def quat_slerp(q1, q2):
if isinstance(q1, PyQuaternion) and isinstance(q2, PyQuaternion):
return PyQuaternion.slerp(q1, q2)
elif isinstance(q1, Quaternion) and isinstance(q2, Quaternion):
q3 = PyQuaternion.slerp(quat_geom_to_py(q1), quat_geom_to_py(q2))
return quat_py_to_geom(q3)
else:
return None
def test_slerp_extensive(self):
for axis in [[1, 0, 0], [0, 1, 0], [0, 0, 1]]:
q1 = Quaternion(axis=axis, angle=0.0)
q2 = Quaternion(axis=axis, angle=pi/2.0)
q3 = Quaternion(axis=axis, angle=pi*3.0/2.0)
for t in np.arange(0.1, 1, 0.1):
q4 = Quaternion.slerp(q1, q2, t)
q5 = Quaternion.slerp(q1, q3, t)
q6 = Quaternion(axis=axis, angle=t*pi/2)
q7 = Quaternion(axis=axis, angle=-t*pi/2)
assert q4 == q6 or q4 == -q6
assert q5 == q7 or q5 == -q7
def interpolate(self, b):
current_model_state = self.get_model_state(model_name="piano2")
quat = Q(current_model_state.pose.orientation.x, current_model_state.pose.orientation.y,\
current_model_state.pose.orientation.z, current_model_state.pose.orientation.w)
a = SE3(current_model_state.pose.position.x, current_model_state.pose.position.y,\
current_model_state.pose.position.z, quat)
x_inc = b.X - a.X
y_inc = b.Y - a.Y
z_inc = b.Z - a.Z
mag = sqrt(x_inc * x_inc + y_inc * y_inc + z_inc * z_inc)
x_inc = x_inc / mag * inc
y_inc = y_inc / mag * inc
z_inc = z_inc / mag * inc
x = a.X
y = a.Y
z = a.Z
q = a.q
cur = a
while SE3.euclid_dist(cur, b) > inc\
or fabs(Q.sym_distance(q, b.q)) > steering_inc:
self.set_position(cur)
self.set_steering_angle(cur.q)
if SE3.euclid_dist(cur, b) > inc:
x += x_inc
y += y_inc
z += z_inc
if Q.sym_distance(q, b.q) > steering_inc:
q = Q.slerp(q, b.q, amount=steering_inc)
cur = SE3(x, y, z, q)
sleep(0.05)
self.set_state(b)
def interpolate_pose_using_slerp(command_matrix):
pos_mat = command_matrix[:, 0:3].copy()
quat_mat = command_matrix[:, 3:7].copy()
distance_mat = numpy.linalg.norm(pos_mat[1:] - pos_mat[:-1], axis=1)
steps = numpy.cumsum(distance_mat, axis=0)
steps /= steps[-1]
qxyzw0 = numpy.asarray(quat_mat[0]).reshape(-1)
qxyzw1 = numpy.asarray(quat_mat[-1]).reshape(-1)
if numpy.dot(qxyzw0, qxyzw1) < 0:
qxyzw0 = -qxyzw0
q0 = Quaternion(
qxyzw0[3],
qxyzw0[0],
qxyzw0[1],
qxyzw0[2],
)
q1 = Quaternion(
qxyzw1[3],
qxyzw1[0],
qxyzw1[1],
qxyzw1[2],
)
interpolated_q = [q0]
for i in steps:
interpolated_q.append(Quaternion.slerp(q0, q1, i))
interpolated_mat = [[
i.elements[1], i.elements[2], i.elements[3], i.elements[0]
] for i in interpolated_q]
command_matrix[:, 3:7] = interpolated_mat
return command_matrix
def precalculate_interpolation(p1, q1, p2, q2, duration, last_pos, start_cmd, joint_names):
q1, q2 = [Quaternion(x) for x in [q1, q2]]
spline = QuinticSpline(p1, p2, duration)
num_queries = int(CONTROL_RATE * duration / INTERP_SKIP) + 1
jas = []
last_cmd = start_cmd
for t in np.linspace(0., duration, num_queries):
cart_pos = spline.get(t)[0][0]
interp_quat = Quaternion.slerp(q1, q2, t / duration)
interp_pose = state_to_pose(cart_pos[:3], interp_quat.elements)
z_angle = interp_quat.yaw_pitch_roll[0] + np.pi
try:
interp_ja = pose_to_ja(interp_pose, last_cmd,
debug_z=z_angle * 180 / np.pi, retry_on_fail=True)
last_cmd = interp_ja
interp_ja = np.array([interp_ja[j] for j in joint_names])
jas.append(interp_ja)
last_pos = interp_ja
except EnvironmentError:
jas.append(last_pos)
logging.getLogger('robot_logger').error('ignoring IK failure')
interp_ja = []
for i in range(len(jas) - 1):
interp_ja.append(jas[i].tolist())
for j in range(1, INTERP_SKIP):
t = float(j) / INTERP_SKIP
interp_point = (1 - t) * jas[i] + t * jas[i + 1]
interp_ja.append(interp_point.tolist())
interp_ja.append(jas[-1].tolist())
return interp_ja
def render(self, pv_matrix: np.ndarray,
tracked_cam_track_pos_float: float):
camera_pos_floor = int(np.floor(tracked_cam_track_pos_float))
assert camera_pos_floor >= 0
camera_pos_ceil = int(np.ceil(tracked_cam_track_pos_float))
