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Copy pathMultirotor+pinpoint_correct_1.py
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Multirotor+pinpoint_correct_1.py
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#!/usr/bin/env python
# coding: utf-8
# In[55]:
import numpy as np
import matplotlib.pyplot as plt
import math
import copy
import matplotlib.pyplot as plt
import cvxpy as cp
import copy
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
Deg2Rad = np.pi/180
Rad2Deg = 1/Deg2Rad
dt = 0.01 # control frequency
tf = 7 # final time
g = 9.8 # m/s^2
l = 1.0 # m
m = 23.56 # kg
Ix = 1.676 # kg m^2
Iy = 1.676 # kg m^2
Iz = 2.9743 # kg m^2
# rotor characteristics
kf = 1.1 # N / V^2
kt = 0.52 # N m / V^2
rotor_limit = 10 # rotor limit
rotor_sr_limit = rotor_limit/0.1 # rotor slew rate limit
omega_rotor, zeta_rotor = 40, 0.8
t_fail = 3
t_detect = 0.2
r_fail = 5
c = l # chord length
nRotors = 8
loc = np.zeros((nRotors,3))
# rotor 0-7 position
# 0,2,4,6: positive yaw rotation
# 1,3,5,7: negative yaw rotation
loc[0] = np.array([ 0.25*c, 2.5*c, 0])
loc[1] = np.array([ 0.25*c, 1.5*c, 0])
loc[2] = np.array([ 0.25*c, -1.5*c, 0])
loc[3] = np.array([ 0.25*c, -2.5*c, 0])
loc[4] = np.array([-0.75*c, -2.5*c, 0])
loc[5] = np.array([-0.75*c, -1.5*c, 0])
loc[6] = np.array([-0.75*c, 1.5*c, 0])
loc[7] = np.array([-0.75*c, 2.5*c, 0])
thrust = np.array([0, 0, -kf])
moments = np.cross(loc, thrust)
plt.figure(num=1, figsize=(6,6), dpi=100)
plt.broken_barh([(-0.5, 1.0)], (-3.0, 5.0), alpha = 0.2) # fuselage
plt.broken_barh([(-3.0, 6.0)], (-0.75, 1.0), alpha = 0.2) # wing
plt.broken_barh([(-1.2, 2.4)], (-3.0, 1.0), alpha = 0.2) # tail
plt.plot(loc[0::2,1]/c, loc[0::2,0]/c, 'o', markersize=6, label='CW rotation')
plt.plot(loc[1::2,1]/c, loc[1::2,0]/c, 'o', markersize=6, label='CCW rotation')
plt.plot(loc[0::2,1]/c, loc[0::2,0]/c, 'o', alpha=0.1, markersize=30)
plt.plot(loc[1::2,1]/c, loc[1::2,0]/c, 'o', alpha=0.1, markersize=30)
for i in range(nRotors) :
plt.text(loc[i,1]+0.2, loc[i,0]/c+0.2, 'R%i' %i)
plt.xlabel(r'$y_B$ (chord)')
plt.ylabel(r'$x_B$ (chord)')
plt.legend()
plt.axis('equal')
plt.grid()
plt.show()
A = np.zeros((4,nRotors)) # rotor speed (sq) to control (thr/torque)
A[0,:] = np.ones(nRotors)*kf # thrust
A[[1,2],:] = moments[:,[0,1]].T # roll moment , pitch moment
A[3,0::2] = -kt # yaw moment (CW rotors)
A[3,1::2] = kt # yaw moment (CCW rotors)
print('location:\n',loc)
print('moments:\n', moments)
print('A:\n',A)
# In[56]:
def compute_location_cvx(destination) :
l_des = destination
L = [-(1/3), 1, 0]
landing_loc = cp.Variable(3)
#print(L@landing_loc)
#print(np.shape(landing_loc-l_des))
obj_loc = cp.sum_squares(landing_loc-l_des)
obj = cp.Minimize(obj_loc)
constr = [#L@landing_loc >= 3,
L@landing_loc <= 0]
cp.Problem(obj, constr).solve(verbose=False)
l_loc = landing_loc.value
#print(l_loc)
#print(np.shape(l_loc))
return l_loc
#compute_location_cvx([3,5,0])
# In[57]:
# guidance command computation
def compute_guidance(state, t, t_index):
if not hasattr(compute_guidance, "counter"):
compute_guidance.counter = 0
compute_guidance.cmd0 = 0
compute_guidance.cmd1 = 0
compute_guidance.cmd2 = 0
compute_guidance.cmd3 = 0
u,v,w,p,q,r,x,y,z,phi,the,psi = state[:12] # state variables
