-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathquadrotor_dynamics.py
300 lines (233 loc) · 12.5 KB
/
quadrotor_dynamics.py
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
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
import numpy as np
from numpy import array, zeros, diag, ones, sin, cos, tan, linspace, dot, pi
from numpy.random import uniform
import time
from scipy import integrate
from numpy import isnan, pi, isinf
from numpy.random import normal
import os
import math
from scipy.spatial.transform import Rotation as R
def world_to_body(state, waypoint_world):
psi, theta, phi = state[5], state[4], state[3]
rot = R.from_euler('zyx', [[psi, theta, phi]], degrees=False).as_dcm()
rot = rot.reshape(3,3)
# R = np.array([[cos(theta)*cos(psi), sin(phi)*sin(theta)*cos(psi)-cos(phi)*sin(psi), cos(phi)*sin(theta)*cos(psi)+sin(phi)*sin(psi)],
# [cos(theta)*sin(psi), sin(phi)*sin(theta)*sin(psi)+cos(phi)*cos(psi), cos(phi)*sin(theta)*sin(psi)-sin(phi)*cos(psi)],
# [-sin(theta), sin(phi)*cos(theta), cos(phi)*cos(theta)]])
waypoint_body = np.dot(rot.T, waypoint_world.reshape(-1,1))
return waypoint_body.ravel()
def body_to_world(state, waypoint_body):
psi, theta, phi = state[5], state[4], state[3]
rot = R.from_euler('zyx', [[psi, theta, phi]], degrees=False).as_dcm()
# R = np.array([[cos(theta)*cos(psi), sin(phi)*sin(theta)*cos(psi)-cos(phi)*sin(psi), cos(phi)*sin(theta)*cos(psi)+sin(phi)*sin(psi)],
# [cos(theta)*sin(psi), sin(phi)*sin(theta)*sin(psi)+cos(phi)*cos(psi), cos(phi)*sin(theta)*sin(psi)-sin(phi)*cos(psi)],
# [-sin(theta), sin(phi)*cos(theta), cos(phi)*cos(theta)]])
waypoint_world = np.dot(rot, waypoint_body.reshape(-1,1))
return waypoint_world.ravel()
class Quadrotor:
def __init__(self, state0, coeff_pos=1.0, coeff_angle = 0.25, coeff_control = 0.0, coeff_final_pos=0.0):
self.state = np.array(state0)
# self.state2 = state0
# self.state3 = state0
self.U = [1, 0., 0., 0.]
# self.U2 = [1, 0., 0., 0.]
# self.U3 = [1, 0., 0., 0.]
self.costValue = 0.
self.coeff_pos = coeff_pos
self.coeff_angle = coeff_angle
self.coeff_control = coeff_control
self.coeff_final_pos = coeff_final_pos
self.Controllers = ["Backstepping_1","Backstepping_2","Backstepping_3","Backstepping_4"]
def model_parameters(self):
g = 9.81
m = 1.52
Ixx, Iyy, Izz = 0.0347563, 0.0458929, 0.0977
I1 = (Iyy - Izz) / Ixx
I2 = (Izz - Ixx) / Iyy
I3 = (Ixx - Iyy) / Izz
Jr = 0.0001
l = 0.09
b = 8.54858e-6
d = 1.6e-2
return g, m, Ixx, Iyy, Izz, I1, I2, I3, Jr, l, b, d
def model_dynamics_2(self, t, state):
g, m, Ixx, Iyy, Izz, I1, I2, I3, Jr, l, b, d = self.model_parameters()
#states: [x,y,z,phi,theta,psi,x_dot,y_dot,z_dot,phi_dot,theta_dot,psi_dot]
x,y,z,phi,theta,psi,x_dot,y_dot,z_dot,phi_dot,theta_dot,psi_dot = state
U1, U2, U3, U4 = self.U
omega = 0.
