add README

README.md

@@ -9,6 +9,7 @@ Now you can see the examples of control theories as following
 - **Nonlinear Model Predictive Control with CGMRES**
 - **Linear Model Predictive Control**(as generic function such as matlab tool box)
 - **Extended Linear Model Predictive Control for vehicle model**
+- **Iterative LQR (linear quadratic regulator)**
 
 # Usage and Details
 you can see the usage in each folder

iLQR/README.md

@@ -3,13 +3,43 @@ This program is about iLQR (Iteratice Linear Quadratic Regulator)
 
 # Problem Formulation
 
+Two wheeled robot is expressed by the following equation.
+It is nonlinear and nonholonomic system. Sometimes, it's extremely difficult to control the 
+steering(or angular velocity) and velocity of the wheeled robot. Therefore, many methods control only steering, like purepersuit, Linear MPC.
+However, sometimes we should consider the velocity and steering simultaneously when the car or robots move fast.
+To solve the problem, we should apply the control methods which can treat the nonlinear system.
+
+<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>
+
+Nonliner Model Predictive Control is one of the famous methods, so I applied the method in the folder of this repository.
+(if you are interested, please look it)
+
+NMPC is very effecitive method to solve nonlinear optimal control problem but it is a handcraft method.
+This program is about one more other methods to solve the nonlinear optimal control problem.
+
+The method is iterative LQR.
+Iterative LQR is one of the DDP(differential dynamic programming) method.
+Recently, this method is used in IRL(inverse reinforcement learning), such as GPS(guided policy search)
+
+If you want to know more about the iLQR, please look the references.
+The paper and website is great.
 
 # Usage
 
+```
 
+```
 
 # Expected Results
 
+- static goal
+
+
+- track the goal
+
+
+# Applied other model
+
 
 
 # Requirement
@@ -17,9 +47,6 @@ This program is about iLQR (Iteratice Linear Quadratic Regulator)
 - python3.5 or more
 - numpy
 - matplotlib
-- cvxopt
-- scipy1.2.0 or more
-- python-control
 
 # Reference