894 lines
28 KiB
Python
894 lines
28 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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import math
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class TwoWheeledSystem():
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"""SampleSystem, this is the simulator
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Attributes
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-----------
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x_1 : float
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system state 1
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x_2 : float
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system state 2
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history_x_1 : list
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time history of system state 1 (x_1)
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history_x_2 : list
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time history of system state 2 (x_2)
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"""
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def __init__(self, init_x_1=0., init_x_2=0., init_x_3=0.):
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"""
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Palameters
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-----------
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init_x_1 : float, optional
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initial value of x_1, default is 0.
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init_x_2 : float, optional
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initial value of x_2, default is 0.
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init_x_3 : float, optional
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initial value of x_3, default is 0.
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"""
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self.x_1 = init_x_1
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self.x_2 = init_x_2
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self.x_3 = init_x_3
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self.history_x_1 = [init_x_1]
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self.history_x_2 = [init_x_2]
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self.history_x_3 = [init_x_3]
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def update_state(self, u_1, u_2, dt=0.01):
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"""
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Palameters
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------------
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u_1 : float
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input of system in some cases this means the reference, u_velocity
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u_2 : float
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input of system in some cases this means the reference, u_omega
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dt : float in seconds, optional
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sampling time of simulation, default is 0.01 [s]
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"""
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# for theta 1, theta 1 dot, theta 2, theta 2 dot
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k0 = [0.0 for _ in range(3)]
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k1 = [0.0 for _ in range(3)]
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k2 = [0.0 for _ in range(3)]
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k3 = [0.0 for _ in range(3)]
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functions = [self._func_x_1, self._func_x_2, self._func_x_3]
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# solve Runge-Kutta
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for i, func in enumerate(functions):
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k0[i] = dt * func(self.x_1, self.x_2, self.x_3, u_1, u_2)
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for i, func in enumerate(functions):
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k1[i] = dt * func(self.x_1 + k0[0]/2., self.x_2 + k0[1]/2., self.x_3 + k0[2]/2., u_1, u_2)
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for i, func in enumerate(functions):
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k2[i] = dt * func(self.x_1 + k1[0]/2., self.x_2 + k1[1]/2., self.x_3 + k1[2]/2., u_1, u_2)
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for i, func in enumerate(functions):
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k3[i] = dt * func(self.x_1 + k2[0], self.x_2 + k2[1], self.x_3 + k2[2], u_1, u_2)
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self.x_1 += (k0[0] + 2. * k1[0] + 2. * k2[0] + k3[0]) / 6.
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self.x_2 += (k0[1] + 2. * k1[1] + 2. * k2[1] + k3[1]) / 6.
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self.x_3 += (k0[2] + 2. * k1[2] + 2. * k2[2] + k3[2]) / 6.
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# save
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self.history_x_1.append(self.x_1)
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self.history_x_2.append(self.x_2)
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self.history_x_3.append(self.x_3)
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def _func_x_1(self, y_1, y_2, y_3, u_1, u_2):
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"""
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Parameters
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------------
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y_1 : float
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y_2 : float
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y_3 : float
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u_1 : float
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system input
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u_2 : float
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system input
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"""
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y_dot = math.cos(y_3) * u_1
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return y_dot
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def _func_x_2(self, y_1, y_2, y_3, u_1, u_2):
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"""
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Parameters
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------------
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y_1 : float
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y_2 : float
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y_3 : float
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u_1 : float
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system input
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u_2 : float
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system input
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"""
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y_dot = math.sin(y_3) * u_1
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return y_dot
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def _func_x_3(self, y_1, y_2, y_3, u_1, u_2):
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"""
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Parameters
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------------
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y_1 : float
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y_2 : float
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y_3 : float
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u_1 : float
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system input
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u_2 : float
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system input
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"""
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y_dot = u_2
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return y_dot
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class NMPCSimulatorSystem():
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"""SimulatorSystem for nmpc, this is the simulator of nmpc
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the reason why I seperate the real simulator and nmpc's simulator is sometimes the modeling error, disturbance can include in real simulator
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Attributes
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-----------
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None
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"""
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def __init__(self):
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"""
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Parameters
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-----------
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None
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"""
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pass
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def calc_predict_and_adjoint_state(self, x_1, x_2, x_3, u_1s, u_2s, N, dt):
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"""main
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Parameters
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------------
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x_1 : float
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current state
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x_2 : float
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current state
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x_3 : float
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current state
