, 2])
assert (SE3.is_valid_matrix(T.as_matrix())
== torch.ByteTensor([1, 0, 1])).all()
T.normalize()
assert SE3.is_valid_matrix(T.as_matrix()).all()
def test_perturb_batch():
T = SE3.exp(0.1 * torch.Tensor([[1, 2, 3, 4, 5, 6],
[7, 8, 9, 10, 11, 12]]))
T_copy1 = copy.deepcopy(T)
T_copy2 = copy.deepcopy(T)
xi = torch.Tensor([0.3, 0.2, 0.1, -0.1, -0.2, -0.3])
T_copy1.perturb(xi)
assert utils.allclose(T_copy1.as_matrix(),
(SE3.exp(xi).dot(T)).as_matrix())
xis = torch.Tensor([[0.3, 0.2, 0.1, -0.1, -0.2, -0.3],
[-0.3, -0.2, -0.1, 0.1, 0.2, 0.3]])
T_copy2.perturb(xis)
assert utils.allclose(T_copy2.as_matrix(),
(SE3.exp(xis).dot(T)).as_matrix())
def correct(self, x, u_odo, u_fog, compute_G=False, full_cov=False):
u_odo_fog = torch.cat((u_odo, u_fog), 1).unsqueeze(0)
u_odo_fog.requires_grad = True
Xnew = self.normalize(u_odo_fog)
# take mean to speed up correction
y_cor_nor, _ = self.gp_f.forward(Xnew, full_cov)
# # sample corrections and take mean
# N = 100
# mean, cov = self.gp_f.forward(Xnew, full_cov=True)
# y_cor_nor = torch.zeros(6)
# dist = torch.distributions.MultivariateNormal(loc=mean, cov)
# for i in range(N):
# y_cor_nor += 1/N * dist.sample()
y_cor = self.unnormalize(y_cor_nor.t(), var="y_odo_fog").squeeze()
G_cor = self.correct_cov(u_odo_fog, y_cor, compute_G)
u_odo_fog.requires_grad = False
y_cor = y_cor.detach()
y_cor[[3, 4]] = 0 # pitch and roll corrections are set to 0
G_cor[[3, 4], :] = 0
Rot = SO3.from_rpy(x[3:6]).as_matrix()
# correct state
dRot_cor = SO3.exp(y_cor[3:]).as_matrix()
x[:3] = x[:3] + Rot.mv(SE3.exp(y_cor).as_matrix()[:3, 3])
x[3:6] = SO3.from_matrix(Rot.mm(dRot_cor)).to_rpy()
return x, G_cor
def mean_position(self, predicted_position):
batch_size = predicted_position.shape[0]
predicted_position = predicted_position.reshape(batch_size * self._head_count,
predicted_position.shape[1] // self._head_count)
logvar = predicted_position[:, 7:]
mean_matrix = self.mean_matrix(predicted_position)
log_mean = SE3.log(SE3.from_matrix(mean_matrix, normalize=False, check=False))
if log_mean.dim() < 2:
log_mean = log_mean[None]
inverse_sigma_matrix = self.get_inverse_sigma_matrix(logvar)
inverse_covariance_matrix = torch.bmm(inverse_sigma_matrix.transpose(1, 2), inverse_sigma_matrix)
result_inverse_covariance_matrix = torch.sum(inverse_covariance_matrix.reshape(-1, self._head_count, 6, 6),
dim=1)
result_covariance_matrix = torch.inverse(result_inverse_covariance_matrix)
