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com.py
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# -*- coding: utf-8 -*-
"""
Created on Tue Jun 2 22:03:15 2020
@author: mocki
"""
import glv
import numpy as np
def norm(x):
return np.sqrt(x @ x)
def antisym(v):
'''
Parameters
----------
v : list (3 entries)
1x3 vector
Returns
-------
Antisymmetric matrix:
'''
if not len(v) == 3:
raise Exception("Vector length large than 3!")
v_ = np.asarray(v)
vx = np.array([
[0, -v_[2], v_[1]],
[v_[2], 0, -v_[0]],
[-v_[1], v_[0], 0]
])
return vx
def quaterAnti(q):
if not len(q) == 4:
raise Exception("Quaternion length large than 4!")
q_ = np.asarray(q)
qx = np.array([
[q_[0], -q_[1], -q_[2], -q_[3]],
[q_[1], q_[0], -q_[3], q_[2]],
[q_[2], q_[3], q_[0], -q_[1]],
[q_[3], -q_[2], q_[1], q_[0]]
])
return qx
def quaterConjugate(q):
q = np.asarray(q)
qc = np.copy(q)
qc[1:] *= -1
return qc
def quaterMultiply(q1, q2):
q1 = np.asarray(q1)
q2 = np.asarray(q2)
return quaterAnti(q1) @ q2
def euler2quater(euler):
'''
euler angles :
[roll, pitch, yaw(heading)], righthand
roll -> phi
pitch -> theta
yaw -> psi
quaternion :
q0, q1, q2, q3
'''
phi, theta, psi = euler
sphi_2,cphi_2 = np.sin(phi/2),np.cos(phi/2)
stheta_2,ctheta_2 = np.sin(theta/2),np.cos(theta/2)
spsi_2,cpsi_2 = np.sin(psi/2),np.cos(psi/2)
q0 = cphi_2*ctheta_2*cpsi_2 + sphi_2*stheta_2*spsi_2
q1 = sphi_2*ctheta_2*cpsi_2 - cphi_2*stheta_2*spsi_2
q2 = cphi_2*stheta_2*cpsi_2 + sphi_2*ctheta_2*spsi_2
q3 = cphi_2*ctheta_2*spsi_2 - sphi_2*stheta_2*cpsi_2
q = quater2unit(np.array([q0,q1,q2,q3]))
return q
def rotvec2quater(eqv):
eqv = np.asarray(eqv)
meqv_2 = norm(eqv/2)
q = np.zeros(4)
if np.abs(meqv_2) < 1e-9:
return q
else:
q[0] = np.cos(meqv_2)
q[1:] = np.sin(meqv_2) / meqv_2 * eqv / 2
return q
def euler2rotation(euler):
phi, theta, psi = euler
sphi,cphi = np.sin(phi),np.cos(phi)
stheta,ctheta = np.sin(theta),np.cos(theta)
spsi,cpsi = np.sin(psi),np.cos(psi)
r = np.array([
[ctheta*cpsi, -cphi*spsi + sphi*stheta*cpsi, sphi*spsi + cphi*stheta*cpsi],
[ctheta*spsi, cphi*cpsi + sphi*stheta*spsi , -sphi*cpsi + cphi*stheta*spsi],
[-stheta , sphi*ctheta , cphi*ctheta]
])
return r
def quater2rotation(q):
q0 = q[0]; q1 = q[1]; q2 = q[2]; q3 = q[3];
r = np.array([
[q0**2 + q1**2 - q2**2 - q3**2, 2 * (q1*q2 - q0*q3) , 2 * (q0*q2 + q1*q3)],
[2 * (q0*q3 + q1*q2) , q0**2 - q1**2 +q2**2 - q3**2, 2 * (q2*q3 - q0*q1)],
[2 * (q1*q3 - q0*q2) , 2 * (q0*q1 + q2*q3) , q0**2 - q1**2 - q2**2 + q3**2]