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u_1s : list of float
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estimated optimal input Us for N steps
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u_2s : list of float
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estimated optimal input Us for N steps
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N : int
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predict step
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dt : float
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sampling time
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Returns
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--------
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x_1s : list of float
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predicted x_1s for N steps
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x_2s : list of float
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predicted x_2s for N steps
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x_3s : list of float
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predicted x_3s for N steps
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lam_1s : list of float
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adjoint state of x_1s, lam_1s for N steps
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lam_2s : list of float
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adjoint state of x_2s, lam_2s for N steps
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lam_3s : list of float
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adjoint state of x_3s, lam_3s for N steps
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"""
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x_1s, x_2s, x_3s = self._calc_predict_states(x_1, x_2, x_3, u_1s, u_2s, N, dt) # by usin state equation
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lam_1s, lam_2s, lam_3s = self._calc_adjoint_states(x_1s, x_2s, x_3s, u_1s, u_2s, N, dt) # by using adjoint equation
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return x_1s, x_2s, x_3s, lam_1s, lam_2s, lam_3s
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def _calc_predict_states(self, x_1, x_2, x_3, u_1s, u_2s, N, dt):
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"""
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Parameters
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------------
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x_1 : float
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current state
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x_2 : float
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current state
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x_3 : float
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current state
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u_1s : list of float
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estimated optimal input Us for N steps
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u_2s : list of float
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estimated optimal input Us for N steps
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N : int
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predict step
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dt : float
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sampling time
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Returns
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--------
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x_1s : list of float
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predicted x_1s for N steps
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x_2s : list of float
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predicted x_2s for N steps
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x_3s : list of float
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predicted x_3s for N steps
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"""
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# initial state
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x_1s = [x_1]
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x_2s = [x_2]
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x_3s = [x_3]
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for i in range(N):
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temp_x_1, temp_x_2, temp_x_3 = self._predict_state_with_oylar(x_1s[i], x_2s[i], x_3s[i], u_1s[i], u_2s[i], dt)
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x_1s.append(temp_x_1)
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x_2s.append(temp_x_2)
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x_3s.append(temp_x_3)
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return x_1s, x_2s, x_3s
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def _calc_adjoint_states(self, x_1s, x_2s, x_3s, u_1s, u_2s, N, dt):
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"""
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Parameters
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------------
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x_1s : list of float
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predicted x_1s for N steps
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x_2s : list of float
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predicted x_2s for N steps
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x_3s : list of float
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predicted x_3s for N steps
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u_1s : list of float
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estimated optimal input Us for N steps
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u_2s : list of float
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estimated optimal input Us for N steps
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N : int
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predict step
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dt : float
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sampling time
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Returns
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--------
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lam_1s : list of float
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adjoint state of x_1s, lam_1s for N steps
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lam_2s : list of float
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adjoint state of x_2s, lam_2s for N steps
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lam_3s : list of float
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adjoint state of x_2s, lam_2s for N steps
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"""
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# final state
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# final_state_func
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lam_1s = [x_1s[-1]]
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lam_2s = [x_2s[-1]]
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lam_3s = [x_3s[-1]]
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for i in range(N-1, 0, -1):
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temp_lam_1, temp_lam_2, temp_lam_3 = self._adjoint_state_with_oylar(x_1s[i], x_2s[i], x_3s[i], lam_1s[0] ,lam_2s[0], lam_3s[0], u_1s[i], u_2s[i], dt)
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lam_1s.insert(0, temp_lam_1)
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lam_2s.insert(0, temp_lam_2)
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lam_3s.insert(0, temp_lam_3)
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return lam_1s, lam_2s, lam_3s
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def final_state_func(self):
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"""this func usually need
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"""
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pass
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def _predict_state_with_oylar(self, x_1, x_2, x_3, u_1, u_2, dt):
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"""in this case this function is the same as simulator
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Parameters
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------------
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x_1 : float
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system state
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x_2 : float
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system state
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x_3 : float
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system state
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u_1 : float
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system input
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u_2 : float
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system input
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dt : float in seconds
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sampling time
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Returns
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--------
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next_x_1 : float
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next state, x_1 calculated by using state equation
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next_x_2 : float
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next state, x_2 calculated by using state equation
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next_x_3 : float
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next state, x_3 calculated by using state equation
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"""
