Cart Pole Demo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.01, 0.0, -2.0, -2.0]\n"
     ]
    },
    {
     "data": {
      "image/png": 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YghsAEkNwA0BiCG4ASIwXc1pp7o3a05J+tMR/fr6kp/tYTgrY5+F3tu2vxD4v1osjYiLPwEKC+0zYnoqIybLrGCT2efidbfsrsc9FolUCAIkhuAEgMVUM7m1lF1AC9nn4nW37K7HPhalcjxsAcHpVnHEDAE6D4AaAxFQmuM+GGxLbvtn2Ads75712nu27bD+a/b2uzBr7zfbFtu+xvdv2Lts3Zq8P7X7bXm77m7a/m+3zR7PXL7H9YLbP/5RdJnlo2B61/R3bd2TPh3p/Jcn2Htvfs73D9lT2WuGf7UoE97wbEv+qpMskXWf7snKrKsQtkrac9NqHJX0tIl4m6WvZ82HSkvTBiHilpKskvS/72Q7zfs9J2hwRr5F0uaQttq+S9OeS/irb52ck3VBijUW4UdLuec+HfX97fikiLp+3frvwz3YlglvzbkgcEQ1JvRsSD5WIuE/SoZNefpukW7PHt0r69YEWVbCI2BcR384eH1H3P/ZFGuL9jq6j2dOx7E9I2izp89nrQ7XPtjdIeoukT2bPrSHe3wUU/tmuSnCf6obEF5VUy6C9MCL2Sd2Qk/SCkuspjO1Nkq6Q9KCGfL+ztsEOSQck3SXph5IOR0QrGzJsn/FPSPqQpE72fL2Ge397QtJXbW/PbpguDeCznetGCgOQ64bESJft1ZK+IOkDETFTxF2+qyQi2pIut71W0pckvfJUwwZbVTFsXyPpQERst/2G3sunGDoU+3uSqyNir+0XSLrL9iODeNOqzLjP5hsS77d9oSRlfx8ouZ6+sz2mbmh/JiK+mL089PstSRFxWNK96vb319ruTZaG6TN+taS32t6jbptzs7oz8GHd3xMiYm/29wF1f0FfqQF8tqsS3GfzDYm/LOn67PH1kv61xFr6Lut1fkrS7oj4+LwvDe1+257IZtqyvULSG9Xt7d8j6e3ZsKHZ54j4SERsiIhN6v7fvTsi3qUh3d8e26tsn9N7LOlNknZqAJ/typw5afvN6v6W7t2Q+GMll9R3tj8r6Q3qXvpxv6Q/kvQvkj4naaOkJyRdGxEnH8BMlu2fl3S/pO/puf7n76vb5x7K/bb9s+oelBpVd3L0uYj4Y9uXqjsjPU/SdyS9OyLmyqu0/7JWye9GxDXDvr/Z/n0pe1qTdFtEfMz2ehX82a5McAMA8qlKqwQAkBPBDQCJIbgBIDEENwAkhuAGgMQQ3ACQGIIbABLz/yyX1Xw9Z1BtAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20b85b86358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.908\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Program Files (x86)\\Microsoft Visual Studio\\Shared\\Anaconda3_64\\lib\\site-packages\\ipykernel_launcher.py:27: RuntimeWarning: invalid value encountered in multiply\n",
      "C:\\Program Files (x86)\\Microsoft Visual Studio\\Shared\\Anaconda3_64\\lib\\site-packages\\scipy\\integrate\\odepack.py:218: ODEintWarning: Excess accuracy requested (tolerances too small). Run with full_output = 1 to get quantitative information.\n",
      "  warnings.warn(warning_msg, ODEintWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.000000\n",
      "         Iterations: 82\n",
      "         Function evaluations: 203\n",
      "[ -0.11873798  -0.11747164 -83.35508944 -71.14178119]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20b85df4320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "from scipy.optimize import minimize\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "class CartPole:\n",
    "    def __init__(self,g,L,M):\n",
    "        self.g=g\n",
    "        self.L=L\n",
    "        self.M=M\n",
    "        self.A_matrix=np.array([[0,1,0,0],[0,0,0,0],[0,0,0,1],[0,0,self.g/self.L,0]])\n",
    "        self.b_vector=np.array([[0],[1/self.M],[0],[1/(self.M*self.L)]])\n",
    "        self.u_func=lambda t: 0\n",
    "        self.fedback=False\n",
    "        self.k_vec=[0,0,0,0]\n",
    "    def make_fedback(self,k_vec):\n",
    "        self.fedback=True\n",
    "        self.k_vec=k_vec\n",
    "    def derivative(self,q,t):\n",
    "        q_vec=np.array([[q[0]],[q[1]],[q[2]],[q[3]]])\n",
    "        part_one=np.matmul(self.A_matrix,q_vec)\n",
    "        u_value=0\n",
    "        if self.fedback:\n",
    "            u_value=np.dot(self.k_vec,q_vec)\n",
    "        else:\n",
    "            u_value=self.u_func(t)\n",
    "        part_two=self.b_vector*u_value\n",
    "        return_value=part_one+part_two\n",
    "        return np.ndarray.flatten(return_value)\n",
    "    def get_trajectory(self,ts,q0,u_func=None):\n",
    "        if not (u_func is None):\n",
    "            self.u_func=u_func\n",
    "        return odeint(self.derivative,q0,ts)\n",
    "    def score_this_feedback(self,q0,ts,k_trial,to_plot=False):\n",
    "        cp.make_fedback(k_trial)\n",
    "        result=cp.get_trajectory(ts,q0)\n",
    "        score=len(list(filter(lambda x: np.abs(x)>np.pi/4,result[:,2])))\n",
    "        if to_plot:\n",
    "            plt.plot(ts,result[:,2])\n",
    "            plt.show()\n",
    "        return (score+.0)/len(ts)\n",
    "        \n",
    "cp=CartPole(9.8,1,1)\n",
    "q0=[.1,.02,0,0]\n",
    "ts=np.linspace(0,50,1000)\n",
    "k0=[.01,.0,-2.0,-2.0]\n",
    "print(k0)\n",
    "print(cp.score_this_feedback(q0,ts,k0,True))\n",
    "to_optimize=lambda k: cp.score_this_feedback(q0,ts,k)\n",
    "res=minimize(to_optimize,k0,method='Nelder-Mead',tol=1e-3,options={'disp': True,'maxiter':200})\n",
    "print(res.x)\n",
    "print(cp.score_this_feedback(q0,ts,res.x,True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}