rotor = state[12:12+nRotors]
rotor_dot = state[12+nRotors:]
s_phi, c_phi = np.sin(phi), np.cos(phi)
s_the, c_the = np.sin(the), np.cos(the)
s_psi, c_psi = np.sin(psi), np.cos(psi)
Cbn = np.array([ [c_psi*c_the, c_psi*s_the*s_phi-s_psi*c_phi, c_psi*s_the*c_phi+s_psi*s_phi], [s_psi*c_the, s_psi*s_the*s_phi+c_psi*c_phi, s_psi*s_the*c_phi-c_psi*s_phi], [ -s_the, c_the*s_phi, c_the*c_phi] ])
x_dot,y_dot,z_dot = np.dot(Cbn,[u,v,w])
h_dot = -z_dot
h = -z
omg_alt, zet_alt = 2, 0.8
omg_pos, zet_pos = 2, 0.8
if t < t_fail+t_detect:
h_cmd = 1
x_cmd = 1
y_cmd = 2
psi_cmd = 10*Deg2Rad
# altitude loop
up_cmd = -2*zet_alt*omg_alt*h_dot + omg_alt**2*(h_cmd-h) + g
thrust = m*up_cmd/(c_phi*c_the)
# horizontal position loop
ax_cmd = -2*zet_pos*omg_pos*x_dot + omg_pos**2*(x_cmd-x)
ay_cmd = -2*zet_pos*omg_pos*y_dot + omg_pos**2*(y_cmd-y)
au_cmd, av_cmd, aw_cmd = np.dot(Cbn.T,[ax_cmd,ay_cmd,0])
the_cmd = np.arctan2(-au_cmd,g)
phi_cmd = np.arctan2( av_cmd,g)
else :
if (compute_guidance.counter%5==0):
thrust, phi_cmd, the_cmd, psi_cmd = compute_guidance_cvx([x,y,z],[x_dot,y_dot,z_dot],psi,tf-t)
compute_guidance.cmd0 = thrust
compute_guidance.cmd1 = phi_cmd
compute_guidance.cmd2 = the_cmd
compute_guidance.cmd3 = psi_cmd
else:
thrust = compute_guidance.cmd0
phi_cmd = compute_guidance.cmd1
the_cmd = compute_guidance.cmd2
psi_cmd = compute_guidance.cmd3
compute_guidance.counter += 1
return np.array([thrust, phi_cmd, the_cmd, psi_cmd])
'''
elif t < t_fail+t_detect:
h_cmd = 2.5
x_cmd = 0.4
y_cmd = 0.6
psi_cmd = 0*Deg2Rad
# altitude loop
up_cmd = -2*zet_alt*omg_alt*h_dot + omg_alt**2*(h_cmd-h) + g
thrust = m*up_cmd/(c_phi*c_the)
# horizontal position loop
ax_cmd = -2*zet_pos*omg_pos*x_dot + omg_pos**2*(x_cmd-x)
ay_cmd = -2*zet_pos*omg_pos*y_dot + omg_pos**2*(y_cmd-y)
au_cmd, av_cmd, aw_cmd = np.dot(Cbn.T,[ax_cmd,ay_cmd,0])
the_cmd = np.arctan2(-au_cmd,g)
phi_cmd = np.arctan2( av_cmd,g)
'''
'''
#compute location
def compute_location_cvx(destination) :
l_des = destination
L = [-(1/3), 1, 0]
landing_loc = cp.Variable(3)
obj_loc = cp.sum_squares(landing_loc-l_des)
obj = cp.Minimize(obj_loc)
constr = [L@landing_loc >= 3,
L@landing_loc <= 0]
cp.Problem(obj, constr).solve(verbose=False)
l_loc = landing_loc.value
return l_loc
'''
# guidance command computation_convex
def compute_guidance_cvx(position, velocity, psi, tgo):
delt = 0.05
T = tgo
N = int(T/delt)
base_loc = np.zeros(3)
base_loc[0] = 3
base_loc[1] = 5
base_loc[2] = 0
r_des = compute_location_cvx(base_loc)
#print(np.shape(r_des))
#print(r_des)
#r_des = np.zeros(3)
#r_des[0] = 1
#r_des[1] = 1
r_des[2] = 0
v_des = np.zeros(3)
g_pin = np.zeros(3)
g_pin[2] = 9.8
T2 = 720
T_c = cp.Variable((3,N+1))
r_pin = cp.Variable((3,N+1))
v_pin = cp.Variable((3,N+1))
mag = cp.norm(T_c,axis=0)
obj = cp.Minimize(cp.norm(mag))
constr = [
v_pin[:,0] == velocity,
r_pin[:,0] == position,
v_pin[:,-1] == v_des,
r_pin[:,-1] == r_des,
#r_pin[2,-1] == 0,
]
# 3축 최적 추력 명령 산출
for t in range(N):
constr += [
#r_pin[:,t+1] == r_pin[:,t] + 0.5*delt*(v_pin[:,t]+v_pin[:,t+1]) + delt**2/12*(T_c[:,t+1]/m-T_c[:,t]/m),
#v_pin[:,t+1] == v_pin[:,t] + 0.5*delt*(T_c[:,t]/m+T_c[:,t+1]/m) + g_pin*delt,
r_pin[:,t+1] == r_pin[:,t] + v_pin[:,t]*delt,
v_pin[:,t+1] == v_pin[:,t] + (T_c[:,t]/m+g_pin)*delt,