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k0 = [0. for _ in range(3)]
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functions = [self.func_x_1, self.func_x_2, self.func_x_3]
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for i, func in enumerate(functions):
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k0[i] = dt * func(x_1, x_2, x_3, u_1, u_2)
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next_x_1 = x_1 + k0[0]
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next_x_2 = x_2 + k0[1]
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next_x_3 = x_3 + k0[2]
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return next_x_1, next_x_2, next_x_3
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def func_x_1(self, y_1, y_2, y_3, u_1, u_2):
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"""
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Parameters
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------------
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y_1 : float
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y_2 : float
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y_3 : float
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u_1 : float
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system input
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u_2 : float
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system input
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"""
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y_dot = math.cos(y_3) * u_1
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return y_dot
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def func_x_2(self, y_1, y_2, y_3, u_1, u_2):
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"""
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Parameters
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------------
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y_1 : float
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y_2 : float
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y_3 : float
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u_1 : float
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system input
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u_2 : float
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system input
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"""
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y_dot = math.sin(y_3) * u_1
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return y_dot
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def func_x_3(self, y_1, y_2, y_3, u_1, u_2):
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"""
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Parameters
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------------
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y_1 : float
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y_2 : float
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y_3 : float
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u_1 : float
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system input
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u_2 : float
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system input
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"""
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y_dot = u_2
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return y_dot
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def _adjoint_state_with_oylar(self, x_1, x_2, x_3, lam_1, lam_2, lam_3, u_1, u_2, dt):
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"""
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Parameters
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------------
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x_1 : float
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system state
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x_2 : float
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system state
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x_3 : float
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system state
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lam_1 : float
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adjoint state
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lam_2 : float
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adjoint state
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lam_3 : float
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adjoint state
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u_1 : float
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system input
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u_2 : float
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system input
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dt : float in seconds
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sampling time
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Returns
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--------
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pre_lam_1 : float
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pre, 1 step before lam_1 calculated by using adjoint equation
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pre_lam_2 : float
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pre, 1 step before lam_2 calculated by using adjoint equation
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pre_lam_3 : float
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pre, 1 step before lam_3 calculated by using adjoint equation
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"""
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k0 = [0. for _ in range(3)]
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functions = [self._func_lam_1, self._func_lam_2, self._func_lam_3]
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for i, func in enumerate(functions):
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k0[i] = dt * func(x_1, x_2, x_3, lam_1, lam_2, lam_3, u_1, u_2)
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pre_lam_1 = lam_1 + k0[0]
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pre_lam_2 = lam_2 + k0[1]
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pre_lam_3 = lam_3 + k0[2]
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return pre_lam_1, pre_lam_2, pre_lam_3
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def _func_lam_1(self, y_1, y_2, y_3, y_4, y_5, y_6, u_1, u_2):
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"""calculating -\dot{lam_1}
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Parameters
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------------
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y_1 : float
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means x_1
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y_2 : float
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means x_2
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y_3 : float
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means x_3
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y_4 : float
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means lam_1
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y_5 : float
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means lam_2
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y_6 : float
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means lam_3
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u_1 : float
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means system input
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u_2 : float
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means system input
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Returns
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---------
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y_dot : float
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means -\dot{lam_1}
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"""
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y_dot = 0.
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return y_dot
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def _func_lam_2(self, y_1, y_2, y_3, y_4, y_5, y_6, u_1, u_2):
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"""calculating -\dot{lam_2}
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Parameters
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------------
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y_1 : float
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means x_1
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y_2 : float
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means x_2
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y_3 : float
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means x_3
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y_4 : float
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means lam_1
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y_5 : float
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means lam_2
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y_6 : float
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means lam_3
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u_1 : float
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means system input
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u_2 : float
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means system input
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Returns
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---------
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y_dot : float
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means -\dot{lam_2}
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"""
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y_dot = 0.
