Capstone/LQR MIP/LQRMIP.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import scipy.integrate as inte\n",
    "from numpy import matmul as mm\n",
    "from control import lqr\n",
    "import scipy.linalg\n",
    "import slycot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "th,phi,dth,dphi,u = symbols('th phi dth dphi u')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "def lqr(A,B,Q,R):\n",
    "    X = np.matrix(scipy.linalg.solve_continuous_are(A, B, Q, R))\n",
    "    K = np.matrix(scipy.linalg.inv(R)*(B.T*X))\n",
    "    eigVals, eigVecs = scipy.linalg.eig(A-B*K)\n",
    "    return K, X, eigVals\n",
    "\n",
    "def dlqr(A,B,Q,R):\n",
    "    X = np.matrix(scipy.linalg.solve_discrete_are(A, B, Q, R))\n",
    "    K = np.matrix(scipy.linalg.inv(B.T*X*B+R)*(B.T*X*A))\n",
    "    eigVals, eigVecs = scipy.linalg.eig(A-B*K)\n",
    "    return K, X, eigVals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def eomsym(params,th,phi,dth,dphi,u):\n",
    "    A = params['mr']*params['r']*params['d']*cos(phi)\n",
    "    B = params['ir']+params['mr']*(params['d']**2)\n",
    "    C = params['mr']*params['g']*params['d']\n",
    "    D = params['mr']*(params['r']**2)\n",
    "    E = params['r']*params['mr']*params['d']*cos(phi) \n",
    "    F = params['mr']*params['r']*params['d']\n",
    "    tau = u\n",
    "    tmp1 = A*F*sin(phi)*dphi**2-C*D*sin(phi)+(A+D)*tau\n",
    "    tmp2 = A*E-B*D; phidd = tmp1/tmp2\n",
    "    thdd = -((A+B)*phidd-C*sin(phi)+tau)/A\n",
    "    qdd = Matrix([thdd,phidd])\n",
    "    return qdd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def eom(params,th,phi,dth,dphi,u):\n",
    "    A = params['mr']*params['r']*params['d']*np.cos(phi)\n",
    "    B = params['ir']+params['mr']*(params['d']**2)\n",
    "    C = params['mr']*params['g']*params['d']\n",
    "    D = params['mr']*(params['r']**2)\n",
    "    E = params['r']*params['mr']*params['d']*np.cos(phi) \n",
    "    F = params['mr']*params['r']*params['d']\n",
    "    tau = u\n",
    "    tmp1 = A*F*np.sin(phi)*dphi**2-C*D*np.sin(phi)+(A+D)*tau\n",
    "    tmp2 = A*E-B*D; phidd = tmp1/tmp2\n",
    "    thdd = -((A+B)*phidd-C*np.sin(phi)+tau)/A\n",
    "    qdd = np.array([thdd,phidd])\n",
    "    return qdd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = {}; params['g'] = 9.81\n",
    "params['mr'] = .25; params['ir'] = .0001\n",
    "params['d'] = .1; params['r'] = .02\n",
    "\n",
    "qdd = eomsym(params,th,phi,dth,dphi,u)\n",
    "f = Matrix([dth,dphi])\n",
    "g = Matrix([qdd])\n",
    "der = Matrix([th,phi,dth,dphi])\n",
    "A = f.jacobian(der)\n",
    "A2= g.jacobian(der)\n",
    "b = f.jacobian(Matrix([u]))\n",
    "b2= g.jacobian(Matrix([u]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 1 & 0\\\\0 & 0 & 0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, 0, 1, 0],\n",