cp.norm(T_c[:,t]) <= T2,
T_c[2,t]<=0,
]
prob = cp.Problem(obj, constr)
prob.solve(verbose=False,solver=cp.ECOS)
if prob.status=='optimal' or prob.status=='optimal_inaccurate':
T_n, T_e, T_d = T_c.value[:,0]
# T_e = T_c.value[1,0]
# T_d = T_c.value[2,0]
# 추력 명령 -> 자세각 명령 변환 loop
T_a = T_n*np.cos(psi) + T_e*np.sin(psi)
T_b = -T_n*np.sin(psi) + T_e*np.cos(psi)
thrust = np.sqrt(T_d**2+T_n**2+T_e**2)
the_cmd = -np.arctan2(T_a,-T_d)
phi_cmd = np.arcsin(T_b/thrust)
psi_cmd = psi
print(tgo, prob.status)
else:
thrust, phi_cmd, the_cmd, psi_cmd = 0, 0, 0, 0
print(tgo, prob.status)
if position[2]>=0:
thrust, phi_cmd, the_cmd, psi_cmd = 0, 0, 0, 0
return np.array([thrust,phi_cmd,the_cmd,psi_cmd])
# control computation
def compute_control(guidance_cmd, state, t):
u,v,w,p,q,r,x,y,z,phi,the,psi = state[:12] # state variables
thrust, phi_cmd, the_cmd, psi_cmd = guidance_cmd
omg_phi, zet_phi = 8, 0.7
omg_the, zet_the = 8, 0.7
omg_psi, zet_psi = 4, 0.9
torque_phi = -2*zet_phi*omg_phi*p + omg_phi**2*(phi_cmd-phi)
torque_the = -2*zet_the*omg_the*q + omg_the**2*(the_cmd-the)
torque_psi = -2*zet_psi*omg_psi*r + omg_psi**2*(psi_cmd-psi)
torque_phi *= Ix
torque_the *= Iy
torque_psi *= Iz
return np.array([thrust,torque_phi,torque_the,torque_psi])
def mix_actuators(control,t):
rotor = pinvA@control
if t>t_fail+t_detect:
rotor[5] = 0
return np.sqrt(np.clip(rotor,0,100))
def mix_actuators_cvx(control, r_p, k, flag_fail):
import cvxpy as cp
W = np.diag([1, 1, 1, 1])
r = cp.Variable(nRotors,nonneg=True)
obj_req = cp.sum_squares(W@(A@r-control))
obj_smooth = 1e-4*cp.sum_squares(r-r_p)
#obj_card = 0.1*cp.norm(r,1)
#obj_max = 0.01*cp.max(r)
#obj_energy = 1e-6*cp.sum_squares(r)
#obj = cp.Minimize( obj_req + obj_smooth + obj_card )
obj = cp.Minimize( obj_req + obj_smooth)
constr = [ r <= 100 ]
if flag_fail and k*dt > t_fail + t_detect:
constr += [r[r_fail]==0]
cp.Problem(obj, constr).solve(verbose=False)
rotor = r.value
return np.sqrt(np.clip(rotor,0,100))
# In[58]:
pinvA = np.linalg.pinv(A)
# quadrotor 6DOF dynamics
def state_derivative(state, t, rotor_cmd, flag_fail): # computes state derivatives
u,v,w,p,q,r,x,y,z,phi,the,psi = state[:12] # state variables
rotor = state[12:12+nRotors]
rotor_dot = state[12+nRotors:]
rotor = np.clip(rotor, 0, rotor_limit) # rotor limit
rotor_dot = np.clip(rotor_dot, -rotor_sr_limit, rotor_sr_limit) # rotor speed slew rate limit
if flag_fail and t > t_fail:
state[12+r_fail] = 0
rotor[r_fail] = 0
rotor_dot[r_fail] = 0
T,L,M,N = A@(rotor**2) # control variable
s_phi, c_phi = np.sin(phi), np.cos(phi)
s_the, c_the = np.sin(the), np.cos(the)
s_psi, c_psi = np.sin(psi), np.cos(psi)
u_dot = -g*s_the - (q*w - r*v)
v_dot = g*c_the*s_phi - (r*u - p*w)
w_dot = g*c_the*c_phi - (p*v - q*u) - T/m
if z>0:
u_dot -= -g*s_the
v_dot -= g*c_the*s_phi
w_dot -= g*c_the*c_phi
p_dot = -(Iz-Iy)/Ix*q*r + L/Ix
q_dot = -(Ix-Iz)/Iy*r*p + M/Iy
r_dot = -(Iy-Ix)/Iz*p*q + N/Iz
Cbn = np.array([ [c_psi*c_the, c_psi*s_the*s_phi-s_psi*c_phi, c_psi*s_the*c_phi+s_psi*s_phi], [s_psi*c_the, s_psi*s_the*s_phi+c_psi*c_phi, s_psi*s_the*c_phi-c_psi*s_phi], [ -s_the, c_the*s_phi, c_the*c_phi] ])
x_dot,y_dot,z_dot = np.dot(Cbn,np.array([u,v,w]))
phi_dot = p + s_phi*s_the/c_the*q + c_phi*s_the/c_the*r
