def test_so3_log_exp(self): r = lie.random_so3() self.assertTrue(lie.is_so3(r)) axis, angle = lie.so3_log(r, return_angle_only=False) self.assertTrue(np.allclose(r, lie.so3_exp(axis, angle), atol=1e-6)) angle = lie.so3_log(r) self.assertTrue(np.allclose(r, lie.so3_exp(axis, angle), atol=1e-6))
def test_so3_log_exp(self): r = lie.random_so3() self.assertTrue(lie.is_so3(r)) rotvec = lie.so3_log(r, return_angle_only=False) self.assertTrue(np.allclose(r, lie.so3_exp(rotvec), atol=1e-6)) angle = lie.so3_log(r) self.assertAlmostEqual(np.linalg.norm(rotvec), angle)
def process_data(self, data, id_pairs=None): """ calculate relative poses on a batch of SE(3) poses :param data: tuple (traj_ref, traj_est) with: traj_ref: reference evo.trajectory.PosePath or derived traj_est: estimated evo.trajectory.PosePath or derived :param id_pairs: pre-computed pair indices if you know what you're doing (ignores delta) """ if len(data) != 2: raise MetricsException( "please provide data tuple as: (traj_ref, traj_est)") traj_ref, traj_est = data if traj_ref.num_poses != traj_est.num_poses: raise MetricsException( "trajectories must have same number of poses") if id_pairs is None: id_pairs = id_pairs_from_delta(traj_est.poses_se3, self.delta, self.delta_unit, self.rel_delta_tol, all_pairs=self.all_pairs) if not self.all_pairs: self.delta_ids = [j for i, j in id_pairs ] # store flat id list e.g. for plotting self.E = [ self.rpe_base(traj_ref.poses_se3[i], traj_ref.poses_se3[j], traj_est.poses_se3[i], traj_est.poses_se3[j]) for i, j in id_pairs ] logger.debug("compared " + str(len(self.E)) + " relative pose pairs, delta = " + str(self.delta) + " (" + str(self.delta_unit.value) + ") " + ("with all possible pairs" if self. all_pairs else "with consecutive pairs")) logger.debug("calculating RPE for " + str(self.pose_relation.value) + " pose relation...") if self.pose_relation == PoseRelation.translation_part: self.error = [np.linalg.norm(E_i[:3, 3]) for E_i in self.E] elif self.pose_relation == PoseRelation.rotation_part: # ideal: rot(E_i) = 3x3 identity self.error = np.array([ np.linalg.norm(lie.so3_from_se3(E_i) - np.eye(3)) for E_i in self.E ]) elif self.pose_relation == PoseRelation.full_transformation: # ideal: E_i = 4x4 identity self.error = np.array( [np.linalg.norm(E_i - np.eye(4)) for E_i in self.E]) elif self.pose_relation == PoseRelation.rotation_angle_rad: self.error = np.array( [abs(lie.so3_log(E_i[:3, :3])) for E_i in self.E]) elif self.pose_relation == PoseRelation.rotation_angle_deg: self.error = np.array([ abs(lie.so3_log(E_i[:3, :3])) * 180 / np.pi for E_i in self.E ]) else: raise MetricsException("unsupported pose_relation: ", self.pose_relation)
def process_data(self, data): """ Calculates the RPE on a batch of SE(3) poses from trajectories. :param data: tuple (traj_ref, traj_est) with: traj_ref: reference evo.trajectory.PosePath or derived traj_est: estimated evo.trajectory.PosePath or derived """ if len(data) != 2: raise MetricsException( "please provide data tuple as: (traj_ref, traj_est)") traj_ref, traj_est = data if traj_ref.num_poses != traj_est.num_poses: raise MetricsException( "trajectories must have same number of poses") id_pairs = filters.id_pairs_from_delta( traj_est.poses_se3, self.delta, self.delta_unit, self.rel_delta_tol, all_pairs=self.all_pairs) if not self.all_pairs: # Store flat id list e.g. for plotting. self.delta_ids = [j for i, j in id_pairs] self.E = [ self.rpe_base(traj_ref.poses_se3[i], traj_ref.poses_se3[j], traj_est.poses_se3[i], traj_est.poses_se3[j]) for i, j in id_pairs ] logger.debug( "Compared {} relative pose pairs, delta = {} ({}) {}".format( len(self.E), self.delta, self.delta_unit.value, ("with all pairs." if self.all_pairs \ else "with consecutive