assert camera_pos_ceil <= len(self._cam_poses) - 1
camera_pos_fraction = tracked_cam_track_pos_float - camera_pos_floor
assert 0 <= camera_pos_fraction <= 1
floor_quaternion = Quaternion(
matrix=self._cam_poses[camera_pos_floor].r_mat)
ceil_quaternion = Quaternion(
matrix=self._cam_poses[camera_pos_ceil].r_mat)
rotation_matrix = Quaternion.slerp(floor_quaternion, ceil_quaternion,
camera_pos_fraction).rotation_matrix
floor_trans_vector = self._cam_poses[camera_pos_floor].t_vec
ceil_trans_vector = self._cam_poses[camera_pos_ceil].t_vec
translation_vector = ceil_trans_vector * camera_pos_fraction + floor_trans_vector * (
1 - camera_pos_fraction)
# cam_model_pose_matrix = _get_pose_matrix(self._cam_poses[camera_pos_floor])
cam_model_pose_matrix = _get_pose_matrix(
data3d.Pose(r_mat=rotation_matrix, t_vec=translation_vector))
cam_mvp = pv_matrix.dot(cam_model_pose_matrix)
self._cam_model_renderer.render(cam_mvp)
self._cam_frustrum_renderer.render(cam_mvp)
def __getitem__(self, time):
times = self.t
if self.circuit:
start = min(times)
time = time - start % (len(self) + start)
x = self.__filter__(self.xfn(time))
y = self.__filter__(self.yfn(time))
z = self.__filter__(self.zfn(time))
q = self.q
pos = Position(x, y, z)
start = min(times)
stop = max(times)
if time < start:
quat = self.wps[0]['pose'].quaternion
elif time > stop:
quat = self.wps[-1]['pose'].quaternion
else:
for start_idx, pair in enumerate(pairwise(times)):
if pair[0] <= time <= pair[1]:
quat1 = q[start_idx]
quat2 = q[start_idx + 1]
quat_times = (pair[0], pair[1])
percent = (time - quat_times[0]) / (quat_times[1] - quat_times[0])
quat = Quaternion.from_py_quaternion(
pyQuaternion.slerp(quat1, quat2, percent))
return Pose(pos, quat)
def get_boxes(self, sample_data_token: str) -> List[Box]:
"""
Instantiates Boxes for all annotation for a particular sample_data record. If the sample_data is a
keyframe, this returns the annotations for that sample. But if the sample_data is an intermediate
sample_data, a linear interpolation is applied to estimate the location of the boxes at the time the
sample_data was captured.
:param sample_data_token: Unique sample_data identifier.
"""
# Retrieve sensor & pose records
sd_record = self.get('sample_data', sample_data_token)
curr_sample_record = self.get('sample', sd_record['sample_token'])
if curr_sample_record['prev'] == "" or sd_record['is_key_frame']:
# If no previous annotations available, or if sample_data is keyframe just return the current ones.
boxes = list(map(self.get_box, curr_sample_record['anns']))
else:
prev_sample_record = self.get('sample', curr_sample_record['prev'])
curr_ann_recs = [self.get('sample_annotation', token) for token in curr_sample_record['anns']]
prev_ann_recs = [self.get('sample_annotation', token) for token in prev_sample_record['anns']]
# Maps instance tokens to prev_ann records
prev_inst_map = {entry['instance_token']: entry for entry in prev_ann_recs}
t0 = prev_sample_record['timestamp']
t1 = curr_sample_record['timestamp']
t = sd_record['timestamp']
# There are rare situations where the timestamps in the DB are off so ensure that t0 < t < t1.
t = max(t0, min(t1, t))
boxes = []
for curr_ann_rec in curr_ann_recs:
if curr_ann_rec['instance_token'] in prev_inst_map:
# If the annotated instance existed in the previous frame, interpolate center & orientation.
prev_ann_rec = prev_inst_map[curr_ann_rec['instance_token']]
# Interpolate center.
center = [np.interp(t, [t0, t1], [c0, c1]) for c0, c1 in zip(prev_ann_rec['translation'],
curr_ann_rec['translation'])]
# Interpolate orientation.
rotation = Quaternion.slerp(q0=Quaternion(prev_ann_rec['rotation']),
q1=Quaternion(curr_ann_rec['rotation']),
amount=(t - t0) / (t1 - t0))
box = Box(center, curr_ann_rec['size'], rotation, name=curr_ann_rec['category_name'],
token=curr_ann_rec['token'])
else:
