File size: 3,192 Bytes
a199a9b |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 |
# Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
import numpy as np
from loguru import logger
from projectaria_tools.core.sophus import SE3
class HandEyeSolver:
def __init__(self, smooth: bool, window: int, skip: int = 240, stride: int = 1):
self.stride = int(stride)
self.smooth = smooth
self.skip = int(skip)
self.window = int(window)
if self.window < 240:
self.smooth = False
def so3xR3(self, T_Wa_A: list[SE3], T_Wb_B: list[SE3]) -> SE3:
"""
\return T_A_B using so3xR3 SVD decomposition.
"""
assert len(T_Wa_A) == len(T_Wb_B)
N = len(T_Wa_A) - self.stride
se3_A1_A2 = [T_Wa_A[i].inverse() @ T_Wa_A[i + self.stride] for i in range(N)]
se3_B1_B2 = [T_Wb_B[i].inverse() @ T_Wb_B[i + self.stride] for i in range(N)]
# solve for R
log_A1_A2 = [x.rotation().log() for x in se3_A1_A2]
log_B1_B2 = [x.rotation().log() for x in se3_B1_B2]
A = np.stack(log_A1_A2, axis=-1).squeeze()
B = np.stack(log_B1_B2, axis=-1).squeeze()
logger.debug(f"{A.shape=}, {B.shape=}")
matrixU, S, matrixVh = np.linalg.svd(
B @ A.transpose(), full_matrices=True, compute_uv=True
)
logger.debug(f"{matrixU.shape=}, {S.shape=}, {matrixVh.shape=}")
RX = matrixVh @ matrixU.transpose()
if np.linalg.det(RX) < 0:
RX[2, :] = RX[2, :] * -1.0
# solve for t
jacobian = [x.rotation().to_matrix() - np.eye(3) for x in se3_A1_A2]
jacobian = np.concatenate(jacobian, axis=0)
assert jacobian.shape == (N * 3, 3)
logger.debug(f"{jacobian.shape=}")
residual = [
RX @ b.translation().reshape(3, 1) - a.translation().reshape(3, 1)
for a, b in zip(se3_A1_A2, se3_B1_B2)
]
residual = np.concatenate(residual, axis=0)
assert residual.shape == (N * 3, 1)
logger.debug(f"{residual.shape=}")
JTJ = jacobian.T @ jacobian
JTr = jacobian.T @ residual
tX = np.linalg.lstsq(JTJ, JTr, rcond=None)[0]
T_A_B = np.ndarray([3, 4])
T_A_B[:3, :3] = RX
T_A_B[:3, 3] = tX.squeeze()
logger.debug(f"{T_A_B=}\n")
T_A_B = SE3.from_matrix3x4(T_A_B)
return T_A_B
def __call__(self, T_Wa_A: list[SE3], T_Wb_B: list[SE3]) -> list[SE3]:
N = len(T_Wa_A)
assert N == len(T_Wb_B)
if self.window >= N or not self.smooth:
T_A_B = self.so3xR3(T_Wa_A, T_Wb_B)
return [T_A_B]
Ts_A_B = []
for i in range(0, N, self.skip):
istart = int(i - self.window / 2)
if istart < 0:
istart = 0
iend = istart + self.window
if iend >= N:
iend = -1
istart = N - self.window
t_wa_a = T_Wa_A[istart:iend]
t_wb_b = T_Wb_B[istart:iend]
T_A_B = self.so3xR3(t_wa_a, t_wb_b)
Ts_A_B.append(T_A_B)
return Ts_A_B
|