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return y_dot
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def _func_lam_3(self, y_1, y_2, y_3, y_4, y_5, y_6, u_1, u_2):
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"""calculating -\dot{lam_3}
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Parameters
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------------
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y_1 : float
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means x_1
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y_2 : float
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means x_2
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y_3 : float
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means x_3
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y_4 : float
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means lam_1
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y_5 : float
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means lam_2
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y_6 : float
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means lam_3
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u_1 : float
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means system input
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u_2 : float
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means system input
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Returns
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---------
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y_dot : float
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means -\dot{lam_3}
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"""
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y_dot = - y_4 * math.sin(y_3) * u_1 + y_5 * math.cos(y_3) * u_1
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return y_dot
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class NMPCController_with_CGMRES():
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"""
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Attributes
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------------
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zeta : float
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gain of optimal answer stability
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ht : float
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update value of NMPC this should be decided by zeta
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tf : float
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predict time
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alpha : float
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gain of predict time
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N : int
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predicte step, discritize value
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threshold : float
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cgmres's threshold value
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input_num : int
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system input length, this should include dummy u and constraint variables
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max_iteration : int
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decide by the solved matrix size
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simulator : NMPCSimulatorSystem class
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u_1s : list of float
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estimated optimal system input
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u_2s : list of float
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estimated optimal system input
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dummy_u_1s : list of float
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estimated dummy input
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dummy_u_2s : list of float
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estimated dummy input
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raw_1s : list of float
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estimated constraint variable
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raw_2s : list of float
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estimated constraint variable
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history_u_1 : list of float
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time history of actual system input
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history_u_2 : list of float
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time history of actual system input
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history_dummy_u_1 : list of float