# If not, simply grab the current annotation.
box = self.get_box(curr_ann_rec['token'])
boxes.append(box)
return boxes
def get_interpolated_quat(interp_time, scan_time, q_array): q_interp_array = [] for i in range(0, len(scan_time)-1): # count the number of quaternion n = np.sum(np.logical_and(interp_time >= scan_time[i], interp_time < scan_time[i+1])) for j in range(1, int(n)+1): q_interp_array.append(Quaternion.slerp(q_array[i], q_array[i+1], float(j)/(n+1))) q_interp_array.append(q_array[-1]) return q_interp_array
def quat_average(input):
"""averaging quaternions
input : nx4 array
"""
if len(input) == 0:
return Quaternion(0, 0, 0, 0)
else:
avg = Quaternion(input[0])
for l1 in range(1, input.shape[0]):
avg = Quaternion.slerp(avg, Quaternion(input[l1]), 1 / (l1 + 1))
return avg
def _interpolate_cam_pose(t: float, p0: data3d.Pose, p1: data3d.Pose):
def to_quat(m):
qr = np.sqrt(1 + m[0][0] + m[1][1] + m[2][2]) / 2
return Quaternion(
np.array([
qr, (m[2][1] - m[1][2]) / 4 / qr, (m[0][2] - m[2][0]) / 4 / qr,
(m[1][0] - m[0][1]) / 4 / qr
]))
return data3d.Pose(
Quaternion.slerp(to_quat(p0.r_mat), to_quat(p1.r_mat),
t).rotation_matrix.astype(np.float32),
p0.t_vec * (1 - t) + p1.t_vec * t)
def act(self, obs):
if self._t == 0:
self._target = np.random.uniform(self._range[0], self._range[1])
y = -(self._target[1] - obs[self._obs_name][1])
x = self._target[0] - obs[self._obs_name][0]
self._target_quat = self._calculate_quat(np.arctan2(y, x))
if np.random.uniform() < self._p:
self._gripper *= -1
quat_t = Quaternion.slerp(self._base_quat, self._target_quat, min(1, float(self._t) / 50))
velocities = self._get_velocities(self._target - obs[self._obs_name], quat_t)
action = np.concatenate((velocities, [self._gripper]))
self._t += 1
return action
def interpolate_pose(pose1, pose2, alpha):
assert alpha >=0 and alpha <= 1
# interpolating rotation component
q1 = Quaternion(matrix = pose1)
q2 = Quaternion(matrix = pose2)
q_interp = Quaternion.slerp(q1, q2, alpha)
rot_interp = q_interp.transformation_matrix
# interpolating translation component
t1 = pose1[0:3, 3]
t2 = pose2[0:3, 3]
trans_interp = t1 * (1. - alpha) + t2 * alpha
rot_interp[0:3, 3] = rot_interp[0:3, 3] + trans_interp
return rot_interp
def handQuatUpd():
#assign an array of a quaternion to the message output
global q_out, q_prev, count
pose = Pose()
Q1 = Quaternion(q_out)
Q0 = Quaternion(q_prev)
Q05 = Quaternion.slerp(Q0, Q1, 1 / (2**(1 + count)))
print(Q05)
pose.orientation.w = Q05[0]
pose.orientation.x = Q05[1]
pose.orientation.y = Q05[2]
pose.orientation.z = Q05[3]
return pose.orientation
def check_collide(a, b):
x_inc = b.X - a.X
y_inc = b.Y - a.Y
z_inc = b.Z - a.Z
mag = sqrt(x_inc * x_inc + y_inc * y_inc + z_inc * z_inc)
x_inc = x_inc / mag * inc
y_inc = y_inc / mag * inc
z_inc = z_inc / mag * inc
x = a.X
y = a.Y
z = a.Z
q = a.q
cur = SE3(x, y, z, q)
T, R = b.get_transition_rotation()
currlerp = 0
if pqp_client(T, R).result:
return False
looping = True
while looping:
looping = False
T, R = cur.get_transition_rotation()
if pqp_client(T, R).result:
# Collision
return False
if SE3.euclid_dist(cur, b) > inc:
looping = True
cur.X += x_inc
cur.Y += y_inc
cur.Z += z_inc
if fabs(Q.sym_distance(cur.q, b.q)) > .1:
looping = True
cur.q = Q.slerp(a.q, b.q, amount=currlerp)
currlerp += steering_inc
T, R = cur.get_transition_rotation()
if pqp_client(T, R).result:
return False
return True
def evaluate(self, t):
t0, data0 = self.data_time.get(block=True)
t1, data1 = self.data_time.get(block=True)
q = []
for i in range(0, len(t)):
while t[i] > t1:
t0 = t1
data0 = data1
t1, data1 = self.data_time.get(block=True)
#Here I assumed roll pitch yaw, but data may come in a different order
q0 = transformations.quaternion_from_euler(data0[0], data0[1],
data0[2])
q1 = transformations.quaternion_from_euler(data1[0], data1[1],
data1[2])
q0 = Quaternion(q0[3], q0[0], q0[1], q0[2])
q1 = Quaternion(q1[3], q1[0], q1[1], q1[2])
w = (t[i] - t0) / (t1 - t0)
yield Quaternion.slerp(q0, q1, w)
def interpolate_tracking_boxes(left_box: TrackingBox, right_box: TrackingBox,
right_ratio: float) -> TrackingBox:
"""
Linearly interpolate box parameters between two boxes.