state_dot = np.zeros(12)
state_dot[0] = x_dot
state_dot[1] = y_dot
state_dot[2] = z_dot
state_dot[3] = phi_dot
state_dot[4] = theta_dot
state_dot[5] = psi_dot
state_dot[6] = (cos(phi)*sin(theta)*cos(psi) + sin(phi)*sin(psi))*U1/m
state_dot[7] = (cos(phi)*sin(theta)*sin(psi) - sin(phi)*cos(psi))*U1/m
state_dot[8] = -g + cos(phi)*cos(theta)*U1/m
state_dot[9] = theta_dot*psi_dot*I1 - Jr / Ixx * theta_dot * omega + l/Ixx*U2
state_dot[10] = phi_dot*psi_dot*I2 + Jr / Iyy * phi_dot * omega + l/Iyy*U3
state_dot[11] = phi_dot*theta_dot*I3 + 1/Izz*U4
return state_dot
def model_dynamics(self, state, U):
g, m, Ixx, Iyy, Izz, I1, I2, I3, Jr, l, b, d = self.model_parameters()
#states: [x,y,z,phi,theta,psi,x_dot,y_dot,z_dot,phi_dot,theta_dot,psi_dot]
x,y,z,phi,theta,psi,x_dot,y_dot,z_dot,phi_dot,theta_dot,psi_dot = state
U1, U2, U3, U4 = U
omega = 0.
state_dot = np.zeros(12)
state_dot[0] = x_dot
state_dot[1] = y_dot
state_dot[2] = z_dot
state_dot[3] = phi_dot
state_dot[4] = theta_dot
state_dot[5] = psi_dot
state_dot[6] = (cos(phi)*sin(theta)*cos(psi) + sin(phi)*sin(psi))*U1/m
state_dot[7] = (cos(phi)*sin(theta)*sin(psi) - sin(phi)*cos(psi))*U1/m
state_dot[8] = -g + cos(phi)*cos(theta)*U1/m
state_dot[9] = theta_dot*psi_dot*I1 - Jr / Ixx * theta_dot * omega + l/Ixx*U2
state_dot[10] = phi_dot*psi_dot*I2 + Jr / Iyy * phi_dot * omega + l/Iyy*U3
state_dot[11] = phi_dot*theta_dot*I3 + 1/Izz*U4
return state_dot
def backstepping(self, A1, A2, A3, A4, A5, A6, state, U_list, ref_traj):
g, m, Ixx, Iyy, Izz, I1, I2, I3, Jr, l, b, d = self.model_parameters()
U1, U2, U3, U4 = U_list
#self.state: [x,y,z,phi,theta,psi,x_dot,y_dot,z_dot,phi_dot,theta_dot,psi_dot]
x, y, z = state[0], state[1], state[2]
phi, theta, psi = state[3], state[4], state[5]
x_dot, y_dot, z_dot = state[6], state[7], state[8]
phi_dot, theta_dot, psi_dot = state[9], state[10], state[11]
# ref_traj = [xd[i], yd[i], zd[i], xd_dot[i], yd_dot[i], zd_dot[i],
# xd_ddot[i], yd_ddot[i], zd_ddot[i], xd_dddot[i], yd_dddot[i],
# xd_ddddot[i], yd_ddddot[i], psid[i], psid_dot[i], psid_ddot[i]]
xd, yd, zd = ref_traj[0], ref_traj[1], ref_traj[2],
xd_dot, yd_dot, zd_dot = ref_traj[3], ref_traj[4], ref_traj[5]
xd_ddot, yd_ddot, zd_ddot = ref_traj[6], ref_traj[7], ref_traj[8]
xd_dddot, yd_dddot = ref_traj[9], ref_traj[10]
xd_ddddot, yd_ddddot = ref_traj[11], ref_traj[12]
psid, psid_dot, psid_ddot = ref_traj[13], ref_traj[14], ref_traj[15]
x1, x2, x3 = array([[x], [y]]), array([[x_dot], [y_dot]]), array([[phi], [theta]])
x4, x5, x6 = array([[phi_dot], [theta_dot]]), array([[psi], [z]]), array([[psi_dot], [z_dot]])
g0 = array([[np.cos(psi), np.sin(psi)], [np.sin(psi), -np.cos(psi)]])
g0_inv = array([[np.cos(psi), np.sin(psi)], [np.sin(psi), -np.cos(psi)]])