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time history of actual dummy u_1
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history_dummy_u_2 : list of float
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time history of actual dummy u_2
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history_raw_1 : list of float
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time history of actual raw_1
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history_raw_2 : list of float
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time history of actual raw_2
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history_f : list of float
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time history of error of optimal
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"""
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def __init__(self):
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"""
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Parameters
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-----------
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None
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"""
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# parameters
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self.zeta = 100. # 安定化ゲイン
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self.ht = 0.01 # 差分近似の幅
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self.tf = 1. # 最終時間
|
||
self.alpha = 0.5 # 時間の上昇ゲイン
|
||
self.N = 10 # 分割数
|
||
self.threshold = 0.001 # break値
|
||
|
||
self.input_num = 6 # dummy, 制約条件に対するuにも合わせた入力の数
|
||
self.max_iteration = self.input_num * self.N
|
||
|
||
# simulator
|
||
self.simulator = NMPCSimulatorSystem()
|
||
|
||
# initial
|
||
self.u_1s = np.ones(self.N) * 1.
|
||
self.u_2s = np.ones(self.N) * 0.1
|
||
self.dummy_u_1s = np.ones(self.N) * 0.1
|
||
self.dummy_u_2s = np.ones(self.N) * 2.5
|
||
self.raw_1s = np.ones(self.N) * 0.8
|
||
self.raw_2s = np.ones(self.N) * 0.8
|
||
|
||
# for fig
|
||
self.history_u_1 = []
|
||
self.history_u_2 = []
|
||
self.history_dummy_u_1 = []
|
||
self.history_dummy_u_2 = []
|
||
self.history_raw_1 = []
|
||
self.history_raw_2 = []
|
||
self.history_f = []
|
||
|
||
def calc_input(self, x_1, x_2, x_3, time):
|
||
"""
|
||
Parameters
|
||
------------
|
||
x_1 : float
|
||
current state
|
||
x_2 : float
|
||
current state
|
||
x_3 : float
|
||
current state
|
||
time : float in seconds
|
||
now time
|
||
Returns
|
||
--------
|
||
u_1s : list of float
|
||
estimated optimal system input
|
||
u_2s : list of float
|
||
estimated optimal system input
|
||
"""
|
||
# calculating sampling time
|
||
dt = self.tf * (1. - np.exp(-self.alpha * time)) / float(self.N)
|
||
|
||
# x_dot
|
||
x_1_dot = self.simulator.func_x_1(x_1, x_2, x_3, self.u_1s[0], self.u_2s[0])
|
||
x_2_dot = self.simulator.func_x_2(x_1, x_2, x_3, self.u_1s[0], self.u_2s[0])
|
||
x_3_dot = self.simulator.func_x_3(x_1, x_2, x_3, self.u_1s[0], self.u_2s[0])
|
||
|
||
dx_1 = x_1_dot * self.ht
|
||
dx_2 = x_2_dot * self.ht
|
||
dx_3 = x_3_dot * self.ht
|
||
|
||
x_1s, x_2s, x_3s, lam_1s, lam_2s, lam_3s = self.simulator.calc_predict_and_adjoint_state(x_1 + dx_1, x_2 + dx_2, x_3 + dx_3, self.u_1s, self.u_2s, self.N, dt)
|
||
|
||
# Fxt
|
||
Fxt = self._calc_f(x_1s, x_2s, x_3s, lam_1s, lam_2s, lam_3s, self.u_1s, self.u_2s, self.dummy_u_1s, self.dummy_u_2s,
|
||
self.raw_1s, self.raw_2s, self.N, dt)
|
||
|
||
# F
|
||
x_1s, x_2s, x_3s, lam_1s, lam_2s, lam_3s = self.simulator.calc_predict_and_adjoint_state(x_1, x_2, x_3, self.u_1s, self.u_2s, self.N, dt)
|
||
|
||
F = self._calc_f(x_1s, x_2s, x_3s, lam_1s, lam_2s, lam_3s, self.u_1s, self.u_2s, self.dummy_u_1s, self.dummy_u_2s,
|
||
self.raw_1s, self.raw_2s, self.N, dt)
|
||
|
||
right = -self.zeta * F - ((Fxt - F) / self.ht)
|
||
|
||
du_1 = self.u_1s * self.ht
|
||
du_2 = self.u_2s * self.ht
|
||
ddummy_u_1 = self.dummy_u_1s * self.ht
|
||
ddummy_u_2 = self.dummy_u_2s * self.ht
|
||
draw_1 = self.raw_1s * self.ht
|
||
draw_2 = self.raw_2s * self.ht
|
||
|
||
x_1s, x_2s, x_3s, lam_1s, lam_2s, lam_3s = self.simulator.calc_predict_and_adjoint_state(x_1 + dx_1, x_2 + dx_2, x_3 + dx_3, self.u_1s + du_1, self.u_2s + du_2, self.N, dt)
|
||
|
||
Fuxt = self._calc_f(x_1s, x_2s, x_3s, lam_1s, lam_2s, lam_3s, self.u_1s + du_1, self.u_2s + du_2, self.dummy_u_1s + ddummy_u_1, self.dummy_u_2s + ddummy_u_2,
|
||
self.raw_1s + draw_1, self.raw_2s + draw_2, self.N, dt)
|
||
|
||
left = ((Fuxt - Fxt) / self.ht)
|
||
|
||
# calculationg cgmres
|
||
r0 = right - left
|
||
r0_norm = np.linalg.norm(r0)
|
||
|
||
vs = np.zeros((self.max_iteration, self.max_iteration + 1)) # 数×iterarion回数
|
||
|
||
vs[:, 0] = r0 / r0_norm # 最初の基底を算出
|
||
|
||
hs = np.zeros((self.max_iteration + 1, self.max_iteration + 1))
|
||
|
||
e = np.zeros((self.max_iteration + 1, 1)) # in this case the state is 3(u and dummy_u)
|
||
e[0] = 1.
