add memo and IOC
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Shunichi09
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# Model Predictive Control Basic Tool
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This program is about template, generic function of linear model predictive control
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# Documentation of the MPC function
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Linear model predicitive control should have state equation.
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So if you want to use this function, you should model the plant as state equation.
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Therefore, the parameters of this class are as following
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**class MpcController()**
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Attributes :
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- A : numpy.ndarray
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- system matrix
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- B : numpy.ndarray
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- input matrix
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- Q : numpy.ndarray
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- evaluation function weight for states
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- Qs : numpy.ndarray
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- concatenated evaluation function weight for states
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- R : numpy.ndarray
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- evaluation function weight for inputs
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- Rs : numpy.ndarray
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- concatenated evaluation function weight for inputs
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- pre_step : int
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- prediction step
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- state_size : int
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- state size of the plant
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- input_size : int
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- input size of the plant
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- dt_input_upper : numpy.ndarray, shape(input_size, ), optional
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- constraints of input dt, default is None
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- dt_input_lower : numpy.ndarray, shape(input_size, ), optional
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- constraints of input dt, default is None
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- input_upper : numpy.ndarray, shape(input_size, ), optional
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- constraints of input, default is None
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- input_lower : numpy.ndarray, shape(input_size, ), optional
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- constraints of input, default is None
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Methods:
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- initialize_controller() initialize the controller
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- calc_input(states, references) calculating optimal input
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More details, please look the **mpc_func_with_scipy.py** and **mpc_func_with_cvxopt.py**
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We have two function, mpc_func_with_cvxopt.py and mpc_func_with_scipy.py
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Both functions have same variable and member function. However the solver is different.
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Plese choose the right method for your environment.
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- example of import
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```py
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from mpc_func_with_scipy import MpcController as MpcController_scipy
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from mpc_func_with_cvxopt import MpcController as MpcController_cvxopt
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```
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# Examples
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## Problem Formulation
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- **first order system**
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<a href="https://www.codecogs.com/eqnedit.php?latex=\frac{d}{dt}&space;\boldsymbol{X}&space;=&space;\begin{bmatrix}&space;-1/&space;\tau&space;&&space;0&space;&&space;0&space;&&space;0\\&space;0&space;&&space;-1/&space;\tau&space;&&space;0&space;&&space;0\\&space;1&space;&&space;0&space;&&space;0&space;&&space;0\\&space;0&space;&&space;1&space;&&space;0&space;&&space;0\\&space;\end{bmatrix}&space;\begin{bmatrix}&space;v_x&space;\\&space;v_y&space;\\&space;x&space;\\&space;y&space;\end{bmatrix}&space;+&space;\begin{bmatrix}&space;1/&space;\tau&space;&&space;0&space;\\&space;0&space;&&space;1/&space;\tau&space;\\&space;0&space;&&space;0&space;\\&space;0&space;&&space;0&space;\\&space;\end{bmatrix}&space;\begin{bmatrix}&space;u_x&space;\\&space;u_y&space;\\&space;\end{bmatrix}&space;=&space;\boldsymbol{A}\boldsymbol{X}&space;+&space;\boldsymbol{B}\boldsymbol{U}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\frac{d}{dt}&space;\boldsymbol{X}&space;=&space;\begin{bmatrix}&space;-1/&space;\tau&space;&&space;0&space;&&space;0&space;&&space;0\\&space;0&space;&&space;-1/&space;\tau&space;&&space;0&space;&&space;0\\&space;1&space;&&space;0&space;&&space;0&space;&&space;0\\&space;0&space;&&space;1&space;&&space;0&space;&&space;0\\&space;\end{bmatrix}&space;\begin{bmatrix}&space;v_x&space;\\&space;v_y&space;\\&space;x&space;\\&space;y&space;\end{bmatrix}&space;+&space;\begin{bmatrix}&space;1/&space;\tau&space;&&space;0&space;\\&space;0&space;&&space;1/&space;\tau&space;\\&space;0&space;&&space;0&space;\\&space;0&space;&&space;0&space;\\&space;\end{bmatrix}&space;\begin{bmatrix}&space;u_x&space;\\&space;u_y&space;\\&space;\end{bmatrix}&space;=&space;\boldsymbol{A}\boldsymbol{X}&space;+&space;\boldsymbol{B}\boldsymbol{U}" title="\frac{d}{dt} \boldsymbol{X} = \begin{bmatrix} -1/ \tau & 0 & 0 & 0\\ 0 & -1/ \tau & 0 & 0\\ 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ \end{bmatrix} \begin{bmatrix} v_x \\ v_y \\ x \\ y \end{bmatrix} + \begin{bmatrix} 1/ \tau & 0 \\ 0 & 1/ \tau \\ 0 & 0 \\ 0 & 0 \\ \end{bmatrix} \begin{bmatrix} u_x \\ u_y \\ \end{bmatrix} = \boldsymbol{A}\boldsymbol{X} + \boldsymbol{B}\boldsymbol{U}" /></a>
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- **ACC (Adaptive cruise control)**
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The two wheeled model are expressed the following equation.
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<a href="https://www.codecogs.com/eqnedit.php?latex=\frac{d}{dt}&space;\boldsymbol{X}=&space;\frac{d}{dt}&space;\begin{bmatrix}&space;x&space;\\&space;y&space;\\&space;\theta&space;\end{bmatrix}&space;=&space;\begin{bmatrix}&space;\cos(\theta)&space;&&space;0&space;\\&space;\sin(\theta)&space;&&space;0&space;\\&space;0&space;&&space;1&space;\\&space;\end{bmatrix}&space;\begin{bmatrix}&space;u_v&space;\\&space;u_\omega&space;\\&space;\end{bmatrix}&space;=&space;\boldsymbol{B}\boldsymbol{U}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\frac{d}{dt}&space;\boldsymbol{X}=&space;\frac{d}{dt}&space;\begin{bmatrix}&space;x&space;\\&space;y&space;\\&space;\theta&space;\end{bmatrix}&space;=&space;\begin{bmatrix}&space;\cos(\theta)&space;&&space;0&space;\\&space;\sin(\theta)&space;&&space;0&space;\\&space;0&space;&&space;1&space;\\&space;\end{bmatrix}&space;\begin{bmatrix}&space;u_v&space;\\&space;u_\omega&space;\\&space;\end{bmatrix}&space;=&space;\boldsymbol{B}\boldsymbol{U}" title="\frac{d}{dt} \boldsymbol{X}= \frac{d}{dt} \begin{bmatrix} x \\ y \\ \theta \end{bmatrix} = \begin{bmatrix} \cos(\theta) & 0 \\ \sin(\theta) & 0 \\ 0 & 1 \\ \end{bmatrix} \begin{bmatrix} u_v \\ u_\omega \\ \end{bmatrix} = \boldsymbol{B}\boldsymbol{U}" /></a>
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However, if we assume the velocity are constant, we can approximate the equation as following,
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<a href="https://www.codecogs.com/eqnedit.php?latex=\frac{d}{dt}&space;\boldsymbol{X}=&space;\frac{d}{dt}&space;\begin{bmatrix}&space;y&space;\\&space;\theta&space;\end{bmatrix}&space;=&space;\begin{bmatrix}&space;0&space;&&space;V&space;\\&space;0&space;&&space;0&space;\\&space;\end{bmatrix}&space;\begin{bmatrix}&space;y&space;\\&space;\theta&space;\end{bmatrix}&space;+&space;\begin{bmatrix}&space;0&space;\\&space;1&space;\end{bmatrix}&space;\begin{bmatrix}&space;u_\omega&space;\\&space;\end{bmatrix}&space;=&space;\boldsymbol{A}\boldsymbol{X}&space;+&space;\boldsymbol{B}\boldsymbol{U}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\frac{d}{dt}&space;\boldsymbol{X}=&space;\frac{d}{dt}&space;\begin{bmatrix}&space;y&space;\\&space;\theta&space;\end{bmatrix}&space;=&space;\begin{bmatrix}&space;0&space;&&space;V&space;\\&space;0&space;&&space;0&space;\\&space;\end{bmatrix}&space;\begin{bmatrix}&space;y&space;\\&space;\theta&space;\end{bmatrix}&space;+&space;\begin{bmatrix}&space;0&space;\\&space;1&space;\end{bmatrix}&space;\begin{bmatrix}&space;u_\omega&space;\\&space;\end{bmatrix}&space;=&space;\boldsymbol{A}\boldsymbol{X}&space;+&space;\boldsymbol{B}\boldsymbol{U}" title="\frac{d}{dt} \boldsymbol{X}= \frac{d}{dt} \begin{bmatrix} y \\ \theta \end{bmatrix} = \begin{bmatrix} 0 & V \\ 0 & 0 \\ \end{bmatrix} \begin{bmatrix} y \\ \theta \end{bmatrix} + \begin{bmatrix} 0 \\ 1 \end{bmatrix} \begin{bmatrix} u_\omega \\ \end{bmatrix} = \boldsymbol{A}\boldsymbol{X} + \boldsymbol{B}\boldsymbol{U}" /></a>
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then we can apply this model to linear mpc, we should give the model reference V although.
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- **evaluation function**
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the both examples have same evaluation function form as following equation.