       "[0, 0, 0, 1]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & \\frac{2000.0 \\left(- u - \\frac{\\left(0.0005 \\cos{\\left(\\phi \\right)} + 0.0026\\right) \\left(2.5 \\cdot 10^{-7} dphi^{2} \\sin{\\left(\\phi \\right)} \\cos{\\left(\\phi \\right)} + u \\left(0.0005 \\cos{\\left(\\phi \\right)} + 0.0001\\right) - 2.4525 \\cdot 10^{-5} \\sin{\\left(\\phi \\right)}\\right)}{2.5 \\cdot 10^{-7} \\cos^{2}{\\left(\\phi \\right)} - 2.6 \\cdot 10^{-7}} + 0.24525 \\sin{\\left(\\phi \\right)}\\right) \\sin{\\left(\\phi \\right)}}{\\cos^{2}{\\left(\\phi \\right)}} + \\frac{2000.0 \\left(- \\frac{\\left(0.0005 \\cos{\\left(\\phi \\right)} + 0.0026\\right) \\left(- 2.5 \\cdot 10^{-7} dphi^{2} \\sin^{2}{\\left(\\phi \\right)} + 2.5 \\cdot 10^{-7} dphi^{2} \\cos^{2}{\\left(\\phi \\right)} - 0.0005 u \\sin{\\left(\\phi \\right)} - 2.4525 \\cdot 10^{-5} \\cos{\\left(\\phi \\right)}\\right)}{2.5 \\cdot 10^{-7} \\cos^{2}{\\left(\\phi \\right)} - 2.6 \\cdot 10^{-7}} - \\frac{5.0 \\cdot 10^{-7} \\left(0.0005 \\cos{\\left(\\phi \\right)} + 0.0026\\right) \\left(2.5 \\cdot 10^{-7} dphi^{2} \\sin{\\left(\\phi \\right)} \\cos{\\left(\\phi \\right)} + u \\left(0.0005 \\cos{\\left(\\phi \\right)} + 0.0001\\right) - 2.4525 \\cdot 10^{-5} \\sin{\\left(\\phi \\right)}\\right) \\sin{\\left(\\phi \\right)} \\cos{\\left(\\phi \\right)}}{\\left(2.5 \\cdot 10^{-7} \\cos^{2}{\\left(\\phi \\right)} - 2.6 \\cdot 10^{-7}\\right)^{2}} + 0.24525 \\cos{\\left(\\phi \\right)} + \\frac{0.0005 \\left(2.5 \\cdot 10^{-7} dphi^{2} \\sin{\\left(\\phi \\right)} \\cos{\\left(\\phi \\right)} + u \\left(0.0005 \\cos{\\left(\\phi \\right)} + 0.0001\\right) - 2.4525 \\cdot 10^{-5} \\sin{\\left(\\phi \\right)}\\right) \\sin{\\left(\\phi \\right)}}{2.5 \\cdot 10^{-7} \\cos^{2}{\\left(\\phi \\right)} - 2.6 \\cdot 10^{-7}}\\right)}{\\cos{\\left(\\phi \\right)}} & 0 & - \\frac{0.001 dphi \\left(0.0005 \\cos{\\left(\\phi \\right)} + 0.0026\\right) \\sin{\\left(\\phi \\right)}}{2.5 \\cdot 10^{-7} \\cos^{2}{\\left(\\phi \\right)} - 2.6 \\cdot 10^{-7}}\\\\0 & \\frac{- 2.5 \\cdot 10^{-7} dphi^{2} \\sin^{2}{\\left(\\phi \\right)} + 2.5 \\cdot 10^{-7} dphi^{2} \\cos^{2}{\\left(\\phi \\right)} - 0.0005 u \\sin{\\left(\\phi \\right)} - 2.4525 \\cdot 10^{-5} \\cos{\\left(\\phi \\right)}}{2.5 \\cdot 10^{-7} \\cos^{2}{\\left(\\phi \\right)} - 2.6 \\cdot 10^{-7}} + \\frac{5.0 \\cdot 10^{-7} \\left(2.5 \\cdot 10^{-7} dphi^{2} \\sin{\\left(\\phi \\right)} \\cos{\\left(\\phi \\right)} + u \\left(0.0005 \\cos{\\left(\\phi \\right)} + 0.0001\\right) - 2.4525 \\cdot 10^{-5} \\sin{\\left(\\phi \\right)}\\right) \\sin{\\left(\\phi \\right)} \\cos{\\left(\\phi \\right)}}{\\left(2.5 \\cdot 10^{-7} \\cos^{2}{\\left(\\phi \\right)} - 2.6 \\cdot 10^{-7}\\right)^{2}} & 0 & \\frac{5.0 \\cdot 10^{-7} dphi \\sin{\\left(\\phi \\right)} \\cos{\\left(\\phi \\right)}}{2.5 \\cdot 10^{-7} \\cos^{2}{\\left(\\phi \\right)} - 2.6 \\cdot 10^{-7}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, 2000.0*(-u - (0.0005*cos(phi) + 0.0026)*(2.5e-7*dphi**2*sin(phi)*cos(phi) + u*(0.0005*cos(phi) + 0.0001) - 2.4525e-5*sin(phi))/(2.5e-7*cos(phi)**2 - 2.6e-7) + 0.24525*sin(phi))*sin(phi)/cos(phi)**2 + 2000.0*(-(0.0005*cos(phi) + 0.0026)*(-2.5e-7*dphi**2*sin(phi)**2 + 2.5e-7*dphi**2*cos(phi)**2 - 0.0005*u*sin(phi) - 2.4525e-5*cos(phi))/(2.5e-7*cos(phi)**2 - 2.6e-7) - 5.0e-7*(0.0005*cos(phi) + 0.0026)*(2.5e-7*dphi**2*sin(phi)*cos(phi) + u*(0.0005*cos(phi) + 0.0001) - 2.4525e-5*sin(phi))*sin(phi)*cos(phi)/(2.5e-7*cos(phi)**2 - 2.6e-7)**2 + 0.24525*cos(phi) + 0.0005*(2.5e-7*dphi**2*sin(phi)*cos(phi) + u*(0.0005*cos(phi) + 0.0001) - 2.4525e-5*sin(phi))*sin(phi)/(2.5e-7*cos(phi)**2 - 2.6e-7))/cos(phi), 0, -0.001*dphi*(0.0005*cos(phi) + 0.0026)*sin(phi)/(2.5e-7*cos(phi)**2 - 2.6e-7)],\n",
       "[0,                                                                                                                                                                                                                                                                                                                                                                                                                                            (-2.5e-7*dphi**2*sin(phi)**2 + 2.5e-7*dphi**2*cos(phi)**2 - 0.0005*u*sin(phi) - 2.4525e-5*cos(phi))/(2.5e-7*cos(phi)**2 - 2.6e-7) + 5.0e-7*(2.5e-7*dphi**2*sin(phi)*cos(phi) + u*(0.0005*cos(phi) + 0.0001) - 2.4525e-5*sin(phi))*sin(phi)*cos(phi)/(2.5e-7*cos(phi)**2 - 2.6e-7)**2, 0,                   5.0e-7*dphi*sin(phi)*cos(phi)/(2.5e-7*cos(phi)**2 - 2.6e-7)]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0],\n",
       "[0]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{2000.0 \\left(- \\frac{\\left(0.0005 \\cos{\\left(\\phi \\right)} + 0.0001\\right) \\left(0.0005 \\cos{\\left(\\phi \\right)} + 0.0026\\right)}{2.5 \\cdot 10^{-7} \\cos^{2}{\\left(\\phi \\right)} - 2.6 \\cdot 10^{-7}} - 1\\right)}{\\cos{\\left(\\phi \\right)}}\\\\\\frac{0.0005 \\cos{\\left(\\phi \\right)} + 0.0001}{2.5 \\cdot 10^{-7} \\cos^{2}{\\left(\\phi \\right)} - 2.6 \\cdot 10^{-7}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[2000.0*(-(0.0005*cos(phi) + 0.0001)*(0.0005*cos(phi) + 0.0026)/(2.5e-7*cos(phi)**2 - 2.6e-7) - 1)/cos(phi)],\n",
       "[                                                  (0.0005*cos(phi) + 0.0001)/(2.5e-7*cos(phi)**2 - 2.6e-7)]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 1 & 0\\\\0 & 0 & 0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, 0, 1, 0],\n",
       "[0, 0, 0, 1]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.subs([(th,0),(phi,0),(dth,0),(dphi,0),(u,0)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & -14714.9999999999 & 0 & 0\\\\0 & 2452.49999999998 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, -14714.9999999999, 0, 0],\n",
       "[0,  2452.49999999998, 0, 0]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A2.subs([(th,0),(phi,0),(dth,0),(dphi,0),(u,0)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  0.           0.           1.           0.        ]\n",
      " [  0.           0.           0.           1.        ]\n",
      " [  0.         698.49085038   0.           0.        ]\n",
      " [  0.         -63.27637257   0.           0.        ]]\n",
      "[[    0.        ]\n",
      " [    0.        ]\n",
      " [17326.11921085]\n",
      " [-1979.22366384]]\n"
     ]
    }
   ],
   "source": [
    "A_1 = np.vstack((np.array(A.subs([(th,0),(phi,1),(dth,0),(dphi,0),(u,0)])),\n",
    "          np.array(A2.subs([(th,0),(phi,1),(dth,0),(dphi,0),(u,0)])))).astype(float)\n",
    "b_1 = np.vstack((np.array(b.subs([(th,0),(phi,1),(dth,0),(dphi,0),(u,0)])),\n",
    "          np.array(b2.subs([(th,0),(phi,1),(dth,0),(dphi,0),(u,0)])))).astype(float)\n",
    "A_1 = np.matrix(A_1)\n",
    "b_1 = np.matrix(b_1)\n",
    "print(A_1)\n",
    "print(b_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 1)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "K,S,E = lqr(A_1,b_1,10000*np.eye(4),1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def circle(x,y,r):\n",
    "    ang = np.arange(0,2*np.pi,0.01)\n",
    "    xp = r*np.cos(ang)\n",
    "    yp = r*np.sin(ang)\n",
    "    plt.plot(x+xp,y+yp,color='k',linewidth=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def controller(params,t,X):\n",
    "    k = -np.array([.0089,1.0553,.0112,.125])\n",
    "    u = -mm(k,X)\n",
    "    return u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dynamics(params,t,X):\n",
    "    Xd = np.zeros(X.shape);\n",
    "    th,phi,dth,dphi = X[0],X[1],X[2],X[3]\n",
    "    u = controller(params,t,X)\n",
    "    Xd[:2] = X[2:]\n",
    "    Xd[2:] = eom(params,th,phi,dth,dphi,u)\n",
    "    return Xd\n",
    "def robotSim():\n",
    "    params = {}; params['g'] = 9.81\n",
    "    params['mr'] = .25; params['ir'] = .0001\n",
    "    params['d'] = .1; params['r'] = .02\n",
    "    t0,t1 = 0,2; y0 = np.array([0,1,0,0])\n",
    "    t = np.linspace(t0,t1,445)\n",
    "    y = np.zeros((len(t),len(y0))); y[0,:] = y0\n",
    "    r = inte.ode(lambda t,y:dynamics(params,t,y)).set_integrator(\"dopri5\") \n",
    "    r.set_initial_value(y0, t0)   # initial values\n",
    "    for i in range(1, t.size):\n",
    "        y[i, :] = r.integrate(t[i]) # get one more value, add it to the array\n",
    "        if not r.successful():\n",
    "           raise RuntimeError(\"Could not integrate\")\n",
    "    return t,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1af1adbd5c8>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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H9nbrgrU1ioWDevmzmiVJP9/WXuRaAQAAAACAckBItET0Z0b1+KE+XbahXpK0ti6h89fW6OePERIBAAAAAICFR0i0RGzZ16MxJ122/vhE1a98drO2HerTvs5UEWsGAAAAAADKASHREvHg3i5FggFd2FI7se8ahpwBAAAAAIBFQki0RDy4p1vnr61WPBKc2Le6Jq6LWmr0M4acAQAAAACABUZItAQMDmf1+KE+Xbq+/oSyVzx7lXa092t3x2ARagYAAAAAAMoFIdESsHlft3JjbmLS6nzjTzm7i95EAAAAAABgARESLQGPH+qTJF3YUnNC2crqmJ7TWsuQMwAAAAAAsKAIiZaAfV1praiKKhkNTVv+imev0lNHB7Tz6MAi1wwAAAAAAJQLQqIlYH9XSuvqkzOWX3PeSpmJ3kQAAAAAAGDBEBItAfu70lpXl5ixvKkqpkta6/Tzbe1yzi1izQAAAAAAQLkgJCqy9EhWxwaG1dowc08iSXrF+au069igth/uX6SaAQAAAACAckJIVGT7u9KSpHX1M/ckkqRrn71KiUhQ//mHfYtQKwAAAAAAUG4IiYpsIiSqO3lPoupEWK+9eI3ufPSQjvVnFqNqAAAAAACgjBASFdn+rpQkqeUUPYkk6W1XrFd2zOmWB/YvdLUAAAAAAECZISQqsn1dadUmwqqOh095bGtDUi85e4W+89B+DY3kFqF2AAAAAACgXDyjkMjM1prZb81sh5ltN7O/8ffXmdmvzWynv6z195uZfcHMdpnZY2Z20Xx+E6XsQHdK6+pPPtQs343PW6+e9Kh+tOXgAtYKAAAAAACUm2fakygr6e+cc2dLukzSe8zsHEkfkXSPc26jpHv8bUm6RtJG/+smSV+eU62XkX2dabUWMNRs3CXr67RpXa3+/d5dSo9kF7BmAAAAAACgnDyjkMg51+6ce9hfH5C0Q9JqSddJ+pZ/2Lckvcpfv07SLc7zoKQaM2ueU82XgeFsTu19Q2qZRU8iM9PfX3OWjg0M86QzAAAAAAAwb+Y8J5GZtUq6UNJDklY459olL0iS1OQftlpS/vioNn9fWWvrGdKY06x6EknSc1rr9OKzm/SV+3arJzWyQLUDAAAAAADlZE4hkZlVSLpV0gecc/0nO3SafW6a17vJzDab2eaOjo65VK0kjD/ZbDZzEo378MvO0uBIVl/87a75rhYAAAAAAChDzzgkMrOwvIDoO8652/zdR8eHkfnLY/7+Nklr805fI+nw1Nd0zt3snNvknNvU2Nj4TKtWMvZ3pSVJ62bZk0iSzlxZqddevEbf/OM+7To2MN9VAwAAAAAAZeaZPt3MJH1d0g7n3L/mFd0p6S3++lsk3ZG3/wb/KWeXSeobH5ZWzvZ3pVURDak+GXlG5/+Pq89SIhLU//zJdjl3QscsAAAAAACAgj3TnkRXSHqzpBeZ2Vb/6+WSPiPpJWa2U9JL/G1JukvSHkm7JH1N0rvnVu3lYX9XSi11CXmZ2+w1VET14avP0gN7unTnoyd0zAIAAAAAAChY6Jmc5Jz7vaafZ0iSrprmeCfpPc/kvZaz9r6M1tTOfqhZvr+8pEU/2nxQ//TzHbryzCZVx8PzVDsAAAAAAFBO5vx0MzxzR/ozaq6Ozek1ggHTP7/qWepOjeiff/7EPNUMAAAAAACUG0KiIsmM5tSbHtXKOYZEkvSsNdV61ws26Ieb23TfU8dOfQIAAAAAAMAUhERFcqQvI0laWTX3kEiS3n/VRm1sqtBHb9um/szovLwmAAAAAAAoH4RERdLuh0RzHW42LhoK6rOvPV/HBob1D7c/ztPOAAAAAADArBASFcmR/iFJ0op5Cokk6YK1NfrAVRt156OH9aMtbfP2ugAAAAAAYPkjJCqSI33DkuZvuNm4d7/wdF22oU6fvGO7dncMzutrAwAAAACA5YuQqEiO9A2pKhZSMhqa19cNBkz/5/UXKhYO6H3ffUTD2dy8vj4AAAAAAFieCImKpL0vMy9PNpvOyuqYPvua8/VEe7/+37ueXJD3AAAAAAAAywshUZEc7c9oZXV8wV7/xees0Fsvb9U3/7hPv3ni6IK9DwAAAAAAWB4IiYqkvS+j5nmej2iqj778LJ3TXKUP/fhRHexOL+h7AQAAAACA0kZIVASjuTF1DA7P65PNphMNBfWlN16k3JjTX317i4ZGmJ8IAAAAAABMj5CoCDoGhuWc1LzAIZEktTYk9fnrL9COI/362O3b5Jxb8PcEAAD/f3t3Hh1HdeZ9/Pd0q7VZsmRbtpGNbAN2WB0bMDaYJSEJhHDC4gkvawATCBOWSSaTN3NC5kySmckkmeQ9TMhkgxBMWAJZgInnDZOEAAkDxBibAGYxYAPBxptk2bL2re/80dVSdavabltSlVr9/ZzTp7tv3Vv1dF+VSvfRrSoAAIDCQ5IoAltbuiRp1C5cne0DR0zXZz/0Hj3053d159Nvh7JNAAAAAABQWEgSRWBbOkk0ytck8rvx9Lk646jp+uqvX9WqN3eGtl0AAAAAAFAYSBJFYNueVJIojNPN0mIx080XLtDsKZW64d7ntGV3Z2jbBgAAAAAAYx9Joghsa+lUWUlMNRWJULdbXZ7QbZcvUndfUp+8a406evpC3T4AAAAAABi7SBJFYGtLl+prymVmoW977rQq/cclx+rVrXv0t/c/r2SSC1kDAAAAAACSRJHYvqcrtItWBzn9iGn6x48epd+9sl3f/O1rkcUBAAAAAADGDpJEEdja0hXqRauDLF86Rx8/cZZ++MeN+vmaTZHGAgAAAAAAokeSKGTOOW3f06XpEc4kkiQz05fPOVqnzqvTPzy0jjueAQAAAABQ5EgShWx3R696+52mV0ebJJKkRDym7156nGZNrtSn7lmrjY1tUYcEAAAAAAAiQpIoZE1t3ZKkuuqyiCNJqalIaMXyxSqJma68Y7V2tHZFHRIAAAAAAIgASaKQNbamkkRTq8ZGkkiSZk2p1I+vPEE723p01Ypn1dbdF3VIAAAAAAAgZCSJQtbozSSaWl0acSSZFjTU6vuXHaf121p1/b3Pqbc/GXVIAAAAAAAgRCSJQjY4kyj6axJlO/2Iafr6svl64vVGfeGBdXLORR0SAAAAAAAISUnUARSbprYelcZjmlgxNr/6C09o0JaWTn37929oRm25Pnfm4VGHBAAAAAAAQjA2MxXjWGNrt+qqSmVmUYeS02c+OE/bWrr0H49t0EE15bpsyeyoQwIAAAAAAKOMJFHImtq6x8ydzXIxM331/GO0o7Vb//ifL2ladbnOOGp61GEBAAAAAIBRxDWJQpaaSTS2k0SSVBKP6buXHqv5M2t040+f0zNv7ow6JAAAAAAAMIpIEoWsqa1bUwsgSSRJlaUlumP5CTp4UoWu+ckavfRuS9QhAQAAAACAUXLASSIzu8PMdpjZS76yyWb2iJm94T1P8srNzL5jZhvM7EUzO24kgi80yaTTzvYe1VWXRh1K3qZUlemea5ZoYkVCV9yxWht2tEUdEgAAAAAAGAXDmUl0p6Szssq+IOlR59w8SY967yXpI5LmeY9rJf1gGNstWLs6etSfdAUzkyitvqZC91yzRDEzffz2Z7SpuSPqkAAAAAAAwAg74CSRc+4JSc1ZxedJ+on3+ieSzveV3+VSVkmqNbP6A912oWps65akMX/h6iCH1E3Q3VcvVkdPny7/8TPa0doVdUgAAAAAAGAEjfQ1iaY757ZKkvc8zSufKWmTr95mr6yoNLX2SFLBzSRKO7J+olZctVjb93Trih+vVktHb9QhAQAAAACAERLWhastoMwNqWR2rZmtMbM1jY2NIYQVrqYCnkmUdvzsSbrtiuP1ZmO7rrpztTp6+qIOCQAAAAAAjICRThJtT59G5j3v8Mo3S2rw1TtY0pbsxs6525xzi5xzi6ZOnTrCoUWvsTWVJJpawOQdP6oAABcESURBVEkiSTp13lR955KFen7Tbn3yrjXq6u2POiQAAAAAADBMI50kWinpSu/1lZJ+5Su/wrvL2YmSWtKnpRWTprZulZbEVF1WEnUow3bWMfX61gUL9PTGnSSKAAAAAAAYBw44SWRm90n6k6TDzWyzmV0t6RuSzjCzNySd4b2XpIclvSlpg6QfSbp+WFEXqMbWbk2tKpNZ0Nl3hedjxx+sf/vYe/XkhiZde/daEkUAAAAAABSwA57S4py7JMeiDwbUdZJuONBtjReNbd0FfT2iIBcuapCc9PcPvKi/vnutbr38eJUn4lGHBQAAAAAA9lNYF66G0jOJSqMOY8RdeEKDvvFX8/XH1xv1qXvWqruPGUUAAAAAABQakkQhamrrKfiLVudy8eJZ+tqy+frDa4267p7nSBQBAAAAAFBgSBKFpD/p1Nzerbqq8ZkkkqRLl8zSvy47Ro+t36HrSRQBAAAAAFBQSBKFpLm9R0mncTuTKO2yJbP11fOP0aPrd+i6e57jYtYAAAAAABQIkkQhaWztlqRxPZMo7eMnztbXls3X46/t0PIVq9XW3Rd1SAAAAAAAYB9IEoWkqa14kkRS6tSzb1+0UM++vUuX3f6Mdnf0RB0SAAAAAADYC5JEIdnlJUmmjMO7m+Vy3sKZ+sFlx+nVLXt00a2rtKO1K+qQAAAAAABADiSJQtLcnkoSTa4sniSRJJ159EFacdUJ2rSrQxf+8E96Z2dH1CEBAAAAAIAAJIlCsqu9RzGTJlYkog4ldCfPrdPdVy/Rro5e/dUPntKLm3dHHRIAAAAAAMhCkigkzR09qq0sVTxmUYcSieNnT9ID1y1VWUlcF926So+v3xF1SAAAAAAAwIckUUia23s0qbL4ZhH5zZ1WpYduWKrDpk3QNXet0X2r34k6JAAAAAAA4CFJFJLm9h5NnlBc1yMKMq26XD+79iSdMrdONz24Tt/67Xolky7qsAAAAAAAKHokiUKyq71Xk4rsotW5TCgr0e1XLtIlixv0vcc36tq716q1qzfqsAAAAAAAKGokiULS3MFMIr9EPKavLZuvfzr3aD3+2g4t+/7TequpPeqwAAAAAAAoWiSJQuCc0672Hk0iSZTBzHTl0jm6++rF2tnWrfO++6T++Hpj1GEBAAAAAFCUSBKFoLW7T31Jp8mcbhZo6WF1WnnjKZpRW6GrVqzWdx59Q/1cpwgAAAAAgFCRJArBrvYeSWIm0V40TK7Ug9cv1bkLZujmR17XZbev0vY9XVGHBQAAAABA0SBJFIJmL0k0eUIi4kjGtsrSEv37RQv1//7PAr2wqUUfueV/9Nj67VGHBQAAAABAUSBJFIJdHd5MIk432ycz0wXHH6z//+lTNH1iuT5x5xr903+9rM6e/qhDAwAAAABgXCNJFILm9tTt3bm7Wf4Om1qlh65fquVL52jFU2/rrFue0J827ow6LAAAAAAAxi2SRCHgmkQHpjwR11fOPVr3ffJESdIlP1qlmx5cpz1dvRFHBgAAAADA+EOSKATNHT1KxE3VZSVRh1KQTjpsin7zmdN07WmH6mfPvqMzb35CD6/bKue4AxoAAAAAACOFJFEIdrX3aFJlqcws6lAKVkVpXF88+0g9dP3Jqq1M6Pp7n9NFt67Sus0tUYcGAAAAAMC4QJIoBM3tPVyPaIQsaKjVrz99qr62bL42NrbpnO8+qc/9/AVt39MVdWgAAAAAABQ0zn8Kwa6OHu5sNoLiMdOlS2bpowvq9b3HN2jFk2/r1+u26LIls/XXpx2qaRPLow4RAAAAAICCw0yiEDCTaHRMLE/opo8cqUf+7jSdPb9edz79tk755uP68q9e0taWzqjDAwAAAACgoJAkCsGujl5NmpCIOoxxa/aUCbr5woV67HPv07KFM3XvM+/ofd/8gz7/ixf00rtcswgAAAAAgHxwutko60867e7o0WRONxt1s6dM0L9d8F7d+IG5uvWJjXpg7bv6xdrNOnZWra44abbOnl+vspJ41GECAAAAADAmMZNolO3p7FXSSZM43Sw0DZMr9dXz52vVFz+oL330KLV09OqzP3tBS7/+mL6y8mU9v2m3nHNRhwkAAAAAwJjCTKJR1tzRI0lckygCNRUJfeKUQ7R86Rw9tbFJ961+Rz9d/Y7ufPptHVI3QectnKFzFszQYVOrog4VAAAAAIDIkSQaZbvaU0ki7m4WnVjMdOq8qTp13lTt6erVb9Zt00N/fle3PPqGvv37N3Ro3QR96Kjp+tCR03XcrFqVxJlgBwAAAAAoPqEmiczsLEm3SIpLut05940wtx+F5nZmEo0lE8sTuvCEBl14QoO2tnTqkVe265FXtmvFU2/ptife1KTKhJYeVqelc6fo5MPqNHtKpcws6rABAAAAABh1oSWJzCwu6XuSzpC0WdKzZrbSOfdKWDFEIZ0k4ppEY099TYWuOGmOrjhpjlq7evU/bzTp0Vd36KkNTfr1uq2SpBk15Trx0Ck6dlatFjZM0hH11Uow0wgAAAAAMA6FOZNosaQNzrk3JcnM7pd0nqTxnSRKX5OI083GtOryhM6eX6+z59fLOae3mtr11MadenpDk554o0kP/vldSVJZSUzHzKzRsQ21WjirVvNn1qhhUqViMWYbAQAAAAAKW5hJopmSNvneb5a0JMTtR2JXe4/KEzFVlHLr9UJhZjp0apUOnVqly0+cLeecNu/q1PObdg887l71F93+5FuSpMrSuOZNr9bh06t0+EETdcRB1XrP9GpNrS6L+JMAAAAAAJC/MJNEQVMtMu5DbmbXSrpWkmbNmhVGTKNu3vRqnb9wZtRhYBjMTA2TK9UwuVLnLJghSertT2r91la9vKVFr21v1WvbWvXoqzv08zWbB9rVVCQ0Z0qlZk+ZoDl1EzRnSqX3PEGTKhNc6wgAAAAAfJxzcm4wUeCck5O8stQyBb3Pqivfcv8yf1sNLAuo68tU+JdPqixVTWVi1L+HKJlzbt+1RmJDZidJ+opz7sPe+5skyTn39aD6ixYtcmvWrAklNmCkNLV167VtrVq/rVVvNbXpLzs79FZTu7bs7lTSt6tVlsZVX1OuGbUVA88zaipUX1uu+poKzagtV2UpNx8EAACImnNOSed7Tg8mnZT0Bp7J9MDWe/aXy2mgXTK7jq/uYLlXN5m5raAB78A2g17vs61/eR7r8bdRQNshdf31cq07z7b7Wmd22+zPmHfb4O8s3Y9DvqeMZUPbpv7+D+63pDcOD+qr5F6SHElvBUH9HLjOvcaf+jlTQLl8n9Ht5XOk8wlelcBtpNulszS5fpYLwec/fLhuOH1u1GEMm5mtdc4tCloW5ij0WUnzzOwQSe9KuljSpSFuHxh1dVVlqptbppPn1mWUd/f1a1Nzp/6ys91LGnVpa0untrR0af22RjW2dg9ZV3VZieqqy1RXVZpab/pR7X9fqpqKhKrLE4pzXSQAQJFLD+KTzmUMwPuTmYP8pHNKJvOv258cXJ50g8sD15t+JJVZ1/nrDi73DwrT2/APVpNZz9l1JSmZDEhUyN82c3A8pL1/G1nbTtcdus5ccUpSdlIlx+fJLpdyJlGC4/RvY3Cwu89tJIe2z1W3UAauxcosdbqKmXnPWa9lmXVyvR5SNtg25s3+T607c50x78WQGNJ1MuLKUZ4r/phkiu1H2+D4M9tkth2MP7ht+nMrx/L0OjP7I6uut01lrzegvgK+w4y6/r7I2o4XpS/ugO8pvZ0c2/K/l6+uf11Hz6jZnx/RghRaksg512dmN0r6raS4pDuccy+HtX0gSmUlcc2dVqW506oCl/f0JbV9T5e27O7UlpZObdndpcbWbjW2dauptVuvb2/V0xt3qqWzN7C9mTSxPKHayoRqKxKqqSxVbUXqfU3F4KO6vEQTylKPqvRzaYkmlMVVwl3bABSR7EFwelDZn04YDAzwU4P7jLrJrLo5kwkaWN7vW1/2uoZTN+nkJSqGbtefBBmo619vVpLEn9BIJrPqDllvZhJgaAxDY95b0sX/fSaTQUmXwW1n1M0e5DOgHxDzBlSxrMFizBvspAeHMbOMcht4H1SWXTdoG977XO0zti2ZxRSLZQ7Ic8Vjsoy6g9vO+jwaXM+Q9r6y9PtYLMe2vA+Z2Tb48/gHw/7vPlf7gbaBn2ewrvwxD3zng4PYjL7IGGwP/Q4HB9MB6/QNrgc/T+4Bf3BCZC/lWUmFjPUFlefZFsDIC/V8Fufcw5IeDnObQCEoLYkNXPdob3r6ktrZ3q2m1h41tXWrub1Huzt71dLZq5aO1OvdHb3a3dmrd3a2p8o7e5XM44/mspLYQOIolUSKp16XlqgsEVN5Iq6KRFzliZjKS+Iq916XJeKZyxJxb3nqdVlJTIl4TImSmBJxUyIW425wKDhBsxP6cwyU862ba3aCf3CfUTc90E9mDdgz1js4uM+MI2jWQ66YR6bu/s6mSAasN+klTIasNyP54Uvm7EfdfH4vjifpAW1s4HnwtXmD5LjZwCB1YHksoK6Z4rG9100vKymJBdY1S20vFhscMMdMQ2OI+epaVt1c640NrZta1/Dqpj53QN2Mz++r6/u+YrGh37t/IJ47MeJLQsQGkyHpZVJQWwbPAIADx0VPgAJSWhJTfU2F6msq8m6TTDq1dveppaNXbd19au/pSz17j7bufrV1BZX3aWdbj97p6VB3b1Jdvf2pR19S/cMcXZXETCVxUyIeU2k8nURKJZAGXqfLvXolsZjisdSgIB6LKe4b1MRjlvna+0N+aJnvYek2g/9BDJp2KgVPPR2YOptelt0me7nvv2Dpb8/5p/8PlLmBZVL2OeqDdbzZ/IHnjGeXKV0/XeYyp9Cnp9dnz6jwn74QlADInongPxXBPxthb+3TpwfsdRu+ZEv2ID8oYRG8LHN2wpAkypAZFZmJn2ITPFDOTBD4EwEDg99YQN08B8qpfdxXd2Dg7O3PATHkWzc42TGYeIgFrCuWscxXN+fnyfxO0r93LMf3s6+6QckIy7XeHMmceEYigqQBAADYN5JEwDgXi9nA6WYjpbc/lTTq7O33JZCS6urrH3ztSyr19SfV259Ub7/znlOve/qS6ksm1duXKu/pT6qvf/B1ajtJtXX1qac/NZDv92YtpB/p2RhJ5y9LDez73WAbV3zj/BEXlCzwD0jNMgfgQ/4L7x+8SxmD3OxB95D2GhwgJwYGyUH/6c+Ox0sEZtcPHKznnp0wdIbEyNTNazZFLKtunkmX+JA4cid+susCAACgOJEkArDf0rN8qssL5/aP6VNi/Emm7GtuOO+WDJmzbLLuvpAuz7