the_dot = c_phi*q - s_phi*r
psi_dot = s_phi/c_the*q + c_phi/c_the*r
rotor_ddot = -2*zeta_rotor*omega_rotor*rotor_dot + omega_rotor**2*(rotor_cmd-rotor)
return np.array([u_dot,v_dot,w_dot,p_dot,q_dot,r_dot,x_dot,y_dot,z_dot, phi_dot,the_dot,psi_dot,*rotor_dot,*rotor_ddot])
# In[59]:
u0, v0, w0 = 0, 0, 0
p0, q0, r0 = 0, 0, 0
x0, y0, z0 = 0, 0, 0
phi0, the0, psi0 = 0, 0, 0
rotor0 = np.zeros(nRotors)
rotor_dot0 = np.zeros(nRotors)
X0 = np.array([u0,v0,w0,p0,q0,r0,x0,y0,z0,phi0,the0,psi0,*rotor0,*rotor_dot0])
G0 = np.zeros(4)
U0 = np.zeros(4)
R0 = np.zeros(nRotors)
t = np.arange(0,tf, dt)
n = len(t)
X = np.zeros((len(X0),n))
dX = np.zeros((len(X0),n))
G = np.zeros((len(G0),n-1))
U = np.zeros((len(U0),n-1))
R = np.zeros((len(R0),n-1))
R2 = np.zeros((len(R0),n-1))
X[:,0] = X0
G[:,0] = G0
U[:,0] = U0
R[:,0] = R0
R2[:,0] = R0
dotX_p = X0*0
for k in range(n-1):
G[:,k] = compute_guidance(X[:,k],t[k],k)
U[:,k] = compute_control(G[:,k],X[:,k],t[k])
if k==0:
R_p = np.zeros(nRotors)
else:
R_p = R[:,k-1]**2
if k%100==0:
print(k, end=' ')
R[:,k] = mix_actuators_cvx(U[:,k],R_p, k, True)
dotX = state_derivative(X[:,k],t[k],R[:,k], True) # fail sim
dX[:,k+1] = dotX
X[:,k+1] = X[:,k] + 0.5*(3*dotX-dotX_p)*dt
dotX_p = dotX
if t[k]>1 and X[8,k+1]>0:
X[:,k+2:] = X[:,k+1].reshape(-1,1)
break
X_ca1, G_ca1, U_ca1, R_ca1 = X, G, U, R
dX_ca1 = dX
Rr_ca1 = X_ca1[12:12+nRotors,:-1]
Ur_ca1 = A@(Rr_ca1**2)
X_ca2, U_ca2, R_ca2 = X_ca1, U_ca1, R_ca1
dX_ca1 = dX
Rr_ca2 = Rr_ca1
Ur_ca2 = Ur_ca1
# In[60]:
u0, v0, w0 = 0, 0, 0
p0, q0, r0 = 0, 0, 0
x0, y0, z0 = 0, 0, 0
phi0, the0, psi0 = 0, 0, 0
rotor0 = np.zeros(nRotors)
rotor_dot0 = np.zeros(nRotors)
X0 = np.array([u0,v0,w0,p0,q0,r0,x0,y0,z0,phi0,the0,psi0,*rotor0,*rotor_dot0])
G0 = np.zeros(4)
U0 = np.zeros(4)
R0 = np.zeros(nRotors)
t = np.arange(0,tf, dt)
n = len(t)
X = np.zeros((len(X0),n))
dX = np.zeros((len(X0),n))
G = np.zeros((len(G0),n-1))
U = np.zeros((len(U0),n-1))
R = np.zeros((len(R0),n-1))
X[:,0] = X0
G[:,0] = G0
U[:,0] = U0
R[:,0] = R0
dotX_p = X0*0
for k in range(n-1):
G[:,k] = compute_guidance(X[:,k],t[k],k)
U[:,k] = compute_control(G[:,k],X[:,k],t[k])
if k==0:
R_p = np.zeros(nRotors)
else:
R_p = R[:,k-1]**2
if k%100==0:
print(k, end=' ')
#R[:,k] = mix_actuators_cvx(U[:,k],R_p, k, False)
R[:,k] = mix_actuators(U[:,k],t[k])
dotX = state_derivative(X[:,k],t[k],R[:,k], False)
dX[:,k+1] = dotX
X[:,k+1] = X[:,k] + 0.5*(3*dotX-dotX_p)*dt
dotX_p = dotX
if t[k]>1 and X[8,k+1]>0:
X[:,k+2:] = X[:,k+1].reshape(-1,1)
break
X_ca2, G_ca2, U_ca2, R_ca2 = X, G, U, R
dX_ca2 = dX
Rr_ca2 = X_ca2[12:12+nRotors,:-1]
Ur_ca2 = A@(Rr_ca2**2)
dX_ca2 = dX
# In[61]:
cmap = plt.get_cmap("tab20")
colors = cmap([0,2,4,6,8,10,12,14])
plt.figure(num=2, figsize=(8,6), dpi=100)
plt.subplot(211)
plt.plot(t[:-1], Ur_ca1[0,:], color=colors[0])
plt.plot(t[:-1], Ur_ca2[0,:], '--', color=colors[0])
plt.axvline(t_fail, linestyle=':', color='r')
plt.ylabel('Thrust (N)')
plt.grid()
plt.subplot(212)
for i in range(3):
plt.plot(t[:-1], G_ca1[i+1,:]*Rad2Deg, color=colors[i])
for i in range(3):
plt.plot(t[:-1], G_ca2[i+1,:]*Rad2Deg, '--', color=colors[i])
plt.axvline(t_fail, linestyle=':', color='r')
plt.xlabel('Time (s)')
#plt.xlim(3,4)
plt.ylabel('Euler angle cmmand (degree)')