:param left_box: A Trackingbox.
:param right_box: Another TrackingBox
:param right_ratio: Weight given to the right box.
:return: The interpolated TrackingBox.
"""
def interp_list(left, right, rratio):
return tuple((1.0 - rratio) * np.array(left, dtype=float) +
rratio * np.array(right, dtype=float))
def interp_float(left, right, rratio):
return (1.0 - rratio) * float(left) + rratio * float(right)
# Interpolate quaternion.
rotation = Quaternion.slerp(q0=Quaternion(left_box.rotation),
q1=Quaternion(right_box.rotation),
amount=right_ratio).elements
# Score will remain -1 for GT.
tracking_score = interp_float(left_box.tracking_score,
right_box.tracking_score, right_ratio)
return TrackingBox(
sample_token=right_box.sample_token,
translation=interp_list(left_box.translation, right_box.translation,
right_ratio),
size=interp_list(left_box.size, right_box.size, right_ratio),
rotation=rotation,
velocity=interp_list(left_box.velocity, right_box.velocity,
right_ratio),
ego_translation=interp_list(left_box.ego_translation,
right_box.ego_translation,
right_ratio), # May be inaccurate.
tracking_id=right_box.tracking_id,
tracking_name=right_box.tracking_name,
tracking_score=tracking_score)
def act(self, obs):
if self._t == 0:
self._start = -1
try:
y = -(obs['{}_pos'.format(self._object_name)][1] - obs[self._obs_name][1])
x = obs['{}_pos'.format(self._object_name)][0] - obs[self._obs_name][0]
except:
import pdb; pdb.set_trace()
angle = np.arctan2(y, x) - np.pi/3 if 'Cereal' in self._object_name else np.arctan2(y, x)
self._target_quat = self._calculate_quat(angle)
if self._start < 0 and self._t < 15:
if np.linalg.norm(obs['{}_pos'.format(self._object_name)] - obs[self._obs_name] + [0, 0, self._hover_delta]) < self._g_tol or self._t == 14:
self._start = self._t
self._rise_t = self._start + 8
quat_t = Quaternion.slerp(self._base_quat, self._target_quat, min(1, float(self._t) / 5))
eef_pose = self._get_target_pose(obs['{}_pos'.format(self._object_name)] - obs[self._obs_name] + [0, 0, self._hover_delta], obs['eef_pos'], quat_t)
action = np.concatenate((eef_pose, [-1]))
elif self._t < self._start + 10:
if self._t < self._rise_t:
eef_pose = self._get_target_pose(obs['{}_pos'.format(self._object_name)] - obs[self._obs_name] - [0, 0, self._clearance], obs['eef_pos'], self._target_quat)
action = np.concatenate((eef_pose, [-1]))
else:
eef_pose = self._get_target_pose(obs['{}_pos'.format(self._object_name)] - obs[self._obs_name] + [0, 0, self._hover_delta], obs['eef_pos'], self._target_quat)
action = np.concatenate((eef_pose, [1]))
elif np.linalg.norm(self._target_loc - obs[self._obs_name]) > self._final_thresh:
target = self._target_loc
eef_pose = self._get_target_pose(target - obs[self._obs_name], obs['eef_pos'], self._target_quat)
action = np.concatenate((eef_pose, [1]))
else:
eef_pose = self._get_target_pose(np.zeros(3), obs['eef_pos'], self._target_quat)
action = np.concatenate((eef_pose, [-1]))
self._t += 1
return action
def move_straight(broker, start_pos, target_pos, **kwargs):
'''
move_straight moves the robot in a straight line
interpolating the positions in between
Kwargs:
num_steps: the number of steps to interpolate between
(default 10)
max_stepwidth: the maximum euclidean distance between two steps
(default 0.05)
by default, the one requiring more steps will be used
time_to_go: the available time to go to target
(default 0.5)
'''
# check the dimensionality of the positions and verify it's either 3 or 7
if (np.asarray(start_pos).size == 7 or np.asarray(start_pos).size == 3) \
and \
(np.asarray(target_pos).size == 7 or np.asarray(target_pos).size == 3) \
and \
(np.asarray(start_pos).size == np.asarray(target_pos).size):
# all parameters seem valid
pass
else:
raise ValueError("The input positions need to be the same size and have"
"either 3 or 7 components")
# check how many steps we need to take
if 'num_steps' in kwargs:
num_steps = kwargs['num_steps']
else:
num_steps = 10
if 'max_stepwidth' in kwargs:
max_stepwidth = kwargs['max_stepwidth']
else:
max_stepwidth = 0.05
if 'time_to_go' in kwargs:
time_to_go = kwargs['time_to_go']
else:
time_to_go = 0.5
# calculate the offset/displacement between start and target
displacement = target_pos - start_pos
distance = np.linalg.norm(displacement[0:3]) # consider only position
# calculate the number of steps by choosing whichever value needs more
num_steps = np.amax(np.asarray([
np.ceil(distance / max_stepwidth),
num_steps]))
num_steps = np.int64(num_steps)
for step in range(num_steps):
fraction = step / num_steps