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<a href="https://www.codecogs.com/eqnedit.php?latex=J&space;=&space;\sum_{i&space;=&space;0}^{prestep}||\boldsymbol{\hat{X}}(k+i|k)-\boldsymbol{r}(k+i|k)&space;||^2_{{\boldsymbol{Q}}(i)}&space;+&space;||\boldsymbol{\Delta&space;{U}}(k+i|k)||^2_{{\boldsymbol{R}}(i)}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?J&space;=&space;\sum_{i&space;=&space;0}^{prestep}||\boldsymbol{\hat{X}}(k+i|k)-\boldsymbol{r}(k+i|k)&space;||^2_{{\boldsymbol{Q}}(i)}&space;+&space;||\boldsymbol{\Delta&space;{U}}(k+i|k)||^2_{{\boldsymbol{R}}(i)}" title="J = \sum_{i = 0}^{prestep}||\boldsymbol{\hat{X}}(k+i|k)-\boldsymbol{r}(k+i|k) ||^2_{{\boldsymbol{Q}}(i)} + ||\boldsymbol{\Delta {U}}(k+i|k)||^2_{{\boldsymbol{R}}(i)}" /></a>
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- <a href="https://www.codecogs.com/eqnedit.php?latex=\boldsymbol{\hat{X}}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\boldsymbol{\hat{X}}" title="\boldsymbol{\hat{X}}" /></a> is predicit state by using predict input
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- <a href="https://www.codecogs.com/eqnedit.php?latex=\boldsymbol{{r}}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\boldsymbol{{r}}" title="\boldsymbol{{r}}" /></a> is reference state
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- <a href="https://www.codecogs.com/eqnedit.php?latex=\boldsymbol{\Delta&space;\boldsymbol{U}}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\boldsymbol{\Delta&space;\boldsymbol{U}}" title="\boldsymbol{\Delta \boldsymbol{U}}" /></a> is predict amount of change of input
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- <a href="https://www.codecogs.com/eqnedit.php?latex=\boldsymbol{\boldsymbol{R}},&space;\boldsymbol{\boldsymbol{Q}}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\boldsymbol{\boldsymbol{R}},&space;\boldsymbol{\boldsymbol{Q}}" title="\boldsymbol{\boldsymbol{R}}, \boldsymbol{\boldsymbol{Q}}" /></a> are evaluation function weights
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## Expected Results
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- first order system
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- time history
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<img src = https://github.com/Shunichi09/linear_nonlinear_control/blob/demo_gif/mpc/basic/first_order_states.png width = 70%>
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- input
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<img src = https://github.com/Shunichi09/linear_nonlinear_control/blob/demo_gif/mpc/basic/first_order_input.png width = 70%>
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- ACC (Adaptive cruise control)
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- time history of states
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<img src = https://github.com/Shunichi09/linear_nonlinear_control/blob/demo_gif/mpc/basic/ACC_states.png width = 70%>
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- animation
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<img src = https://github.com/Shunichi09/linear_nonlinear_control/blob/demo_gif/mpc/basic/ACC.gif width = 70%>
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# Usage
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- for example(first order system)
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```
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$ python main_example.py
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```
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- for example(ACC (Adaptive cruise control))
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```
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$ python main_ACC.py
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```
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- for comparing two methods of optimization solvers
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```
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$ python test_compare_methods.py
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```
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# Requirement
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- python3.5 or more
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- numpy
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- matplotlib
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- cvxopt
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- scipy1.2.0 or more
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- python-control
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# Reference
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I`m sorry that main references are written in Japanese
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- モデル予測制御―制約のもとでの最適制御 著：Jan M. Maciejowski 訳：足立修一 東京電機大学出版局
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import numpy as np
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import matplotlib.pyplot as plt
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import matplotlib.animation as ani
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import matplotlib.font_manager as fon
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import sys
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import math
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# default setting of figures
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plt.rcParams["mathtext.fontset"] = 'stix' # math fonts
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plt.rcParams['xtick.direction'] = 'in' # x axis in
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plt.rcParams['ytick.direction'] = 'in' # y axis in
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plt.rcParams["font.size"] = 10
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plt.rcParams['axes.linewidth'] = 1.0 # axis line width
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plt.rcParams['axes.grid'] = True # make grid
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def coordinate_transformation_in_angle(positions, base_angle):
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'''
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Transformation the coordinate in the angle
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Parameters
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-------
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positions : numpy.ndarray
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this parameter is composed of xs, ys
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should have (2, N) shape
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base_angle : float [rad]
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Returns
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-------
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traslated_positions : numpy.ndarray
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the shape is (2, N)
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'''
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if positions.shape[0] != 2:
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raise ValueError('the input data should have (2, N)')
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positions = np.array(positions)
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positions = positions.reshape(2, -1)
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rot_matrix = [[np.cos(base_angle), np.sin(base_angle)],
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[-1*np.sin(base_angle), np.cos(base_angle)]]
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rot_matrix = np.array(rot_matrix)
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translated_positions = np.dot(rot_matrix, positions)
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return translated_positions
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def square_make_with_angles(center_x, center_y, size, angle):
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'''
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Create square matrix with angle line matrix(2D)
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Parameters
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-------
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center_x : float in meters
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the center x position of the square
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center_y : float in meters
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the center y position of the square
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size : float in meters
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the square's half-size
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angle : float in radians
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Returns
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-------
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square xs : numpy.ndarray
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lenght is 5 (counterclockwise from right-up)
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square ys : numpy.ndarray
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length is 5 (counterclockwise from right-up)
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angle line xs : numpy.ndarray
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angle line ys : numpy.ndarray
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'''
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# start with the up right points
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# create point in counterclockwise
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square_xys = np.array([[size, 0.5 * size], [-size, 0.5 * size], [-size, -0.5 * size], [size, -0.5 * size], [size, 0.5 * size]])
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trans_points = coordinate_transformation_in_angle(square_xys.T, -angle) # this is inverse type
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trans_points += np.array([[center_x], [center_y]])
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square_xs = trans_points[0, :]
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square_ys = trans_points[1, :]
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angle_line_xs = [center_x, center_x + math.cos(angle) * size]
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angle_line_ys = [center_y, center_y + math.sin(angle) * size]
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return square_xs, square_ys, np.array(angle_line_xs), np.array(angle_line_ys)
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class AnimDrawer():
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"""create animation of path and robot
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Attributes
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------------
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cars :
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anim_fig : figure of matplotlib
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axis : axis of matplotlib
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"""
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def __init__(self, objects):
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"""
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Parameters
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------------
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objects : list of objects
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"""
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self.lead_car_history_state = objects[0]
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self.follow_car_history_state = objects[1]
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self.history_xs = [self.lead_car_history_state[:, 0], self.follow_car_history_state[:, 0]]
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self.history_ys = [self.lead_car_history_state[:, 1], self.follow_car_history_state[:, 1]]
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self.history_ths = [self.lead_car_history_state[:, 2], self.follow_car_history_state[:, 2]]
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# setting up figure
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self.anim_fig = plt.figure(dpi=150)
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self.axis = self.anim_fig.add_subplot(111)
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# imgs
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self.object_imgs = []
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self.traj_imgs = []
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def draw_anim(self, interval=50):
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"""draw the animation and save
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Parameteres
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-------------
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interval : int, optional
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animation's interval time, you should link the sampling time of systems
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default is 50 [ms]
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"""
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self._set_axis()
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self._set_img()
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self.skip_num = 1
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frame_num = int((len(self.history_xs[0])-1) / self.skip_num)
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animation = ani.FuncAnimation(self.anim_fig, self._update_anim, interval=interval, frames=frame_num)
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# self.axis.legend()
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print('save_animation?')
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shuold_save_animation = int(input())
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if shuold_save_animation:
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print('animation_number?')
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num = int(input())
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animation.save('animation_{0}.mp4'.format(num), writer='ffmpeg')
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# animation.save("Sample.gif", writer = 'imagemagick') # gif保存
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plt.show()
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def _set_axis(self):
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""" initialize the animation axies
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"""
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# (1) set the axis name
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self.axis.set_xlabel(r'$\it{x}$ [m]')
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self.axis.set_ylabel(r'$\it{y}$ [m]')
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self.axis.set_aspect('equal', adjustable='box')
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# (2) set the xlim and ylim
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self.axis.set_xlim(-5, 50)
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self.axis.set_ylim(-2, 5)
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def _set_img(self):
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""" initialize the imgs of animation
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this private function execute the make initial imgs for animation
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"""
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# object imgs
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obj_color_list = ["k", "k", "m", "m"]
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obj_styles = ["solid", "solid", "solid", "solid"]
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for i in range(len(obj_color_list)):
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temp_img, = self.axis.plot([], [], color=obj_color_list[i], linestyle=obj_styles[i])
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self.object_imgs.append(temp_img)
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traj_color_list = ["k", "m"]
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for i in range(len(traj_color_list)):
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temp_img, = self.axis.plot([],[], color=traj_color_list[i], linestyle="dashed")
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self.traj_imgs.append(temp_img)
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def _update_anim(self, i):
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"""the update animation
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this function should be used in the animation functions
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Parameters
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------------
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i : int
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time step of the animation
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the sampling time should be related to the sampling time of system
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Returns
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-----------
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object_imgs : list of img
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traj_imgs : list of img
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"""
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i = int(i * self.skip_num)
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self._draw_objects(i)
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self._draw_traj(i)
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return self.object_imgs, self.traj_imgs,
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def _draw_objects(self, i):
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"""
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This private function is just divided thing of
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the _update_anim to see the code more clear
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Parameters
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------------
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i : int
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time step of the animation
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the sampling time should be related to the sampling time of system
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"""
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# cars
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for j in range(2):
|
||||
fix_j = j * 2
|
||||
object_x, object_y, angle_x, angle_y = square_make_with_angles(self.history_xs[j][i],
|
||||
self.history_ys[j][i],
|
||||
1.0,
|
||||
self.history_ths[j][i])
|
||||
|
||||
self.object_imgs[fix_j].set_data([object_x, object_y])
|
||||
self.object_imgs[fix_j + 1].set_data([angle_x, angle_y])
|
||||
|
||||
def _draw_traj(self, i):
|
||||
"""
|
||||
This private function is just divided thing of
|
||||
the _update_anim to see the code more clear
|
||||
|
||||
Parameters
|
||||
------------
|
||||
i : int
|
||||
time step of the animation
|
||||
the sampling time should be related to the sampling time of system
|
||||
"""
|
||||
for j in range(2):
|
||||
self.traj_imgs[j].set_data(self.history_xs[j][:i], self.history_ys[j][:i])
|
||||
|
|
@ -0,0 +1,246 @@
|
|||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
import math
|
||||
import copy
|
||||
|
||||
from mpc_func_with_cvxopt import MpcController as MpcController_cvxopt
|
||||
from animation import AnimDrawer
|
||||
from control import matlab
|
||||
|
||||
class TwoWheeledSystem():
|
||||
"""SampleSystem, this is the simulator
|
||||
Attributes
|
||||
-----------
|
||||
xs : numpy.ndarray
|
||||
system states, [x, y, theta]
|
||||
history_xs : list
|
||||
time history of state
|
||||
"""
|
||||
def __init__(self, init_states=None):
|
||||
"""
|
||||
Palameters
|
||||
-----------
|
||||
init_state : float, optional, shape(3, )
|
||||
initial state of system default is None
|
||||
"""
|
||||
self.xs = np.zeros(3)
|
||||
|
||||
if init_states is not None:
|
||||
self.xs = copy.deepcopy(init_states)
|
||||
|
||||
self.history_xs = [init_states]
|
||||
|
||||
def update_state(self, us, dt=0.01):
|
||||
"""
|
||||
Palameters
|
||||
------------
|
||||
u : numpy.ndarray
|
||||
inputs of system in some cases this means the reference
|
||||
dt : float in seconds, optional
|
||||
sampling time of simulation, default is 0.01 [s]
|
||||
"""
|
||||
# for theta 1, theta 1 dot, theta 2, theta 2 dot
|
||||
k0 = [0.0 for _ in range(3)]
|
||||
k1 = [0.0 for _ in range(3)]
|
||||
k2 = [0.0 for _ in range(3)]
|
||||
k3 = [0.0 for _ in range(3)]
|
||||
|
||||
functions = [self._func_x_1, self._func_x_2, self._func_x_3]
|
||||
|
||||
# solve Runge-Kutta
|
||||
for i, func in enumerate(functions):
|
||||
k0[i] = dt * func(self.xs[0], self.xs[1], self.xs[2], us[0], us[1])
|
||||
|
||||
for i, func in enumerate(functions):
|
||||
k1[i] = dt * func(self.xs[0] + k0[0]/2., self.xs[1] + k0[1]/2., self.xs[2] + k0[2]/2., us[0], us[1])
|
||||
|
||||
for i, func in enumerate(functions):
|
||||
k2[i] = dt * func(self.xs[0] + k0[0]/2., self.xs[1] + k0[1]/2., self.xs[2] + k0[2]/2., us[0], us[1])
|
||||
|
||||
for i, func in enumerate(functions):
|
||||
k3[i] = dt * func(self.xs[0] + k2[0], self.xs[1] + k2[1], self.xs[2] + k2[2], us[0], us[1])
|
||||
|
||||
self.xs[0] += (k0[0] + 2. * k1[0] + 2. * k2[0] + k3[0]) / 6.