|
||
|
||
for i in range(self.max_iteration):
|
||
du_1 = vs[::self.input_num, i] * self.ht
|
||
du_2 = vs[1::self.input_num, i] * self.ht
|
||
ddummy_u_1 = vs[2::self.input_num, i] * self.ht
|
||
ddummy_u_2 = vs[3::self.input_num, i] * self.ht
|
||
draw_1 = vs[4::self.input_num, i] * self.ht
|
||
draw_2 = vs[5::self.input_num, i] * self.ht
|
||
|
||
x_1s, x_2s, x_3s, lam_1s, lam_2s, lam_3s = self.simulator.calc_predict_and_adjoint_state(x_1 + dx_1, x_2 + dx_2, x_3 + dx_3, self.u_1s + du_1, self.u_2s + du_2, self.N, dt)
|
||
|
||
Fuxt = self._calc_f(x_1s, x_2s, x_3s, lam_1s, lam_2s, lam_3s, self.u_1s + du_1, self.u_2s + du_2, self.dummy_u_1s + ddummy_u_1, self.dummy_u_2s + ddummy_u_2,
|
||
self.raw_1s + draw_1, self.raw_2s + draw_2, self.N, dt)
|
||
|
||
Av = (( Fuxt - Fxt) / self.ht)
|
||
|
||
sum_Av = np.zeros(self.max_iteration)
|
||
|
||
for j in range(i + 1): # グラムシュミットの直交化法です、和を取って差分を取って算出します
|
||
hs[j, i] = np.dot(Av, vs[:, j])
|
||
sum_Av = sum_Av + hs[j, i] * vs[:, j]
|
||
|
||
v_est = Av - sum_Av
|
||
|
||
hs[i+1, i] = np.linalg.norm(v_est)
|
||
|
||
vs[:, i+1] = v_est / hs[i+1, i]
|
||
|
||
inv_hs = np.linalg.pinv(hs[:i+1, :i]) # この辺は教科書（実時間の方）にのっています
|
||
ys = np.dot(inv_hs, r0_norm * e[:i+1])
|
||
|
||
judge_value = r0_norm * e[:i+1] - np.dot(hs[:i+1, :i], ys[:i])
|
||
|
||
if np.linalg.norm(judge_value) < self.threshold or i == self.max_iteration-1:
|
||
update_value = np.dot(vs[:, :i-1], ys_pre[:i-1]).flatten()
|
||
du_1_new = du_1 + update_value[::self.input_num]
|
||
du_2_new = du_2 + update_value[1::self.input_num]
|
||
ddummy_u_1_new = ddummy_u_1 + update_value[2::self.input_num]
|
||
ddummy_u_2_new = ddummy_u_2 + update_value[3::self.input_num]
|
||
draw_1_new = draw_1 + update_value[4::self.input_num]
|
||
draw_2_new = draw_2 + update_value[5::self.input_num]
|
||
break
|
||
|
||
ys_pre = ys
|
||
|
||
# update
|
||
self.u_1s += du_1_new * self.ht
|
||
self.u_2s += du_2_new * self.ht
|
||
self.dummy_u_1s += ddummy_u_1_new * self.ht
|
||
self.dummy_u_2s += ddummy_u_2_new * self.ht
|
||
self.raw_1s += draw_1_new * self.ht
|
||
self.raw_2s += draw_2_new * self.ht
|
||
|
||
x_1s, x_2s, x_3s, lam_1s, lam_2s, lam_3s = self.simulator.calc_predict_and_adjoint_state(x_1, x_2, x_3, self.u_1s, self.u_2s, self.N, dt)
|
||
|
||
F = self._calc_f(x_1s, x_2s, x_3s, lam_1s, lam_2s, lam_3s, self.u_1s, self.u_2s, self.dummy_u_1s, self.dummy_u_2s,
|
||
self.raw_1s, self.raw_2s, self.N, dt)
|
||
|
||
print("check F = {0}".format(np.linalg.norm(F)))
|
||
|
||
# for save
|
||
self.history_f.append(np.linalg.norm(F))
|
||
self.history_u_1.append(self.u_1s[0])
|
||
self.history_u_2.append(self.u_2s[0])
|
||
self.history_dummy_u_1.append(self.dummy_u_1s[0])
|
||
self.history_dummy_u_2.append(self.dummy_u_2s[0])