new_xyz = start_pos[0:3] + fraction * displacement[0:3]
if start_pos.size == 7 and target_pos.size == 7:
new_quat = Quaternion.slerp(
Quaternion(start_pos[3:]),
Quaternion(target_pos[3:]),
fraction)
new_pos = np.concatenate([new_xyz, np.asarray(new_quat.q)])
else:
new_pos = new_xyz
set_new_pos(broker, new_pos, ctrl_mode=0, time_to_go=time_to_go)
wait_til_ready(broker)
def catmull_rom_spline(camera_poses: List[np.ndarray],
num_points: int) -> List[np.ndarray]:
"""
Interpolate points on a Catmull-Rom spline
Reading: Edwin Catmull, Raphael Rom, A CLASS OF LOCAL INTERPOLATING SPLINES,
Computer Aided Geometric Design, Academic Press, 1974, Pages 317-326
:param camera_poses: List of 4 camera poses. Points are interpolated on the curve segment between pose 1 and 2
:param num_points: Number of points to interpolate between pose 1 and 2
:return: A list of num_points point on the curve segment between pose 1 and 2
"""
# Formulas from https://en.wikipedia.org/wiki/Centripetal_Catmull%E2%80%93Rom_spline
assert len(
camera_poses) == 4, "Need exactly 4 camera poses for interpolation"
interpolated_cameras = []
# rotations
q1 = Quaternion(
matrix=find_closest_orthogonal_matrix(camera_poses[1][:3, :3]))
q2 = Quaternion(
matrix=find_closest_orthogonal_matrix(camera_poses[2][:3, :3]))
# translations
translations = [pose[:3, 3] for pose in camera_poses]
if np.linalg.norm(translations[1] - translations[2]) < 0.001:
for i in range(num_points):
ext = np.eye(4)
ext[:3, :3] = Quaternion.slerp(q1, q2,
float(i) /
num_points).rotation_matrix
ext[:3, 3] = translations[1]
interpolated_cameras.append(ext)
else:
eps = 0.001
alpha = 0.5 # Default for centripetal catmull rom splines
# Calculate knot parameters
t0 = 0.0
t1 = np.linalg.norm(translations[1] - translations[0])**alpha + t0
t2 = np.linalg.norm(translations[2] - translations[1])**alpha + t1
t3 = np.linalg.norm(translations[3] - translations[2])**alpha + t2
# Calculate points on curve segment C
new_points = []
for t in np.arange(t1, t2, (t2 - t1) / float(num_points)):
A1 = (t1 - t) / max(eps, t1 - t0) * translations[0] + (
t - t0) / max(eps, t1 - t0) * translations[1]
A2 = (t2 - t) / max(eps, t2 - t1) * translations[1] + (
t - t1) / max(eps, t2 - t1) * translations[2]
A3 = (t3 - t) / max(eps, t3 - t2) * translations[2] + (
t - t2) / max(eps, t3 - t2) * translations[3]
B1 = (t2 - t) / max(eps, t2 - t0) * A1 + (t - t0) / max(
eps, t2 - t0) * A2
B2 = (t3 - t) / max(eps, t3 - t1) * A2 + (t - t1) / max(
eps, t3 - t1) * A3
C = (t2 - t) / max(eps, t2 - t1) * B1 + (t - t1) / max(
eps, t2 - t1) * B2
new_points.append(C)
# For each point, also slerp the rotation matrix
for idx, point in enumerate(new_points):
ext = np.eye(4)
ext[:3, :3] = Quaternion.slerp(q1, q2,
float(idx) /
len(new_points)).rotation_matrix
ext[:3, 3] = point
interpolated_cameras.append(ext)
return interpolated_cameras
def imu_callback(data):
# sample time
global dt
dt = 1 / 200.0
# get gyro data
w = np.array([
data.angular_velocity.x, data.angular_velocity.y,
data.angular_velocity.z
])
# get accelerometer data: specific force in body frame
f_b = np.array([
data.linear_acceleration.x, data.linear_acceleration.y,
data.linear_acceleration.z
])
### Update state ###
# get current state
global state
# current position
p = state[0]
# current velocity
v = state[1]
# current orientation
b = state[2]
# current accel bias
x_a = state[3]
# current gyro bias
x_g = state[4]
# subtract out gyroscope bias. w_bn = (-w_nb)
w = -1 * (w - x_g) #
w_norm = np.linalg.norm(w)
# subtract out accelerometer bias
f_b = f_b - x_a
# differential rotation: [w, x, y, z]
db = np.concatenate(
([math.cos(w_norm * dt / 2)], math.sin(w_norm * dt / 2) * w / w_norm))
# convert to pyquaternion format
b_prev = Quaternion(array=b)
db = Quaternion(array=db)
# update orientation
b_next = db * b_prev
# get average quaternion by interpolation
b_avg = Quaternion.slerp(b_prev, b_next, amount=0.5)
# b is the nav to body transformation. we need body to nav transformation -> invert
b_body_to_nav_avg = b_avg.inverse # for specific force (5.9 Principles of GNSS book)
# rotate specific force into inertial frame
f_i = b_body_to_nav_avg.rotate(f_b)
# gravity vector
global g
g_vec = np.array([0, 0, g])
# get acceleration in inertial frame. (acceleration of body wrt inertial frame in inertial frame)
a_i = f_i + g_vec
# update position (5.16 Principles of GNSS book)
p = p + v * dt + 0.5 * a_i * dt**2
# DEBUG:
if np.linalg.norm(v * dt + 0.5 * a_i * dt**2) > 0.1:
print("IMU update crazy")
print(state)
