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SC_subproblem.py
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SC_subproblem.py
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#subproblem: x^ v^ sigma^ => next x y sigma
#对应原论文 Problem 2. : Convex Discrete-Time Fixed-Final-Time Problem
from cvxpy import *
import cvxpy_codegen as cpg
from time import time
import numpy as np
import sys
import SC_params
#codegen时params为None,super必须提供 K
#超参数贯穿整个codegen
def solve(params, params_super = None, codegen = False):
#super params
if (params_super == None):
params_super = SC_params.SuperParams() # default
K = params_super.K
#优化变量
x = Variable(14, K, name='x')
u = Variable(3, K, name='u')
s = Variable(1, 1, name='s')
nu = Variable(14, K-1, name='nu')
delta = Variable(1, K, name='delta')
delta_s = Variable(1, 1, name='delta_s')
#参数
# A = [Parameter(14, 14, name='A_%s'%i) for i in range(K)]
# B = [Parameter(14, 3, name='B_%s'%i) for i in range(K)]
# C = [Parameter(14, 3, name='C_%s'%i) for i in range(K)]
# S = [Parameter(14, 1, name='S_%s'%i) for i in range(K)]
# z = [Parameter(14, 1, name='z_%s'%i) for i in range(K)]
#暴力数组会超python255参数限制。。。
A = Parameter(14 * K, 14, name='A')
B = Parameter(14 * K, 3, name='B')
C = Parameter(14 * K, 3, name='C')
S = Parameter(14 * K, 1, name='S')
z = Parameter(14 * K, 1, name='z')
x_last = Parameter(14, K, name='x_last')
u_last = Parameter(3, K, name='u_last')
u_last_dir = Parameter(3, K, name='u_last_dir')
s_last = Parameter(2, 1, name='s_last') #2行1列,第二列占位用,因为1行1列在codegen会出bug
w_nu = Parameter(2, 1, name='w_nu', sign="positive") #权重非负,保证dcp
w_delta = Parameter(2, 1, name='w_delta', sign="positive")
w_delta_s = Parameter(2, 1, name='w_delta_s', sign="positive")
x_initial = Parameter(14, 1, name='x_initial')
x_final = Parameter(14, 1, name='x_final')
#sparse
m_dry = Parameter(2, 1, name='m_dry')
tan_gamma_gs = Parameter(2, 1, name='tan_gamma_gs', sign="positive")
cos_theta_max = Parameter(1, K, name='cos_theta_max')
omega_max = Parameter(2, 1, name='omega_max')
cos_delta_max = Parameter(2, 1, name='cos_delta_max', sign="positive")
T_max = Parameter(2, 1, name='T_max')
T_min = Parameter(2, 1, name='T_min')
if (not codegen): #填入实际参数
A.value = params.A.reshape(K * 14, 14)
B.value = params.B.reshape(K * 14, 3)
C.value = params.C.reshape(K * 14, 3)
S.value = params.S.reshape(K * 14, 1)
z.value = params.z.reshape(K * 14, 1)
x_last.value = params.x_last
u_last.value = params.u_last
u_last_dir.value = params.u_last_dir
s_last.value = [params.s_last, 0]
w_nu.value = [params.w_nu, 0]
w_delta.value = [params.w_delta, 0]
w_delta_s.value = [params.w_delta_s, 0]
x_initial.value = params.x_initial
x_final.value = params.x_final
#sparse
m_dry.value = [params.m_dry, 0]
tan_gamma_gs.value = [params.tan_gamma_gs, 0]
cos_theta_max.value = np.array([params.cos_theta_max] * K).reshape(1, K) if type(params.cos_theta_max)!=np.ndarray else params.cos_theta_max
omega_max.value = [params.omega_max, 0]
cos_delta_max.value = [params.cos_delta_max, 0]
T_max.value = [params.T_max, 0]
T_min.value = [params.T_min, 0]
#限制条件
cons = []
#(1)边界条件
#初始
cons += [
x[0, 0] == x_initial[0, 0], # mass
x[1:4, 0] == x_initial[1:4, 0], # position
x[4:7, 0] == x_initial[4:7, 0], # velocity
x[7:11, 0] == x_initial[7:11, 0], # quanternion 更改:初态姿态固定
x[11:14, 0] == x_initial[11:14, 0], # angular vel
]
#结束
cons += [
# x[0, K-1] == x_final[0, 0], # mass
x[1:4, K-1] == x_final[1:4, 0], # position
x[4:7, K-1] == x_final[4:7, 0], # velocity
#x[7:11, K-1] == x_final[7:11, 0], # quanternion
x[11:14, K-1] == x_final[11:14, 0], # angular vel
]
#thrust最后朝下
cons += [
u[1, K-1] == 0,
u[2, K-1] == 0,
]
#(2)动力学方程
for k in range(K - 1):
cons += [
x[:, k+1] == A[14*k:14*(k+1),:]*x[:, k] + B[14*k:14*(k+1),:]*u[:, k] + C[14*k:14*(k+1),:]*u[:, k+1] + S[14*k:14*(k+1),:]*s + z[14*k:14*(k+1),:] + nu[:, k]
]
#(3)状态限制
for k in range(K):
cons += [
x[0, k] >= m_dry[0,0], #燃料耗尽
norm(x[2:4, k]) * tan_gamma_gs[0,0] <= x[1, k], #在锥内部
cos_theta_max[0,k] <= 1 - 2 * sum_squares(x[9:11, k]), # 倾角
norm(x[11:14, k]) <= omega_max[0,0], #角速度
]
cons += [0 == x[9:11, K-1]] # 规定最终头朝上但是滚转轴随意 即四元数jk分量为0
#cons += [0 == x[8, 0]]
cons += [s >= 0]
#(4)输入量(推力)限制
for k in range(K):
cons += [
#T_min[0,0] <= u_last_dir[:, k].T * u[:, k], #最小推力线性近似
T_min[0,0] <= u_last_dir[0, k]*u[0, k] + u_last_dir[1, k]*u[1, k] + u_last_dir[2, k]*u[2, k], #点乘展开写
norm(u[:, k]) <= T_max[0,0], #最大推力凸约束
norm(u[:, k]) * cos_delta_max[0,0] <= u[0, k], #gimbal限制
]
#(5)trust region
for k in range(K):
dx = x[:, k] - x_last[:, k]
du = u[:, k] - u_last[:, k]
cons += [
sum_squares(dx) + sum_squares(du) <= delta[:, k]
]
cons += [norm(s - s_last[0,0], 1) <= delta_s]
# Objective:
objective = Minimize(
-x[0,K-1]
+ w_nu[0,0] * norm(nu, 1) # virtual control(1范数)
+ w_delta[0,0] * norm(delta) # trust region on dynamics(2范数)
+ w_delta_s[0,0] * norm(delta_s, 1) # trust region on sigma(1范数)
)
# Problem
problem = Problem(objective, cons)
#print('is DCP: %s' % problem.is_dcp()) #检查是否符合凸优化规则
# Solve or Codegen
if (codegen):
cpg.codegen(problem, codegen_path)
else:
obj_opt = problem.solve(solver=ECOS, verbose=False)
return (obj_opt,
np.array(x.value),
np.array(u.value),
s.value,
np.array(nu.value),
np.array(delta.value),
delta_s.value) #tuple(结果,状态,控制,时间scale)
if __name__ == '__main__':
if (len(sys.argv) > 2 and sys.argv[1] == 'codegen'):
codegen_path = sys.argv[2]
solve(None, None, True)
else:
print("invalid input")
print(sys.argv)