triangle_platform/triangle.py at master · git-alice/triangle_platform · GitHub

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
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Apr 23 14:44:31 2018

@author: eval
"""

from sympy.abc import *
from sympy import *


# ИНИЦИАЛИЗАЦИЯ СИМВОЛОВ

# Время
t = symbols('t')
# Индексы
# i, P, C = symbols('i, P, C', cls=Idx)
# (проекция вилки на e_z, проекция вилки на e_wheel, радиус, масса)
h, d, r = symbols('h,d,r')
# Тензор инерции
# J = symbols('J') # J = IndexedBase('J')
# Углы
psi = symbols('psi');
beta = 0;
alpha = symbols('alpha');
theta = symbols('theta');
#управляющие моменты
W, T = symbols ('W, T');
# элементы матрицы моментов инерций для разных тел (ВРЕМЕННО)
a,b,c = symbols('a,b,c')
J0, J1, J3 = symbols('J0, J1, J3')

# Виртуальные перемещения
delta_x, delta_y, delta_alpha = symbols('delta_x, delta_y, delta_alpha')
delta_theta = symbols('delta_theta')
delta_psi = symbols('delta_psi');
nu1, nu2 = symbols('nu1, nu2')
dnu1, dnu2, ddalpha = symbols('dnu1, dnu2, ddalpha')
m1, m2 = symbols('m1, m2')

#ЗАВИСИМОСТИ
x = x(t); y = y(t); alpha = alpha(t);theta = theta(t); psi = psi(t);
nu1 = nu1(t); nu2 = nu2(t);

#СТРОЕНИЕ ВЕКТОРОВ
e_x = Matrix([1,0,0])
e_y = Matrix([0,1,0])
e_z = Matrix([0,0,1])
e_xi = Matrix([cos(alpha),sin(alpha),0])
e_eta = Matrix([-sin(alpha),cos(alpha),0])

n_wheel = -sin(theta)*e_xi + cos(theta)*e_eta # нормаль к колесу
e_wheel = cos(theta)*e_xi + sin(theta)*e_eta # e_z и нормаль к колесу дополняет до правой тройки?


#СТРОЕНИЕ ПЛАТФОРМЫ НА КОЛЁСАХ
SP = a* (cos(beta)*e_xi + sin(beta)*e_eta)
PC = d*e_wheel - h*e_z
# check!!!
CP = -PC
PS = -SP
DC = r*e_z

omega_platform= Derivative(alpha,t)*e_z
omega_fork    = omega_platform + Derivative(theta,t)*e_z
omega_wheel = omega_fork + Derivative(psi,t)*n_wheel

v_c = omega_wheel.cross(DC)
v_p = v_c + omega_fork.cross(CP)
v_s = v_p + omega_platform.cross(PS)

eq_deltax = delta_x - v_s[0].subs(Derivative(theta,t),delta_theta).subs(Derivative(alpha,t),delta_alpha).subs(Derivative(psi,t),delta_psi)
eq_deltay = delta_y - v_s[1].subs(Derivative(theta,t),delta_theta).subs(Derivative(alpha,t),delta_alpha).subs(Derivative(psi,t),delta_psi)
sols_delta = solve([eq_deltax,eq_deltay],[delta_theta,delta_psi], dict = True)
delta_theta = sols_delta[0][delta_theta];
delta_psi = sols_delta[0][delta_psi];

eq_nu1 = nu1 - v_s.dot(e_xi)
eq_nu2 = nu2 - v_s.dot(e_eta)
sols_nu = solve([eq_nu1,eq_nu2],[Derivative(theta,t),Derivative(psi,t)], dict = True)
dtheta = sols_nu[0][Derivative(theta,t)];
dpsi = sols_nu[0][Derivative(psi,t)];

#print(dtheta)
#print(dpsi)
# платформа
acc_s = Matrix([diff(nu1*e_xi[0] + nu2*e_eta[0],t),diff(nu1*e_xi[1] + nu2*e_eta[1],t),0])
delta_rs = delta_x * e_x + delta_y * e_y
dks = J0 * diff(alpha*e_z[2],t,2)
dp_term1 = m1 * acc_s.dot(delta_rs)
dp_term2 = (dks + T)*delta_alpha
dp = Poly(dp_term1 + dp_term2, [delta_x,delta_y,delta_alpha])

#вилка
df_term2 = T*(delta_alpha+delta_theta)
#print(delta_alpha+delta_theta);


