Merge branch 'master' of github.com:Shunichi09/nonlinear_control
This commit is contained in:
Shunichi09
commit
004dffa8d7
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@ -0,0 +1,21 @@
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MIT License
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Copyright (c) 2018 Shunichi Sekiguchi
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Permission is hereby granted, free of charge, to any person obtaining a copy
|
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of this software and associated documentation files (the "Software"), to deal
|
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in the Software without restriction, including without limitation the rights
|
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
|
||||
furnished to do so, subject to the following conditions:
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||||
|
||||
The above copyright notice and this permission notice shall be included in all
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||||
copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
|
||||
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
|
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
|
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SOFTWARE.
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15
README.md
15
README.md
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@ -1,2 +1,17 @@
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[](LICENSE)
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# nonlinear_control
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Implementing the nonlinear model predictive control, sliding mode control
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# Usage
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you can see the usage in each folder
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# Requirement
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You should install following software
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- python(3.5>)
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- numpy
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- matplotlib
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# License
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MIT
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@ -519,8 +519,8 @@ class NMPCController_with_CGMRES():
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if np.linalg.norm(judge_value) < self.threshold or i == self.max_iteration-1:
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update_value = np.dot(vs[:, :i-1], ys_pre[:i-1]).flatten()
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du_new = du + update_value[::3]
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ddummy_u_new = du + update_value[1::3]
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draw_new = du + update_value[2::3]
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ddummy_u_new = ddummy_u + update_value[1::3]
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draw_new = draw + update_value[2::3]
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break
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ys_pre = ys
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|
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@ -2,7 +2,7 @@ import numpy as np
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import matplotlib.pyplot as plt
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import math
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class SampleSystem():
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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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@ -15,7 +15,7 @@ class SampleSystem():
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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.):
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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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@ -23,73 +23,101 @@ class SampleSystem():
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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, dt=0.01):
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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 : float
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input of system in some cases this means the reference
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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(2)]
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k1 = [0.0 for _ in range(2)]
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k2 = [0.0 for _ in range(2)]
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k3 = [0.0 for _ in range(2)]
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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]
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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, u)
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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., u)
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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., u)
