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utils.py
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utils.py
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import pandas as pd
import numpy as np
import math
from scipy.spatial.transform import Rotation as R
import os
import math
q_a = np.array([0.462, 0.191, 0.462, 0.733]) # Auxillary quaternion
unit_quaternion = np.array([0, 0, 0, 1])
def get_all_file_paths(directory):
file_paths = []
for root, dirs, files in os.walk(directory):
for file in files:
file_paths.append(os.path.join(root, file))
return file_paths
def get_transformed_trajectory(file_name, base_bias, cut_data=False, orientation=False, tg_based = False):
"""
Transform keypoints' trajectory into specified coordinate
tg_based: 转换到target坐标系下
"""
base_cols, eb_cols, wr_cols, ee_cols, target_cols = get_col_index(file_name)
T_w2base = read_data(file_name, base_cols, cut_data)
T_w2eb = read_data(file_name, eb_cols, cut_data)
T_w2wr = read_data(file_name, wr_cols, cut_data)
T_w2ee = read_data(file_name, ee_cols, cut_data)
T_w2tg = read_data(file_name, target_cols, cut_data)
if not tg_based:
qs_base2eb, ts_base2eb = keypoint_transform(T_w2base, T_w2eb, base_bias)
qs_base2wr, ts_base2wr = keypoint_transform(T_w2base, T_w2wr, base_bias)
qs_base2ee, ts_base2ee = keypoint_transform(T_w2base, T_w2ee, base_bias)
qs_base2tg, ts_base2tg = keypoint_transform(T_w2base, T_w2tg, base_bias)
if orientation:
return qs_base2eb, ts_base2eb, qs_base2wr, ts_base2wr, qs_base2ee, ts_base2ee, qs_base2tg, ts_base2tg
else:
return ts_base2eb, ts_base2wr, ts_base2ee, ts_base2tg
elif tg_based:
qs_tg2eb, ts_tg2eb = keypoint_transform(T_w2tg, T_w2eb, 0)
qs_tg2wr, ts_tg2wr = keypoint_transform(T_w2tg, T_w2wr, 0)
qs_tg2ee, ts_tg2ee = keypoint_transform(T_w2tg, T_w2ee, 0)
qs_tg2base, ts_tg2base = keypoint_transform(T_w2tg, T_w2base, 0)
if orientation:
return qs_tg2eb, ts_tg2eb, qs_tg2wr, ts_tg2wr, qs_tg2ee, ts_tg2ee, qs_tg2base, ts_tg2base
else:
return ts_tg2eb, ts_tg2wr, ts_tg2ee, ts_tg2base
def get_col_index(file_name):
data_cols = [i for i in range(2, 37)]
col_name_list = np.array(pd.read_csv(file_name, usecols=data_cols, skiprows=2, nrows=1)).reshape(-1)
# 找出每个字符串首次出现的索引
unique_elements, indices = np.unique(col_name_list, return_index=True)
# 按索引排序，以保持原始数组的顺序
sorted_indices = np.sort(indices)
# 结果
col_name_dict = {col_name_list[i]: i+2 for i in sorted_indices}
target_cols = [i for i in range(col_name_dict['target'], col_name_dict['target']+7)]
base_cols = [i for i in range(col_name_dict['base'], col_name_dict['base']+7)]
eb_cols = [i for i in range(col_name_dict['elbow'], col_name_dict['elbow']+7)]
wr_cols = [i for i in range(col_name_dict['wrist'], col_name_dict['wrist']+7)]
for key in col_name_dict.keys():
if key not in ['target', 'base', 'elbow', 'wrist']:
ee_key = key
break
ee_cols = [i for i in range(col_name_dict[ee_key], col_name_dict[ee_key]+7)]
return base_cols, eb_cols, wr_cols, ee_cols, target_cols
def read_data(file_name, data_cols, cut_data=False):
df_raw = pd.read_csv(file_name, usecols=data_cols, skiprows=6)
if cut_data:
T_w2data = np.array(df_raw)[cut_data[0]:cut_data[1]]
else:
T_w2data = np.array(df_raw)
return T_w2data
def keypoint_transform(T_w2base, T_w2k, base_bias):
"""
Transform Tw2k into Tbase2k (in all time)
"""
qs_w2base = T_w2base[:, :4]
ts_w2base = T_w2base[:, 4:7]
qs_w2k = T_w2k[:, :4]
ts_w2k = T_w2k[:, 4:7]
num_frame = T_w2base.shape[0]
qs_base2k = np.zeros((1, 4))
ts_base2k = np.zeros((1, 3))
for i in range(num_frame):
# base
q_w2base = qs_w2base[i, :]
t_w2base = ts_w2base[i, :]
# keypoint
q_w2k = qs_w2k[i, :]
t_w2k = ts_w2k[i, :]
# Transformation
q_base2k, t_base2k, _ = coordinate_transform(q_w2k, t_w2k, q_w2base, t_w2base)
# Concatenateis=0)
qs_base2k = np.concatenate((qs_base2k, q_base2k.reshape(1, 4)), axis=0)
ts_base2k = np.concatenate((ts_base2k, t_base2k.reshape(1, 3)), axis=0)
qs_base2k = qs_base2k[1:, :]