plt.legend([r'$\phi$',r'$\theta$',r'$\psi$'], loc='upper right')
plt.grid()
plt.show()
plt.figure(num=2, figsize=(8,6), dpi=100)
plt.subplot(211)
plt.plot(t[:-1], G_ca1[0,:], color=colors[0])
plt.plot(t[:-1], G_ca2[0,:], '--', color=colors[0])
plt.axvline(t_fail, linestyle=':', color='r')
plt.ylabel('Thrust command (N)')
plt.grid()
plt.subplot(212)
for i in range(3):
plt.plot(t, X_ca1[i+9,:]*Rad2Deg, color=colors[i])
for i in range(3):
plt.plot(t, X_ca2[i+9,:]*Rad2Deg, '--', color=colors[i])
for i in range(3):
plt.plot(t[:-1], G_ca1[i+1,:]*Rad2Deg, ':', color=colors[i])
for i in range(3):
plt.plot(t[:-1], G_ca2[i+1,:]*Rad2Deg, ':', color=colors[i])
plt.axvline(t_fail, linestyle=':', color='r')
plt.xlabel('Time (s)')
plt.ylabel('Euler angle (deg)')
#plt.ylim(-25,25)
plt.legend([r'$\phi$',r'$\theta$',r'$\psi$'])
plt.grid()
plt.show()
'''
plt.subplot(212)
for i in range(3):
plt.plot(t[:-1], Ur_ca1[i+1,:], color=colors[i])
#for i in range(3):
# plt.plot(t[:-1], Ur_ca2[i+1,:], '--', color=colors[i])
plt.axvline(t_fail, linestyle=':', color='r')
plt.xlabel('Time (s)')
plt.ylabel('Torque (Nm)')
plt.legend([r'$\tau_{\phi}$',r'$\tau_{\theta}$',r'$\tau_{\psi}$'])
plt.grid()
plt.show()
'''
# In[62]:
plt.figure(num=2, figsize=(8,6), dpi=100)
plt.subplot(211)
plt.plot(t[:-1], Ur_ca1[0,:], color=colors[0])
plt.plot(t[:-1], Ur_ca2[0,:], '--', color=colors[0])
plt.axvline(t_fail, linestyle=':', color='r')
plt.ylabel('Thrust (N)')
plt.grid()
plt.subplot(212)
for i in range(3):
plt.plot(t[:-1], Ur_ca1[i+1,:], color=colors[i])
#for i in range(3):
# plt.plot(t[:-1], Ur_ca2[i+1,:], '--', color=colors[i])
plt.axvline(t_fail, linestyle=':', color='r')
plt.xlabel('Time (s)')
plt.ylabel('Torque (Nm)')
plt.legend([r'$\tau_{\phi}$',r'$\tau_{\theta}$',r'$\tau_{\psi}$'])
plt.grid()
plt.show()
# In[ ]:
plt.figure(num=3, figsize=(8,6), dpi=100)
for i in range(nRotors):
plt.plot(t[:-1], (Rr_ca1[i,:]), color=colors[i], label='$R_{%i}$'%(i+1))
plt.plot(t[:-1], (Rr_ca2[i,:]), '--', color=colors[i])
plt.axvline(t_fail, linestyle=':', color='r')
plt.ylabel('Rotor speed')
plt.xlabel('Time (s)')
plt.legend()
#plt.xlim(0,1)
plt.grid()
plt.show()
'''
plt.figure(num=4, figsize=(8,12), dpi=100)
plt.title('Rotor speed')
for i in range(nRotors):
plt.subplot(nRotors, 1, i+1)
plt.plot(t[:-1], (Rr_ca1[i,:]), color=colors[i], label='$R_{%i}$'%(i+1))
plt.plot(t[:-1], (Rr_ca2[i,:]), '--', color=colors[i])
plt.axvline(t_fail, linestyle=':', color='r')
plt.ylim(0,10)
plt.legend()
plt.grid()
plt.show()
plt.figure(num=5, figsize=(47,6), dpi=100)
plt.title('Rotor voltage (V)')
for i in range(nRotors):
plt.subplot(1, nRotors, i+1)
plt.plot(t[:-1], (Rr_ca1[i,:]), color=colors[i], label='$R_{%i}$'%(i+1))
plt.plot(t[:-1], (Rr_ca2[i,:]), '--', color=colors[i])
plt.axvline(t_fail, linestyle=':', color='r')
plt.ylim(0,10)
plt.legend()
plt.grid()
plt.show()
'''
# In[ ]:
plt.figure(num=6, figsize=(8,6), dpi=100)
plt.subplot(211)
for i in range(3):
plt.plot(t, dX_ca1[i+6,:], color=colors[i])
for i in range(3):
plt.plot(t, dX_ca2[i+6,:], '--', color=colors[i])
plt.axvline(t_fail, linestyle=':', color='r')
plt.xlabel('Time (s)')
plt.ylabel('NED velocity (m)')
#plt.xlim(2,3)
plt.legend([r'$N$',r'$E$',r'$D$'])
plt.grid()
'''
