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kinkit.py
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kinkit.py
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import numpy as np
from numpy import cos as c
from numpy import sin as s
# Base Rotation DCMs
def R3(t):
return np.array([[c(t), s(t), 0],
[-1*s(t), c(t), 0],
[0, 0, 1]])
def R2(t):
return np.array([[c(t), 0, -s(t)],
[0, 1, 0],
[s(t), 0, c(t)]])
def R1(t):
return np.array([[1, 0, 0],
[0, c(t), s(t)],
[0,-1*s(t), c(t)]])
# Euler Angle Mappings
def EAtoDCM(seq, ang1, ang2, ang3):
ax1 = int(str(seq)[0])
ax2 = int(str(seq)[1])
ax3 = int(str(seq)[2])
# Find sequence
match ax1:
case 1:
rot1 = R1(ang1)
case 2:
rot1 = R2(ang1)
case 3:
rot1 = R3(ang1)
match ax2:
case 1:
rot2 = R1(ang2)
case 2:
rot2 = R2(ang2)
case 3:
rot2 = R3(ang2)
match ax3:
case 1:
rot3 = R1(ang3)
case 2:
rot3 = R2(ang3)
case 3:
rot3 = R3(ang3)
# compute DCM
DCM = np.matmul(rot3, np.matmul(rot2, rot1))
return DCM
def DCMtoEA(sequence, DCM):
match sequence:
case 121:
return np.flip(np.array([np.arctan2(DCM[1][0], DCM[2][0]),
np.arccos(DCM[0][0]),
np.arctan2(DCM[0][1], -DCM[0][2])]))
case 123:
return np.flip(np.array([np.arctan2(DCM[1][2], DCM[2][2]),
-np.arcsin(DCM[0][2]),
np.arctan2(DCM[0][1], DCM[0][0])]))
case 131:
return np.flip(np.array([np.arctan2(DCM[2][0], -DCM[1][0]),
np.arccos(DCM[0][0]),
np.arctan2(DCM[0][2], DCM[0][1])]))
case 132:
return np.flip(np.array([np.arctan2(-DCM[2][1], DCM[1][1]),
np.arcsin(DCM[0][1]),
np.arctan2(-DCM[0][2], DCM[0][0])]))
case 212:
return np.flip(np.array([np.arctan2(DCM[0][1], -DCM[2][1]),
np.arccos(DCM[1][1]),
np.arctan2(DCM[1][0], DCM[1][2])]))
case 213:
return np.flip(np.array([np.arctan2(-DCM[0][2], DCM[2][2]),
np.arcsin(DCM[1][2]),
np.arctan2(-DCM[1][0], DCM[1][1])]))
case 231:
return np.flip(np.array([np.arctan2(DCM[2][0], DCM[0][0]),
-np.arcsin(DCM[1][0]),
np.arctan2(DCM[1][2], DCM[1][1])]))
case 232:
return np.flip(np.array([np.arctan2(DCM[2][1], DCM[0][1]),
np.arccos(DCM[1][1]),
np.arctan2(DCM[1][2], -DCM[1][0])]))
case 312:
return np.flip(np.array([np.arctan2(DCM[0][1], DCM[1][1]),
-np.arcsin(DCM[2][1]),
np.arctan2(DCM[2][0], DCM[2][2])]))
case 313:
return np.flip(np.array([np.arctan2(DCM[0][2], DCM[1][2]),
np.arccos(DCM[2][2]),
np.arctan2(DCM[2][0], -DCM[2][1])]))
case 321:
return np.flip(np.array([np.arctan2(-DCM[1][0], DCM[0][0]),
np.arcsin(DCM[2][0]),
np.arctan2(-DCM[2][1], DCM[2][2])]))
case 323:
return np.flip(np.array([np.arctan2(DCM[1][2], -DCM[0][2]),
np.arccos(DCM[2][2]),
np.arctan2(DCM[2][1], DCM[2][0])]))
# PRP Mappings
def DCMtoPRP(DCM):
theta = np.arccos(0.5*(DCM[0][0]+DCM[1][1]+DCM[2][2]-1))
lamHat = (1/(2*np.sin(theta))) * np.array([DCM[1][2]-DCM[2][1],
DCM[2][0]-DCM[0][2],
DCM[0][1]-DCM[1][0]])
return (theta, lamHat)
def PRPtoDCM(PRP):
th, lh = PRP
DCM = np.array([[((lh[0] ** 2) * (1 - c(th)) + c(th)), ((lh[0] * lh[1]) * (1 - c(th)) + (lh[2] * s(th))),
((lh[0] * lh[2]) * (1 - c(th)) - (lh[1] * s(th)))],
[((lh[1] * lh[0]) * (1 - c(th)) - (lh[2] * s(th))), ((lh[1] ** 2) * (1 - c(th)) + c(th)),
((lh[1] * lh[2]) * (1 - c(th)) + (lh[0] * s(th)))],
[((lh[2] * lh[0]) * (1 - c(th)) + (lh[1] * s(th))),