# print(np.linalg.norm(v*dt + 0.5*a_i*dt**2) )
# print(v)
# print(a_i)
# print(x_a)
# print(x_g)
# print(w)
# print()
# rospy.sleep(100)
# update velocity
v = v + a_i * dt
# store in state -> this is time propagation step.
state[0] = p
state[1] = v
state[2] = b_next.elements
### Update covariance ###
# get rotation matrix corresponding to b_next
b_body_to_nav = b_next.inverse
R_body_to_nav = b_body_to_nav.rotation_matrix
# compute F matrix: F is 15 x 15
F = np.zeros((15, 15))
# store relevant values in F (see writeup)
F[:3, 3:6] = np.identity(3)
f_i_skew = to_skew(f_i)
F[3:6, 6:9] = -1 * f_i_skew
F[3:6, 9:12] = -1 * R_body_to_nav
F[6:9, 12:15] = R_body_to_nav
F_gg = -1.0 / 1000 * np.identity(3)
F_aa = -1.0 / 1000 * np.identity(3)
F[9:12, 9:12] = F_aa
F[12:15, 12:15] = F_gg
# compute system transition matrix Phi
Phi = expm(F * dt)
# compute G. G is 15 x 12.
G = np.zeros((15, 12))
G[3:6, :3] = -R_body_to_nav
G[6:9, 3:6] = R_body_to_nav
G[9:12, 6:9] = np.identity(3)
G[12:15, 9:12] = np.identity(3)
# get noise matrix
global Q
# compute Qdk (discrete noise). Qdk is 15 x 15
Qdk = G.dot(Q).dot(G.T) * dt
# get previous covariance
global cov
# update covariance (15x15)
cov = Phi.dot(cov).dot(Phi.T) + Qdk
### Measurement update stuff for acceleration. Helps correct roll and pitch ###
# if 50 accelerometer readings were close enough to the gravity vector, robot is stationary
global accel_counter, rover_stationary, g_pred_sum
# predict gravity in navigation frame and store prediction in global variable. used in filter.
num_g_pred = 50
global g_pred_sum
# check if current measurement is stationary
if np.abs(
np.linalg.norm(f_b) - g
) < 0.03: # tuned. test: you should never be able to hold the imu in your hand and have an update.
accel_counter += 1
g_pred_sum += R_body_to_nav.dot(-1 * f_b)
else:
accel_counter = 0
g_pred_sum = 0
rover_stationary = False
# if 50 consecutive stationary, use accel_data
if accel_counter == num_g_pred:
global g_pred
# averaging
g_pred = g_pred_sum / num_g_pred
rover_stationary = True
accel_counter = 0
g_pred_sum = 0
### Visualization ###
# for visualization: publish tf
if True:
b_vis = b_body_to_nav
# useful for visualization
br = tf.TransformBroadcaster()
# send world to IMU transformation
br.sendTransform((p[0], p[1], p[2]),
(b_vis[1], b_vis[2], b_vis[3], b_vis[0]),
rospy.Time.now(), "IMU", "ENU") # ENU to quat
def process(self, df, participant=None, video=None):
print("Process LowPassFilter", participant, video)
df = df.sort_values(by="time")
## get all sensors
sensors = list(
set(
df.columns.map(lambda row: row
if row == "time" else (row.split("_")[0]))))
sensors.remove("time")
low = max(min(self.hbias - (self.hrange / 2), 1), 0)
high = max(min(self.hbias + (self.hrange / 2), 1), 0)
hrangeLimited = high - low
y = {}
result = {}
for sensor in sensors:
yrow = df.iloc[[0]][[
"%s_orientation_q_w" % sensor,
"%s_orientation_q_x" % sensor,
"%s_orientation_q_y" % sensor,
"%s_orientation_q_z" % sensor
]]
y[sensor] = Quaternion(yrow["%s_orientation_q_w" % sensor],
yrow["%s_orientation_q_x" % sensor],
yrow["%s_orientation_q_y" % sensor],
yrow["%s_orientation_q_z" % sensor])
if y[sensor].norm == 0.0:
y[sensor] = Quaternion(1, 0, 0, 0)
if sensor not in result:
result[sensor] = []
result[sensor].append(list(y[sensor]))
for i in range(1, len(df)):
rowresult = []
for sensor in sensors:
xrow = df.iloc[[i]][[
"%s_orientation_q_w" % sensor,
"%s_orientation_q_x" % sensor,
"%s_orientation_q_y" % sensor,
"%s_orientation_q_z" % sensor
]]
x = Quaternion(xrow["%s_orientation_q_w" % sensor],
xrow["%s_orientation_q_x" % sensor],
xrow["%s_orientation_q_y" % sensor],
