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computation_v2-2.py
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from sympy import *
import numpy as np
import math
import matplotlib.pyplot as plt
from scipy.linalg import svd
from scipy.linalg import expm
from scipy.linalg import eigh
import matplotlib.animation as animation
from spb import *
def plot_reachable_sets(A, B, thrusttime, terminaltime, l1, integer):
A = Matrix(A)
B = Matrix(B)
theta = Symbol("theta")
q1 = A @ Matrix([cos(theta), sin(theta)])
q2 = B @ Matrix([cos(theta), sin(theta)])
"""
p = plot_parametric(
(q1[0], q1[1]),
(q2[0], q2[1]),
(theta, 0, 2 * math.pi),
xlabel="X Reachable Set",
ylabel="Y Reachable Set",
show=False,
title="Impulsive vs Constant Thrust Reachable Sets",
)
p.save(f"plots/{round(thrusttime, 3)}tt{round(terminaltime, 3)}{l1}.png")
"""
p = graphics(
line_parametric_2d(
q1[0],
q1[1],
(theta, 0, 2 * math.pi),
use_cm=False,
label="Impulsive RRS",
),
line_parametric_2d(
q2[0],
q2[1],
(theta, 0, 2 * math.pi),
use_cm=False,
label="Constant Thrust RRS",
),
xlabel="x (meters)",
ylabel="y (meters)",
legend=True,
show=False,
title="X-Y Position Relative Reachable Set",
)
p.save(f"plots/{integer}tt{l1}.png")
def phi_calc(A, B, th):
A = Matrix(A)
B = Matrix(B)
theta = Symbol("theta")
res_vec_B = B.inv() @ Matrix([cos(theta), sin(theta)]).subs(theta, th)
res_vec_A = A.inv() @ Matrix([cos(theta), sin(theta)]).subs(theta, th)
return sqrt(res_vec_B.dot(res_vec_B)) / sqrt(res_vec_A.dot(res_vec_A))
t2 = 10
t1 = 0.1
def reachable_set_calcs(t2, t1, l1, i):
print(f"Computing statistics for terminal time: {t2}, thrust time: {t1}")
STM = lambda t, n: expm(
[
[0, 0, 0, 1 * t, 0, 0],
[0, 0, 0, 0, 1 * t, 0],
[0, 0, 0, 0, 0, 1 * t],
[3 * t * n**2, 0, 0, 0, 2 * n * t, 0],
[0, 0, 0, -2 * n * t, 0, 0],
[0, 0, -t * n**2, 0, 0, 0],
]
)
ITM = lambda t, n: [
[(1 - np.cos(t * n)) / n**2, -2 * (-t * n + np.sin(t * n)) / n**2, 0],
[
2 * (-t * n + np.sin(t * n)) / n**2,
(-3 * t**2) / 2 + 4 * (1 - np.cos(t * n)) / n**2,
0,
],
[0, 0, (1 - np.cos(t * n)) / n**2],
[np.sin(t * n) / n, 2 * (-1 + np.cos(t * n)) / n, 0],
[2 * (-1 + np.cos(t * n)) / n, -3 * t + 4 * np.sin(t * n) / n, 0],
[0, 0, np.sin(t * n) / n],
]
U_1, S_1, V_1 = svd(STM(t2, 1)[0:2, 3:5])
transform_mat_1 = [U_1.T[0] * S_1[0], U_1.T[1] * S_1[1]]
transform_mat_1 = np.array(transform_mat_1).T
itm = np.array(ITM(t1, 1))
stm = np.array(STM(t2 - t1, 1))
U_2, S_2, V_2 = svd((stm[0:2, 0:6] @ itm)[:2, :2] / t1)
transform_mat_2 = [U_2.T[0] * S_2[0], U_2.T[1] * S_2[1]]
transform_mat_2 = np.array(transform_mat_2).T
# plot_reachable_sets(transform_mat_1, transform_mat_2, t1, t2, l1, i)
phis = np.linspace(0, 2 * math.pi, 628)
res = [phi_calc(transform_mat_1, transform_mat_2, phi) for phi in phis]
res_min = min(res)
res_max = max(res)
a_ = np.array(STM(t2, 1)[0:2, 3:5])
aT = STM(t2, 1)[0:2, 3:5].T
b_ = np.array((stm[0:2, 0:6] @ itm)[:2, :2] / t1)
bT = np.array((stm[0:2, 0:6] @ itm)[:2, :2] / t1).T
w, v = eigh(
a=np.linalg.inv(aT) @ np.linalg.inv(a_), b=np.linalg.inv(bT) @ np.linalg.inv(b_)
)
v0 = v[:, 0]
v1 = v[:, 1]
# print(np.sqrt(w))
# print(v0, v1)
t0 = np.arctan2(v0[1], v0[0])
t1 = np.arctan2(v1[1], v1[0])
# print(t0, t1)
#
# plt.plot(phis, res)
# plt.axvline(x=t0)
# plt.axvline(x=t1)
# plt.show()
# print()
return np.sqrt(w), t0, t1
def plotsaver(terminal_time=4 * math.pi, max_thrust_time=3 * math.pi, num_plots=200):
for i in range(np.linspace(0.01, max_thrust_time, num_plots).shape[0]):
cur_thrust_time = np.linspace(0.01, max_thrust_time, num_plots)[i]
tt = terminal_time
print(
f"Computing statistics for terminal time: {tt}, thrust time: {cur_thrust_time}"
)
STM = lambda t, n: expm(
[
[0, 0, 0, 1 * t, 0, 0],
[0, 0, 0, 0, 1 * t, 0],
[0, 0, 0, 0, 0, 1 * t],
[3 * t * n**2, 0, 0, 0, 2 * n * t, 0],
[0, 0, 0, -2 * n * t, 0, 0],
[0, 0, -t * n**2, 0, 0, 0],
]
)
ITM = lambda t, n: [
[(1 - np.cos(t * n)) / n**2, -2 * (-t * n + np.sin(t * n)) / n**2, 0],
[
2 * (-t * n + np.sin(t * n)) / n**2,
(-3 * t**2) / 2 + 4 * (1 - np.cos(t * n)) / n**2,
0,
],
[0, 0, (1 - np.cos(t * n)) / n**2],
[np.sin(t * n) / n, 2 * (-1 + np.cos(t * n)) / n, 0],
[2 * (-1 + np.cos(t * n)) / n, -3 * t + 4 * np.sin(t * n) / n, 0],
[0, 0, np.sin(t * n) / n],
]
U_1, S_1, V_1 = svd(STM(tt, 1)[0:2, 3:5])
transform_mat_1 = [U_1.T[0] * S_1[0], U_1.T[1] * S_1[1]]
transform_mat_1 = np.array(transform_mat_1).T
itm = np.array(ITM(cur_thrust_time, 1))
stm = np.array(STM(tt - cur_thrust_time, 1))
U_2, S_2, V_2 = svd((stm[0:2, 0:6] @ itm)[:2, :2] / cur_thrust_time)
transform_mat_2 = [U_2.T[0] * S_2[0], U_2.T[1] * S_2[1]]
transform_mat_2 = np.array(transform_mat_2).T
plot_reachable_sets(
STM(t2, 1)[0:2, 3:5],
(stm[0:2, 0:6] @ itm)[:2, :2] / cur_thrust_time,
cur_thrust_time,
tt,
)
# plot_reachable_sets(transform_mat_1, transform_mat_2, cur_thrust_time, tt)
# plotsaver()
l1 = [reachable_set_calcs(8, i / 4, "l1", i) for i in range(1, 20)]
l2 = [reachable_set_calcs(10, i / 4, "l2", i) for i in range(1, 20)]
l3 = [reachable_set_calcs(12, i / 2, "l3", i) for i in range(1, 20)]
val_mins_l1 = [ele[0][0] for ele in l1]
val_maxs_l1 = [ele[0][1] for ele in l1]
val_mins_l2 = [ele[0][0] for ele in l2]
val_maxs_l2 = [ele[0][1] for ele in l2]
val_mins_l3 = [ele[0][0] for ele in l3]
val_maxs_l3 = [ele[0][1] for ele in l3]
theta_min_l1 = [ele[1] for ele in l1]
theta_max_l1 = [ele[2] for ele in l1]
theta_min_l2 = [ele[1] for ele in l2]
theta_max_l2 = [ele[2] for ele in l2]
theta_min_l3 = [ele[1] for ele in l3]
theta_max_l3 = [ele[2] for ele in l3]
plt.xlabel("Terminal Time")
plt.ylabel("Reacahble Set min/max Ratios")
plt.title("Reachable Set min/max Ratios vs Thrust Time ")
plt.yscale("log")
plt.plot([i / 4 for i in range(1, 20)], val_mins_l1, label="l1 min")
plt.plot([i / 4 for i in range(1, 20)], val_maxs_l1, label="l1 max")
plt.legend()
plt.savefig("figs/ratiosvstimel1.png")
plt.clf()
plt.xlabel("Terminal Time")
plt.ylabel("Reacahble Set min/max Ratios")
plt.title("Reachable Set min/max Ratios vs Thrust Time ")
plt.yscale("log")
plt.plot([i / 4 for i in range(1, 20)], val_mins_l2, label="l2 min")
plt.plot([i / 4 for i in range(1, 20)], val_maxs_l2, label="l2 max")
plt.legend()
plt.savefig("figs/ratiosvstimel2.png")
plt.clf()
plt.xlabel("Terminal Time")
plt.ylabel("Reacahble Set min/max Ratios")
plt.title("Reachable Set min/max Ratios vs Thrust Time ")
plt.yscale("log")
plt.plot([i / 4 for i in range(1, 20)], val_mins_l3, label="l3 min")
plt.plot([i / 4 for i in range(1, 20)], val_maxs_l3, label="l3 max")
plt.legend()
plt.savefig("figs/ratiosvstimel3.png")
plt.clf()
plt.legend()
plt.xlabel("Terminal Time")
plt.ylabel("Reacahble Set min/max Angles")
plt.title("Reachable Set min/max Angles vs Thrust Time")
plt.plot([i / 4 for i in range(1, 20)], theta_min_l1, label="l1 min")
plt.plot([i / 4 for i in range(1, 20)], theta_max_l1, label="l1 max")
plt.legend()
plt.savefig("figs/thetassvstimel1.png")
plt.clf()
plt.legend()
plt.xlabel("Terminal Time")
plt.ylabel("Reacahble Set min/max Angles")
plt.title("Reachable Set min/max Angles vs Thrust Time")
plt.plot([i / 4 for i in range(1, 20)], theta_min_l2, label="l2 min")
plt.plot([i / 4 for i in range(1, 20)], theta_max_l2, label="l2 max")
plt.legend()
plt.savefig("figs/thetassvstimel2.png")
plt.clf()
plt.legend()
plt.xlabel("Terminal Time")
plt.ylabel("Reacahble Set min/max Angles")
plt.title("Reachable Set min/max Angles vs Thrust Time")
plt.plot([i / 4 for i in range(1, 20)], theta_min_l3, label="l3 min")
plt.plot([i / 4 for i in range(1, 20)], theta_max_l3, label="l3 max")
plt.legend()
plt.savefig("figs/thetasvstimel3.png")
plt.clf()