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k2[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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k3[i] = dt * func(self.x_1 + k2[0], self.x_2 + k2[1], u)
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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_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, u):
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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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u : 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 = y_2
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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, u):
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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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u : 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 = (1. - y_1**2 - y_2**2) * y_2 - y_1 + u
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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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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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|
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@ -107,7 +135,7 @@ class NMPCSimulatorSystem():
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"""
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pass
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def calc_predict_and_adjoint_state(self, x_1, x_2, us, N, dt):
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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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|
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@ -115,7 +143,11 @@ class NMPCSimulatorSystem():
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current state
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x_2 : float
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current state
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us : list of float
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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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@ -128,18 +160,21 @@ class NMPCSimulatorSystem():
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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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x_1s, x_2s = self._calc_predict_states(x_1, x_2, us, N, dt) # by usin state equation
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lam_1s, lam_2s = self._calc_adjoint_states(x_1s, x_2s, us, 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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return x_1s, x_2s, lam_1s, lam_2s
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def _calc_predict_states(self, x_1, x_2, us, N, dt):
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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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|
|
@ -147,7 +182,11 @@ class NMPCSimulatorSystem():
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current state
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x_2 : float
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current state
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us : list of float
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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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|
|
@ -160,19 +199,23 @@ class NMPCSimulatorSystem():
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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 = self._predict_state_with_oylar(x_1s[i], x_2s[i], us[i], dt)
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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
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return x_1s, x_2s, x_3s
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def _calc_adjoint_states(self, x_1s, x_2s, us, N, dt):
|
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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
|
||||
------------
|
||||
|
|
@ -180,7 +223,11 @@ class NMPCSimulatorSystem():
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predicted x_1s for N steps
|
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x_2s : list of float
|
||||
predicted x_2s for N steps
|
||||
us : list of float
|
||||
x_3s : list of float
|
||||
predicted x_3s for N steps
|
||||
u_1s : list of float
|
||||
estimated optimal input Us for N steps
|
||||
u_2s : list of float
|
||||
estimated optimal input Us for N steps
|
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N : int
|
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predict step
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||||
|
|
@ -193,25 +240,29 @@ class NMPCSimulatorSystem():
|
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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
|
||||
lam_3s : list of float
|
||||
adjoint state of x_2s, lam_2s for N steps
|
||||
"""
|
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# final state
|
||||
# final_state_func
|
||||
lam_1s = [x_1s[-1]]
|
||||
lam_2s = [x_2s[-1]]
|
||||
lam_3s = [x_3s[-1]]
|
||||
|
||||
for i in range(N-1, 0, -1):
|
||||
temp_lam_1, temp_lam_2 = self._adjoint_state_with_oylar(x_1s[i], x_2s[i], lam_1s[0] ,lam_2s[0], us[i], dt)
|
