CPG-AND-PERTURBATION-REJECTION.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1 Design gait and basic functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import matplotlib as mpl\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.ion()\n",
    "\n",
    "# for the symbolic manipulation of jacobian\n",
    "import sympy as sp\n",
    "# from sympy import symbols\n",
    "# from sympy import sin, cos, asin, acos, pi, atan2, sqrt\n",
    "from sympy.utilities.lambdify import lambdify\n",
    "# from sympy import Matrix\n",
    "\n",
    "from scipy.optimize import minimize\n",
    "from scipy.optimize import fsolve\n",
    "from scipy import interpolate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Motor constants\n",
    "K = 0.0285;                 # Nm / A\n",
    "peak_amp = 30;              # A\n",
    "peak_torque = K * peak_amp; # Nm\n",
    "m_motor = 0.2;              # kg\n",
    "m_assembly = 0.2;           # kg\n",
    "\n",
    "m_total = 2*m_motor + m_assembly; # kg\n",
    "\n",
    "gravity = 9.8;              # m/s^2\n",
    "\n",
    "weight = m_total * gravity  # N\n",
    "\n",
    "l1 = 0.09;                  # m \n",
    "l2 = 0.16;                  # m\n",
    "w = 0.07;                   # m\n",
    "\n",
    "T = 0.25;                   # s\n",
    "d = 0.5;\n",
    "N = 100;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# solve jacobian of constraint equation\n",
    "(thetaL_sym, \n",
    " thetaR_sym, \n",
    " link1_sym, \n",
    " link2_sym, \n",
    " width_sym) = sp.symbols(\"\"\"thetaL_sym \n",
    "                            thetaR_sym \n",
    "                            link1_sym \n",
    "                            link2_sym \n",
    "                            width_sym\"\"\", real = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def T(theta, x, y):\n",
    "    return sp.Matrix([[sp.cos(theta), -sp.sin(theta), x], \n",
    "                      [sp.sin(theta), sp.cos(theta), y],\n",
    "                      [0, 0, 1]])\n",
    "\n",
    "def sym_to_np(T):\n",
    "    return np.array(T).astype(np.float64)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1 FK Through transformation matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_r = width_sym/2 + link1_sym*sp.cos(thetaR_sym)\n",
    "x_l = -width_sym/2 + link1_sym*sp.cos(thetaL_sym)\n",
    "\n",
    "y_r = link1_sym*sp.sin(thetaR_sym)\n",
    "y_l = link1_sym*sp.sin(thetaL_sym)\n",
    "\n",
    "theta3_sym = sp.atan2(y_r - y_l, x_r - x_l)\n",
    "L = sp.sqrt((x_l - x_r)**2 + (y_l - y_r)**2)\n",
    "\n",
    "FK = T(thetaL_sym, -width_sym/2, 0)@T(-(thetaL_sym - theta3_sym), link1_sym, 0)@sp.Matrix([L/2, sp.sqrt(link2_sym**2 - (L/2)**2), 1])\n",
    "FK = FK[:2,:]\n",
    "FK.simplify()\n",
    "FK_fast = FK.subs([(link1_sym, l1), (link2_sym, l2), (width_sym, w)]).evalf()\n",
    "# lambdify the forward kinematics (makes it faster)\n",