|
||
self.history_raw_1.append(self.raw_1s[0])
|
||
self.history_raw_2.append(self.raw_2s[0])
|
||
|
||
return self.u_1s, self.u_2s
|
||
|
||
def _calc_f(self, x_1s, x_2s, x_3s, lam_1s, lam_2s, lam_3s, u_1s, u_2s, dummy_u_1s, dummy_u_2s, raw_1s, raw_2s, N, dt):
|
||
"""
|
||
Parameters
|
||
------------
|
||
x_1s : list of float
|
||
predicted x_1s for N steps
|
||
x_2s : list of float
|
||
predicted x_2s for N steps
|
||
x_3s : list of float
|
||
predicted x_3s for N steps
|
||
lam_1s : list of float
|
||
adjoint state of x_1s, lam_1s for N steps
|
||
lam_2s : list of float
|
||
adjoint state of x_2s, lam_2s for N steps
|
||
lam_3s : list of float
|
||
adjoint state of x_2s, lam_3s for N steps
|
||
u_1s : list of float
|
||
estimated optimal system input
|
||
u_2s : list of float
|
||
estimated optimal system input
|
||
dummy_u_1s : list of float
|
||
estimated dummy input
|
||
dummy_u_2s : list of float
|
||
estimated dummy input
|
||
raw_1s : list of float
|
||
estimated constraint variable
|
||
raw_2s : list of float
|
||
estimated constraint variable
|
||
N : int
|
||
predict time step
|
||
dt : float
|
||
sampling time of system
|
||
"""
|
||
F = []
|
||
|
||
for i in range(N):
|
||
F.append(u_1s[i] + lam_1s[i] * math.cos(x_3s[i]) + lam_2s[i] * math.sin(x_3s[i]) + 2 * raw_1s[i] * u_1s[i])
|
||
F.append(u_2s[i] + lam_3s[i] + 2 * raw_2s[i] * u_2s[i])
|
||
F.append(-0.01 + 2. * raw_1s[i] * dummy_u_1s[i])
|
||
F.append(-0.01 + 2. * raw_2s[i] * dummy_u_2s[i])
|
||
F.append(u_1s[i]**2 + dummy_u_1s[i]**2 - 1.**2)
|
||
F.append(u_2s[i]**2 + dummy_u_2s[i]**2 - 1.5**2)
|
||
|
||
return np.array(F)
|
||
|
||
def circle_make_with_angles(center_x, center_y, radius, angle):
|
||
'''
|
||
Create circle matrix with angle line matrix
|
||
|
||
Parameters
|
||
-------
|
||
center_x : float
|
||
the center x position of the circle
|
||
center_y : float
|
||
the center y position of the circle
|
||
radius : float
|
||
angle : float [rad]
|
||
|
||
Returns
|
||
-------
|
||
circle xs : numpy.ndarray
|
||
circle ys : numpy.ndarray
|
||
angle line xs : numpy.ndarray
|
||
angle line ys : numpy.ndarray
|
||
'''
|
||
|
||
point_num = 100 # 分解能
|
||
|
||
circle_xs = []
|
||
circle_ys = []
|
||
|
||
for i in range(point_num + 1):
|
||
circle_xs.append(center_x + radius * math.cos(i*2*math.pi/point_num))
|
||
circle_ys.append(center_y + radius * math.sin(i*2*math.pi/point_num))
|
||
|
||
angle_line_xs = [center_x, center_x + math.cos(angle) * radius]
|
||
angle_line_ys = [center_y, center_y + math.sin(angle) * radius]
|
||
|
||
return np.array(circle_xs), np.array(circle_ys), np.array(angle_line_xs), np.array(angle_line_ys)
|
||
|
||
def main():
|
||
# simulation time
|
||
dt = 0.01
|
||
iteration_time = 15.