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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)
|
||||
lam_2s.insert(0, temp_lam_2)
|
||||
lam_3s.insert(0, temp_lam_3)
|
||||
|
||||
return lam_1s, lam_2s
|
||||
return lam_1s, lam_2s, lam_3s
|
||||
|
||||
def final_state_func(self):
|
||||
"""this func usually need
|
||||
"""
|
||||
pass
|
||||
|
||||
def _predict_state_with_oylar(self, x_1, x_2, u, dt):
|
||||
def _predict_state_with_oylar(self, x_1, x_2, x_3, u_1, u_2, dt):
|
||||
"""in this case this function is the same as simulator
|
||||
Parameters
|
||||
------------
|
||||
|
|
@ -219,7 +270,11 @@ class NMPCSimulatorSystem():
|
|||
system state
|
||||
x_2 : float
|
||||
system state
|
||||
u : float
|
||||
x_3 : float
|
||||
system state
|
||||
u_1 : float
|
||||
system input
|
||||
u_2 : float
|
||||
system input
|
||||
dt : float in seconds
|
||||
sampling time
|
||||
|
|
@ -229,56 +284,68 @@ class NMPCSimulatorSystem():
|
|||
next state, x_1 calculated by using state equation
|
||||
next_x_2 : float
|
||||
next state, x_2 calculated by using state equation
|
||||
next_x_3 : float
|
||||
next state, x_3 calculated by using state equation
|
||||
"""
|
||||
k0 = [0. for _ in range(2)]
|
||||
k0 = [0. for _ in range(3)]
|
||||
|
||||
functions = [self.func_x_1, self.func_x_2]
|
||||
functions = [self.func_x_1, self.func_x_2, self.func_x_3]
|
||||
|
||||
for i, func in enumerate(functions):
|
||||
k0[i] = dt * func(x_1, x_2, u)
|
||||
k0[i] = dt * func(x_1, x_2, x_3, u_1, u_2)
|
||||
|
||||
next_x_1 = x_1 + k0[0]
|
||||
next_x_2 = x_2 + k0[1]
|
||||
next_x_3 = x_3 + k0[2]
|
||||
|
||||
return next_x_1, next_x_2
|
||||
return next_x_1, next_x_2, next_x_3
|
||||
|
||||
def func_x_1(self, y_1, y_2, u):
|
||||
"""calculating \dot{x_1}
|
||||
def func_x_1(self, y_1, y_2, y_3, u_1, u_2):
|
||||
"""
|
||||
Parameters
|
||||
------------
|
||||
y_1 : float
|
||||
means x_1
|
||||
y_2 : float
|
||||
means x_2
|
||||
u : float
|
||||
means system input
|
||||
Returns
|
||||
---------
|
||||
y_dot : float
|
||||
means \dot{x_1}
|
||||
y_3 : float
|
||||
u_1 : float
|
||||
system input
|
||||
u_2 : float
|
||||
system input
|
||||
"""
|
||||
y_dot = y_2
|
||||
y_dot = math.cos(y_3) * u_1
|
||||
return y_dot
|
||||
|
||||
def func_x_2(self, y_1, y_2, u):
|
||||
"""calculating \dot{x_2}
|
||||
def func_x_2(self, y_1, y_2, y_3, u_1, u_2):
|
||||
"""
|
||||
Parameters
|
||||
------------
|
||||
y_1 : float
|
||||
means x_1
|
||||
y_2 : float
|
||||
means x_2
|
||||
u : float
|
||||
means system input
|
||||
Returns
|
||||
---------
|
||||
y_dot : float
|
||||
means \dot{x_2}
|
||||
y_3 : float
|
||||
u_1 : float
|
||||
system input
|
||||
u_2 : float
|
||||
system input
|
||||
"""
|
||||
y_dot = (1. - y_1**2 - y_2**2) * y_2 - y_1 + u
|
||||
y_dot = math.sin(y_3) * u_1
|
||||
return y_dot
|
||||
|
||||
def func_x_3(self, y_1, y_2, y_3, u_1, u_2):
|
||||
"""
|
||||
Parameters
|
||||
------------
|
||||
y_1 : float
|
||||
y_2 : float
|
||||
y_3 : float
|
||||
u_1 : float
|
||||
system input
|
||||
u_2 : float
|
||||
system input
|
||||
"""
|
||||
y_dot = u_2
|
||||
return y_dot
|
||||
|
||||
def _adjoint_state_with_oylar(self, x_1, x_2, lam_1, lam_2, u, dt):
|
||||
def _adjoint_state_with_oylar(self, x_1, x_2, x_3, lam_1, lam_2, lam_3, u_1, u_2, dt):
|
||||
"""
|
||||
Parameters
|
||||
------------
|
||||
|
|
@ -286,11 +353,17 @@ class NMPCSimulatorSystem():
|
|||
system state
|
||||
x_2 : float
|
||||
system state
|
||||
x_3 : float
|
||||
system state
|
||||
lam_1 : float
|
||||
adjoint state
|
||||
lam_2 : float
|
||||
adjoint state
|
||||
u : float
|
||||
lam_3 : float
|
||||
adjoint state
|
||||
u_1 : float
|
||||
system input
|
||||
u_2 : float
|
||||
system input
|
||||
dt : float in seconds
|
||||
sampling time
|
||||
|
|
@ -300,20 +373,23 @@ class NMPCSimulatorSystem():
|
|||
pre, 1 step before lam_1 calculated by using adjoint equation
|
||||
pre_lam_2 : float
|
||||
pre, 1 step before lam_2 calculated by using adjoint equation
|
||||
pre_lam_3 : float
|
||||
pre, 1 step before lam_3 calculated by using adjoint equation
|
||||
"""
|
||||
k0 = [0. for _ in range(2)]
|
||||
k0 = [0. for _ in range(3)]
|
||||
|
||||
functions = [self._func_lam_1, self._func_lam_2]
|
||||
functions = [self._func_lam_1, self._func_lam_2, self._func_lam_3]
|
||||
|
||||
for i, func in enumerate(functions):
|
||||
k0[i] = dt * func(x_1, x_2, lam_1, lam_2, u)
|
||||
k0[i] = dt * func(x_1, x_2, x_3, lam_1, lam_2, lam_3, u_1, u_2)
|
||||
|
||||
pre_lam_1 = lam_1 + k0[0]
|
||||
pre_lam_2 = lam_2 + k0[1]
|
||||
pre_lam_3 = lam_3 + k0[2]
|
||||
|
||||
return pre_lam_1, pre_lam_2
|
||||
return pre_lam_1, pre_lam_2, pre_lam_3
|
||||
|
||||
def _func_lam_1(self, y_1, y_2, y_3, y_4, u):
|
||||
def _func_lam_1(self, y_1, y_2, y_3, y_4, y_5, y_6, u_1, u_2):
|
||||
"""calculating -\dot{lam_1}
|
||||
Parameters
|
||||
------------
|
||||
|
|
@ -322,20 +398,26 @@ class NMPCSimulatorSystem():
|
|||
y_2 : float
|
||||
means x_2
|
||||
y_3 : float
|
||||
means lam_1
|
||||
means x_3
|
||||
y_4 : float
|
||||
means lam_1
|
||||
y_5 : float
|
||||
means lam_2
|
||||
u : float
|
||||
y_6 : float
|
||||
means lam_3
|
||||
u_1 : float
|
||||
means system input
|
||||
u_2 : float
|
||||
means system input
|
||||
Returns
|
||||
---------
|
||||
y_dot : float
|
||||
means -\dot{lam_1}
|
||||
"""
|
||||
y_dot = y_1 - (2. * y_1 * y_2 + 1.) * y_4
|
||||
y_dot = 0.