|
||||
self.xs[1] += (k0[1] + 2. * k1[1] + 2. * k2[1] + k3[1]) / 6.
|
||||
self.xs[2] += (k0[2] + 2. * k1[2] + 2. * k2[2] + k3[2]) / 6.
|
||||
|
||||
# save
|
||||
save_states = copy.deepcopy(self.xs)
|
||||
self.history_xs.append(save_states)
|
||||
print(self.xs)
|
||||
|
||||
def _func_x_1(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 = math.cos(y_3) * u_1
|
||||
return y_dot
|
||||
|
||||
def _func_x_2(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 = 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 main():
|
||||
dt = 0.05
|
||||
simulation_time = 10 # in seconds
|
||||
iteration_num = int(simulation_time / dt)
|
||||
|
||||
# you must be care about this matrix
|
||||
# these A and B are for continuos system if you want to use discret system matrix please skip this step
|
||||
# lineared car system
|
||||
V = 5.0
|
||||
A = np.array([[0., V], [0., 0.]])
|
||||
B = np.array([[0.], [1.]])
|
||||
|
||||
C = np.eye(2)
|
||||
D = np.zeros((2, 1))
|
||||
|
||||
# make simulator with coninuous matrix
|
||||
init_xs_lead = np.array([5., 0., 0.])
|
||||
init_xs_follow = np.array([0., 0., 0.])
|
||||
lead_car = TwoWheeledSystem(init_states=init_xs_lead)
|
||||
follow_car = TwoWheeledSystem(init_states=init_xs_follow)
|
||||
|
||||
# create system
|
||||
sysc = matlab.ss(A, B, C, D)
|
||||
# discrete system
|
||||
sysd = matlab.c2d(sysc, dt)
|
||||
|
||||
Ad = sysd.A
|
||||
Bd = sysd.B
|
||||
|
||||
# evaluation function weight
|
||||
Q = np.diag([1., 1.])
|
||||
R = np.diag([5.])
|
||||
pre_step = 15
|
||||
|
||||
# make controller with discreted matrix
|
||||
# please check the solver, if you want to use the scipy, set the MpcController_scipy
|
||||
lead_controller = MpcController_cvxopt(Ad, Bd, Q, R, pre_step,
|
||||
dt_input_upper=np.array([30 * dt]), dt_input_lower=np.array([-30 * dt]),
|
||||
input_upper=np.array([30.]), input_lower=np.array([-30.]))
|
||||
|
||||
follow_controller = MpcController_cvxopt(Ad, Bd, Q, R, pre_step,
|
||||
dt_input_upper=np.array([30 * dt]), dt_input_lower=np.array([-30 * dt]),
|
||||
input_upper=np.array([30.]), input_lower=np.array([-30.]))
|
||||
|
||||
lead_controller.initialize_controller()
|
||||
follow_controller.initialize_controller()
|
||||
|
||||
# reference
|
||||
lead_reference = np.array([[0., 0.] for _ in range(pre_step)]).flatten()
|
||||
|
||||
for i in range(iteration_num):
|
||||
print("simulation time = {0}".format(i))
|
||||
# make lead car's move
|
||||
if i > int(iteration_num / 3):
|
||||
lead_reference = np.array([[4., 0.] for _ in range(pre_step)]).flatten()
|
||||
|
||||
lead_states = lead_car.xs
|
||||
lead_opt_u = lead_controller.calc_input(lead_states[1:], lead_reference)
|
||||
lead_opt_u = np.hstack((np.array([V]), lead_opt_u))
|
||||
|
||||
# make follow car
|
||||
follow_reference = np.array([lead_states[1:] for _ in range(pre_step)]).flatten()
|
||||
follow_states = follow_car.xs
|
||||
|
||||
follow_opt_u = follow_controller.calc_input(follow_states[1:], follow_reference)
|
||||
follow_opt_u = np.hstack((np.array([V]), follow_opt_u))
|
||||
|
||||
lead_car.update_state(lead_opt_u, dt=dt)
|
||||
follow_car.update_state(follow_opt_u, dt=dt)
|
||||
|
||||
# figures and animation
|
||||
lead_history_states = np.array(lead_car.history_xs)
|
||||
follow_history_states = np.array(follow_car.history_xs)
|
||||
|
||||
time_history_fig = plt.figure()
|
||||
x_fig = time_history_fig.add_subplot(311)
|
||||
y_fig = time_history_fig.add_subplot(312)
|
||||
theta_fig = time_history_fig.add_subplot(313)
|
||||
|
||||
car_traj_fig = plt.figure()
|
||||
traj_fig = car_traj_fig.add_subplot(111)
|
||||
traj_fig.set_aspect('equal')
|
||||
|
||||
x_fig.plot(np.arange(0, simulation_time+0.01, dt), lead_history_states[:, 0], label="lead")
|
||||
x_fig.plot(np.arange(0, simulation_time+0.01, dt), follow_history_states[:, 0], label="follow")
|
||||
x_fig.set_xlabel("time [s]")
|
||||
x_fig.set_ylabel("x")
|
||||
x_fig.legend()
|
||||
|
||||
y_fig.plot(np.arange(0, simulation_time+0.01, dt), lead_history_states[:, 1], label="lead")
|
||||
y_fig.plot(np.arange(0, simulation_time+0.01, dt), follow_history_states[:, 1], label="follow")
|
||||
y_fig.plot(np.arange(0, simulation_time+0.01, dt), [4. for _ in range(iteration_num+1)], linestyle="dashed")
|
||||
y_fig.set_xlabel("time [s]")
|
||||
y_fig.set_ylabel("y")
|
||||
y_fig.legend()
|
||||
|
||||
theta_fig.plot(np.arange(0, simulation_time+0.01, dt), lead_history_states[:, 2], label="lead")
|
||||
theta_fig.plot(np.arange(0, simulation_time+0.01, dt), follow_history_states[:, 2], label="follow")
|
||||
theta_fig.plot(np.arange(0, simulation_time+0.01, dt), [0. for _ in range(iteration_num+1)], linestyle="dashed")
|
||||
theta_fig.set_xlabel("time [s]")
|
||||
theta_fig.set_ylabel("theta")
|
||||
theta_fig.legend()
|
||||
|
||||
time_history_fig.tight_layout()
|
||||
|
||||
traj_fig.plot(lead_history_states[:, 0], lead_history_states[:, 1], label="lead")
|
||||
traj_fig.plot(follow_history_states[:, 0], follow_history_states[:, 1], label="follow")
|
||||
traj_fig.set_xlabel("x")
|
||||
traj_fig.set_ylabel("y")
|
||||
traj_fig.legend()
|
||||
plt.show()
|
||||
|
||||
lead_history_us = np.array(lead_controller.history_us)
|
||||
follow_history_us = np.array(follow_controller.history_us)
|
||||
input_history_fig = plt.figure()
|
||||
u_1_fig = input_history_fig.add_subplot(111)
|
||||
|
||||
u_1_fig.plot(np.arange(0, simulation_time+0.01, dt), lead_history_us[:, 0], label="lead")
|
||||
u_1_fig.plot(np.arange(0, simulation_time+0.01, dt), follow_history_us[:, 0], label="follow")
|
||||
u_1_fig.set_xlabel("time [s]")
|
||||
u_1_fig.set_ylabel("u_omega")
|
||||
|
||||
input_history_fig.tight_layout()
|
||||
plt.show()
|
||||
|
||||
animdrawer = AnimDrawer([lead_history_states, follow_history_states])
|
||||
animdrawer.draw_anim()
|
||||
|
||||
if __name__ == "__main__":
|
||||
main()
|
||||
|
|
@ -0,0 +1,243 @@
|
|||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
import math
|
||||
import copy
|
||||
|
||||
from mpc_func_with_cvxopt import MpcController as MpcController_cvxopt
|
||||
from animation import AnimDrawer
|
||||
# from control import matlab
|
||||
|
||||
class TwoWheeledSystem():
|
||||
"""SampleSystem, this is the simulator
|
||||
Attributes
|
||||
-----------
|
||||
xs : numpy.ndarray
|
||||
system states, [x, y, theta]
|
||||
history_xs : list
|
||||
time history of state
|
||||
"""
|
||||
def __init__(self, init_states=None):
|
||||
"""
|
||||
Palameters
|
||||
-----------
|
||||
init_state : float, optional, shape(3, )
|
||||
initial state of system default is None
|
||||
"""
|
||||
self.xs = np.zeros(3)
|
||||
|
||||
if init_states is not None:
|
||||
self.xs = copy.deepcopy(init_states)
|
||||
|
||||
self.history_xs = [init_states]
|
||||
|
||||
def update_state(self, us, dt=0.01):
|
||||
"""
|
||||
Palameters
|
||||
------------
|
||||
u : numpy.ndarray
|
||||
inputs of system in some cases this means the reference
|
||||
dt : float in seconds, optional
|
||||
sampling time of simulation, default is 0.01 [s]
|
||||
"""
|
||||
# for theta 1, theta 1 dot, theta 2, theta 2 dot
|
||||
k0 = [0.0 for _ in range(3)]
|
||||
k1 = [0.0 for _ in range(3)]
|
||||
k2 = [0.0 for _ in range(3)]
|
||||
k3 = [0.0 for _ in range(3)]
|
||||
|
||||
functions = [self._func_x_1, self._func_x_2, self._func_x_3]
|
||||
|
||||
# solve Runge-Kutta
|
||||
for i, func in enumerate(functions):
|
||||
k0[i] = dt * func(self.xs[0], self.xs[1], self.xs[2], us[0], us[1])
|
||||
|
||||
for i, func in enumerate(functions):
|
||||
k1[i] = dt * func(self.xs[0] + k0[0]/2., self.xs[1] + k0[1]/2., self.xs[2] + k0[2]/2., us[0], us[1])
|
||||
|
||||
for i, func in enumerate(functions):
|
||||
k2[i] = dt * func(self.xs[0] + k0[0]/2., self.xs[1] + k0[1]/2., self.xs[2] + k0[2]/2., us[0], us[1])
|
||||
|
||||
for i, func in enumerate(functions):
|
||||
k3[i] = dt * func(self.xs[0] + k2[0], self.xs[1] + k2[1], self.xs[2] + k2[2], us[0], us[1])
|
||||
|
||||
self.xs[0] += (k0[0] + 2. * k1[0] + 2. * k2[0] + k3[0]) / 6.