factors = torch.bmm(result_covariance_matrix.repeat_interleave(self._head_count, 0), inverse_covariance_matrix)
scaled_log_mean = torch.bmm(factors, log_mean[:, :, None])[:, :, 0]
result_log_mean = torch.sum(scaled_log_mean.reshape(-1, self._head_count, 6), dim=1)
mean_matrix = SE3.exp(result_log_mean).as_matrix()
if mean_matrix.dim() < 3:
mean_matrix = mean_matrix[None]
return mean_matrix
def test_dot():
T = torch.Tensor([[0, 0, -1, 0.1],
[0, 1, 0, 0.5],
[1, 0, 0, -0.5],
[0, 0, 0, 1]])
T_SE3 = SE3.from_matrix(T)
pt = torch.Tensor([1, 2, 3])
pth = torch.Tensor([1, 2, 3, 1])
TT = torch.mm(T, T)
TT_SE3 = T_SE3.dot(T_SE3).as_matrix()
assert utils.allclose(TT_SE3, TT)
Tpt = torch.matmul(T[0:3, 0:3], pt) + T[0:3, 3]
Tpt_SE3 = T_SE3.dot(pt)
assert utils.allclose(Tpt_SE3, Tpt)
Tpth = torch.matmul(T, pth)
Tpth_SE3 = T_SE3.dot(pth)
assert utils.allclose(Tpth_SE3, Tpth) and \
utils.allclose(Tpth_SE3[0:3], Tpt)
def test_curlywedge_curlyvee_batch():
xis = torch.Tensor([[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12]])
Psis = SE3.curlywedge(xis)
assert (xis == SE3.curlyvee(Psis)).all()
def test_dot_batch():
T1 = torch.Tensor([[0, 0, -1, 0.1],
[0, 1, 0, 0.5],
[1, 0, 0, -0.5],
[0, 0, 0, 1]]).expand(5, 4, 4)
T2 = torch.Tensor([[0, 0, -1, 0.1],
[0, 1, 0, 0.5],
[1, 0, 0, -0.5],
[0, 0, 0, 1]])
T1_SE3 = SE3.from_matrix(T1)
T2_SE3 = SE3.from_matrix(T2)
pt1 = torch.Tensor([1, 2, 3])
pt2 = torch.Tensor([4, 5, 6])
pt3 = torch.Tensor([7, 8, 9])
pts = torch.cat([pt1.unsqueeze(dim=0),
pt2.unsqueeze(dim=0),
pt3.unsqueeze(dim=0)], dim=0) # 3x3
ptsbatch = pts.unsqueeze(dim=0).expand(5, 3, 3)
pt1h = torch.Tensor([1, 2, 3, 1])
pt2h = torch.Tensor([4, 5, 6, 1])
pt3h = torch.Tensor([7, 8, 9, 1])
ptsh = torch.cat([pt1h.unsqueeze(dim=0),
pt2h.unsqueeze(dim=0),
pt3h.unsqueeze(dim=0)], dim=0) # 3x4
ptshbatch = ptsh.unsqueeze(dim=0).expand(5, 3, 4)
T1T1 = torch.bmm(T1, T1)
T1T1_SE3 = T1_SE3.dot(T1_SE3).as_matrix()
assert T1T1_SE3.shape == T1.shape and utils.allclose(T1T1_SE3, T1T1)
T1T2 = torch.matmul(T1, T2)
T1T2_SE3 = T1_SE3.dot(T2_SE3).as_matrix()
assert T1T2_SE3.shape == T1.shape and utils.allclose(T1T2_SE3, T1T2)
T1pt1 = torch.matmul(T1[:, 0:3, 0:3], pt1) + T1[:, 0:3, 3]
T1pt1_SE3 = T1_SE3.dot(pt1)
assert T1pt1_SE3.shape == (T1.shape[0], pt1.shape[0]) \
and utils.allclose(T1pt1_SE3, T1pt1)
T1pt1h = torch.matmul(T1, pt1h)
T1pt1h_SE3 = T1_SE3.dot(pt1h)
assert T1pt1h_SE3.shape == (T1.shape[0], pt1h.shape[0]) \
and utils.allclose(T1pt1h_SE3, T1pt1h) \
and utils.allclose(T1pt1h_SE3[:, 0:3], T1pt1_SE3)