|
||
iteration_num = int(iteration_time/dt)
|
||
|
||
# plant
|
||
plant_system = TwoWheeledSystem(init_x_1=-4.5, init_x_2=1.5, init_x_3=0.25)
|
||
|
||
# controller
|
||
controller = NMPCController_with_CGMRES()
|
||
|
||
# for i in range(iteration_num)
|
||
for i in range(1, iteration_num):
|
||
time = float(i) * dt
|
||
x_1 = plant_system.x_1
|
||
x_2 = plant_system.x_2
|
||
x_3 = plant_system.x_3
|
||
# make input
|
||
u_1s, u_2s = controller.calc_input(x_1, x_2, x_3, time)
|
||
# update state
|
||
plant_system.update_state(u_1s[0], u_2s[0])
|
||
|
||
# figure
|
||
# time history
|
||
fig_p = plt.figure()
|
||
fig_u = plt.figure()
|
||
fig_f = plt.figure()
|
||
|
||
# traj
|
||
fig_t = plt.figure()
|
||
fig_traj = fig_t.add_subplot(111)
|
||
fig_traj.set_aspect('equal')
|
||
|
||
x_1_fig = fig_p.add_subplot(311)
|
||
x_2_fig = fig_p.add_subplot(312)
|
||
x_3_fig = fig_p.add_subplot(313)
|
||
|
||
u_1_fig = fig_u.add_subplot(411)
|
||
u_2_fig = fig_u.add_subplot(412)
|
||
dummy_1_fig = fig_u.add_subplot(413)
|
||
dummy_2_fig = fig_u.add_subplot(414)
|
||
|
||
raw_1_fig = fig_f.add_subplot(311)
|
||
raw_2_fig = fig_f.add_subplot(312)
|
||
f_fig = fig_f.add_subplot(313)
|
||
|
||
x_1_fig.plot(np.arange(iteration_num)*dt, plant_system.history_x_1)
|
||
x_1_fig.set_xlabel("time [s]")
|
||
x_1_fig.set_ylabel("x_1")
|
||
|
||
x_2_fig.plot(np.arange(iteration_num)*dt, plant_system.history_x_2)
|
||
x_2_fig.set_xlabel("time [s]")
|
||
x_2_fig.set_ylabel("x_2")
|
||
|
||
x_3_fig.plot(np.arange(iteration_num)*dt, plant_system.history_x_3)
|
||
x_3_fig.set_xlabel("time [s]")
|
||
x_3_fig.set_ylabel("x_3")
|
||
|
||
u_1_fig.plot(np.arange(iteration_num - 1)*dt, controller.history_u_1)
|
||
u_1_fig.set_xlabel("time [s]")
|
||
u_1_fig.set_ylabel("u_v")
|
||
|
||
u_2_fig.plot(np.arange(iteration_num - 1)*dt, controller.history_u_2)
|
||
u_2_fig.set_xlabel("time [s]")
|
||
u_2_fig.set_ylabel("u_omega")
|
||
|
||
dummy_1_fig.plot(np.arange(iteration_num - 1)*dt, controller.history_dummy_u_1)
|
||
dummy_1_fig.set_xlabel("time [s]")
|
||
dummy_1_fig.set_ylabel("dummy u_1")
|
||
|
||
dummy_2_fig.plot(np.arange(iteration_num - 1)*dt, controller.history_dummy_u_2)
|
||
dummy_2_fig.set_xlabel("time [s]")
|
||
dummy_2_fig.set_ylabel("dummy u_2")
|
||
|
||
raw_1_fig.plot(np.arange(iteration_num - 1)*dt, controller.history_raw_1)
|
||
raw_1_fig.set_xlabel("time [s]")
|
||
raw_1_fig.set_ylabel("raw_1")
|
||
|
||
raw_2_fig.plot(np.arange(iteration_num - 1)*dt, controller.history_raw_2)
|
||
raw_2_fig.set_xlabel("time [s]")
|
||
raw_2_fig.set_ylabel("raw_2")
|
||
|
||
f_fig.plot(np.arange(iteration_num - 1)*dt, controller.history_f)
|
||
f_fig.set_xlabel("time [s]")
|
||
f_fig.set_ylabel("optimal error")
|
||
|
||
fig_traj.plot(plant_system.history_x_1, plant_system.history_x_2, color="b", linestyle="dashed")
|
||
fig_traj.set_xlabel("x [m]")
|
||
fig_traj.set_ylabel("y [m]")
|
||
|
||
write_obj_num = 5
|
||
count_num = int(iteration_num / write_obj_num)
|
||
|
||
for i in np.arange(0, iteration_num, count_num):
|
||
obj_xs, obj_ys, obj_line_xs, obj_line_ys = circle_make_with_angles(plant_system.history_x_1[i], plant_system.history_x_2[i], 0.5, plant_system.history_x_3[i])
|
||
fig_traj.plot(obj_xs, obj_ys, color="k")
|
||
fig_traj.plot(obj_line_xs, obj_line_ys, color="k")
|
||
|
||
fig_p.tight_layout()
|
||
fig_u.tight_layout()
|
||
fig_f.tight_layout()
|
||
|
||
plt.show()
|
||
|
||
|
||
if __name__ == "__main__":
|
||
main()
|
||
|
||
|
||
|