plt.subplot(212)
for i in range(3):
plt.plot(t[:-1], G_ca1[i+7,:], color=colors[i])
#plt.plot(t, G_ca1[i+3,:], color=colors[i])
#for i in range(3):
# plt.plot(t, X_ca2[i,:], '--', color=colors[i])
plt.axvline(t_fail, linestyle=':', color='r')
plt.ylabel('NED velocity command (m/s)')
#plt.ylim(-1.6,1.6)
plt.legend([r'$N$',r'$E$',r'$D$'])
plt.grid()
plt.show()
'''
plt.figure(num=6, figsize=(8,6), dpi=100)
'''
plt.subplot(211)
for i in range(3):
plt.plot(t[:-1], G_ca1[i+4,:], color=colors[i])
#plt.plot(t, G_ca1[i+3,:], color=colors[i])
#for i in range(3):
# plt.plot(t, X_ca2[i,:], '--', color=colors[i])
plt.axvline(t_fail, linestyle=':', color='r')
plt.ylabel('NED command (m)')
#plt.ylim(-1.6,1.6)
plt.legend([r'$N$',r'$E$',r'$D$'])
plt.grid()
'''
plt.subplot(212)
for i in range(3):
plt.plot(t, X_ca1[i+6,:], color=colors[i])
for i in range(3):
plt.plot(t, X_ca2[i+6,:], '--', color=colors[i])
plt.axvline(t_fail, linestyle=':', color='r')
plt.xlabel('Time (s)')
plt.ylabel('NED position (m)')
#plt.ylim(-1,1)
plt.legend([r'$N$',r'$E$',r'$D$'])
plt.grid()
plt.show()
plt.figure(num=7, figsize=(8,6), dpi=100)
plt.subplot(211)
for i in range(3):
plt.plot(t, X_ca1[i+3,:]*Rad2Deg, color=colors[i])
for i in range(3):
plt.plot(t, X_ca2[i+3,:]*Rad2Deg, '--', color=colors[i])
plt.axvline(t_fail, linestyle=':', color='r')
plt.ylabel('Body rate (deg/s)')
#plt.ylim(-150,150)
plt.legend([r'$p$',r'$q$',r'$r$'])
plt.grid()
plt.subplot(212)
for i in range(3):
plt.plot(t, X_ca1[i+9,:]*Rad2Deg, color=colors[i])
for i in range(3):
plt.plot(t, X_ca2[i+9,:]*Rad2Deg, '--', color=colors[i])
plt.axvline(t_fail, linestyle=':', color='r')
plt.xlabel('Time (s)')
plt.ylabel('Euler angle (deg)')
#plt.ylim(-25,25)
plt.legend([r'$\phi$',r'$\theta$',r'$\psi$'])
plt.grid()
plt.show()
# In[ ]:
from mpl_toolkits.mplot3d import Axes3D
plt.figure(figsize=(8,6), dpi=100)
plt.gca(projection='3d')
plt.plot(X_ca1[7,:], X_ca1[6,:], -X_ca1[8,:], color=colors[0], alpha=1.0, linewidth=2, label='Fault')
plt.plot(X_ca2[7,:], X_ca2[6,:], -X_ca2[8,:], '--', color=colors[0], alpha=1.0, linewidth=2, label='Normal')
plt.plot(X_ca2[7,[int(t_fail/dt),int(t_fail/dt)]], X_ca2[6,[int(t_fail/dt),int(t_fail/dt)]], -X_ca2[8,[int(t_fail/dt),int(t_fail/dt)]], 'r*', markersize=10)
plt.plot(X_ca2[7,[int((t_fail+t_detect)/dt),int((t_fail+t_detect)/dt)]], X_ca2[6,[int((t_fail+t_detect)/dt),int((t_fail+t_detect)/dt)]], -X_ca2[8,[int((t_fail+t_detect)/dt),int((t_fail+t_detect)/dt)]], 'b^', markersize=10)
plt.xlabel('East (m)')
plt.ylabel('North (m)')
#plt.zlabel('h (m)')
plt.legend()
plt.show()
plt.figure(figsize=(8,6), dpi=100)
plt.plot(X_ca1[7,:], X_ca1[6,:], color=colors[0], alpha=1.0, linewidth=2)
plt.plot(X_ca2[7,:], X_ca2[6,:], '--', color=colors[0], alpha=1.0, linewidth=2)
plt.plot(X_ca2[7,[int(t_fail/dt),int(t_fail/dt)]], X_ca2[6,[int(t_fail/dt),int(t_fail/dt)]], 'r*', markersize=10)
plt.plot(X_ca2[7,[int((t_fail+t_detect)/dt),int((t_fail+t_detect)/dt)]], X_ca2[6,[int((t_fail+t_detect)/dt),int((t_fail+t_detect)/dt)]], 'b^', markersize=10)
plt.xlabel('East (m)')
plt.ylabel('North (m)')
plt.axis('equal')
plt.grid()
plt.show()
plt.figure(figsize=(8,6), dpi=100)
plt.plot(X_ca1[7,:], -X_ca1[8,:], color=colors[0], alpha=1.0, linewidth=2)