g1 = array([[theta_dot*psi_dot*I1], [phi_dot*psi_dot*I2]])
g2 = array([[phi_dot*theta_dot*I3], [-g]])
l0 = array([[np.cos(phi)*np.sin(theta)], [np.sin(phi)]])*U1/m
dl0_dx3 = array([[-np.sin(phi)*np.sin(theta), np.cos(phi)*np.cos(theta)], [np.cos(phi), 0]])*U1/m
dl0_dx3_inv = array([[0, 1/np.cos(phi)], [1/np.cos(theta)*1/np.cos(phi), 1/np.cos(phi)*np.tan(theta)*np.tan(phi)]])*m/U1
dl0_dx3_inv_dot = array([[0, 1/np.cos(phi)*np.tan(phi)*phi_dot],
[1/np.cos(theta)*1/np.cos(phi)*(np.tan(theta)*theta_dot + np.tan(phi)*phi_dot), 1/np.cos(phi)*((1/np.cos(theta))**2*np.tan(phi)*theta_dot + (-1+2*(1/np.cos(phi))**2)*np.tan(theta)*phi_dot)]])*m/U1
# Omega_square = Omega_coef_inv * abs([U1/b U2/b U3/b U4/d])
# Omega_param = sqrt(Omega_square)
# omega = Omega_param(2) + Omega_param[3] - Omega_param(1) - Omega_param(3)
# h1 = [-Jr/Ixx*theta_dot*omega Jr/Iyy*phi_dot*omega]
h1 = 0
k1 = diag([l/Ixx, l/Iyy])
k1_inv = diag([Ixx/l, Iyy/l])
k2 = diag([1/Izz, np.cos(phi)*np.cos(theta)/m])
k2_inv = diag([Izz, m/(np.cos(phi)*np.cos(theta))])
x1d = array([[xd], [yd]])
x1d_dot = array([[xd_dot], [yd_dot]])
x1d_ddot = array([[xd_ddot], [yd_ddot]])
x1d_dddot = array([[xd_dddot], [yd_dddot]])
x1d_ddddot = array([[xd_ddddot], [yd_ddddot]])
x5d = array([[psid], [zd]])
x5d_dot = array([[psid_dot], [zd_dot]])
x5d_ddot = array([[psid_ddot], [zd_ddot]])
z1 = x1d - x1
v1 = x1d_dot + dot(A1,z1)
z2 = v1 - x2
z1_dot = -dot(A1,z1) + z2
v1_dot = x1d_ddot + dot(A1,z1_dot)
v2 = dot(g0_inv, z1 + v1_dot + dot(A2,z2))
z3 = v2 - l0
z2_dot = -z1 - dot(A2,z2) + dot(g0,z3)
z1_ddot = -dot(A1,z1_dot) + z2_dot
v1_ddot = x1d_dddot + dot(A1, z1_ddot)
v2_dot = dot(g0_inv, z1_dot + v1_ddot + dot(A2,z2_dot))
v3 = dot(dl0_dx3_inv, dot(g0.T,z2) + v2_dot + dot(A3, z3))
z4 = v3 - x4
z3_dot = -dot(g0.T, z2) - dot(A3,z3) + dot(dl0_dx3, z4)
z2_ddot = - z1_dot - dot(A2, z2_dot) + dot(g0, z3_dot)
z1_dddot = -dot(A1, z1_ddot) + z2_ddot
v1_dddot = x1d_ddddot + dot(A1, z1_dddot)
v2_ddot = dot(g0_inv, z1_ddot + v1_dddot + dot(A2, z2_ddot))
v3_dot = dot(dl0_dx3_inv, dot(g0.T, z2_dot) + v2_ddot + dot(A3, z3_dot)) + dot(dl0_dx3_inv_dot, dot(g0.T, z2) + v2_dot + dot(A3, z3))
l1 = dot(k1_inv, dot(dl0_dx3.T, z3) + v3_dot - g1 - h1 + dot(A4, z4)).ravel()
z5 = x5d - x5
v5 = x5d_dot + dot(A5, z5)
z6 = v5 - x6
z5_dot = - dot(A5, z5) + z6
v5_dot = x5d_ddot + dot(A5, z5_dot)
l2 = dot(k2_inv, z5 + v5_dot - g2 + dot(A6, z6)).ravel()
U1, U2, U3, U4 = l2[1], l1[0], l1[1], l2[0]
U1 = np.clip(U1, 0.0, 1e5)
U2 = np.clip(U2, -1e5, 1e5)
U3 = np.clip(U3, -1e5, 1e5)
U4 = np.clip(U4, -1e5, 1e5)
U = np.array([U1, U2, U3, U4])
return U
def get_control_input(self, state, U0, cont, current_traj):
if (cont == self.Controllers[0]): #Backstepping_1
A1, A2, A3 = 15*diag([1,1]), 10*diag([1,1]), 15*diag([1,1])