pairs."))) logger.debug("Calculating RPE for {} pose relation...".format( self.pose_relation.value)) if self.pose_relation == PoseRelation.translation_part: self.error = [np.linalg.norm(E_i[:3, 3]) for E_i in self.E] elif self.pose_relation == PoseRelation.rotation_part: # ideal: rot(E_i) = 3x3 identity self.error = np.array([ np.linalg.norm(lie.so3_from_se3(E_i) - np.eye(3)) for E_i in self.E ]) elif self.pose_relation == PoseRelation.full_transformation: # ideal: E_i = 4x4 identity self.error = np.array( [np.linalg.norm(E_i - np.eye(4)) for E_i in self.E]) elif self.pose_relation == PoseRelation.rotation_angle_rad: self.error = np.array( [abs(lie.so3_log(E_i[:3, :3])) for E_i in self.E]) elif self.pose_relation == PoseRelation.rotation_angle_deg: self.error = np.array([ abs(lie.so3_log(E_i[:3, :3])) * 180 / np.pi for E_i in self.E ]) else: raise MetricsException("unsupported pose_relation: ", self.pose_relation)
def process_data(self, data): """ Calculates the RPE on a batch of SE(3) poses from trajectories. :param data: tuple (traj_ref, traj_est) with: traj_ref: reference evo.trajectory.PosePath or derived traj_est: estimated evo.trajectory.PosePath or derived """ if len(data) != 2: raise MetricsException( "please provide data tuple as: (traj_ref, traj_est)") traj_ref, traj_est = data if traj_ref.num_poses != traj_est.num_poses: raise MetricsException( "trajectories must have same number of poses") id_pairs = filters.id_pairs_from_delta( traj_est.poses_se3, self.delta, self.delta_unit, self.rel_delta_tol, all_pairs=self.all_pairs) if not self.all_pairs: # Store flat id list e.g. for plotting. self.delta_ids = [j for i, j in id_pairs] self.E = [self.rpe_base(traj_ref.poses_se3[i], traj_ref.poses_se3[j], traj_est.poses_se3[i], traj_est.poses_se3[j]) for i, j in id_pairs] logger.debug( "Compared {} relative pose pairs, delta = {} ({}) {}".format( len(self.E), self.delta, self.delta_unit.value, ("with all pairs." if self.all_pairs \ else "with consecutive pairs."))) logger.debug("Calculating RPE for {} pose relation...".format( self.pose_relation.value)) if self.pose_relation == PoseRelation.translation_part: self.error = [np.linalg.norm(E_i[:3, 3]) for E_i in self.E] elif self.pose_relation == PoseRelation.rotation_part: # ideal: rot(E_i) = 3x3 identity self.error = np.array( [np.linalg.norm( lie.so3_from_se3(E_i) - np.eye(3)) for E_i in self.E]) elif self.pose_relation == PoseRelation.full_transformation: # ideal: E_i = 4x4 identity self.error = np.array( [np.linalg.norm(E_i - np.eye(4)) for E_i in self.E]) elif self.pose_relation == PoseRelation.rotation_angle_rad: self.error = np.array( [abs(lie.so3_log(E_i[:3, :3])) for E_i in self.E]) elif self.pose_relation == PoseRelation.rotation_angle_deg: self.error = np.array( [abs( lie.so3_log(E_i[:3, :3])) * 180 / np.pi for E_i in self.E]) else: raise MetricsException( "unsupported pose_relation: ", self.pose_relation)
def process_data(self, data: PathPair) -> None: """ Calculates the APE on a batch of SE(3) poses from trajectories. :param data: tuple (traj_ref, traj_est) with: traj_ref: reference evo.trajectory.PosePath or derived traj_est: estimated evo.trajectory.PosePath or derived """ if len(data) != 2: raise MetricsException( "please provide data tuple as: (traj_ref, traj_est)") traj_ref, traj_est = data if traj_ref.num_poses != traj_est.num_poses: raise MetricsException( "trajectories must have same number of poses") if self.pose_relation == PoseRelation.translation_part: # don't require full SE(3) matrices for faster computation self.E = traj_est.positions_xyz - traj_ref.positions_xyz elif self.pose_relation == PoseRelation.z: self.E = traj_est.positions_xyz - traj_ref.positions_xyz elif self.pose_relation == PoseRelation.xy: self.E = traj_est.positions_xyz - traj_ref.positions_xyz else: self.E = [ self.ape_base(x_t, x_t_star) for x_t, x_t_star in zip( traj_est.poses_se3, traj_ref.poses_se3) ] logger.debug("Compared {} absolute pose pairs.".format(len(self.E))) logger.debug("Calculating APE for {} pose relation...".format( (self.pose_relation.value))) if self.pose_relation == PoseRelation.translation_part: # E is an array of position vectors only in this case self.error = np.array([np.linalg.norm(E_i) for E_i in self.E]) elif self.pose_relation == PoseRelation.z: self.error = np.array([E_i[2] for E_i in self.E]) elif self.pose_relation == PoseRelation.xy: self.error = np.array([np.linalg.norm(E_i[0:2]) for E_i in self.E]) elif self.pose_relation == PoseRelation.rotation_part: self.error = np.array([ np.linalg.norm(lie.so3_from_se3(E_i) - np.eye(3)) for E_i in self.E ]) elif self.pose_relation == PoseRelation.full_transformation: self.error = np.array( [np.linalg.norm(E_i - np.eye(4)) for E_i in self.E]) elif self.pose_relation == PoseRelation.rotation_angle_rad: self.error = np.array( [abs(lie.so3_log(E_i[:3, :3])) for E_i in self.E]) elif self.pose_relation == PoseRelation.rotation_angle_deg: self.error = np.array([ abs(lie.so3_log(E_i[:3, :3])) * 180 / np.pi for E_i in self.E ]) else: raise MetricsException("unsupported pose_relation")
def test_so3_log_exp(self): r = lie.random_so3() self.assertTrue(lie.is_so3(r)) axis, angle = lie.so3_log(r, return_angle_only=False) self.assertTrue(np.allclose(r, lie.so3_exp(axis, angle), atol=1e-6)) angle = lie.so3_log(r) # we ignore signs here, therefore check also transpose self.assertTrue( np.allclose(r, lie.so3_exp(axis, angle).T) or np.allclose(r, lie.so3_exp(axis, angle)))
def filter_pairs_by_angle(poses, delta, tol=0.0, degrees=False, all_pairs=False): """ filters pairs in a list of SE(3) poses by their absolute relative angle - by default, the angle accumulated on the path between the two pair poses is considered - if <all_pairs> is set to True, the direct angle between the two pair poses is considered :param poses: list of SE(3) poses :param delta: the angle in radians used for filtering :param tol: absolute angle tolerance to accept or reject pairs in all_pairs mode :param degrees: set to True if <delta> is in degrees instead of radians :param all_pairs: use all pairs instead of consecutive pairs :return: list of index tuples of the filtered pairs """ if all_pairs: upper_bound = delta + tol lower_bound = delta - tol id_pairs = [] ids = range(len(poses)) if degrees: angles = [lie.so3_log(p[:3, :3]) * 180 / np.pi for p in poses] else: angles = [lie.so3_log(p[:3, :3]) for p in poses] for i in ids: for j in ids[i + 1:]: current_angle = abs(angles[i] - angles[j]) if lower_bound <= current_angle <= upper_bound: id_pairs.append((i, j)) else: ids = [] if degrees: angles = [lie.so3_log(p[:3, :3]) * 180 / np.pi for p in poses] else: angles = [lie.so3_log(p[:3, :3]) for p in poses] previous_angle = angles[0] current_delta = 0.0 ids.append(0) for i, current_angle in enumerate(angles): current_delta += abs(current_angle - previous_angle) previous_angle = current_angle if current_delta >= delta: ids.append(i) current_delta = 0.0 id_pairs = [(i, j) for i, j in zip(ids, ids[1:])] return id_pairs
def test_so3_log_exp_skew(self): r = lie.random_so3() log = lie.so3_log(r, return_skew=True) # skew-symmetric tangent space # here, axis is a rotation vector with norm = angle axis = lie.vee(log) angle = np.linalg.norm(axis) self.assertTrue(np.allclose(r, lie.so3_exp(axis, angle)))
