add ACC.py of mpc

mpc/README.md

@@ -1,110 +0,0 @@
-# Model Predictive Control Tool
-This program is about template, generic function of linear model predictive control
-
-# Documentation of the MPC function
-Linear model predicitive control should have state equation.
-So if you want to use this function, you should model the plant as state equation.
-Therefore, the parameters of this class are as following
-
-**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
-
-Methods:
-
-- initialize_controller() initialize the controller
-- calc_input(states, references) calculating optimal input
-
-More details, please look the **mpc_func_with_scipy.py** and **mpc_func_with_cvxopt.py**
-
-We have two function, mpc_func_with_cvxopt.py and mpc_func_with_scipy.py
-Both functions have same variable and member function. However the solver is different. 
-Plese choose the right method for your environment.
-
-- example of import
-
-```py
-from mpc_func_with_scipy import MpcController as MpcController_scipy
-from mpc_func_with_cvxopt import MpcController as MpcController_cvxopt
-```
-
-# Examples
-## Problem Formulation
-
-** updating soon !!
-
-- first order system
-
-
-- ACC (Adaptive cruise control)
-
-
-
-## Expected Results
-
-- first order system
-
-
-- ACC (Adaptive cruise control)
-
-
-# Usage
-
-- for example(first order system)
-
-```
-$ python main_example.py
-```
-
-- for example(ACC (Adaptive cruise control))
-
-```
-$ python main_ACC.py
-```
-
-- for comparing two methods of optimization solvers
-
-```
-$ python test_compare_methods.py
-```
-
-# Requirement
-
-- python3.5 or more
-- numpy
-- matplotlib
-- cvxopt
-- scipy1.2.0 or more
-- python-control
-
-# Reference
-I`m sorry that main references are written in Japanese
-
-- 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

mpc/basic/README.md

@@ -0,0 +1,144 @@
+# Model Predictive Control Basic Tool
+This program is about template, generic function of linear model predictive control
+
+# Documentation of the MPC function
+Linear model predicitive control should have state equation.
+So if you want to use this function, you should model the plant as state equation.
+Therefore, the parameters of this class are as following
+
+**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
+
+Methods:
+
+- initialize_controller() initialize the controller
+- calc_input(states, references) calculating optimal input
+
+More details, please look the **mpc_func_with_scipy.py** and **mpc_func_with_cvxopt.py**
+
+We have two function, mpc_func_with_cvxopt.py and mpc_func_with_scipy.py
+Both functions have same variable and member function. However the solver is different. 
+Plese choose the right method for your environment.
+
+- example of import
+
+```py
+from mpc_func_with_scipy import MpcController as MpcController_scipy
+from mpc_func_with_cvxopt import MpcController as MpcController_cvxopt
+```
+
+# Examples
+## Problem Formulation
+
+- **first order system**
+
+<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;&plus;&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;&plus;&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;&plus;&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;&plus;&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>
+
+- **ACC (Adaptive cruise control)**
+
+The two wheeled model are expressed the following equation.
+
+<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>
+
+However, if we assume the velocity are constant, we can approximate the equation as following, 
+
+<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;&plus;&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;&plus;&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;&plus;&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;&plus;&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>
+
+then we can apply this model to linear mpc, we should give the model reference V although.
+
+- **evaluation function**
+
+the both examples have same evaluation function form as following equation.
+
+<a href="https://www.codecogs.com/eqnedit.php?latex=J&space;=&space;\sum_{i&space;=&space;0}^{prestep}||\boldsymbol{\hat{X}}(k&plus;i|k)-\boldsymbol{r}(k&plus;i|k)&space;||^2_{{\boldsymbol{Q}}(i)}&space;&plus;&space;||\boldsymbol{\Delta&space;{U}}(k&plus;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&plus;i|k)-\boldsymbol{r}(k&plus;i|k)&space;||^2_{{\boldsymbol{Q}}(i)}&space;&plus;&space;||\boldsymbol{\Delta&space;{U}}(k&plus;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>
+
+- <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
+
+- <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
+
+- <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
+
+- <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
+
+## Expected Results
+
+- first order system
+
+- time history
+
+
+
+- input
+
+
+
+- ACC (Adaptive cruise control)
+
+<img src = https://github.com/Shunichi09/linear_nonlinear_control/blob/demo_gifs/ACC.gif width = 70%>
+
+
+- animation
+
+
+
+# Usage
+
+- for example(first order system)
+
+```
+$ python main_example.py
+```
+
+- for example(ACC (Adaptive cruise control))
+
+```
+$ python main_ACC.py
+```
+
+- for comparing two methods of optimization solvers
+
+```
+$ python test_compare_methods.py
+```
+
+# Requirement
+
+- python3.5 or more
+- numpy
+- matplotlib
+- cvxopt
+- scipy1.2.0 or more
+- python-control
+
+# Reference
+I`m sorry that main references are written in Japanese
+
+- 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

mpc/basic/animation.py

@@ -127,7 +127,7 @@ class AnimDrawer():
         self._set_axis()
         self._set_img()
 
-        self.skip_num = 3
+        self.skip_num = 1
         frame_num = int((len(self.history_xs[0])-1) / self.skip_num)
 
         animation = ani.FuncAnimation(self.anim_fig, self._update_anim, interval=interval, frames=frame_num)

mpc/basic/main_ACC.py

@@ -218,7 +218,6 @@ def main():
     theta_fig.legend()
 
     time_history_fig.tight_layout()
-    time_history_fig.legend()
 
     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")

mpc/basic/main_example.py

@@ -85,7 +85,7 @@ class FirstOrderSystem():
 
 def main():
     dt = 0.05
-    simulation_time = 100 # in seconds
+    simulation_time = 30 # in seconds
     iteration_num = int(simulation_time / dt)
 
     # you must be care about this matrix
@@ -116,9 +116,9 @@ def main():
     Bd = sysd.B
 
     # evaluation function weight
-    Q = np.diag([1., 1., 10., 10.])
+    Q = np.diag([1., 1., 1., 1.])
-    R = np.diag([0.01, 0.01])
+    R = np.diag([1., 1.])
-    pre_step = 5
+    pre_step = 10
 
     # make controller with discreted matrix
     # please check the solver, if you want to use the scipy, set the MpcController_scipy