A4, A5, A6 = 10*diag([1,1]), 15*diag([1,1]), 10*diag([1,1])
U = self.backstepping(A1, A2, A3, A4, A5, A6, state, U0, current_traj)
elif (cont == self.Controllers[1]): #Backstepping_2
A1, A2, A3 = 10*diag([1,1]), 5*diag([1,1]), 10*diag([1,1])
A4, A5, A6 = 5*diag([1,1]), 10*diag([1,1]), 5*diag([1,1])
U = self.backstepping(A1, A2, A3, A4, A5, A6, state, U0, current_traj)
elif (cont == self.Controllers[2]): #Backstepping_3
A1, A2, A3 = 5*diag([1,1]), 3*diag([1,1]), 10*diag([1,1])
A4, A5, A6 = 7*diag([1,1]), 1*diag([1,1]), 1*diag([1,1])
U = self.backstepping(A1, A2, A3, A4, A5, A6, state, U0, current_traj)
elif (cont == self.Controllers[3]): #Backstepping_4
A1, A2, A3 = 2*diag([1,1]), 5*diag([1,1]), 2*diag([1,1])
A4, A5, A6 = 5*diag([1,1]), 2*diag([1,1]), 5*diag([1,1])
U = self.backstepping(A1, A2, A3, A4, A5, A6, state, U0, current_traj)
return U
def euler(self, state, U):
state_dot = self.model_dynamics(state, U)
return state_dot
def runge_kutta(self, state, U, dtau):
k1 = self.euler(state, U)
k2 = self.euler(state + k1/2., U + dtau/2.)
k3 = self.euler(state + k2/2., U + dtau/2.)
k4 = self.euler(state + k3, U + dtau)
state_dot = (k1 + 2*k2 + 2*k3 + k4) / 6.
return state_dot
def simulate(self, current_traj, dtau=1e-3, method="Backstepping_3"):
# states: [x,y,z,phi,theta,psi,x_dot,y_dot,z_dot,phi_dot,theta_dot,psi_dot]
std_list = [0, 0, 0, 0]
r_std, phi_std, theta_std, psi_std = std_list[0], std_list[1], std_list[2], std_list[3]
fail_check = False
## Add noise, if you wish ##
self.state[6] = normal(self.state[6], 0*r_std / 3.0)
self.state[7] = normal(self.state[7], 0*r_std / 3.0)
self.state[8] = normal(self.state[8], 0*r_std / 3.0)
self.state[9] = normal(self.state[9], 0*phi_std)
self.state[10] = normal(self.state[10], 0*theta_std)
self.state[11] = normal(self.state[11], 0*psi_std)
# Scipy diff solver
# U = self.get_control_input(self.state, self.U, method, current_traj)
# self.U = U
# sol = integrate.solve_ivp(fun=self.model_dynamics_2, t_span=(0, dtau), y0=self.state)
# self.state = sol.y[:,-1]
# Euler Solver
self.U = self.get_control_input(self.state, self.U, method, current_traj)
state_dot = self.euler(self.state, self.U)
self.state = self.state + state_dot * dtau
# Runge-Kutta Solver
# U3 = self.get_control_input(self.state3, self.U3, method, current_traj)
# self.U3 = U3
# state_dot = self.runge_kutta(self.state3, self.U3, dtau)
# self.state3 = self.state3 + state_dot * dtau
# diff12 = np.sum((self.state - self.state2)**2)
# diff13 = np.sum((self.state - self.state3)**2)
# diff23 = np.sum((self.state2 - self.state3)**2)
# diff = np.array([diff12, diff13, diff23])
if (np.abs(self.state[3]) > np.pi/2) | (np.abs(self.state[4]) > np.pi/2):
self.costValue = 1e12
fail_check = True
return fail_check