|
||||
self.xs[1] += (k0[1] + 2. * k1[1] + 2. * k2[1] + k3[1]) / 6.
|
||||
self.xs[2] += (k0[2] + 2. * k1[2] + 2. * k2[2] + k3[2]) / 6.
|
||||
|
||||
# save
|
||||
save_states = copy.deepcopy(self.xs)
|
||||
self.history_xs.append(save_states)
|
||||
print(self.xs)
|
||||
|
||||
def _func_x_1(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 = math.cos(y_3) * u_1
|
||||
return y_dot
|
||||
|
||||
def _func_x_2(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 = 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 main():
|
||||
dt = 0.05
|
||||
simulation_time = 10 # in seconds
|
||||
iteration_num = int(simulation_time / dt)
|
||||
|
||||
# you must be care about this matrix
|
||||
# these A and B are for continuos system if you want to use discret system matrix please skip this step
|
||||
# lineared car system
|
||||
V = 5.0
|
||||
Ad = np.array([[1., V * dt], [0., 1.]])
|
||||
Bd = np.array([[0.], [1. * dt]])
|
||||
|
||||
C = np.eye(2)
|
||||
D = np.zeros((2, 1))
|
||||
|
||||
# make simulator with coninuous matrix
|
||||
init_xs_lead = np.array([5., 0., 0.])
|
||||
init_xs_follow = np.array([0., 0., 0.])
|
||||
lead_car = TwoWheeledSystem(init_states=init_xs_lead)
|
||||
follow_car = TwoWheeledSystem(init_states=init_xs_follow)
|
||||
|
||||
# create system
|
||||
# sysc = matlab.ss(A, B, C, D)
|
||||
# discrete system
|
||||
# sysd = matlab.c2d(sysc, dt)
|
||||
|
||||
# evaluation function weight
|
||||
Q = np.diag([1., 1.])
|
||||
R = np.diag([5.])
|
||||
pre_step = 15
|
||||
|
||||
# make controller with discreted matrix
|
||||
# please check the solver, if you want to use the scipy, set the MpcController_scipy
|
||||
lead_controller = MpcController_cvxopt(Ad, Bd, Q, R, pre_step,
|
||||
dt_input_upper=np.array([30 * dt]), dt_input_lower=np.array([-30 * dt]),
|
||||
input_upper=np.array([30.]), input_lower=np.array([-30.]))
|
||||
|
||||
follow_controller = MpcController_cvxopt(Ad, Bd, Q, R, pre_step,
|
||||
dt_input_upper=np.array([30 * dt]), dt_input_lower=np.array([-30 * dt]),
|
||||
input_upper=np.array([30.]), input_lower=np.array([-30.]))
|
||||
|
||||
lead_controller.initialize_controller()
|
||||
follow_controller.initialize_controller()
|
||||
|
||||
# reference
|
||||
lead_reference = np.array([[0., 0.] for _ in range(pre_step)]).flatten()
|
||||
|
||||
for i in range(iteration_num):
|
||||
print("simulation time = {0}".format(i))
|
||||
# make lead car's move
|
||||
if i > int(iteration_num / 3):
|
||||
lead_reference = np.array([[4., 0.] for _ in range(pre_step)]).flatten()
|
||||
|
||||
lead_states = lead_car.xs
|
||||
lead_opt_u = lead_controller.calc_input(lead_states[1:], lead_reference)
|
||||
lead_opt_u = np.hstack((np.array([V]), lead_opt_u))
|
||||
|
||||
# make follow car
|
||||
follow_reference = np.array([lead_states[1:] for _ in range(pre_step)]).flatten()
|
||||
follow_states = follow_car.xs
|
||||
|
||||
follow_opt_u = follow_controller.calc_input(follow_states[1:], follow_reference)
|
||||
follow_opt_u = np.hstack((np.array([V]), follow_opt_u))
|
||||
|
||||
lead_car.update_state(lead_opt_u, dt=dt)
|
||||
follow_car.update_state(follow_opt_u, dt=dt)
|
||||
|
||||
# figures and animation
|
||||
lead_history_states = np.array(lead_car.history_xs)
|
||||
follow_history_states = np.array(follow_car.history_xs)
|
||||
|
||||
time_history_fig = plt.figure()
|
||||
x_fig = time_history_fig.add_subplot(311)
|
||||
y_fig = time_history_fig.add_subplot(312)
|
||||
theta_fig = time_history_fig.add_subplot(313)
|
||||
|
||||
car_traj_fig = plt.figure()
|
||||
traj_fig = car_traj_fig.add_subplot(111)
|
||||
traj_fig.set_aspect('equal')
|
||||
|
||||
x_fig.plot(np.arange(0, simulation_time+0.01, dt), lead_history_states[:, 0], label="lead")
|
||||
x_fig.plot(np.arange(0, simulation_time+0.01, dt), follow_history_states[:, 0], label="follow")
|
||||
x_fig.set_xlabel("time [s]")
|
||||
x_fig.set_ylabel("x")
|
||||
x_fig.legend()
|
||||
|
||||
y_fig.plot(np.arange(0, simulation_time+0.01, dt), lead_history_states[:, 1], label="lead")
|
||||
y_fig.plot(np.arange(0, simulation_time+0.01, dt), follow_history_states[:, 1], label="follow")
|
||||
y_fig.plot(np.arange(0, simulation_time+0.01, dt), [4. for _ in range(iteration_num+1)], linestyle="dashed")
|
||||
y_fig.set_xlabel("time [s]")
|
||||
y_fig.set_ylabel("y")
|
||||
y_fig.legend()
|
||||
|
||||
theta_fig.plot(np.arange(0, simulation_time+0.01, dt), lead_history_states[:, 2], label="lead")
|
||||
theta_fig.plot(np.arange(0, simulation_time+0.01, dt), follow_history_states[:, 2], label="follow")
|
||||
theta_fig.plot(np.arange(0, simulation_time+0.01, dt), [0. for _ in range(iteration_num+1)], linestyle="dashed")
|
||||
theta_fig.set_xlabel("time [s]")
|
||||
theta_fig.set_ylabel("theta")
|
||||
theta_fig.legend()
|
||||
|
||||
time_history_fig.tight_layout()
|
||||
|
||||
traj_fig.plot(lead_history_states[:, 0], lead_history_states[:, 1], label="lead")
|
||||
traj_fig.plot(follow_history_states[:, 0], follow_history_states[:, 1], label="follow")
|
||||
traj_fig.set_xlabel("x")
|
||||
traj_fig.set_ylabel("y")
|
||||
traj_fig.legend()
|
||||
plt.show()
|
||||
|
||||
lead_history_us = np.array(lead_controller.history_us)
|
||||
follow_history_us = np.array(follow_controller.history_us)
|
||||
input_history_fig = plt.figure()
|
||||
u_1_fig = input_history_fig.add_subplot(111)
|
||||
|
||||
u_1_fig.plot(np.arange(0, simulation_time+0.01, dt), lead_history_us[:, 0], label="lead")
|
||||
u_1_fig.plot(np.arange(0, simulation_time+0.01, dt), follow_history_us[:, 0], label="follow")
|
||||
u_1_fig.set_xlabel("time [s]")
|
||||
u_1_fig.set_ylabel("u_omega")
|
||||
|
||||
input_history_fig.tight_layout()
|
||||
plt.show()
|
||||
|
||||
animdrawer = AnimDrawer([lead_history_states, follow_history_states])
|
||||
animdrawer.draw_anim()
|
||||
|
||||
if __name__ == "__main__":
|
||||
main()
|
||||
|
|
@ -0,0 +1,184 @@
|
|||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
import math
|
||||
import copy
|
||||
|
||||
from mpc_func_with_scipy import MpcController as MpcController_scipy
|
||||
from mpc_func_with_cvxopt import MpcController as MpcController_cvxopt
|
||||
from control import matlab
|
||||
|
||||
class FirstOrderSystem():
|
||||
"""FirstOrderSystemWithStates
|
||||
|
||||
Attributes
|
||||
-----------
|
||||
xs : numpy.ndarray
|
||||
system states
|
||||
A : numpy.ndarray
|
||||
system matrix
|
||||
B : numpy.ndarray
|
||||
control matrix
|
||||
C : numpy.ndarray
|
||||
observation matrix
|
||||
history_xs : list
|
||||
time history of state
|
||||
"""
|
||||
def __init__(self, A, B, C, D=None, init_states=None):
|
||||
"""
|
||||
Parameters
|
||||
-----------
|
||||
A : numpy.ndarray
|
||||
system matrix
|
||||
B : numpy.ndarray
|
||||
control matrix
|
||||
C : numpy.ndarray
|
||||
observation matrix
|
||||
D : numpy.ndarray
|
||||
directly matrix
|
||||
init_state : float, optional
|
||||
initial state of system default is None
|
||||
history_xs : list
|
||||
time history of system states
|
||||
"""
|
||||
|
||||
self.A = A
|
||||
self.B = B
|
||||
self.C = C
|
||||
|
||||
if D is not None:
|
||||
self.D = D
|
||||
|
||||
self.xs = np.zeros(self.A.shape[0])
|
||||
|
||||
if init_states is not None:
|
||||
self.xs = copy.deepcopy(init_states)
|
||||
|
||||
self.history_xs = [init_states]
|
||||
|
||||
def update_state(self, u, dt=0.01):
|
||||
"""calculating input
|
||||
Parameters
|
||||
------------
|
||||
u : numpy.ndarray
|
||||
inputs of system in some cases this means the reference
|
||||
dt : float in seconds, optional
|
||||
sampling time of simulation, default is 0.01 [s]
|
||||
"""
|
||||
temp_x = self.xs.reshape(-1, 1)
|
||||
temp_u = u.reshape(-1, 1)
|
||||
|
||||
# solve Runge-Kutta
|
||||
k0 = dt * (np.dot(self.A, temp_x) + np.dot(self.B, temp_u))
|
||||
k1 = dt * (np.dot(self.A, temp_x + k0/2.) + np.dot(self.B, temp_u))
|
||||
k2 = dt * (np.dot(self.A, temp_x + k1/2.) + np.dot(self.B, temp_u))
|
||||
k3 = dt * (np.dot(self.A, temp_x + k2) + np.dot(self.B, temp_u))
|
||||
|
||||
self.xs += ((k0 + 2 * k1 + 2 * k2 + k3) / 6.).flatten()
|
||||
|
||||
# for oylar
|
||||
# self.xs += k0.flatten()
|
||||
# print("xs = {0}".format(self.xs))
|
||||
|
||||
# save
|
||||
save_states = copy.deepcopy(self.xs)
|
||||
self.history_xs.append(save_states)
|
||||
|
||||
def main():
|
||||
dt = 0.05
|
||||
simulation_time = 30 # in seconds
|
||||
iteration_num = int(simulation_time / dt)
|
||||
|
||||
# you must be care about this matrix
|
||||
# these A and B are for continuos system if you want to use discret system matrix please skip this step
|
||||
tau = 0.63
|
||||
A = np.array([[-1./tau, 0., 0., 0.],
|
||||
[0., -1./tau, 0., 0.],
|
||||
[1., 0., 0., 0.],
|
||||
[0., 1., 0., 0.]])