])
return r
def rotvec2rotation(eqv):
'''
eqv :
eqv_x, eqv_y, eqv_z
'''
eqv = np.asarray(eqv)
meqv = norm(eqv)
anti_eqv = antisym(eqv)
r = np.identity(3) + np.sin(meqv) / meqv * anti_eqv + (1 - np.cos(meqv)) / meqv**2 * (anti_eqv @ anti_eqv)
return r
def rotation2euler(r):
phi = np.arctan2(r[2][1], r[2][2])
theta = np.arctan(-r[2][0]/np.sqrt(r[2][1]**2 + r[2][2]**2))
psi = np.arctan2(r[1][0], r[0][0])
euler = np.array([phi, theta, psi])
return euler
def quater2unit(q):
q = np.asarray(q)
mq = norm(q)
return q / mq
def mcucradius(lat):
'''
Parameters
----------
lat : float(rad)
latitude of local
Returns
-------
Rm,Rn
Radius of meridian circle & Radius of unitary circle
'''
dump = 1 - glv.E2_WGS84 * np.sin(lat) ** 2
Rm = glv.RE_WGS84 * (1 - glv.E2_WGS84) / dump ** 1.5
Rn = glv.RE_WGS84 / np.sqrt(dump)
return Rm, Rn
def earthrotatvec(loc,vel):
lat = loc[0]
h = loc[2]
vn = vel[0]
ve = vel[1]
Rm,Rn = mcucradius(lat)
omega_n_ie = np.array([glv.EARTH_ROTATE * np.cos(lat), 0, -glv.EARTH_ROTATE * np.sin(lat)])
omega_n_en = np.array([ve / (Rn + h), -vn / (Rm + h), -ve * np.tan(lat) / (Rn + h)])
return omega_n_ie, omega_n_en
def getgravity(lat, h):
sinlat = np.sin(lat)
coslat = np.cos(lat)
m = glv.EARTH_ROTATE**2 * glv.RE_WGS84**2 * glv.BE_WGS84 / glv.GM
gama_lat = (glv.RE_WGS84 * glv.GAMA_A * coslat**2 + glv.BE_WGS84 * glv.GAMA_B * sinlat**2) \
/ np.sqrt(glv.RE_WGS84**2 * coslat**2 + glv.BE_WGS84**2 * sinlat**2)
gama = gama_lat * (1 - \
2 / glv.RE_WGS84 * (1 + glv.FR_WGS84 + m - 2 * glv.FR_WGS84 * sinlat**2) * h \
+ 3 * h**2 / glv.RE_WGS84**2)
gama_n = np.array([0 , 0, gama])
return gama_n
def DrMat(loc, itype = 0):
Rm, Rn = mcucradius(loc[0])
if not itype:
Dr = np.diag([Rm + loc[2], (Rn + loc[2]) * np.cos(loc[0]), -1])
else:
Dr = np.diag([1 / (Rm + loc[2]), 1 / ((Rn + loc[2]) * np.cos(loc[0])), -1])
return Dr
def rv2m(rv):
mat = antisym(rv)
mat = np.identity(3) - mat
return mat
# inpos = [0.0107951084511778 * glv.D2R, -2.14251290749072 * glv.D2R, -75.7498049314083 * glv.D2R]
# qua = euler2quater(inpos)
# rot = euler2rotation(inpos)
# rot_ = quater2rotation(qua)
# pos_ = rotation2euler(rot)
# eqv = [0.0107951084511778 * glv.D2R, -2.14251290749072 * glv.D2R, -75.7498049314083 * glv.D2R]
# qua = rotvec2quater(eqv)
# rot = rotvec2rotation(eqv)
# rot_ = quater2rotation(qua)
# eqv = [1,2,3]
# q = rotvec2quater(eqv)
# r = quater2rotation(q)
# euler = rotation2euler(r)
# print(q)
# print(e)
# print(e_)