|
||||
return y_dot
|
||||
|
||||
def _func_lam_2(self, y_1, y_2, y_3, y_4, u):
|
||||
def _func_lam_2(self, y_1, y_2, y_3, y_4, y_5, y_6, u_1, u_2):
|
||||
"""calculating -\dot{lam_2}
|
||||
Parameters
|
||||
------------
|
||||
|
|
@ -344,17 +426,51 @@ class NMPCSimulatorSystem():
|
|||
y_2 : float
|
||||
means x_2
|
||||
y_3 : float
|
||||
means lam_1
|
||||
means x_3
|
||||
y_4 : float
|
||||
means lam_1
|
||||
y_5 : float
|
||||
means lam_2
|
||||
u : float
|
||||
y_6 : float
|
||||
means lam_3
|
||||
u_1 : float
|
||||
means system input
|
||||
u_2 : float
|
||||
means system input
|
||||
Returns
|
||||
---------
|
||||
y_dot : float
|
||||
means -\dot{lam_2}
|
||||
"""
|
||||
y_dot = y_2 + y_3 + (-3. * (y_2**2) - y_1**2 + 1. ) * y_4
|
||||
y_dot = 0.
|
||||
return y_dot
|
||||
|
||||
def _func_lam_3(self, y_1, y_2, y_3, y_4, y_5, y_6, u_1, u_2):
|
||||
"""calculating -\dot{lam_3}
|
||||
Parameters
|
||||
------------
|
||||
y_1 : float
|
||||
means x_1
|
||||
y_2 : float
|
||||
means x_2
|
||||
y_3 : float
|
||||
means x_3
|
||||
y_4 : float
|
||||
means lam_1
|
||||
y_5 : float
|
||||
means lam_2
|
||||
y_6 : float
|
||||
means lam_3
|
||||
u_1 : float
|
||||
means system input
|
||||
u_2 : float
|
||||
means system input
|
||||
Returns
|
||||
---------
|
||||
y_dot : float
|
||||
means -\dot{lam_3}
|
||||
"""
|
||||
y_dot = - y_4 * math.sin(y_3) * u_1 + y_5 * math.cos(y_3) * u_1
|
||||
return y_dot
|
||||
|
||||
class NMPCController_with_CGMRES():
|
||||
|
|
@ -378,18 +494,30 @@ class NMPCController_with_CGMRES():
|
|||
max_iteration : int
|
||||
decide by the solved matrix size
|
||||
simulator : NMPCSimulatorSystem class
|
||||
us : list of float
|
||||
u_1s : list of float
|
||||
estimated optimal system input
|
||||
dummy_us : list of float
|
||||
u_2s : list of float
|
||||
estimated optimal system input
|
||||
dummy_u_1s : list of float
|
||||
estimated dummy input
|
||||
raws : list of float
|
||||
dummy_u_2s : list of float
|
||||
estimated dummy input
|
||||
raw_1s : list of float
|
||||
estimated constraint variable
|
||||
history_u : list of float
|
||||
raw_2s : list of float
|
||||
estimated constraint variable
|
||||
history_u_1 : list of float
|
||||
time history of actual system input
|
||||
history_dummy_u : list of float
|
||||
time history of actual dummy u
|
||||
history_raw : list of float
|
||||
time history of actual raw
|
||||
history_u_2 : list of float
|
||||
time history of actual system input
|
||||
history_dummy_u_1 : list of float
|
||||
time history of actual dummy u_1
|
||||
history_dummy_u_2 : list of float
|
||||
time history of actual dummy u_2
|
||||
history_raw_1 : list of float
|
||||
time history of actual raw_1
|
||||
history_raw_2 : list of float
|
||||
time history of actual raw_2
|
||||
history_f : list of float
|
||||
time history of error of optimal
|
||||
"""
|
||||
|
|
@ -407,24 +535,30 @@ class NMPCController_with_CGMRES():
|
|||
self.N = 10 # 分割数
|
||||
self.threshold = 0.001 # break値
|
||||
|
||||
self.input_num = 3 # dummy, 制約条件に対するuにも合わせた入力の数
|
||||
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.us = np.zeros(self.N)
|
||||
self.dummy_us = np.ones(self.N) * 0.49
|
||||
self.raws = np.ones(self.N) * 0.011
|
||||
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 = []
|
||||
self.history_dummy_u = []
|
||||
self.history_raw = []
|
||||
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, time):
|
||||
def calc_input(self, x_1, x_2, x_3, time):
|
||||
"""
|
||||
Parameters
|
||||
------------
|
||||
|
|
@ -432,45 +566,54 @@ class NMPCController_with_CGMRES():
|
|||
current state
|
||||
x_2 : float
|
||||
current state
|
||||
x_3 : float
|
||||
current state
|
||||
time : float in seconds
|
||||
now time
|
||||
Returns
|
||||
--------
|