    "FK_lambda = lambdify((thetaR_sym, thetaL_sym), FK_fast)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.2 IK Through Fsolve method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def IK_constraint_eqn(x, x_pt, y_pt, l1, l2, w):\n",
    "    theta_R = x[0]\n",
    "    theta_L = x[1]\n",
    "    \n",
    "    return (l1**2 - l2**2 + (x_pt - w/2)**2 + y_pt**2 - 2*l1 * (y_pt * np.sin(theta_R) + (x_pt - w/2)*np.cos(theta_R)),\n",
    "            l1**2 - l2**2 + (x_pt + w/2)**2 + y_pt**2 - 2*l1 * (y_pt * np.sin(theta_L) + (x_pt + w/2)*np.cos(theta_L)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.3 define a function to transport gait to angle versus time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def add_arrow(line, position=None, direction='right', size=15, color=None):\n",
    "    \"\"\"\n",
    "    add an arrow to a line.\n",
    "\n",
    "    line:       Line2D object\n",
    "    position:   x-position of the arrow. If None, mean of xdata is taken\n",
    "    direction:  'left' or 'right'\n",
    "    size:       size of the arrow in fontsize points\n",
    "    color:      if None, line color is taken.\n",
    "    \"\"\"\n",
    "    if color is None:\n",
    "        color = line.get_color()\n",
    "\n",
    "    xdata = line.get_xdata()\n",
    "    ydata = line.get_ydata()\n",
    "\n",
    "    if position is None:\n",
    "        position = xdata.mean()\n",
    "    # find closest index\n",
    "    start_ind = np.argmin(np.absolute(xdata - position))\n",
    "    if direction == 'right':\n",
    "        end_ind = start_ind + 1\n",
    "    else:\n",
    "        end_ind = start_ind - 1\n",
    "\n",
    "    line.axes.annotate('',\n",
    "        xytext=(xdata[start_ind], ydata[start_ind]),\n",
    "        xy=(xdata[end_ind], ydata[end_ind]),\n",
    "        arrowprops=dict(arrowstyle=\"->\", color=color),\n",
    "        size=size\n",
    "    )\n",
    "\n",
    "def gait2angle(x_on, y_on, x_off, y_off, x_sw, y_sw, T, d, N, leg_position):    \n",
    "    if leg_position == 1:\n",
    "        x_on = -x_on\n",
    "        x_off = -x_off\n",
    "        x_sw = -x_sw\n",
    "    \n",
    "    N_st = np.int64(N*d)  \n",
    "    N_sw = np.int64(N*(1-d))\n",
    "\n",
    "    # generate line of stance\n",
    "    x = np.array([x_on,x_off])\n",
    "    y = np.array([y_on,y_off])\n",
    "    z = np.polyfit(x, y, deg = 1)\n",
    "    poly_st = np.poly1d(z)\n",
    "    x_st = np.linspace(x_on, x_off, N_st+1)\n",
    "    \n",
    "    # generate poly of swing\n",
    "    x = np.array([x_off,x_sw,x_on])\n",
    "    y = np.array([y_off,y_sw,y_on])\n",
    "    z = np.polyfit(x, y, deg = 2)\n",
    "    poly_sw = np.poly1d(z)\n",
    "    x_sw = np.linspace(x_off, x_on, N_sw+1)\n",
    "\n",
    "    # plot gait\n",
    "    plt.figure()\n",
    "    st_line = plt.plot(x_st, poly_st(x_st),'b', label=\"Stance phase\")[0]\n",