T1pt2 = torch.matmul(T1[:, 0:3, 0:3], pt2) + T1[:, 0:3, 3]
T1pt2_SE3 = T1_SE3.dot(pt2)
assert T1pt2_SE3.shape == (T1.shape[0], pt2.shape[0]) \
and utils.allclose(T1pt2_SE3, T1pt2)
T1pt2h = torch.matmul(T1, pt2h)
T1pt2h_SE3 = T1_SE3.dot(pt2h)
assert T1pt2h_SE3.shape == (T1.shape[0], pt2h.shape[0]) \
and utils.allclose(T1pt2h_SE3, T1pt2h) \
and utils.allclose(T1pt2h_SE3[:, 0:3], T1pt2_SE3)
T1pts = torch.bmm(T1[:, 0:3, 0:3],
pts.unsqueeze(dim=0).expand(
T1.shape[0],
pts.shape[0],
pts.shape[1]).transpose(2, 1)).transpose(2, 1) + \
T1[:, 0:3, 3].unsqueeze(dim=1).expand(
T1.shape[0], pts.shape[0], pts.shape[1])
T1pts_SE3 = T1_SE3.dot(pts)
assert T1pts_SE3.shape == (T1.shape[0], pts.shape[0], pts.shape[1]) \
and utils.allclose(T1pts_SE3, T1pts) \
and utils.allclose(T1pt1, T1pts[:, 0, :]) \
and utils.allclose(T1pt2, T1pts[:, 1, :])
T1ptsh = torch.bmm(T1, ptsh.unsqueeze(dim=0).expand(
T1.shape[0],
ptsh.shape[0],
ptsh.shape[1]).transpose(2, 1)).transpose(2, 1)
T1ptsh_SE3 = T1_SE3.dot(ptsh)
assert T1ptsh_SE3.shape == (T1.shape[0], ptsh.shape[0], ptsh.shape[1]) \
and utils.allclose(T1ptsh_SE3, T1ptsh) \
and utils.allclose(T1pt1h, T1ptsh[:, 0, :]) \
and utils.allclose(T1pt2h, T1ptsh[:, 1, :]) \
and utils.allclose(T1ptsh_SE3[:, :, 0:3], T1pts_SE3)
T1ptsbatch = torch.bmm(T1[:, 0:3, 0:3],
ptsbatch.transpose(2, 1)).transpose(2, 1) + \
T1[:, 0:3, 3].unsqueeze(dim=1).expand(ptsbatch.shape)
T1ptsbatch_SE3 = T1_SE3.dot(ptsbatch)
assert T1ptsbatch_SE3.shape == ptsbatch.shape \
and utils.allclose(T1ptsbatch_SE3, T1ptsbatch) \
and utils.allclose(T1pt1, T1ptsbatch[:, 0, :]) \
and utils.allclose(T1pt2, T1ptsbatch[:, 1, :])
T1ptshbatch = torch.bmm(T1, ptshbatch.transpose(2, 1)).transpose(2, 1)
T1ptshbatch_SE3 = T1_SE3.dot(ptshbatch)
assert T1ptshbatch_SE3.shape == ptshbatch.shape \
and utils.allclose(T1ptshbatch_SE3, T1ptshbatch) \
and utils.allclose(T1pt1h, T1ptshbatch[:, 0, :]) \
and utils.allclose(T1pt2h, T1ptshbatch[:, 1, :]) \
and utils.allclose(T1ptshbatch_SE3[:, :, 0:3], T1ptsbatch_SE3)
T2ptsbatch = torch.matmul(T2[0:3, 0:3],
ptsbatch.transpose(2, 1)).transpose(2, 1) + \
T1[:, 0:3, 3].unsqueeze(dim=1).expand(ptsbatch.shape)
T2ptsbatch_SE3 = T2_SE3.dot(ptsbatch)
assert T2ptsbatch_SE3.shape == ptsbatch.shape \
and utils.allclose(T2ptsbatch_SE3, T2ptsbatch) \
and utils.allclose(T2_SE3.dot(pt1), T2ptsbatch[:, 0, :]) \
and utils.allclose(T2_SE3.dot(pt2), T2ptsbatch[:, 1, :])
T2ptshbatch = torch.matmul(T2, ptshbatch.transpose(2, 1)).transpose(2, 1)