||||
us : list of float
|
||||
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, self.us[0])
|
||||
x_2_dot = self.simulator.func_x_2(x_1, x_2, self.us[0])
|
||||
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, lam_1s, lam_2s = self.simulator.calc_predict_and_adjoint_state(x_1 + dx_1, x_2 + dx_2, self.us, self.N, dt)
|
||||
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, lam_1s, lam_2s, self.us, self.dummy_us,
|
||||
self.raws, self.N, dt)
|
||||
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, lam_1s, lam_2s = self.simulator.calc_predict_and_adjoint_state(x_1, x_2, self.us, self.N, dt)
|
||||
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, lam_1s, lam_2s, self.us, self.dummy_us,
|
||||
self.raws, 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 = self.us * self.ht
|
||||
ddummy_u = self.dummy_us * self.ht
|
||||
draw = self.raws * 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, lam_1s, lam_2s = self.simulator.calc_predict_and_adjoint_state(x_1 + dx_1, x_2 + dx_2, self.us + du, self.N, dt)
|
||||
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, lam_1s, lam_2s, self.us + du, self.dummy_us + ddummy_u,
|
||||
self.raws + draw, 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)
|
||||
|
||||
|
|
@ -488,14 +631,17 @@ class NMPCController_with_CGMRES():
|
|||
e[0] = 1.
|
||||
|
||||
for i in range(self.max_iteration):
|
||||
du = vs[::3, i] * self.ht
|
||||
ddummy_u = vs[1::3, i] * self.ht
|
||||
draw = vs[2::3, i] * self.ht
|
||||
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, lam_1s, lam_2s = self.simulator.calc_predict_and_adjoint_state(x_1 + dx_1, x_2 + dx_2, self.us + du, self.N, dt)
|
||||
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, lam_1s, lam_2s, self.us + du, self.dummy_us + ddummy_u,
|
||||
self.raws + draw, 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)
|
||||
|
||||
|
|
@ -518,34 +664,43 @@ class NMPCController_with_CGMRES():
|
|||
|
||||
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_new = du + update_value[::3]
|
||||
ddummy_u_new = du + update_value[1::3]
|
||||
draw_new = du + update_value[2::3]
|
||||
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.us += du_new * self.ht
|
||||
self.dummy_us += ddummy_u_new * self.ht
|
||||
self.raws += draw_new * self.ht
|
||||
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, lam_1s, lam_2s = self.simulator.calc_predict_and_adjoint_state(x_1, x_2, self.us, self.N, dt)
|
||||
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, lam_1s, lam_2s, self.us, self.dummy_us,
|
||||
self.raws, 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.append(self.us[0])
|
||||
self.history_dummy_u.append(self.dummy_us[0])
|
||||
self.history_raw.append(self.raws[0])
|
||||
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.us
|
||||
return self.u_1s, self.u_2s
|
||||
|
||||
def _calc_f(self, x_1s, x_2s, lam_1s, lam_2s, us, dummy_us, raws, N, dt):
|
||||
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
|
||||
------------
|
||||
|
|
@ -553,15 +708,25 @@ class NMPCController_with_CGMRES():
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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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us : list of float
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lam_3s : list of float
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adjoint state of x_2s, lam_3s for N steps
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u_1s : list of float
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estimated optimal system input
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dummy_us : list of float
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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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raws : list of float