    "    add_arrow(st_line)\n",
    "    sw_curve = plt.plot(x_sw, poly_sw(x_sw),'r', label=\"Swing phase\")[0]\n",
    "    add_arrow(sw_curve)\n",
    "    plt.plot(x_st[0], poly_st(x_st[0]), 's', label=\"ON position\")\n",
    "    plt.plot(x_st[-1], poly_st(x_st[-1]), 'o', label=\"OFF position\")\n",
    "    if leg_position == 1:\n",
    "        plt.plot(x_st[-1], poly_st(x_st[-1]), 'o', markersize=12, label=\"START position\")\n",
    "    else:\n",
    "        plt.plot(x_st[0], poly_st(x_st[0]), 'o', markersize=12, label=\"START position\")\n",
    "    plt.title('Gait trajectory')\n",
    "    plt.xlabel('x (m)')\n",
    "    plt.ylabel('y (m)')\n",
    "    plt.legend()\n",
    "    \n",
    "    all_pts  = []\n",
    "    \n",
    "    y_st = poly_st(x_st)\n",
    "    y_sw = poly_sw(x_sw)\n",
    "    \n",
    "    all_x = np.append(x_st, x_sw)\n",
    "    all_y = np.append(y_st, y_sw)\n",
    "    \n",
    "    for idx, x in enumerate(all_x):\n",
    "        all_pts.append((x, all_y[idx]))\n",
    "        \n",
    "    \n",
    "    print('gait origin is ', np.mean(all_x), np.mean(all_y))\n",
    "    \n",
    "    # stance gait to angle\n",
    "    theta_st = np.zeros(shape=(N_st+1,2))\n",
    "    i = 0\n",
    "    for j in x_st:\n",
    "        theta_st[i] = fsolve(lambda x: IK_constraint_eqn(x, j, poly_st(j), l1, l2,w), (0,np.pi))\n",
    "        i = i+1\n",
    "    \n",
    "    # swing gait to angle\n",
    "    theta_sw = np.zeros(shape=(N_sw+1,2))\n",
    "    i = 0\n",
    "    for j in x_sw:\n",
    "        theta_sw[i] = fsolve(lambda x: IK_constraint_eqn(x, j, poly_sw(j), l1, l2,w), (0,np.pi))\n",
    "        i = i+1\n",
    "    \n",
    "    # plot angle versus time\n",
    "    plt.figure()\n",
    "    if leg_position == 0:\n",
    "        theta_sw = np.delete(theta_sw, 0, 0)\n",
    "        theta = np.append(theta_st, theta_sw, axis = 0)\n",
    "    elif leg_position == 1:\n",
    "        theta_st = np.delete(theta_st, 0, 0)\n",
    "        theta = np.append(theta_sw, theta_st, axis = 0)\n",
    "         \n",
    "    t = np.linspace(0, T, N+1)\n",
    "    plt.plot(t, theta[:, 0],'r')\n",
    "    plt.plot(t, theta[:, 1],'b')\n",
    "    plt.title('Angle versus time')\n",
    "    plt.xlabel('t (s)')\n",
    "    plt.ylabel('θ (rad)')\n",
    "    plt.legend(['${θ_R}$','${θ_L}$'])\n",
    "        \n",
    "    return (theta, np.mean(all_x), np.mean(all_y), all_pts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.4 plot the gait(top) & angle versus time(bottom)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gait origin is  -5.442269728554689e-19 