#Ref: https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=9230365&casa_token=paW6MkN65vUAAAAA:JFJZQ3nC7fJ-6evzYq8DGWNrRAfd6qXUO
import numpy as np
from cpsim import Simulator
from cpsim.controllers.LQR import LQR
# system dynamics
kp = 2 # proportional gains of an on-board PD controller
kd = 1.5 # derivative gains of an on-board PD controller
beta = -0.1 # characterizes the loss of velocity as a result of friction
d_star = 2 # desired distance
A = np.array([[0, 0, 0, -1, 1, 0, 0],
[0, 0, 0, 0, -1, 1, 0],
[0, 0, 0, 0, 0, -1, 1],
[kp, 0, 0, beta - kd, kd, 0, 0],
[-kp, kp, 0, kd, beta - 2 * kd, kd, 0],
[0, -kp, kp, 0, kd, beta - 2 * kd, kd],
[0, 0, -kp, 0, 0, kd, beta - kd]])
B = np.concatenate((np.zeros((4, 3)), np.eye(4)), axis=1).T
x_0 = np.array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])
# utils parameters
R = np.eye(4) * 0.0008
Q = np.eye(7) * 1.2
control_limit = {
'lo': np.array([-5]),
'up': np.array([5])
}
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class Controller:
def __init__(self, dt, control_limit=None):
self.lqr = LQR(A, B, Q, R)
self.set_control_limit(control_lo=control_limit['lo'], control_up=control_limit['up'])
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def update(self, ref: np.ndarray, feedback_value: np.ndarray, current_time) -> np.ndarray:
self.lqr.set_reference(ref)
cin = self.lqr.update(feedback_value, current_time)
return cin
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def set_control_limit(self, control_lo, control_up):
self.control_lo = control_lo
self.control_up = control_up
self.lqr.set_control_limit(self.control_lo[0], self.control_up[0])
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def clear(self):
self.lqr.clear()
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class Platoon(Simulator):
"""
States: (7,)
x[0]: e12 relative distance error with car 1 and 2
x[1]: e23 relative distance error with car 2 and 3
x[2]: e34 relative distance error with car 3 and 4
x[3]: velocity of car 1
x[4]: velocity of car 2
x[5]: velocity of car 3
x[6]: velocity of car 4
Control Input: (4,)
u[0]: acceleration of car 1
u[1]: acceleration of car 2
u[2]: acceleration of car 3
u[3]: acceleration of car 4
State Feedback
Controller: PID
"""
def __init__(self, name, dt, max_index, noise=None):
super().__init__('Platoon' + name, dt, max_index)
self.linear(A, B)
controller = Controller(dt, control_limit)
settings = {
'init_state': x_0,
'feedback_type': 'state',
'controller': controller
}
if noise:
settings['noise'] = noise
self.sim_init(settings)
if __name__ == "__main__":
max_index = 800
dt = 0.02
ref = [np.array([1])] * 301 + [np.array([2])] * 300 + [np.array([1])] * 200
noise = {
'process': {
'type': 'white',
'param': {'C': np.eye(7) * 0.01}
}
}
platoon = Platoon('test', dt, max_index, noise)
for i in range(0, max_index + 1):
assert platoon.cur_index == i
platoon.update_current_ref(ref[i])
# attack here
platoon.evolve()
# print results
import matplotlib.pyplot as plt
t_arr = np.linspace(0, 10, max_index + 1)
ref = [x[0] for x in platoon.refs[:max_index + 1]]
y_arr = [x[0] for x in platoon.outputs[:max_index + 1]]
plt.plot(t_arr, y_arr, t_arr, ref)
plt.show()