T2ptshbatch_SE3 = T2_SE3.dot(ptshbatch)
assert T2ptshbatch_SE3.shape == ptshbatch.shape \
and utils.allclose(T2ptshbatch_SE3, T2ptshbatch) \
and utils.allclose(T2_SE3.dot(pt1h), T2ptshbatch[:, 0, :]) \
and utils.allclose(T2_SE3.dot(pt2h), T2ptshbatch[:, 1, :]) \
and utils.allclose(T2ptshbatch_SE3[:, :, 0:3], T2ptsbatch_SE3)
def test_exp_log():
T = SE3.exp(torch.Tensor([1, 2, 3, 4, 5, 6]))
assert utils.allclose(SE3.exp(SE3.log(T)).as_matrix(), T.as_matrix())
def test_identity_batch():
T = SE3.identity(5)
assert isinstance(T, SE3) \
and isinstance(T.rot, SO3) \
and T.rot.mat.dim() == 3 \
and T.trans.shape == (5, 3)
def test_perturb():
T = SE3.exp(torch.Tensor([1, 2, 3, 4, 5, 6]))
T_copy = copy.deepcopy(T)
xi = torch.Tensor([0.3, 0.2, 0.1, -0.1, -0.2, -0.3])
T.perturb(xi)
assert utils.allclose(T.as_matrix(), (SE3.exp(xi).dot(T_copy)).as_matrix())
def test_adjoint_batch():
T = SE3.exp(0.1 * torch.Tensor([[1, 2, 3, 4, 5, 6],
[7, 8, 9, 10, 11, 12]]))
assert T.adjoint().shape == (2, 6, 6)
def test_adjoint():
T = SE3.exp(torch.Tensor([1, 2, 3, 4, 5, 6]))
assert T.adjoint().shape == (6, 6)
def test_inv_batch():
T = SE3.exp(0.1 * torch.Tensor([[1, 2, 3, 4, 5, 6],
[7, 8, 9, 10, 11, 12],
[13, 14, 15, 16, 17, 18]]))
assert utils.allclose(T.dot(T.inv()).as_matrix(),
SE3.identity(T.trans.shape[0]).as_matrix())
def test_wedge_vee_batch():
xis = 0.1 * torch.Tensor([[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12]])
Xis = SE3.wedge(xis)
assert (xis == SE3.vee(Xis)).all()
def box_minus(self, chi_1, chi_2):
return SE3.from_matrix(chi_2).inv().dot(SE3.from_matrix(chi_1)).log()
def test_normalize():
T = SE3.exp(torch.Tensor([1, 2, 3, 4, 5, 6]))
T.rot.mat.add_(0.1)
T.normalize()
assert SE3.is_valid_matrix(T.as_matrix()).all()
def test_curlywedge_curlyvee():
xi = torch.Tensor([1, 2, 3, 4, 5, 6])
Psi = SE3.curlywedge(xi)
assert (xi == SE3.curlyvee(Psi)).all()
def test_identity():
T = SE3.identity()
assert isinstance(T, SE3) \
and isinstance(T.rot, SO3) \
and T.rot.mat.dim() == 2 \
and T.trans.shape == (3,)
def test_exp_log_batch():
T = SE3.exp(0.1 * torch.Tensor([[1, 2, 3, 4, 5, 6],
[7, 8, 9, 10, 11, 12]]))
assert utils.allclose(SE3.exp(SE3.log(T)).as_matrix(), T.as_matrix())
def test_inv():
T = SE3.exp(torch.Tensor([1, 2, 3, 4, 5, 6]))
assert utils.allclose((T.dot(T.inv())).as_matrix(), torch.eye(4))
def test_wedge_vee():
xi = 0.1 * torch.Tensor([1, 2, 3, 4, 5, 6])
Xi = SE3.wedge(xi)
assert (xi == SE3.vee(Xi)).all()