((lh[2] * lh[1]) * (1 - c(th)) - (lh[0] * s(th))), ((lh[2] ** 2) * (1 - c(th)) + c(th))]])
return DCM
# CRP Mappings
def DCMtoCRP(DCM):
theta, lamHat = DCMtoPRP(DCM)
rho = lamHat*np.tan(theta/2)
return rho
def CRPtoDCM(CRP):
eps4 = 1/np.sqrt(1 + np.dot(CRP, CRP))
eps13 = CRP/np.sqrt(1 + np.dot(CRP, CRP))
return EPtoDCM(np.array([eps13[0], eps13[1], eps13[2], eps4]))
# MRP Mappings
def DCMtoMRP(DCM):
theta, lamHat = DCMtoPRP(DCM)
sigma = lamHat*np.tan(theta/4)
return sigma
def MRPtoDCM(MRP):
eps4 = (1-np.dot(MRP, MRP))/(1+np.dot(MRP, MRP))
eps13 = (2*MRP)/(1+np.dot(MRP, MRP))
return EPtoDCM(np.array([eps13[0], eps13[1], eps13[2], eps4]))
# Euler Parameter (Quaternion) mappings
def DCMtoEP(DCM): # Sheppard's method
e1sq = (1 / 4) * (1 + (2 * DCM[0][0]) - np.trace(DCM))
e2sq = (1 / 4) * (1 + (2 * DCM[1][1]) - np.trace(DCM))
e3sq = (1 / 4) * (1 + (2 * DCM[2][2]) - np.trace(DCM))
e4sq = (1 / 4) * (1 + np.trace(DCM))
if np.max([e1sq, e2sq, e3sq, e4sq]) == e1sq:
eps = (1 / (4 * np.sqrt(e1sq))) * np.array(
[4 * e1sq, DCM[0][1] + DCM[1][0], DCM[2][0] + DCM[0][2], DCM[1][2] - DCM[2][1]])
elif np.max([e1sq, e2sq, e3sq, e4sq]) == e2sq:
eps = (1 / (4 * np.sqrt(e2sq))) * np.array(
[DCM[0][1] + DCM[1][0], 4 * e2sq, DCM[1][2] + DCM[2][1], DCM[2][0] - DCM[0][2]])
elif np.max([e1sq, e2sq, e3sq, e4sq]) == e3sq:
eps = (1 / (4 * np.sqrt(e3sq))) * np.array(
[DCM[2][0] + DCM[0][2], DCM[1][2] + DCM[2][1], 4 * e3sq, DCM[0][1] - DCM[1][0]])
elif np.max([e1sq, e2sq, e3sq, e4sq]) == e4sq:
eps = (1 / (4 * np.sqrt(e4sq))) * np.array(
[DCM[1][2] - DCM[2][1], DCM[2][0] - DCM[0][2], DCM[0][1] - DCM[1][0], 4 * e4sq])
if eps[3] < 0:
return -1 * eps
else:
return eps
def EPtoDCM(E):
DCM = np.array([[1-(2*E[1]**2) - (2*E[2]**2), 2*(E[0]*E[1] + E[2]*E[3]), 2*(E[0]*E[2] - E[1]*E[3])],
[2*(E[0]*E[1] - E[2]*E[3]), 1-(2*E[0]**2) - (2*E[2]**2), 2*(E[1]*E[2] + E[0]*E[3])],
[2*(E[0]*E[2] + E[1]*E[3]), 2*(E[1]*E[2] - E[0]*E[3]), 1-(2*E[0]**2) - (2*E[1]**2)]])
return DCM
def DCMtoEP_standard(DCM):
theta, lamHat = DCMtoPRP(DCM)
eps13 = lamHat * np.sin(theta / 2)
eps4 = np.cos(theta / 2)
if eps4 < 0:
return -1 * np.array([eps13[0], eps13[1], eps13[2], eps4])
else:
return np.array([eps13[0], eps13[1], eps13[2], eps4])
def dwdt_Bframe(t, omega, I, L):
omedot = [((-(I[2]-I[1])*omega[1]*omega[2]) + (L[0]))/I[0],
((-(I[0]-I[2])*omega[0]*omega[2]) + (L[1]))/I[1],
((-(I[1]-I[0])*omega[0]*omega[1]) + (L[2]))/I[2]]
return omedot
def EP_KDE(t, epsilon, omega):
omegaA = np.array([omega[0], omega[1], omega[2], 0])
magic = np.array([[EP[3], -EP[2], EP[1], EP[0]],
[EP[2], EP[3], -EP[0], EP[1]],
[-EP[1], EP[0], EP[3], EP[2]],
[-EP[0], -EP[1], -EP[2], EP[3]]])
epsilonDot = (0.5)*np.matmul(magic, omegaA)
return epsilonDot
def MRP_KDE_std(t, MRP, omega):
ss = np.dot(MRP, MRP)
omegaA = np.array([omega[0], omega[1], omega[2]])
magic = np.array([[1-ss+2*(MRP[0]**2), 2*(MRP[0]*MRP[1] - MRP[2]), 2*(MRP[0]*MRP[2] + MRP[1])],
[2*(MRP[1]*MRP[0] + MRP[2]), 1-ss+2*(MRP[1]**2), 2*(MRP[1]*MRP[2] - MRP[0])],
[2*(MRP[2]*MRP[0] - MRP[1]), 2*(MRP[2]*MRP[1] + MRP[0]), 1-ss+2*(MRP[2]**2)]])
sigmaDot = (0.25)*np.matmul(magic, omegaA)
return sigmaDot