xrow["%s_orientation_q_z" % sensor])
if x.norm == 0.0:
x = Quaternion(1, 0, 0, 0)
d = Quaternion.distance(y[sensor], x)
hlpf = d / math.pi * hrangeLimited + low
y[sensor] = Quaternion.slerp(y[sensor], x, amount=hlpf)
result[sensor].append(list(y[sensor]))
dfs = []
dfs.append(pd.DataFrame({"time": df.time}))
for sensor in sensors:
newdf = pd.DataFrame(result[sensor],
columns=[
"%s_orientation_q_%s" % (sensor, s)
for s in list("wxyz")
])
dfs.append(newdf)
newdf = pd.concat(dfs, axis=1, join='inner')
return newdf
def interpolate(source, target, alpha):
iquat = Quaternion.slerp(source.q, target.q, alpha)
it = source.t * (1 - alpha) + target.t * alpha
return Isometry(q=iquat, t=it)
def merge_pose_to_gps_interpolate(pose_df, gps_imu_df, time_key='Timestamp'):
gps_imu_df = gps_imu_df.sort_values(time_key, ignore_index=True)
with tqdm(total=pose_df.shape[0]) as pbar:
x_list = []
y_list = []
z_list = []
qw_list = []
qx_list = []
qy_list = []
qz_list = []
roll_list = []
pitch_list = []
yaw_list = []
time_list = []
for index, row in pose_df.iterrows():
index_p = index + 1
if index_p >= pose_df.shape[0]:
pbar.update(1)
continue
ref_time = pose_df[time_key][index]
time_diff = pose_df[time_key][index_p] - pose_df[time_key][index]
x_diff = pose_df['x'][index_p] - pose_df['x'][index]
y_diff = pose_df['y'][index_p] - pose_df['y'][index]
z_diff = pose_df['z'][index_p] - pose_df['z'][index]
q_imu_0 = Quaternion(pose_df[['qw', 'qx', 'qy', 'qz']].loc[index])
q_imu_1 = Quaternion(pose_df[['qw', 'qx', 'qy', 'qz']].loc[index_p])
check_df = gps_imu_df[(gps_imu_df[time_key] > pose_df[time_key][index]) &
(gps_imu_df[time_key] <= pose_df[time_key][index_p])]
for idx, crow in check_df.iterrows():
inter_time = crow[time_key] - ref_time
ratio = inter_time / time_diff
x = pose_df['x'][index] + x_diff * ratio
y = pose_df['y'][index] + y_diff * ratio
z = pose_df['z'][index] + z_diff * ratio
q_inter = Quaternion.slerp(q_imu_0, q_imu_1, ratio)
r_obj = sc_Rotation.from_quat([q_inter.x, q_inter.y, q_inter.z, q_inter.w])
np_euler = r_obj.as_euler('xyz', degrees=False)
roll = np_euler[0]
pitch = np_euler[1]
yaw = np_euler[2]
qw_list.append(q_inter.w)
qx_list.append(q_inter.x)
qy_list.append(q_inter.y)
qz_list.append(q_inter.z)
x_list.append(x)
y_list.append(y)
z_list.append(z)
roll_list.append(roll)
pitch_list.append(pitch)
yaw_list.append(yaw)
pbar.update(1)
if gps_imu_df.shape[0] != len(x_list):
raise Exception('invalid data frame size', 'please check first time and last time')
gps_imu_df['pose_x'] = x_list
gps_imu_df['pose_y'] = y_list
gps_imu_df['pose_z'] = z_list
gps_imu_df['pose_roll'] = roll_list
gps_imu_df['pose_pitch'] = pitch_list
gps_imu_df['pose_yaw'] = yaw_list
gps_imu_df['pose_qx'] = np.array(qx_list)
gps_imu_df['pose_qy'] = np.array(qy_list)
gps_imu_df['pose_qz'] = np.array(qz_list)
gps_imu_df['pose_qw'] = np.array(qw_list)
return gps_imu_df
def update_ori(self, roll, pitch, yaw, slerp_amount=1.0): new_ori = self.__convert_from_euler_angles_to_quat(roll, pitch, yaw) interp_ori = Quaternion.slerp(self.ori, new_ori, slerp_amount) print(interp_ori) self.ori = interp_ori
def test_slerp(self):
q1 = Quaternion(axis=[1, 0, 0], angle=0.0)
q2 = Quaternion(axis=[1, 0, 0], angle=pi/2)
q3 = Quaternion.slerp(q1, q2, 0.5)
self.assertEqual(q3, Quaternion(axis=[1,0,0], angle=pi/4))
def calculate(self, body):
bone_state = {}
for bone in body:
if bone in MMD_TO_VAM_BONE_MAPPINGS.keys():
bone_name = MMD_TO_VAM_BONE_MAPPINGS[bone]
frames = self.md.boneAnimation[bone]
bone_state[bone_name] = {}
last_frame = -1
bone_dep = None
if bone_name in Body.DEPS.keys():
bone_dep = Body.DEPS[bone_name]