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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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N : int
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predict time step
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|
@ -571,20 +736,58 @@ class NMPCController_with_CGMRES():
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F = []
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for i in range(N):
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F.append(us[i] + lam_2s[i] + 2. * raws[i] * us[i])
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F.append(-0.01 + 2. * raws[i] * dummy_us[i])
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F.append(us[i]**2 + dummy_us[i]**2 - 0.5**2)
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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])
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F.append(u_2s[i] + lam_3s[i] + 2 * raw_2s[i] * u_2s[i])
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F.append(-0.01 + 2. * raw_1s[i] * dummy_u_1s[i])
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F.append(-0.01 + 2. * raw_2s[i] * dummy_u_2s[i])
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F.append(u_1s[i]**2 + dummy_u_1s[i]**2 - 1.**2)
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F.append(u_2s[i]**2 + dummy_u_2s[i]**2 - 1.5**2)
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return np.array(F)
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|
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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 = 20.
|
||||
iteration_time = 15.
|
||||
iteration_num = int(iteration_time/dt)
|
||||
|
||||
# plant
|
||||
plant_system = SampleSystem(init_x_1=2., init_x_2=0.)
|
||||
plant_system = TwoWheeledSystem(init_x_1=-4.5, init_x_2=1.5, init_x_3=0.25)
|
||||
|
||||
# controller
|
||||
controller = NMPCController_with_CGMRES()
|
||||
|
|
@ -594,20 +797,35 @@ def main():
|
|||
time = float(i) * dt
|
||||
x_1 = plant_system.x_1
|
||||
x_2 = plant_system.x_2
|
||||
x_3 = plant_system.x_3
|
||||
# make input
|
||||
us = controller.calc_input(x_1, x_2, time)
|
||||
u_1s, u_2s = controller.calc_input(x_1, x_2, x_3, time)
|
||||
# update state
|
||||
plant_system.update_state(us[0])
|
||||
plant_system.update_state(u_1s[0], u_2s[0])
|
||||
|
||||
# figure
|
||||
fig = plt.figure()
|
||||
# time history
|
||||
fig_p = plt.figure()
|
||||
fig_u = plt.figure()
|
||||
fig_f = plt.figure()
|
||||
|
||||
x_1_fig = fig.add_subplot(321)
|
||||
x_2_fig = fig.add_subplot(322)
|
||||
u_fig = fig.add_subplot(323)
|
||||
dummy_fig = fig.add_subplot(324)
|
||||
raw_fig = fig.add_subplot(325)
|
||||
f_fig = fig.add_subplot(326)
|
||||
# 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]")
|
||||
|
|
@ -616,24 +834,54 @@ def main():
|
|||
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_fig.plot(np.arange(iteration_num - 1)*dt, controller.history_u)
|
||||
u_fig.set_xlabel("time [s]")
|
||||
u_fig.set_ylabel("u")
|
||||
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")
|
||||
|
||||
dummy_fig.plot(np.arange(iteration_num - 1)*dt, controller.history_dummy_u)
|
||||
dummy_fig.set_xlabel("time [s]")
|
||||
dummy_fig.set_ylabel("dummy u")
|
||||
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")
|
||||
|
||||
raw_fig.plot(np.arange(iteration_num - 1)*dt, controller.history_raw)
|
||||
raw_fig.set_xlabel("time [s]")
|
||||
raw_fig.set_ylabel("raw")
|
||||
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.tight_layout()
|
||||
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()
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue