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from typing import Union
import numbers
import numpy as np
import scipy.interpolate as si
import scipy.spatial.transform as st
def rotation_distance(a: st.Rotation, b: st.Rotation) -> float:
return (b * a.inv()).magnitude()
def pose_distance(start_pose, end_pose):
start_pose = np.array(start_pose)
end_pose = np.array(end_pose)
start_pos = start_pose[:3]
end_pos = end_pose[:3]
start_rot = st.Rotation.from_rotvec(start_pose[3:])
end_rot = st.Rotation.from_rotvec(end_pose[3:])
pos_dist = np.linalg.norm(end_pos - start_pos)
rot_dist = rotation_distance(start_rot, end_rot)
return pos_dist, rot_dist
class PoseTrajectoryInterpolator:
def __init__(self, times: np.ndarray, poses: np.ndarray):
assert len(times) >= 1
assert len(poses) == len(times)
if not isinstance(times, np.ndarray):
times = np.array(times)
if not isinstance(poses, np.ndarray):
poses = np.array(poses)
if len(times) == 1:
# special treatment for single step interpolation
self.single_step = True
self._times = times
self._poses = poses
else:
self.single_step = False
assert np.all(times[1:] >= times[:-1])
pos = poses[:,:3]
rot = st.Rotation.from_rotvec(poses[:,3:])
self.pos_interp = si.interp1d(times, pos,
axis=0, assume_sorted=True)
self.rot_interp = st.Slerp(times, rot)
@property
def times(self) -> np.ndarray:
if self.single_step:
return self._times
else:
return self.pos_interp.x
@property
def poses(self) -> np.ndarray:
if self.single_step:
return self._poses
else:
n = len(self.times)
poses = np.zeros((n, 6))
poses[:,:3] = self.pos_interp.y
poses[:,3:] = self.rot_interp(self.times).as_rotvec()
return poses
def trim(self,
start_t: float, end_t: float
) -> "PoseTrajectoryInterpolator":
assert start_t <= end_t
times = self.times
should_keep = (start_t < times) & (times < end_t)
keep_times = times[should_keep]
all_times = np.concatenate([[start_t], keep_times, [end_t]])
# remove duplicates, Slerp requires strictly increasing x
all_times = np.unique(all_times)
# interpolate
all_poses = self(all_times)
return PoseTrajectoryInterpolator(times=all_times, poses=all_poses)
def drive_to_waypoint(self,
pose, time, curr_time,
max_pos_speed=np.inf,
max_rot_speed=np.inf
) -> "PoseTrajectoryInterpolator":
assert(max_pos_speed > 0)
assert(max_rot_speed > 0)
time = max(time, curr_time)
curr_pose = self(curr_time)
pos_dist, rot_dist = pose_distance(curr_pose, pose)
pos_min_duration = pos_dist / max_pos_speed
rot_min_duration = rot_dist / max_rot_speed
duration = time - curr_time
duration = max(duration, max(pos_min_duration, rot_min_duration))
assert duration >= 0
last_waypoint_time = curr_time + duration
# insert new pose
trimmed_interp = self.trim(curr_time, curr_time)
times = np.append(trimmed_interp.times, [last_waypoint_time], axis=0)
poses = np.append(trimmed_interp.poses, [pose], axis=0)
# create new interpolator
final_interp = PoseTrajectoryInterpolator(times, poses)
return final_interp
def schedule_waypoint(self,
pose, time,
max_pos_speed=np.inf,
max_rot_speed=np.inf,
curr_time=None,
last_waypoint_time=None
) -> "PoseTrajectoryInterpolator":
assert(max_pos_speed > 0)
assert(max_rot_speed > 0)
if last_waypoint_time is not None:
assert curr_time is not None
# trim current interpolator to between curr_time and last_waypoint_time
start_time = self.times[0]
end_time = self.times[-1]
assert start_time <= end_time
if curr_time is not None:
if time <= curr_time:
# if insert time is earlier than current time
# no effect should be done to the interpolator
return self
# now, curr_time < time
start_time = max(curr_time, start_time)
if last_waypoint_time is not None:
# if last_waypoint_time is earlier than start_time
# use start_time
if time <= last_waypoint_time:
end_time = curr_time
else:
end_time = max(last_waypoint_time, curr_time)
else:
end_time = curr_time
end_time = min(end_time, time)
start_time = min(start_time, end_time)
# end time should be the latest of all times except time
# after this we can assume order (proven by zhenjia, due to the 2 min operations)
# Constraints:
# start_time <= end_time <= time (proven by zhenjia)
# curr_time <= start_time (proven by zhenjia)
# curr_time <= time (proven by zhenjia)
# time can't change
# last_waypoint_time can't change
# curr_time can't change
assert start_time <= end_time
assert end_time <= time
if last_waypoint_time is not None:
if time <= last_waypoint_time:
assert end_time == curr_time
else:
assert end_time == max(last_waypoint_time, curr_time)
if curr_time is not None:
assert curr_time <= start_time
assert curr_time <= time
trimmed_interp = self.trim(start_time, end_time)
# after this, all waypoints in trimmed_interp is within start_time and end_time
# and is earlier than time
# determine speed
duration = time - end_time
end_pose = trimmed_interp(end_time)
pos_dist, rot_dist = pose_distance(pose, end_pose)
pos_min_duration = pos_dist / max_pos_speed
rot_min_duration = rot_dist / max_rot_speed
duration = max(duration, max(pos_min_duration, rot_min_duration))
assert duration >= 0
last_waypoint_time = end_time + duration
# insert new pose
times = np.append(trimmed_interp.times, [last_waypoint_time], axis=0)
poses = np.append(trimmed_interp.poses, [pose], axis=0)
# create new interpolator
final_interp = PoseTrajectoryInterpolator(times, poses)
return final_interp
def __call__(self, t: Union[numbers.Number, np.ndarray]) -> np.ndarray:
is_single = False
if isinstance(t, numbers.Number):
is_single = True
t = np.array([t])
pose = np.zeros((len(t), 6))
if self.single_step:
pose[:] = self._poses[0]
else:
start_time = self.times[0]
end_time = self.times[-1]
t = np.clip(t, start_time, end_time)
pose = np.zeros((len(t), 6))
pose[:,:3] = self.pos_interp(t)
pose[:,3:] = self.rot_interp(t).as_rotvec()
if is_single:
pose = pose[0]
return pose
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