|
||||
B = np.array([[1./tau, 0.],
|
||||
[0., 1./tau],
|
||||
[0., 0.],
|
||||
[0., 0.]])
|
||||
|
||||
C = np.eye(4)
|
||||
D = np.zeros((4, 2))
|
||||
|
||||
# make simulator with coninuous matrix
|
||||
init_xs = np.array([0., 0., 0., 0.])
|
||||
plant = FirstOrderSystem(A, B, C, init_states=init_xs)
|
||||
|
||||
# create system
|
||||
sysc = matlab.ss(A, B, C, D)
|
||||
# discrete system
|
||||
sysd = matlab.c2d(sysc, dt)
|
||||
|
||||
Ad = sysd.A
|
||||
Bd = sysd.B
|
||||
|
||||
# evaluation function weight
|
||||
Q = np.diag([1., 1., 1., 1.])
|
||||
R = np.diag([1., 1.])
|
||||
pre_step = 10
|
||||
|
||||
# make controller with discreted matrix
|
||||
# please check the solver, if you want to use the scipy, set the MpcController_scipy
|
||||
controller = MpcController_cvxopt(Ad, Bd, Q, R, pre_step,
|
||||
dt_input_upper=np.array([0.25 * dt, 0.25 * dt]), dt_input_lower=np.array([-0.5 * dt, -0.5 * dt]),
|
||||
input_upper=np.array([1. ,3.]), input_lower=np.array([-1., -3.]))
|
||||
|
||||
controller.initialize_controller()
|
||||
|
||||
for i in range(iteration_num):
|
||||
print("simulation time = {0}".format(i))
|
||||
reference = np.array([[0., 0., -5., 7.5] for _ in range(pre_step)]).flatten()
|
||||
states = plant.xs
|
||||
opt_u = controller.calc_input(states, reference)
|
||||
plant.update_state(opt_u, dt=dt)
|
||||
|
||||
history_states = np.array(plant.history_xs)
|
||||
|
||||
time_history_fig = plt.figure()
|
||||
x_fig = time_history_fig.add_subplot(411)
|
||||
y_fig = time_history_fig.add_subplot(412)
|
||||
v_x_fig = time_history_fig.add_subplot(413)
|
||||
v_y_fig = time_history_fig.add_subplot(414)
|
||||
|
||||
v_x_fig.plot(np.arange(0, simulation_time+0.01, dt), history_states[:, 0])
|
||||
v_x_fig.plot(np.arange(0, simulation_time+0.01, dt), [0. for _ in range(iteration_num+1)], linestyle="dashed")
|
||||
v_x_fig.set_xlabel("time [s]")
|
||||
v_x_fig.set_ylabel("v_x")
|
||||
|
||||
v_y_fig.plot(np.arange(0, simulation_time+0.01, dt), history_states[:, 1])
|
||||
v_y_fig.plot(np.arange(0, simulation_time+0.01, dt), [0. for _ in range(iteration_num+1)], linestyle="dashed")
|
||||
v_y_fig.set_xlabel("time [s]")
|
||||
v_y_fig.set_ylabel("v_y")
|
||||
|
||||
x_fig.plot(np.arange(0, simulation_time+0.01, dt), history_states[:, 2])
|
||||
x_fig.plot(np.arange(0, simulation_time+0.01, dt), [-5. for _ in range(iteration_num+1)], linestyle="dashed")
|
||||
x_fig.set_xlabel("time [s]")
|
||||
x_fig.set_ylabel("x")
|
||||
|
||||
y_fig.plot(np.arange(0, simulation_time+0.01, dt), history_states[:, 3])
|
||||
y_fig.plot(np.arange(0, simulation_time+0.01, dt), [7.5 for _ in range(iteration_num+1)], linestyle="dashed")
|
||||
y_fig.set_xlabel("time [s]")
|
||||
y_fig.set_ylabel("y")
|
||||
time_history_fig.tight_layout()
|
||||
plt.show()
|
||||
|
||||
history_us = np.array(controller.history_us)
|
||||
input_history_fig = plt.figure()
|
||||
u_1_fig = input_history_fig.add_subplot(211)
|
||||
u_2_fig = input_history_fig.add_subplot(212)
|
||||
|
||||
u_1_fig.plot(np.arange(0, simulation_time+0.01, dt), history_us[:, 0])
|
||||
u_1_fig.set_xlabel("time [s]")
|
||||
u_1_fig.set_ylabel("u_x")
|
||||
|
||||
u_2_fig.plot(np.arange(0, simulation_time+0.01, dt), history_us[:, 1])
|
||||
u_2_fig.set_xlabel("time [s]")
|
||||
u_2_fig.set_ylabel("u_y")
|
||||
input_history_fig.tight_layout()
|
||||
plt.show()
|
||||
|
||||
if __name__ == "__main__":
|
||||
main()
|
||||
|
|
@ -0,0 +1,5 @@
|
|||
# ラプラス近似
|
||||
参考
|
||||
- http://triadsou.hatenablog.com/entry/20090217/1234865055
|
||||
|
||||
#
|
||||
|
|
@ -0,0 +1,256 @@
|
|||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
import math
|
||||
import copy
|
||||
|
||||
from cvxopt import matrix, solvers
|
||||
|
||||
class MpcController():
|
||||
"""
|
||||
Attributes
|
||||
------------
|
||||
A : numpy.ndarray
|
||||
system matrix
|
||||
B : numpy.ndarray
|
||||
input matrix
|
||||
Q : numpy.ndarray
|
||||
evaluation function weight for states
|
||||
Qs : numpy.ndarray
|
||||
concatenated evaluation function weight for states
|
||||
R : numpy.ndarray
|
||||
evaluation function weight for inputs
|
||||
Rs : numpy.ndarray
|
||||
concatenated evaluation function weight for inputs
|
||||
pre_step : int
|
||||
prediction step
|
||||
state_size : int
|
||||
state size of the plant
|
||||
input_size : int
|
||||
input size of the plant
|
||||
dt_input_upper : numpy.ndarray, shape(input_size, ), optional
|
||||
constraints of input dt, default is None
|
||||
dt_input_lower : numpy.ndarray, shape(input_size, ), optional
|
||||
constraints of input dt, default is None
|
||||
input_upper : numpy.ndarray, shape(input_size, ), optional
|
||||
constraints of input, default is None
|
||||
input_lower : numpy.ndarray, shape(input_size, ), optional
|
||||
constraints of input, default is None
|
||||
"""
|
||||
def __init__(self, A, B, Q, R, pre_step, initial_input=None, dt_input_upper=None, dt_input_lower=None, input_upper=None, input_lower=None):
|
||||
"""
|
||||
Parameters
|
||||
------------
|
||||
A : numpy.ndarray
|
||||
system matrix
|
||||
B : numpy.ndarray
|
||||
input matrix
|
||||
Q : numpy.ndarray
|
||||
evaluation function weight for states
|
||||
R : numpy.ndarray
|
||||
evaluation function weight for inputs
|
||||
pre_step : int
|
||||
prediction step
|
||||
dt_input_upper : numpy.ndarray, shape(input_size, ), optional
|
||||
constraints of input dt, default is None
|
||||
dt_input_lower : numpy.ndarray, shape(input_size, ), optional
|
||||
constraints of input dt, default is None
|
||||
input_upper : numpy.ndarray, shape(input_size, ), optional
|
||||
constraints of input, default is None
|
||||
input_lower : numpy.ndarray, shape(input_size, ), optional
|
||||
constraints of input, default is None
|
||||
history_us : list
|
||||
time history of optimal input us(numpy.ndarray)
|
||||
"""
|
||||
self.A = np.array(A)
|
||||
self.B = np.array(B)
|
||||
self.Q = np.array(Q)
|
||||
self.R = np.array(R)
|
||||
self.pre_step = pre_step
|
||||
|
||||
self.Qs = None
|
||||
self.Rs = None
|
||||
|
||||
self.state_size = self.A.shape[0]
|
||||
self.input_size = self.B.shape[1]
|
||||
|
||||
self.history_us = [np.zeros(self.input_size)]
|
||||
|
||||
# initial state
|
||||
if initial_input is not None:
|
||||
self.history_us = [initial_input]
|
||||
|
||||
# constraints
|
||||
self.dt_input_lower = dt_input_lower
|
||||
self.dt_input_upper = dt_input_upper
|
||||
self.input_upper = input_upper
|
||||
self.input_lower = input_lower
|
||||
|
||||
# about mpc matrix
|
||||
self.W = None
|
||||
self.omega = None
|
||||
self.F = None
|
||||
self.f = None
|
||||
|
||||
def initialize_controller(self):
|
||||
"""
|
||||
make matrix to calculate optimal control input
|
||||
|
||||
"""
|
||||
A_factorials = [self.A]
|
||||
|
||||
self.phi_mat = copy.deepcopy(self.A)
|
||||
|
||||
for _ in range(self.pre_step - 1):
|
||||
temp_mat = np.dot(A_factorials[-1], self.A)
|
||||
self.phi_mat = np.vstack((self.phi_mat, temp_mat))
|
||||
|
||||
A_factorials.append(temp_mat) # after we use this factorials
|
||||
|
||||
print("phi_mat = \n{0}".format(self.phi_mat))
|
||||
|
||||
self.gamma_mat = copy.deepcopy(self.B)
|
||||
gammma_mat_temp = copy.deepcopy(self.B)
|
||||
|
||||
for i in range(self.pre_step - 1):
|
||||
temp_1_mat = np.dot(A_factorials[i], self.B)
|
||||
gammma_mat_temp = temp_1_mat + gammma_mat_temp
|
||||
self.gamma_mat = np.vstack((self.gamma_mat, gammma_mat_temp))
|
||||
|
||||
print("gamma_mat = \n{0}".format(self.gamma_mat))
|
||||
|
||||
self.theta_mat = copy.deepcopy(self.gamma_mat)
|
||||
|
||||
for i in range(self.pre_step - 1):
|
||||
temp_mat = np.zeros_like(self.gamma_mat)
|
||||
temp_mat[int((i + 1)*self.state_size): , :] = self.gamma_mat[:-int((i + 1)*self.state_size) , :]
|
||||
|
||||
self.theta_mat = np.hstack((self.theta_mat, temp_mat))
|
||||
|
||||
print("theta_mat = \n{0}".format(self.theta_mat))
|
||||
|
||||
# evaluation function weight
|
||||
diag_Qs = np.array([np.diag(self.Q) for _ in range(self.pre_step)])
|
||||
diag_Rs = np.array([np.diag(self.R) for _ in range(self.pre_step)])
|
||||
|
||||
self.Qs = np.diag(diag_Qs.flatten())
|
||||
self.Rs = np.diag(diag_Rs.flatten())
|
||||
|
||||
print("Qs = \n{0}".format(self.Qs))
|
||||
print("Rs = \n{0}".format(self.Rs))
|
||||
|
||||
# constraints
|
||||
# about dt U
|
||||
if self.input_lower is not None:
|
||||
# initialize
|
||||
self.F = np.zeros((self.input_size * 2, self.pre_step * self.input_size))
|
||||
for i in range(self.input_size):
|
||||
self.F[i * 2: (i + 1) * 2, i] = np.array([1., -1.])
|
||||
temp_F = copy.deepcopy(self.F)
|
||||
|
||||
print("F = \n{0}".format(self.F))
|
||||
|
||||
for i in range(self.pre_step - 1):
|
||||
temp_F = copy.deepcopy(temp_F)
|
||||
|
||||
for j in range(self.input_size):
|
||||
temp_F[j * 2: (j + 1) * 2, ((i+1) * self.input_size) + j] = np.array([1., -1.])
|
||||
|
||||
self.F = np.vstack((self.F, temp_F))
|
||||
|
||||
self.F1 = self.F[:, :self.input_size]
|
||||
|
||||
temp_f = []
|
||||
|
||||
for i in range(self.input_size):
|
||||
temp_f.append(-1 * self.input_upper[i])
|
||||
temp_f.append(self.input_lower[i])
|
||||
|
||||
self.f = np.array([temp_f for _ in range(self.pre_step)]).flatten()
|
||||
|
||||
print("F = \n{0}".format(self.F))
|
||||
print("F1 = \n{0}".format(self.F1))
|
||||
print("f = \n{0}".format(self.f))
|
||||
|
||||
# about dt_u
|
||||
if self.dt_input_lower is not None:
|
||||
self.W = np.zeros((2, self.pre_step * self.input_size))
|
||||
self.W[:, 0] = np.array([1., -1.])
|
||||
|
||||
for i in range(self.pre_step * self.input_size - 1):
|
||||
temp_W = np.zeros((2, self.pre_step * self.input_size))
|
||||
temp_W[:, i+1] = np.array([1., -1.])
|
||||
self.W = np.vstack((self.W, temp_W))
|
||||
|
||||
temp_omega = []
|
||||
|
||||
for i in range(self.input_size):
|
||||
temp_omega.append(self.dt_input_upper[i])
|
||||
temp_omega.append(-1. * self.dt_input_lower[i])
|
||||
|
||||
self.omega = np.array([temp_omega for _ in range(self.pre_step)]).flatten()
|
||||
|
||||
print("W = \n{0}".format(self.W))
|
||||
print("omega = \n{0}".format(self.omega))
|
||||
|
||||
# about state
|
||||
print("check the matrix!! if you think rite, plese push enter")
|
||||
input()
|
||||
|
||||
def calc_input(self, states, references):
|
||||
"""calculate optimal input
|
||||
Parameters
|
||||
-----------
|
||||
states : numpy.ndarray, shape(state length, )
|
||||
current state of system
|
||||
references : numpy.ndarray, shape(state length * pre_step, )
|
||||
reference of the system, you should set this value as reachable goal
|
||||
|
||||
References
|
||||
------------
|
||||
opt_input : numpy.ndarray, shape(input_length, )
|
||||
optimal input
|
||||
"""
|
||||
temp_1 = np.dot(self.phi_mat, states.reshape(-1, 1))
|
||||
temp_2 = np.dot(self.gamma_mat, self.history_us[-1].reshape(-1, 1))
|
||||
|
||||
error = references.reshape(-1, 1) - temp_1 - temp_2
|
||||
|
||||
G = 2. * np.dot(self.theta_mat.T, np.dot(self.Qs, error))
|
||||
|
||||
H = np.dot(self.theta_mat.T, np.dot(self.Qs, self.theta_mat)) + self.Rs
|
||||
|
||||
# constraints
|
||||
A = []
|
||||
b = []
|
||||
|
||||
if self.W is not None:
|
||||
A.append(self.W)
|
||||
b.append(self.omega.reshape(-1, 1))
|
||||
|
||||
if self.F is not None:
|
||||
b_F = - np.dot(self.F1, self.history_us[-1].reshape(-1, 1)) - self.f.reshape(-1, 1)
|
||||
A.append(self.F)
|
||||
b.append(b_F)
|
||||
|
||||
A = np.array(A).reshape(-1, self.input_size * self.pre_step)
|
||||
|
||||
ub = np.array(b).flatten()
|
||||
|
||||
# make cvxpy problem formulation
|
||||
P = 2*matrix(H)
|
||||
q = matrix(-1 * G)
|
||||
A = matrix(A)
|
||||
b = matrix(ub)
|
||||
|
||||
# constraint
|
||||
if self.W is not None or self.F is not None :
|
||||
opt_result = solvers.qp(P, q, G=A, h=b)
|
||||
|
||||
opt_dt_us = list(opt_result['x'])
|
||||
|
||||
opt_u = opt_dt_us[:self.input_size] + self.history_us[-1]
|
||||
|
||||
# save
|
||||
self.history_us.append(opt_u)
|
||||
|
||||
return opt_u
|
||||
|
|
@ -0,0 +1,262 @@
|
|||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
import math
|
||||
import copy
|
||||
|
||||
from scipy.optimize import minimize
|
||||
from scipy.optimize import LinearConstraint
|
||||
|
||||
class MpcController():
|
||||
"""
|
||||
Attributes
|
||||
------------
|
||||
A : numpy.ndarray
|
||||
system matrix
|
||||
B : numpy.ndarray
|
||||
input matrix
|
||||
Q : numpy.ndarray
|
||||
evaluation function weight for states
|
||||
Qs : numpy.ndarray
|
||||
concatenated evaluation function weight for states
|
||||
R : numpy.ndarray
|
||||
evaluation function weight for inputs
|
||||
Rs : numpy.ndarray
|
||||
concatenated evaluation function weight for inputs
|
||||
pre_step : int
|
||||
prediction step
|
||||
state_size : int
|
||||
state size of the plant
|
||||
input_size : int
|
||||
input size of the plant
|
||||
dt_input_upper : numpy.ndarray, shape(input_size, ), optional
|
||||
constraints of input dt, default is None
|
||||
dt_input_lower : numpy.ndarray, shape(input_size, ), optional
|
||||
constraints of input dt, default is None
|
||||
input_upper : numpy.ndarray, shape(input_size, ), optional
|
||||
constraints of input, default is None
|
||||
input_lower : numpy.ndarray, shape(input_size, ), optional
|
||||
constraints of input, default is None
|
||||
"""
|
||||
def __init__(self, A, B, Q, R, pre_step, initial_input=None, dt_input_upper=None, dt_input_lower=None, input_upper=None, input_lower=None):
|
||||
"""
|
||||
Parameters
|
||||
------------
|
||||
A : numpy.ndarray
|
||||
system matrix
|
||||
B : numpy.ndarray
|
||||
input matrix
|
||||
Q : numpy.ndarray
|
||||
evaluation function weight for states
|
||||
R : numpy.ndarray
|
||||
evaluation function weight for inputs
|
||||
pre_step : int
|
||||
prediction step
|
||||
dt_input_upper : numpy.ndarray, shape(input_size, ), optional
|
||||
constraints of input dt, default is None
|
||||
dt_input_lower : numpy.ndarray, shape(input_size, ), optional
|
||||
constraints of input dt, default is None
|
||||
input_upper : numpy.ndarray, shape(input_size, ), optional
|
||||
constraints of input, default is None
|
||||
input_lower : numpy.ndarray, shape(input_size, ), optional
|
||||
constraints of input, default is None
|
||||
history_us : list
|
||||
time history of optimal input us(numpy.ndarray)
|
||||
"""
|
||||
self.A = np.array(A)
|
||||
self.B = np.array(B)
|
||||
self.Q = np.array(Q)
|
||||
self.R = np.array(R)
|
||||
self.pre_step = pre_step
|
||||
|
||||
self.Qs = None
|
||||
self.Rs = None
|
||||
|
||||
self.state_size = self.A.shape[0]
|
||||
self.input_size = self.B.shape[1]
|
||||
|
||||
self.history_us = [np.zeros(self.input_size)]
|
||||
|
||||
# initial state
|
||||
if initial_input is not None:
|
||||
self.history_us = [initial_input]
|
||||
|
||||
# constraints
|
||||
self.dt_input_lower = dt_input_lower
|
||||
self.dt_input_upper = dt_input_upper
|
||||
self.input_upper = input_upper
|
||||
self.input_lower = input_lower
|
||||
|
||||
self.W = None
|
||||
self.omega = None
|
||||
self.F = None
|
||||
self.f = None
|
||||
|
||||
def initialize_controller(self):
|
||||
"""
|
||||
make matrix to calculate optimal control input
|
||||
"""
|
||||
A_factorials = [self.A]
|
||||
|
||||
self.phi_mat = copy.deepcopy(self.A)
|
||||
|
||||
for _ in range(self.pre_step - 1):
|
||||
temp_mat = np.dot(A_factorials[-1], self.A)
|
||||
self.phi_mat = np.vstack((self.phi_mat, temp_mat))
|
||||
|
||||
A_factorials.append(temp_mat) # after we use this factorials
|
||||
|
||||
print("phi_mat = \n{0}".format(self.phi_mat))
|
||||
|
||||
self.gamma_mat = copy.deepcopy(self.B)
|
||||
gammma_mat_temp = copy.deepcopy(self.B)
|
||||
|
||||
for i in range(self.pre_step - 1):
|
||||
temp_1_mat = np.dot(A_factorials[i], self.B)
|
||||
gammma_mat_temp = temp_1_mat + gammma_mat_temp
|
||||
self.gamma_mat = np.vstack((self.gamma_mat, gammma_mat_temp))
|
||||
|
||||
print("gamma_mat = \n{0}".format(self.gamma_mat))
|
||||
|
||||
self.theta_mat = copy.deepcopy(self.gamma_mat)
|
||||
|
||||
for i in range(self.pre_step - 1):
|
||||
temp_mat = np.zeros_like(self.gamma_mat)
|
||||
temp_mat[int((i + 1)*self.state_size): , :] = self.gamma_mat[:-int((i + 1)*self.state_size) , :]
|
||||
|
||||
self.theta_mat = np.hstack((self.theta_mat, temp_mat))
|
||||
|
||||
print("theta_mat = \n{0}".format(self.theta_mat))
|
||||
|
||||
# evaluation function weight
|
||||
diag_Qs = np.array([np.diag(self.Q) for _ in range(self.pre_step)])
|
||||
diag_Rs = np.array([np.diag(self.R) for _ in range(self.pre_step)])
|
||||
|
||||
self.Qs = np.diag(diag_Qs.flatten())
|
||||
self.Rs = np.diag(diag_Rs.flatten())
|
||||
|
||||
print("Qs = \n{0}".format(self.Qs))
|
||||
print("Rs = \n{0}".format(self.Rs))
|
||||
|
||||
# constraints
|
||||
# about dt U
|
||||
if self.input_lower is not None:
|
||||
# initialize
|
||||
self.F = np.zeros((self.input_size * 2, self.pre_step * self.input_size))
|
||||
for i in range(self.input_size):
|
||||
self.F[i * 2: (i + 1) * 2, i] = np.array([1., -1.])
|
||||
temp_F = copy.deepcopy(self.F)
|
||||
|
||||
print("F = \n{0}".format(self.F))
|
||||
|
||||
for i in range(self.pre_step - 1):
|
||||
temp_F = copy.deepcopy(temp_F)
|
||||
|
||||
for j in range(self.input_size):
|
||||
temp_F[j * 2: (j + 1) * 2, ((i+1) * self.input_size) + j] = np.array([1., -1.])
|
||||
|
||||
self.F = np.vstack((self.F, temp_F))
|
||||
|
||||
self.F1 = self.F[:, :self.input_size]
|
||||
|
||||
temp_f = []
|
||||
|
||||
for i in range(self.input_size):
|
||||
temp_f.append(-1 * self.input_upper[i])
|
||||
temp_f.append(self.input_lower[i])
|
||||
|
||||
self.f = np.array([temp_f for _ in range(self.pre_step)]).flatten()
|
||||
|
||||
print("F = \n{0}".format(self.F))
|
||||
print("F1 = \n{0}".format(self.F1))
|
||||
print("f = \n{0}".format(self.f))
|
||||
|
||||
# about dt_u
|
||||
if self.dt_input_lower is not None:
|
||||
self.W = np.zeros((2, self.pre_step * self.input_size))
|
||||
self.W[:, 0] = np.array([1., -1.])
|
||||
|
||||
for i in range(self.pre_step * self.input_size - 1):
|
||||
temp_W = np.zeros((2, self.pre_step * self.input_size))
|
||||
temp_W[:, i+1] = np.array([1., -1.])
|
||||
self.W = np.vstack((self.W, temp_W))
|
||||
|
||||
temp_omega = []
|
||||
|
||||
for i in range(self.input_size):
|
||||
temp_omega.append(self.dt_input_upper[i])
|
||||
temp_omega.append(-1. * self.dt_input_lower[i])
|
||||
|
||||
self.omega = np.array([temp_omega for _ in range(self.pre_step)]).flatten()
|
||||
|
||||
print("W = \n{0}".format(self.W))
|
||||
print("omega = \n{0}".format(self.omega))
|
||||
|
||||
# about state
|
||||
print("check the matrix!! if you think rite, plese push enter")
|
||||
input()
|
||||
|
||||
def calc_input(self, states, references):
|
||||
"""calculate optimal input
|
||||
Parameters
|
||||
-----------
|
||||
states : numpy.ndarray, shape(state length, )
|
||||
current state of system
|
||||
references : numpy.ndarray, shape(state length * pre_step, )
|
||||
reference of the system, you should set this value as reachable goal
|
||||
|
||||
References
|
||||
------------
|
||||
opt_input : numpy.ndarray, shape(input_length, )
|
||||
optimal input
|
||||
"""
|
||||
temp_1 = np.dot(self.phi_mat, states.reshape(-1, 1))
|
||||
temp_2 = np.dot(self.gamma_mat, self.history_us[-1].reshape(-1, 1))
|
||||
|
||||
error = references.reshape(-1, 1) - temp_1 - temp_2
|
||||
|
||||
G = 2. * np.dot(self.theta_mat.T, np.dot(self.Qs, error) )
|
||||
|
||||
H = np.dot(self.theta_mat.T, np.dot(self.Qs, self.theta_mat)) + self.Rs
|
||||
|
||||
# constraints
|
||||
A = []
|
||||
b = []
|
||||
|
||||
if self.W is not None:
|
||||
A.append(self.W)
|
||||
b.append(self.omega.reshape(-1, 1))
|
||||
|
||||
if self.F is not None:
|
||||
b_F = - np.dot(self.F1, self.history_us[-1].reshape(-1, 1)) - self.f.reshape(-1, 1)
|
||||
A.append(self.F)
|
||||
b.append(b_F)
|
||||
|
||||
A = np.array(A).reshape(-1, self.input_size * self.pre_step)
|
||||
|
||||
ub = np.array(b).flatten()
|
||||
|
||||
def optimized_func(dt_us):
|
||||
"""
|
||||
"""
|
||||
temp_dt_us = np.array([dt_us[i] for i in range(self.input_size * self.pre_step)])
|
||||
|
||||
return (np.dot(temp_dt_us, np.dot(H, temp_dt_us.reshape(-1, 1))) - np.dot(G.T, temp_dt_us.reshape(-1, 1)))[0]
|
||||
|
||||
# constraint
|
||||
lb = np.array([-np.inf for _ in range(len(ub))])
|
||||
linear_cons = LinearConstraint(A, lb, ub)
|
||||
|
||||
init_dt_us = np.zeros(self.input_size * self.pre_step)
|
||||
|
||||
# constraint
|
||||
if self.W is not None or self.F is not None :
|
||||
opt_result = minimize(optimized_func, init_dt_us, constraints=[linear_cons])
|
||||
|
||||
opt_dt_us = opt_result.x
|
||||
|
||||
opt_u = opt_dt_us[:self.input_size] + self.history_us[-1]
|
||||
|
||||
# save
|
||||
self.history_us.append(opt_u)
|
||||
|
||||
return opt_u
|
||||
|
|
@ -0,0 +1,211 @@
|
|||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
import math
|
||||
import copy
|
||||
|
||||
from mpc_func_with_scipy import MpcController as MpcController_scipy
|
||||
from mpc_func_with_cvxopt import MpcController as MpcController_cvxopt
|
||||
from control import matlab
|
||||
|
||||
class FirstOrderSystem():
|
||||
"""FirstOrderSystemWithStates
|
||||
|
||||
Attributes
|
||||
-----------
|
||||
states : float
|
||||
system states
|
||||
A : numpy.ndarray
|
||||
system matrix
|
||||
B : numpy.ndarray
|
||||
control matrix
|
||||
C : numpy.ndarray
|
||||
observation matrix
|
||||
history_state : list
|
||||
time history of state
|
||||
"""
|
||||
def __init__(self, A, B, C, D=None, init_states=None):
|
||||
"""
|
||||
Parameters
|
||||
-----------
|
||||
A : numpy.ndarray
|
||||
system matrix
|
||||
B : numpy.ndarray
|
||||
control matrix
|
||||
C : numpy.ndarray
|
||||
observation matrix
|
||||
C : numpy.ndarray
|
||||
directly matrix
|
||||
init_state : float, optional
|
||||
initial state of system default is None
|
||||
history_xs : list
|
||||
time history of system states
|
||||
"""
|
||||
|
||||
self.A = A
|
||||
self.B = B
|
||||
self.C = C
|
||||
|
||||
if D is not None:
|
||||
self.D = D
|
||||
|
||||
self.xs = np.zeros(self.A.shape[0])
|
||||
|
||||
if init_states is not None:
|
||||
self.xs = copy.deepcopy(init_states)
|
||||
|
||||
self.history_xs = [init_states]
|
||||
|
||||
def update_state(self, u, dt=0.01):
|
||||
"""calculating input
|
||||
Parameters
|
||||
------------
|
||||
u : float
|
||||
input of system in some cases this means the reference
|
||||
dt : float in seconds, optional
|
||||
sampling time of simulation, default is 0.01 [s]
|
||||
"""
|
||||
temp_x = self.xs.reshape(-1, 1)
|
||||
temp_u = u.reshape(-1, 1)
|
||||
|
||||
# solve Runge-Kutta
|
||||
k0 = dt * (np.dot(self.A, temp_x) + np.dot(self.B, temp_u))
|
||||
k1 = dt * (np.dot(self.A, temp_x + k0/2.) + np.dot(self.B, temp_u))
|
||||
k2 = dt * (np.dot(self.A, temp_x + k1/2.) + np.dot(self.B, temp_u))
|
||||
k3 = dt * (np.dot(self.A, temp_x + k2) + np.dot(self.B, temp_u))
|
||||
|
||||
self.xs += ((k0 + 2 * k1 + 2 * k2 + k3) / 6.).flatten()
|
||||
|
||||
# for oylar
|
||||
# self.xs += k0.flatten()
|
||||
|
||||
# print("xs = {0}".format(self.xs))
|
||||
# a = input()
|
||||
# save
|
||||
save_states = copy.deepcopy(self.xs)
|
||||
self.history_xs.append(save_states)
|
||||
# print(self.history_xs)
|
||||
|
||||
def main():
|
||||
dt = 0.05
|
||||
simulation_time = 50 # in seconds
|
||||
iteration_num = int(simulation_time / dt)
|
||||
|
||||
# you must be care about this matrix
|
||||
# these A and B are for continuos system if you want to use discret system matrix please skip this step
|
||||
tau = 0.63
|
||||
A = np.array([[-1./tau, 0., 0., 0.],
|
||||
[0., -1./tau, 0., 0.],
|
||||
[1., 0., 0., 0.],
|
||||
[0., 1., 0., 0.]])