# Sometimes a dep wont have any info, so take the dep of the dep.
# E.g. Foot depends on knee, but knee has no motion info so use thigh as the dep.
while bone_dep not in bone_state.keys() or len(
bone_state[bone_dep].keys()) <= 1:
if bone_dep == 'hip':
break
bone_dep = Body.DEPS[bone_dep]
frames.sort(key=lambda g: g.frame_number)
print('Calculating motion for: ' + bone_name)
for boneFrameKey in frames:
if last_frame == -1:
# This is the first frame
bone_state[bone_name][0] = {}
bone_state[bone_name][0]['pos'] = {
'x': boneFrameKey.location[0],
'y': boneFrameKey.location[1],
'z': boneFrameKey.location[2]
}
# If all the rotation data is 0 (null rotation) then set the rotation to off for this bone
# at frame 0.
if boneFrameKey.rotation[0] == 0 and boneFrameKey.rotation[1] == 0\
and boneFrameKey.rotation[2] == 0:
bone_state[bone_name][0]['rot_on'] = False
# Get the initial rotation
q = Quaternion(boneFrameKey.rotation[3],
boneFrameKey.rotation[0],
boneFrameKey.rotation[1],
boneFrameKey.rotation[2])
# If bone has a parent then add the first frame rotation with the parent.
if bone_dep:
q = bone_state[bone_dep][0]['rot'] * q
bone_state[bone_name][0]['rot'] = q
else:
# Try to calculate the positions and rotations between frames via interpolation.
for current_frame in range(
last_frame + 1, boneFrameKey.frame_number + 1):
bone_state[bone_name][current_frame] = {}
diff = boneFrameKey.frame_number - last_frame
# Use simple math to calculate where the intermediate points would be.
factor = float(1 / diff)
bone_state[bone_name][current_frame]['pos'] = {
'x':
bone_state[bone_name][last_frame]['pos']['x'] *
(diff - (current_frame - last_frame)) / diff +
(boneFrameKey.location[0] *
(current_frame - last_frame) / diff),
'y':
bone_state[bone_name][last_frame]['pos']['y'] *
(diff - (current_frame - last_frame)) / diff +
(boneFrameKey.location[1] *
(current_frame - last_frame) / diff),
'z':
bone_state[bone_name][last_frame]['pos']['z'] *
(diff - (current_frame - last_frame)) / diff +
(boneFrameKey.location[2] *
(current_frame - last_frame) / diff),
}
# This is the tricky part. The calculation for a rotation goes as follows:
# 1. Find the rotation of the parent bone at this frame. Should be a quaternion.
# 2. If not found, go to the previous frame until one is found.
# 3. If the parent is not found at all just start with a null rotation for the dep.
# 4. If it's not null then turn on rotation, put the rotation it in a new quaternion.
# 5. Calculate the absolute rotation of the next frame by adding the parent and the
# child's rot.
# 6. Get the absolute rotation that was already stored previously.
# 7. Use the slerp function to interpolate the current rotation based on both previous and
# next rotations.
# 8. Save the calculated rotation, and proceed to the next frame.
rot_next_frame_parent = None
if bone_name in Body.DEPS.keys():
fr = boneFrameKey.frame_number
while not rot_next_frame_parent:
try:
# 1
rot_next_frame_parent = bone_state[
bone_dep][fr]['rot']
except KeyError: # 2
fr = fr - 1
if not rot_next_frame_parent:
rot_next_frame_parent = Quaternion(1, 0, 0,
0) # 3
bone_state[bone_name][current_frame][
'rot_on'] = True
# 4
rot_next_frame_child_relative = Quaternion(
boneFrameKey.rotation[3],
boneFrameKey.rotation[0],
boneFrameKey.rotation[1],
boneFrameKey.rotation[2])
# 5
rot_next_frame = rot_next_frame_parent * rot_next_frame_child_relative
rot_prev_frame = bone_state[bone_name][last_frame][
'rot'] # 6
# 7
rot_current_frame = \
Quaternion.slerp(rot_prev_frame, rot_next_frame, (current_frame - last_frame) * factor)
bone_state[bone_name][current_frame][
'rot'] = rot_current_frame # 8
last_frame = boneFrameKey.frame_number
else:
print('Unknown body part: ' + bone)
return bone_state