# колесо
v_c1 = Matrix([0,0,0])
v_c1[0] = v_c[0].subs(Derivative(psi,t),dpsi).subs(Derivative(theta,t),dtheta);
v_c1[1] = v_c[1].subs(Derivative(psi,t),dpsi).subs(Derivative(theta,t),dtheta);
acc_c = Matrix([diff(v_c1[0],t),diff(v_c1[1],t),0])
delta_rc = Matrix([0,0,0])
delta_rc[0] = v_c[0].subs(Derivative(psi,t),delta_psi).subs(Derivative(theta,t),delta_theta).subs(Derivative(alpha,t),delta_alpha);
delta_rc[1] = v_c[1].subs(Derivative(psi,t),delta_psi).subs(Derivative(theta,t),delta_theta).subs(Derivative(alpha,t),delta_alpha);
acc_c[0] = acc_c[0].subs(Derivative(psi,t),dpsi).subs(Derivative(theta,t),dtheta);
acc_c[1] = acc_c[1].subs(Derivative(psi,t),dpsi).subs(Derivative(theta,t),dtheta);
dw_term1 = m2 * acc_c.dot(delta_rc)
#print(v_c[0]);
#print(diff(v_c1[0],t));
#print(acc_c[0]);
K = J1*omega_wheel.dot(e_wheel)*e_wheel + J3*omega_wheel.dot(n_wheel)*n_wheel + J1*omega_wheel.dot(e_z)*e_z
Ksubs = Matrix([0,0,0])
Ksubs[0] = K[0].subs(Derivative(psi,t),dpsi).subs(Derivative(theta,t),dtheta);
Ksubs[1] = K[1].subs(Derivative(psi,t),dpsi).subs(Derivative(theta,t),dtheta);
Ksubs[2] = K[2].subs(Derivative(psi,t),dpsi).subs(Derivative(theta,t),dtheta);
omega_delta_wheel = Matrix([0,0,0])
omega_delta_wheel[0] = omega_wheel[0].subs(Derivative(psi,t),delta_psi).subs(Derivative(theta,t),delta_theta).subs(Derivative(alpha,t),delta_alpha);
omega_delta_wheel[1] = omega_wheel[1].subs(Derivative(psi,t),delta_psi).subs(Derivative(theta,t),delta_theta).subs(Derivative(alpha,t),delta_alpha);
omega_delta_wheel[2] = omega_wheel[2].subs(Derivative(psi,t),delta_psi).subs(Derivative(theta,t),delta_theta).subs(Derivative(alpha,t),delta_alpha);
dK = trigsimp(diff(Ksubs,t) - W*e_z)
#print(dK)
#dw_term2 = trigsimp(dK.dot(omega_delta_wheel))
#print(dK)
#print('dw-term2 done')
#print(trigsimp(dw_term2));


#d = Poly(dp_term1 + dp_term2 + df_term2 + dw_term1, [delta_x,delta_y,delta_alpha])
d = Poly(trigsimp(dp_term1 + dp_term2 + df_term2 + dw_term1 + dw_term2), [delta_x,delta_y,delta_alpha])
#d = Poly((dp_term1 + dp_term2 + df_term2 + dw_term1 + dw_term2), [delta_x,delta_y,delta_alpha])
print('d  - done');


eq_dal_delta_x = d.coeff_monomial(delta_x).subs(Derivative(nu1,t),dnu1).subs(Derivative(nu2,t),dnu2).subs(Derivative(alpha,t,t),ddalpha);
eq_dal_delta_y = d.coeff_monomial(delta_y).subs(Derivative(nu1,t),dnu1).subs(Derivative(nu2,t),dnu2).subs(Derivative(alpha,t,t),ddalpha);
eq_dal_delta_alpha = d.coeff_monomial(delta_alpha).subs(Derivative(nu1,t),dnu1).subs(Derivative(nu2,t),dnu2).subs(Derivative(alpha,t,t),ddalpha);

print('Eq1')
print(eq_dal_delta_x.subs([(alpha,0), (theta,0), (nu1,0), (nu2,0), (Derivative(alpha,t),0)]));

print('Eq2')
print(eq_dal_delta_y.subs([(alpha,0), (theta,0), (nu1,0), (nu2,0), (Derivative(alpha,t),0)]));

print('Eq3')
print(eq_dal_delta_alpha.subs([(alpha,0), (theta,0), (nu1,0), (nu2,0), (Derivative(alpha,t),0)]));

EqMatrix, EqRHS = linear_eq_to_matrix([eq_dal_delta_x,eq_dal_delta_y,eq_dal_delta_alpha],[dnu1,dnu2,ddalpha]);
print('begin to invert')
EqS = EqMatrix.inv()
print('finished')
print(EqS[0,0]);

#dyn_eq = solve([eq_dal_delta_x,eq_dal_delta_y,eq_dal_delta_alpha],[Derivative(nu1,t), Derivative(nu2,t), Derivative(alpha,t,2)], dict = True)
#dyn_eq = solve(, dict = True)
#eq_nu1 = dyn_eq[0][Derivative(nu1,t)]
#eq_nu2 = dyn_eq[0][Derivative(nu2,t)]
#eq_ddalpha = dyn_eq[0][Derivative(alpha,t,2)]
#eq_nu1 = dyn_eq[0][dnu1]
#eq_nu2 = dyn_eq[0][dnu2]
#eq_ddalpha = dyn_eq[0][ddalpha]
#print(eq_nu1);
#print(trigsimp(eq_nu1));
print('end');
#print(eq_nu2);
#print(eq_ddalpha);