ts_base2k = ts_base2k[1:, :] + base_bias
return qs_base2k, ts_base2k
def coordinate_transform(q_w2k, t_w2k, q_w2base, t_w2base):
"""
Transform Tw2k into Tbase2k (in unit time)
"""
r_w2base = R.from_quat(q_w2base).as_matrix() # Get object rotation matrix from quaternion
r_w2k = R.from_quat(q_w2k).as_matrix() # Get hand rotation matrix from quaternion
# Transform
r_base2k = (np.linalg.inv(r_w2base)).dot(r_w2k)
q_base2k = R.from_matrix(r_base2k).as_quat()
t_base2k = np.linalg.inv(r_w2base).dot(t_w2k + (-t_w2base))
tf_base2k = np.concatenate((q_base2k, t_base2k), axis=0)
return q_base2k, t_base2k, tf_base2k
def rgbody_transform(q_base2tg, t_base2tg, q_tg2k, t_tg2k):
"""
对空间中某一刚体k进行坐标变换，即将其从tg坐标系转换到base坐标系下
"""
R_base2tg = R.from_quat(q_base2tg).as_matrix()
R_tg2k = R.from_quat(q_tg2k).as_matrix()
q = R.from_matrix(R_base2tg.dot(R_tg2k)).as_quat()
t = R_base2tg.dot(t_tg2k) + t_base2tg
return q, t
def down_sample(data, interval=1):
return data[::interval, :]
def quaternion_product(q1, q2, conjugate=False):
"""
计算四元数q1与q2的共轭的乘积。
q1: 第一个四元数，形式为 ((x, y, z), v)，v 是实部，(x, y, z) 是虚部（一个三维向量）。
q2: 第二个四元数，形式为 ((x, y, z), v)。
返回值: 乘积后的四元数，形式为 ((x, y, z), v)。
"""
# 提取四元数的实部和虚部
u1, v1 = q1
u2, v2 = q2
# 虚部的分量
x1, y1, z1 = u1
if conjugate:
x2, y2, z2 = (-u2[0], -u2[1], -u2[2])
else:
x2, y2, z2 = (u2[0], u2[1], u2[2])
# 计算实部 v
v = v1 * v2 - (x1 * x2 + y1 * y2 + z1 * z2)
# 计算虚部 u = (x, y, z)
x = v1 * x2 + x1 * v2 + y1 * z2 - z1 * y2
y = v1 * y2 + y1 * v2 + z1 * x2 - x1 * z2
z = v1 * z2 + z1 * v2 + x1 * y2 - y1 * x2
# 返回结果，形式为 ((x, y, z), v)
return ((x, y, z), v)
def quaternion2euler(q_n):
q = quaternion_product(((q_n[0], q_n[1], q_n[2]), q_n[3]), ((q_a[0], q_a[1], q_a[2]), q_a[3]), conjugate=True) # (u, v)
u, v = q
if u == (0, 0, 0):
log_q = np.array([0, 0, 0])
else:
log_q = math.acos(v) * np.array(u) / np.linalg.norm(u, ord=2)
return log_q
def euler2quaternion(log_q):
norm_log_q = np.linalg.norm(log_q, ord=2)
if np.all(log_q[:]==0):
exp_log_q = ((0, 0, 0), 1)
else:
exp_log_q = (tuple((math.sin(np.linalg.norm(log_q, ord=2))) * log_q / norm_log_q), math.cos(norm_log_q))
print(exp_log_q)
q_n = quaternion_product(exp_log_q, ((q_a[0], q_a[1], q_a[2]), q_a[3]), conjugate=False)
q_n = np.hstack((np.array(q_n[0]), np.array(q_n[1])))
return q_n
def calculate_speed_3d(displacement_matrix, time_interval=0.01):
displacement_diff = np.diff(displacement_matrix, axis=0)
speed_matrix = displacement_diff / time_interval
speed_matrix = np.vstack((speed_matrix, [0, 0, 0]))
return speed_matrix
def calculate_angular_speed(quaternions, time_interval=0.01):
"""
计算每个时间点的角速度。
参数：
- quaternions: 形状为 (N, 4) 的四元数序列，N 是时间点数量。
- time_interval: 固定的时间间隔。
返回：
- angular_velocities: 形状为 (N, 3) 的角速度序列，每个时刻对应的角速度向量。
"""
angular_velocities = []
# 遍历每一对相邻的四元数
for i in range(1, len(quaternions)):
# 当前四元数和前一个四元数
q1 = R.from_quat(quaternions[i-1])
q2 = R.from_quat(quaternions[i])
# 计算相对旋转: q_rel = q1.inverse() * q2
q_rel = q1.inv() * q2
# 提取旋转向量
rotvec = q_rel.as_rotvec() # 旋转向量，单位是弧度
# 角速度: ω = Δθ / Δt
angular_velocity = rotvec / time_interval
angular_velocities.append(angular_velocity)
# 末尾时刻速度为零
angular_velocities.append([0, 0, 0])
return np.array(angular_velocities)
def compute_point_dist(A, B):
for (a, b) in zip(A, B):
d = math.sqrt(math.pow(a[0]-b[0],2)
+math.pow(a[1]-b[1],2)
+math.pow(a[2]-b[2],2))
print(d)
def hand_init_bias(y, bias):
for i in range(len(y.T)):
y[2,i] = y[2,i] + bias # bias on z axis
return y
colors = [[142, 207, 201],
[255, 190, 122],
[250, 127, 111],
[130, 176, 210],
[190, 184, 220],
[153, 153, 153],
[231, 218, 210],
[40, 120, 181],
[154, 201, 219],
[195, 36, 35],
[20, 81, 124],
[231, 239, 245],
[150, 195, 125],
[243, 210, 102],
[196, 151, 178],
[73, 108, 136],
[169, 184, 198],
[169, 144, 126],
[243, 222, 186],
[171, 196, 170],
[103, 93, 80],
[252, 115, 0],
[191, 219, 56],
[31, 138, 112]]
colorlib = []
for color in colors:
color = np.array(color) / 255
colorlib.append(color)
# if __name__ == "__main__":