def calc_angular_speed(p_1: np.ndarray, p_2: np.ndarray, t_1: float, t_2: float, degrees: bool = False) -> float: """ :param p_1: pose at timestamp 1 :param p_2: pose at timestamp 2 :param t_1: timestamp 1 :param t_2: timestamp 2 :param degrees: set to True to return deg/s :return: speed in rad/s """ if (t_2 - t_1) <= 0: raise TrajectoryException("bad timestamps: " + str(t_1) + " & " + str(t_2)) angle_1 = lie.so3_log(p_1[:3, :3], degrees) angle_2 = lie.so3_log(p_2[:3, :3], degrees) return (angle_2 - angle_1) / (t_2 - t_1)
def calc_angular_speed(p_1, p_2, t_1, t_2, degrees=False): """ :param p_1: pose at timestamp 1 :param p_2: pose at timestamp 2 :param t_1: timestamp 1 :param t_2: timestamp 2 :param degrees: set to True to return deg/s :return: speed in rad/s """ if (t_2 - t_1) <= 0: raise TrajectoryException("bad timestamps: " + str(t_1) + " & " + str(t_2)) if degrees: angle_1 = lie.so3_log(p_1[:3, :3]) * 180 / np.pi angle_2 = lie.so3_log(p_2[:3, :3]) * 180 / np.pi else: angle_1 = lie.so3_log(p_1[:3, :3]) angle_2 = lie.so3_log(p_2[:3, :3]) return (angle_2 - angle_1) / (t_2 - t_1)
def process_data(self, data): """ Calculates the APE on a batch of SE(3) poses from trajectories. :param data: tuple (traj_ref, traj_est) with: traj_ref: reference evo.trajectory.PosePath or derived traj_est: estimated evo.trajectory.PosePath or derived """ if len(data) != 2: raise MetricsException( "please provide data tuple as: (traj_ref, traj_est)") traj_ref, traj_est = data if traj_ref.num_poses != traj_est.num_poses: raise MetricsException( "trajectories must have same number of poses") if self.pose_relation == PoseRelation.translation_part: # don't require full SE(3) matrices for faster computation self.E = traj_est.positions_xyz - traj_ref.positions_xyz else: self.E = [self.ape_base(x_t, x_t_star) for x_t, x_t_star in zip(traj_est.poses_se3, traj_ref.poses_se3)] logger.debug("Compared {} absolute pose pairs.".format(len(self.E))) logger.debug("Calculating APE for {} pose relation...".format( (self.pose_relation.value))) if self.pose_relation == PoseRelation.translation_part: # E is an array of position vectors only in this case self.error = [np.linalg.norm(E_i) for E_i in self.E] elif self.pose_relation == PoseRelation.rotation_part: self.error = np.array( [np.linalg.norm( lie.so3_from_se3(E_i) - np.eye(3)) for E_i in self.E]) elif self.pose_relation == PoseRelation.full_transformation: self.error = np.array( [np.linalg.norm(E_i - np.eye(4)) for E_i in self.E]) elif self.pose_relation == PoseRelation.rotation_angle_rad: self.error = np.array( [abs(lie.so3_log(E_i[:3, :3])) for E_i in self.E]) elif self.pose_relation == PoseRelation.rotation_angle_deg: self.error = np.array( [abs(lie.so3_log(E_i[:3, :3])) * 180 / np.pi for E_i in self.E]) else: raise MetricsException("unsupported pose_relation")
def process_data(self, data: PathPair, align=False, align_origin=False, align_odom=False) -> None: """ Calculate the APE of segments from a batch of SE(3) poses from trajectories :param data: tuple (traj_ref, traj_est) with: traj_ref: reference evo.trajectory.PosePath or derived traj_est: estimated evo.trajectory.PosePath or derived """ if len(data) != 2: raise MetricsException( "please provide data tuple as: (traj_ref, traj_est)") traj_ref, traj_est = data if traj_ref.num_poses != traj_est.num_poses: raise MetricsException( "trajectories must have same number of poses") step_size = 10 i = 0 for first_pose in range(0, traj_ref.num_poses, step_size): print('processing segment ', i) i = i + 1 last_pose = self.last_pose_from_segment_length( traj_ref, first_pose) if (last_pose == -1): break traj_ref_segment = trajectory.PosePath3D( poses_se3=traj_ref.poses_se3[first_pose:last_pose]) traj_est_segment = trajectory.PosePath3D( poses_se3=traj_est.poses_se3[first_pose:last_pose]) # if align or correct_scale: if align: alignment_transformation = lie.sim3(*traj_est_segment.align( traj_ref_segment, False, False, -1)) elif align_origin: print('align origin: ', align_origin) alignment_transformation = traj_est_segment.align_origin( traj_ref_segment) elif align_odom: alignment_transformation = traj_est_segment.align_odom( traj_ref_segment) self.segment_index.append([first_pose, last_pose]) if i == 1: print('starting idx: ', first_pose) print('ending idx: ', last_pose) # print('origin 0 position: ', traj_est_segment.poses_se3[0]) # print('origin 1 position: ', traj_est_segment.poses_se3[1]) # print('ref 0 position: ', traj_ref_segment.poses_se3[0]) # print('results 1 position: ', traj_ref_segment.poses_se3[1]) fig = plt.figure() plot_option = '3D' if plot_option == '2D': ax = fig.add_subplot() #projection="3d" elif plot_option == '3D': ax = fig.add_subplot(projection="3d") x_ref = traj_ref_segment.positions_xyz[:, 0] y_ref = traj_ref_segment.positions_xyz[:, 1] z_ref = traj_ref_segment.positions_xyz[:, 2] front_vector_origin = np.array([1, 0, 0, 1]) f_vecs = np.array([ (np.dot(pose, front_vector_origin) - pose[:, 3]) * 10 for pose in traj_ref_segment.poses_se3 ]) if plot_option == '2D': ax.plot(x_ref, y_ref) #, z_ref) # plt.quiver(x_ref, y_ref, f_vecs[:,0], f_vecs[:,1], color='g')#, arrow_length_ratio=0.05) elif plot_option == '3D': ax.plot(x_ref, y_ref, z_ref) plt.quiver(x_ref, y_ref, z_ref, f_vecs[:, 0], f_vecs[:, 1], f_vecs[:, 2], color='g', arrow_length_ratio=0.05) x_est = traj_est_segment.positions_xyz[:, 0] y_est = traj_est_segment.positions_xyz[:, 1] z_est = traj_est_segment.positions_xyz[:, 2] f_vecs = np.array([ (np.dot(pose, front_vector_origin) - pose[:, 3]) * 10 for pose in traj_est_segment.poses_se3 ]) if plot_option == '2D': ax.plot(x_est, y_est, color='r') # plt.quiver(x_est, y_est, f_vecs[:,0], f_vecs[:,1], color='b') elif plot_option == '3D': ax.plot(x_est, y_est, z_est, color='r') plt.quiver(x_est, y_est, z_est, f_vecs[:, 0], f_vecs[:, 1], f_vecs[:, 2], color='b', arrow_length_ratio=0.05) plt.title('segment_length: ' + str(self.segment_length) + 'm') plt.savefig('first_segment_aligned.png') if self.plot_show: plt.show() if self.pose_relation == PoseRelation.translation_part: segment_E = traj_est_segment.positions_xyz - traj_ref_segment.positions_xyz elif self.pose_relation == PoseRelation.z: segment_E = traj_est_segment.positions_xyz - traj_ref_segment.positions_xyz elif self.pose_relation == PoseRelation.xy: segment_E = traj_est_segment.positions_xyz - traj_ref_segment.positions_xyz else: segment_E = [ self.ape_base(x_t, x_t_star) for x_t, x_t_star in zip( traj_est_segment.poses_se3, traj_ref_segment.poses_se3) ] logger.debug("Compared {} absolute pose pairs.".format(len( self.E))) logger.debug("Calculating APE for {} pose relation...".format( (self.pose_relation.value))) if self.pose_relation == PoseRelation.translation_part: segment_error = np.array( [np.linalg.norm(E_i) for E_i in segment_E]) elif self.pose_relation == PoseRelation.z: segment_error = np.array([E_i[2] for E_i in segment_E]) elif self.pose_relation == PoseRelation.xy: segment_error = np.array( [np.linalg.norm(E_i[0:2]) for E_i in segment_E]) elif self.pose_relation == PoseRelation.rotation_part: segment_error = np.array([ np.linalg.norm(lie.so3_from_se3(E_i) - np.eye(3)) for E_i in segment_E ]) elif self.pose_relation == PoseRelation.full_transformation: segment_error = np.array( [np.linalg.norm(E_i - np.eye(4)) for E_i in segment_E]) elif self.pose_relation == PoseRelation.rotation_angle_rad: segment_error = np.array( [abs(lie.so3_log(E_i[:3, :3])) for E_i in segment_E]) elif self.pose_relation == PoseRelation.rotation_angle_deg: segment_error = np.array([ abs(lie.so3_log(E_i[:3, :3])) * 180 / np.pi for E_i in segment_E ]) else: raise MetricsException("unsupported pose_relation") self.E.append(segment_E) self.seg_error.append(segment_error)