V8YFnwDB/nfLOSlH49eI2AzDLvvTJnI6WlEyG5ZiylG2eXZZ/zLylwBog/EUTiAAAAABj/SBIBKApmqVPc+KUHAAAAAMG4nREAAAAAAABIEgEAAAAAAIAkEQAAAAAAACSZG6O3/DGzRkl/iTqOEVInqSnqIBAJ+r540ffFi74vTvR78aLvixd9X7zo++I1Xvp+tnNuatCCMZskGk/MbI1zblHUcSB89H3xou+LF31fnOj34kXfFy/6vnjR98WrGPqe080AAAAAAABAkggAAAAAAAAkicJyW9QBIDL0ffGi74sXfV+c6PfiRd8XL/q+eNH3xWvc9z3XJAIAAAAAAAAziQAAAAAAAECSaNjM7Cwze83MNpjZFwKWl5nZz7zlz5jZHN+ym7zy18zsw2HGjeHJo9//zsxeMbMXzexRM5vtW9ZvZs97j5XhRo7hyqPvl5tZo6+Pr/Etu9LM3vAeV4YbOYYrj77/d1+/v25mu33L2O8LmJndYWY7zOylHMvNzL7j/Wy8aGbH+Zax3xeoPPr9Mq+/XzSzp81sgW/Z22a2ztvn14QXNUZCHn3/fjNr8f1e/5Jv2V6PFRjb8uj7z/v6/SXv+D7ZW8Z+X6DMrMHMHjezV83sZTP7TECdojnWc7rZMJhZXNLrks6QtFnSs5Iucc694qtzvaT3Ouc+ZWYXS1rmnLvIzI6SdJ+kxZJmSPq9pPc45/rD/hzYP3n2++mSnnHOdZjZdZLe75y7yFvW5pyriiB0DFOefb9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      "text/plain": [
       "<Figure size 1440x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t,y = robotSim()\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.subplot(4,1,1)\n",
    "plt.plot(t,y[:,1])\n",
    "\n",
    "plt.subplot(4,1,2)\n",
    "plt.plot(t,y[:,3])\n",
    "\n",
    "plt.subplot(4,1,3)\n",
    "plt.plot(t,y[:,0])\n",
    "\n",
    "plt.subplot(4,1,4)\n",
    "plt.plot(t,y[:,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(15,5))\n",
    "plt.ylim([-.3,.3]); plt.xlim([-2,2])\n",
    "j=0\n",
    "for i in np.array([0,20,40,60,80,100]):\n",
    "    ax = plt.subplot(3,2,j+1)\n",
    "    th,phi,dth,dphi = y[i,0],y[i,1],y[i,2],y[i,3]\n",
    "    x = th*.02\n",
    "    plt.ylim([-.3,.3]); plt.xlim([-2,2])\n",
    "    plt.gca().set_aspect('equal', adjustable='box')\n",
    "    ax.plot(np.array([x,x+.1*2*np.sin(phi)]),\n",
    "            np.array([0,2*.1*np.cos(phi)]),\n",
    "            color=.5*np.array([1,1,1]),linewidth=12)\n",
    "    circle(x,0,.02)\n",
    "    ax.plot(np.array([-2,2]),\n",
    "           np.array([-.02,-.02]),\n",
    "           color=.3*np.array([1,1,1]))  \n",
    "    j+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib notebook\n",
    "\n",
    "fig = plt.figure(figsize=(10,10))\n",
    "plt.ylim([-.3,.3]); plt.xlim([-2,2])\n",
    "ax = plt.gca()\n",
    "plt.ion()\n",
    "fig.show()\n",
    "fig.canvas.draw()\n",
    "\n",
    "for i in range(len(t)):\n",
    "    th,phi,dth,dphi = y[i,0],y[i,1],y[i,2],y[i,3]\n",
    "    x = th*.02\n",
    "    ax.clear()\n",
    "    plt.ylim([-.3,.3]); plt.xlim([-2,2])\n",
    "    plt.gca().set_aspect('equal', adjustable='box')\n",
    "    ax.plot(np.array([x,x+.1*2*np.sin(phi)]),\n",
    "            np.array([0,2*.1*np.cos(phi)]),\n",
    "            color=.5*np.array([1,1,1]),linewidth=12)\n",
    "    circle(x,0,.02)\n",
    "    ax.plot(np.array([-2,2]),\n",
    "           np.array([-.02,-.02]),\n",
    "           color=.3*np.array([1,1,1]))\n",
    "    \n",
    "    fig.canvas.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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