|
||||
B = np.array([[1./tau, 0.],
|
||||
[0., 1./tau],
|
||||
[0., 0.],
|
||||
[0., 0.]])
|
||||
|
||||
C = np.eye(4)
|
||||
D = np.zeros((4, 2))
|
||||
|
||||
# make simulator with coninuous matrix
|
||||
init_xs = np.array([0., 0., 0., 0.])
|
||||
plant_cvxopt = FirstOrderSystem(A, B, C, init_states=init_xs)
|
||||
plant_scipy = FirstOrderSystem(A, B, C, init_states=init_xs)
|
||||
|
||||
# create system
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sysc = matlab.ss(A, B, C, D)
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# discrete system
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sysd = matlab.c2d(sysc, dt)
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Ad = sysd.A
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Bd = sysd.B
|
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|
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# evaluation function weight
|
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Q = np.diag([1., 1., 10., 10.])
|
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R = np.diag([0.01, 0.01])
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pre_step = 5
|
||||
|
||||
# make controller with discreted matrix
|
||||
# please check the solver, if you want to use the scipy, set the MpcController_scipy
|
||||
controller_cvxopt = MpcController_cvxopt(Ad, Bd, Q, R, pre_step,
|
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dt_input_upper=np.array([0.25 * dt, 0.25 * dt]), dt_input_lower=np.array([-0.5 * dt, -0.5 * dt]),
|
||||
input_upper=np.array([1. ,3.]), input_lower=np.array([-1., -3.]))
|
||||
|
||||
controller_scipy = MpcController_scipy(Ad, Bd, Q, R, pre_step,
|
||||
dt_input_upper=np.array([0.25 * dt, 0.25 * dt]), dt_input_lower=np.array([-0.5 * dt, -0.5 * dt]),
|
||||
input_upper=np.array([1. ,3.]), input_lower=np.array([-1., -3.]))
|
||||
|
||||
controller_cvxopt.initialize_controller()
|
||||
controller_scipy.initialize_controller()
|
||||
|
||||
for i in range(iteration_num):
|
||||
print("simulation time = {0}".format(i))
|
||||
reference = np.array([[0., 0., -5., 7.5] for _ in range(pre_step)]).flatten()
|
||||
|
||||
states_cvxopt = plant_cvxopt.xs
|
||||
states_scipy = plant_scipy.xs
|
||||
|
||||
opt_u_cvxopt = controller_cvxopt.calc_input(states_cvxopt, reference)
|
||||
opt_u_scipy = controller_scipy.calc_input(states_scipy, reference)
|
||||
|
||||
plant_cvxopt.update_state(opt_u_cvxopt)
|
||||
plant_scipy.update_state(opt_u_scipy)
|
||||
|
||||
history_states_cvxopt = np.array(plant_cvxopt.history_xs)
|
||||
history_states_scipy = np.array(plant_scipy.history_xs)
|
||||
|
||||
time_history_fig = plt.figure(dpi=75)
|
||||
x_fig = time_history_fig.add_subplot(411)
|
||||
y_fig = time_history_fig.add_subplot(412)
|
||||
v_x_fig = time_history_fig.add_subplot(413)
|
||||
v_y_fig = time_history_fig.add_subplot(414)
|
||||
|
||||
v_x_fig.plot(np.arange(0, simulation_time+0.01, dt), history_states_cvxopt[:, 0], label="cvxopt")
|
||||
v_x_fig.plot(np.arange(0, simulation_time+0.01, dt), history_states_scipy[:, 0], label="scipy", linestyle="dashdot")
|
||||
v_x_fig.plot(np.arange(0, simulation_time+0.01, dt), [0. for _ in range(iteration_num+1)], linestyle="dashed")
|
||||
v_x_fig.set_xlabel("time [s]")
|
||||
v_x_fig.set_ylabel("v_x")
|
||||
v_x_fig.legend()
|
||||
|
||||
v_y_fig.plot(np.arange(0, simulation_time+0.01, dt), history_states_cvxopt[:, 1], label="cvxopt")
|
||||
v_y_fig.plot(np.arange(0, simulation_time+0.01, dt), history_states_scipy[:, 1], label="scipy", linestyle="dashdot")
|
||||
v_y_fig.plot(np.arange(0, simulation_time+0.01, dt), [0. for _ in range(iteration_num+1)], linestyle="dashed")
|
||||
v_y_fig.set_xlabel("time [s]")
|
||||
v_y_fig.set_ylabel("v_y")
|
||||
v_y_fig.legend()
|
||||
|
||||
x_fig.plot(np.arange(0, simulation_time+0.01, dt), history_states_cvxopt[:, 2], label="cvxopt")
|
||||
x_fig.plot(np.arange(0, simulation_time+0.01, dt), history_states_scipy[:, 2], label="scipy", linestyle="dashdot")
|
||||
x_fig.plot(np.arange(0, simulation_time+0.01, dt), [-5. for _ in range(iteration_num+1)], linestyle="dashed")
|
||||
x_fig.set_xlabel("time [s]")
|
||||
x_fig.set_ylabel("x")
|
||||
|
||||
y_fig.plot(np.arange(0, simulation_time+0.01, dt), history_states_cvxopt[:, 3], label ="cvxopt")
|
||||
y_fig.plot(np.arange(0, simulation_time+0.01, dt), history_states_scipy[:, 3], label="scipy", linestyle="dashdot")
|
||||
y_fig.plot(np.arange(0, simulation_time+0.01, dt), [7.5 for _ in range(iteration_num+1)], linestyle="dashed")
|
||||
y_fig.set_xlabel("time [s]")
|
||||
y_fig.set_ylabel("y")
|
||||
time_history_fig.tight_layout()
|
||||
plt.show()
|
||||
|
||||
history_us_cvxopt = np.array(controller_cvxopt.history_us)
|
||||
history_us_scipy = np.array(controller_scipy.history_us)
|
||||
|
||||
input_history_fig = plt.figure(dpi=75)
|
||||
u_1_fig = input_history_fig.add_subplot(211)
|
||||
u_2_fig = input_history_fig.add_subplot(212)
|
||||
|
||||
u_1_fig.plot(np.arange(0, simulation_time+0.01, dt), history_us_cvxopt[:, 0], label="cvxopt")
|
||||
u_1_fig.plot(np.arange(0, simulation_time+0.01, dt), history_us_scipy[:, 0], label="scipy", linestyle="dashdot")
|
||||
u_1_fig.set_xlabel("time [s]")
|
||||
u_1_fig.set_ylabel("u_x")
|
||||
u_1_fig.legend()
|
||||
|
||||
u_2_fig.plot(np.arange(0, simulation_time+0.01, dt), history_us_cvxopt[:, 1], label="cvxopt")
|
||||
u_2_fig.plot(np.arange(0, simulation_time+0.01, dt), history_us_scipy[:, 1], label="scipy", linestyle="dashdot")
|
||||
u_2_fig.set_xlabel("time [s]")
|
||||
u_2_fig.set_ylabel("u_y")
|
||||
u_2_fig.legend()
|
||||
input_history_fig.tight_layout()
|
||||
plt.show()
|
||||
|
||||
if __name__ == "__main__":
|
||||
main()
|
||||
|
|
@ -317,7 +317,7 @@ def main():
|
|||
# input()
|
||||
|
||||
# evaluation function weight
|
||||
Q = np.diag([100., 1000., 1.])
|
||||
Q = np.diag([1000000., 10., 1.])
|
||||
R = np.diag([0.1])
|
||||
|
||||
# System model update
|
||||
|
|
|
|||
Loading…
Reference in New Issue