plt.plot(X_ca2[7,:], -X_ca2[8,:], '--', color=colors[0], alpha=1.0, linewidth=2)
plt.plot(X_ca2[7,[int(t_fail/dt),int(t_fail/dt)]], -X_ca2[8,[int(t_fail/dt),int(t_fail/dt)]], 'r*', markersize=10)
plt.plot(X_ca2[7,[int((t_fail+t_detect)/dt),int((t_fail+t_detect)/dt)]], -X_ca2[8,[int((t_fail+t_detect)/dt),int((t_fail+t_detect)/dt)]], 'b^', markersize=10)
plt.xlabel('East (m)')
plt.ylabel('Altitude (m)')
plt.axis('equal')
plt.grid()
plt.show()
# In[ ]:
'''
#3D animation
from matplotlib.ticker import LinearLocator, FormatStrFormatter
from matplotlib.animation import FuncAnimation
import matplotlib.animation as animation
thrust_vec = np.zeros((3,len(dX_ca1[6,:])-1))
for i in range(len(dX_ca1[6,:])-1):
thrust_vec[0,i] =Ur_ca1[0,i] * (dX_ca1[6,i+1]- dX_ca1[6,i])/dt
thrust_vec[1,i] =Ur_ca1[0,i] * (dX_ca1[7,i+1]- dX_ca1[7,i])/dt
thrust_vec[2,i] =Ur_ca1[0,i] * ((dX_ca1[8,i+1]- dX_ca1[8,i])/dt+g)
X_new = X_ca1[7,:-1]
Y_new = X_ca1[6,:-1]
Z_new = X_ca1[8,:-1]
def get_arrow(i):
x = X_new[i]
y = Y_new[i]
z = -Z_new[i]
u = 10e-5* thrust_vec[0,i]
v = 10e-5* thrust_vec[1,i]
w = 10e-5* thrust_vec[2,i]
return x,y,z,u,v,w
fig, ax = plt.subplots(subplot_kw=dict(projection="3d"))
quiver = ax.quiver(*get_arrow(0))
ax.plot(X_new[:], Y_new[:], -Z_new[:],label="Problem1",color ='green',alpha=0.2)
plt.plot(X_ca2[7,[int(t_fail/dt),int(t_fail/dt)]], X_ca2[6,[int(t_fail/dt),int(t_fail/dt)]], -X_ca2[8,[int(t_fail/dt),int(t_fail/dt)]], '*', markersize=10)
ax.legend()
def update(i):
global quiver
quiver.remove()
quiver = ax.quiver(*get_arrow(i),color='r',arrow_length_ratio=0)
ani = FuncAnimation(fig, update, frames=int(tf/dt)-1, interval=10)
Writer = animation.writers['ffmpeg']
writer = Writer(fps=30, metadata=dict(artist='Me'), bitrate=1800, extra_args=['-vcodec', 'libx264'])
ani.save('Sim1.mp4', writer=writer,dpi = 300)
'''
# In[ ]:
#3D animation
Thrust_ani = np.zeros((3,len(X_ca1[9,:])))
X_ani = np.zeros((3,len(X_ca1[9,:])))
Y_ani = np.zeros((3,len(X_ca1[9,:])))
Z_ani = np.zeros((3,len(X_ca1[9,:])))
def convert_Cbn(phi,the,psi):
s_phi, c_phi = np.sin(phi), np.cos(phi)
s_the, c_the = np.sin(the), np.cos(the)
s_psi, c_psi = np.sin(psi), np.cos(psi)
Cbn = np.array([ [c_psi*c_the, c_psi*s_the*s_phi-s_psi*c_phi, c_psi*s_the*c_phi+s_psi*s_phi], [s_psi*c_the, s_psi*s_the*s_phi+c_psi*c_phi, s_psi*s_the*c_phi-c_psi*s_phi], [ -s_the, c_the*s_phi, c_the*c_phi] ])
return Cbn
for i in range(int(len(X_ca1[9,:]))-1):
Thrust = np.zeros(3)
Thrust[2] = -Ur_ca1[0,i]
Thrust_ani[:,i] = np.dot(convert_Cbn(X_ca1[9,i],X_ca1[10,i],X_ca1[11,i]),Thrust)
X_vec = np.zeros((3,1))
X_vec[0,0] = 1
X_ani[:,i] = np.dot(convert_Cbn(X_ca1[9,i],X_ca1[10,i],X_ca1[11,i]),X_vec[:,0])
Y_vec = np.zeros((3,1))
Y_vec[1,0] = 1
Y_ani[:,i] = np.dot(convert_Cbn(X_ca1[9,i],X_ca1[10,i],X_ca1[11,i]),Y_vec[:,0])
Z_vec = np.zeros((3,1))
Z_vec[2,0] = 1
Z_ani[:,i] = np.dot(convert_Cbn(X_ca1[9,i],X_ca1[10,i],X_ca1[11,i]),Y_vec[:,0])
from matplotlib.ticker import LinearLocator, FormatStrFormatter
from matplotlib.animation import FuncAnimation
import matplotlib.animation as animation
thrust_vec = np.zeros((3,len(dX_ca1[6,:])-1))
for i in range(len(dX_ca1[6,:])-1):
thrust_vec[0,i] =Ur_ca1[0,i] * (dX_ca1[6,i+1]- dX_ca1[6,i])/dt
thrust_vec[1,i] =Ur_ca1[0,i] * (dX_ca1[7,i+1]- dX_ca1[7,i])/dt
thrust_vec[2,i] =Ur_ca1[0,i] * ((dX_ca1[8,i+1]- dX_ca1[8,i])/dt+g)
X_new = X_ca1[7,:-1]
Y_new = X_ca1[6,:-1]
Z_new = X_ca1[8,:-1]
def get_arrow(i):
x = X_new[i]
y = Y_new[i]
z = -Z_new[i]
u = 10e-4*Thrust_ani[0,i]
v = 10e-4*Thrust_ani[1,i]
w = 10e-4*Thrust_ani[2,i]
return x,y,z,u,v,w
def get_arrow_x(i):
x = X_new[i]
y = Y_new[i]
z = -Z_new[i]
u = 10e-2*X_ani[0,i]
v = 10e-2*X_ani[1,i]
w = 10e-2*X_ani[2,i]
return x,y,z,u,v,w
def get_arrow_y(i):
x = X_new[i]
y = Y_new[i]
z = -Z_new[i]
u = 0.15*Y_ani[0,i]
v = 0.15*Y_ani[1,i]
w = 0.15*Y_ani[2,i]
return x,y,z,u,v,w
def get_arrow_z(i):
x = X_new[i]
y = Y_new[i]
z = -Z_new[i]
u = 10e-2*Z_ani[0,i]
v = 10e-2*Z_ani[1,i]
w = 10e-2*Z_ani[2,i]
return x,y,z,u,v,w
fig, ax = plt.subplots(subplot_kw=dict(projection="3d"))
quiver = ax.quiver(*get_arrow(0))
quiver_x = ax.quiver(*get_arrow_x(0))
quiver_y = ax.quiver(*get_arrow_y(0))
quiver_z = ax.quiver(*get_arrow_z(0))
ax.plot(X_new[:], Y_new[:], -Z_new[:],label="Problem1",color ='green',alpha=0.2)
plt.plot(X_ca2[7,[int(t_fail/dt),int(t_fail/dt)]], X_ca2[6,[int(t_fail/dt),int(t_fail/dt)]], -X_ca2[8,[int(t_fail/dt),int(t_fail/dt)]], '*', markersize=10)
ax.legend()
def update(i):
global quiver
global quiver_x
global quiver_y
global quiver_z
quiver.remove()
quiver_x.remove()
quiver_y.remove()
quiver_z.remove()
quiver = ax.quiver(*get_arrow(i),arrow_length_ratio=0)
quiver_x = ax.quiver(*get_arrow_x(i),color='r')
quiver_y = ax.quiver(*get_arrow_y(i),color='g')
quiver_z = ax.quiver(*get_arrow_z(i),color='b')
ani = FuncAnimation(fig, update, frames=int(tf/dt)-1, interval=10)
Writer = animation.writers['ffmpeg']
writer = Writer(fps=30, metadata=dict(artist='Me'), bitrate=1800, extra_args=['-vcodec', 'libx264'])
ani.save('Simulation1.mp4', writer=writer,dpi = 300)
# In[ ]:
Thrust_ani[0,:]
# In[ ]:
Y_ani[2,:]
# In[ ]:
#3D animation
Thrust_ani = np.zeros((3,len(X_ca1[9,:])))
X_ani = np.zeros((3,len(X_ca1[9,:])))
Y_ani = np.zeros((3,len(X_ca1[9,:])))
Z_ani = np.zeros((3,len(X_ca1[9,:])))
def convert_Cbn(phi,the,psi):
s_phi, c_phi = np.sin(phi), np.cos(phi)
s_the, c_the = np.sin(the), np.cos(the)
s_psi, c_psi = np.sin(psi), np.cos(psi)
Cbn = np.array([ [c_psi*c_the, c_psi*s_the*s_phi-s_psi*c_phi, c_psi*s_the*c_phi+s_psi*s_phi], [s_psi*c_the, s_psi*s_the*s_phi+c_psi*c_phi, s_psi*s_the*c_phi-c_psi*s_phi], [ -s_the, c_the*s_phi, c_the*c_phi] ])
return Cbn
for i in range(int(len(X_ca1[9,:]))-1):
Thrust = np.zeros(3)
Thrust[2] = -Ur_ca1[0,i]*0.001
Thrust_ani[:,i] = np.dot(convert_Cbn(X_ca1[9,i],X_ca1[10,i],X_ca1[11,i]),Thrust)
X_vec = np.zeros((3,1))
X_vec[0,0] = 1
X_ani[:,i] = np.dot(convert_Cbn(X_ca1[9,i],X_ca1[10,i],X_ca1[11,i]),X_vec[:,0])
Y_vec = np.zeros((3,1))
Y_vec[1,0] = 1
Y_ani[:,i] = np.dot(convert_Cbn(X_ca1[9,i],X_ca1[10,i],X_ca1[11,i]),Y_vec[:,0])
Z_vec = np.zeros((3,1))
Z_vec[2,0] = 1
Z_ani[:,i] = np.dot(convert_Cbn(X_ca1[9,i],X_ca1[10,i],X_ca1[11,i]),Z_vec[:,0])
from matplotlib.ticker import LinearLocator, FormatStrFormatter
from matplotlib.animation import FuncAnimation
import matplotlib.animation as animation
#thrust_vec = np.zeros((3,len(dX_ca1[6,:])-1))
#for i in range(len(dX_ca1[6,:])-1):
# thrust_vec[0,i] =Ur_ca1[0,i] * (dX_ca1[6,i+1]- dX_ca1[6,i])/dt