0.16713333333333336\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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aB388bwzv7Of0wQdWo+mf/7RppqmQqPPbqnL69OlkZmZSokQJLrzwQk4++eQiv5cnApc0MjPhk09scdLYsbBpE5QqZf3MDz1kV5XHHAORXf5cAjnvPHj5Zbj8crjiCnj99dTdA3nMmDFRf01PBC6hrVxpu18NG2ZdPllZNpB76aVW0KxNG1us5BLfZZfZTK2BA21g/tFHw44oeXgicAln/Xr78H/nHeszzs62Ad1//ct2wmrWzAd0k9WAAfDbb/DYY5bwb7wx7IiSgycClxB27bL+/tdft66f7duhdm37YLj4Yjj6aP/wTwUi8NRT8Mcf0K+fJYMLvZB9kXkicHFt4UIYMgRee83++CtVgl69bOVu8+b+4Z+KiheHN9+0MZ9u3Wwtx0knRf99VBVJwF+wfdnk0ROBizs7dti+vi++aF0/xYvb1MErrrB+/5Ilw47Qha1MGWsZnnACdOhgeyEfdVT0Xr906dJkZmZSoUKFhEoGqkpmZial93IqnCcCFzeWL7cP/xdftAVfNWrA/ffbTJGqVcOOzsWbChWsu7BlSzj7bFsYWLlydF67evXqZGRksGrVqui8YAyVLl2a6tWr79VzPBG40KWnwxNP2FzxrCz7o+7TB846y6d6uj2rWdPWFbRuba3Fr76yzW6KqmTJkv9f3iEVpOhMXBe27Gzr/mnd2vr6P/0Urr/eVvx++ql1BXkScIVx7LG2s9nMmbaXwa5dYUeUeDwRuJjavt0Gf+vXt6mey5bBoEH27xNP2Ewg5/bWeefBs8/aRcR11/21UKArWGBdQyJyOPA6UBnIBgar6pO5jjkFGAEsiXxruKreG1RMLjxbtsBLL8Ejj9hYQJMm8O670LGjFXlzrqh694YlS+x3rFYtW1fiCifIP8FdQH9VnS4iBwLTRGSsqs7LddwkVT0vwDhciDZtsiu1xx+HVavglFPg1VdtT98EmozhEsSDD9p+EbfeapMNolybLWkFlghU9Xfg98j9jSLyE1ANyJ0IXBLanQAefdRqAJ11lm3Y0qpV2JG5ZFasGAwdaquPu3e3BWf+O1ewmIwRiEga0ASYksfDLUVkloiMEZE89yESkV4iki4i6Yk4nSuVbNtmff61asFtt9lA8OTJNs3P/yBdLJQubRMR0tJsjcHChWFHFP8CTwQicgDwIXCjqm7I9fB0oIaqNgaeBj7O6zVUdbCqNlPVZpVSaWeKBLJzJwwebIO9/frZ7l3ffWebkR93XNjRuVRToQKMHm0thLPPtm5Jl79AE4GIlMSSwFuqOjz346q6QVU3Re6PBkqKSMUgY3LRpWoF4I4+Gq6+Go44wlYDjxtnC32cC8s//mGrj3/7zVoGW7eGHVH8CiwRiK3LHgL8pKpP5HNM5chxiEiLSDyZQcXkomvSJPuw79TJZv6MHGlL/U89NezInDMtW1pdosmTbcwgOzvsiOJTkC2CE4FuQBsRmRm5nSMivUWkd+SYTsAcEZkFPAV01n2pmORiasEC2ymqdWub/z9kiG343q6dzwRy8adjR5u0MGyYjVu5vwty1tA3wB4/FlT1GeCZoGJw0bV2Ldx3Hzz9tO38dd99Nh5QtmzYkTm3Z/36weLFlhBq1bI1B+5PvpTHFSgryxaD3XEHrFkDPXtaEohWgS/ngiYCTz5pawz69LGxrHPOCTuq+OElJtweTZpktVyuucYGhKdPt6TgScAlmhIlbDV748a20GzmzLAjih+eCFyeli+3fX9bt7YuofffhwkTbPN35xLVAQfAqFFQrpxVK83ICDui+OCJwP3Fzp1W/K1ePZsW+u9/w08/2XaAPhDskkHVqrbGYONGSwYbcq9uSkGeCNz/+/ZbaNoU+ve3lsDcuXDvvT4Y7JJPw4Y2i2juXLjoIi9d7YnAsWYNXHWVlYDYsMGW548aZQtynEtWZ54JL7wAn3/upat91lAKU4W33rKpdWvWwC23wF13wf77hx2Zc7Fx5ZXw88/w0EN24XPLLWFHFA5PBClq8WKbCfTFF3D88VYSolGjsKNyLvYeeMD2MfjXv6xQ3YUXhh1R7HnXUIrJyrLB4KOPtqJwTz8N33zjScClrt2lq084Abp1g++/Dzui2PNEkELmzLFf9v794bTTYN486xv1vYFdqitdGkaMgOrVrUDd4sVhRxRbnghSwM6dNvunaVP7BX/nHSsQd/jhYUfmXPyoWNH2PN61y6aVrl0bdkSx44kgyc2cCS1a2CBwp062JqBzZ18T4Fxe6tWzWXM//2yFFXfsCDui2PBEkKR27oR77rEdwv74w365337brnqcc/lr3RpeeQUmToRevVJjWqnPGkpCc+da7fXp061MxFNPwSGHhB2Vc4mja1dYtMgupurWhdtvDzuiYHmLIIlkZVmZ3aZNbZ+A4cNtUw5PAs7tvbvusgupgQPhvffCjiZY3iJIEkuWQI8eVi30ggvgxRfBt3d2bt+J2KZLv/xif1tHHJG82696iyDBqdoc6EaNYNYseO01KxbnScC5oitVCj766M9ppUuXhh1RMDwRJLDMTFsFefnl0KyZbRfZvbvPCHIumnZPK925E847D9avDzui6PNEkKB2l4QYORIeeQS+/BJq1Ag7KueS0+6y7PPn26Y2yVat1BNBgtmxw2qinHEGHHwwTJlihbKK+U/SuUC1aQPPP2/VSvv3Dzua6PLB4gSycCF06QLTptnm248/7nsFOBdLV15pizKfeAKOOsr+DpNBYNeRInK4iEwQkZ9EZK6I9M3jGBGRp0RkkYjMFpGmQcWT6N54A5o0sRIRw4fblYknAedi75FHrATFdddZl2wyCLJDYRfQX1WPAo4H+ohI/VzHnA3Uidx6Ac8HGE9C2rTJpq51726byM+ebdNDnXPhKF7cVukfdZSVbVmwIOyIii6wRKCqv6vq9Mj9jcBPQLVch3UAXlczGSgnIlWCiinRzJ5tH/5vvgl33w3jx9s0NudcuA46CD75BEqUgPbtE38mUUyGGEUkDWgCTMn1UDVgWY6vM/h7skBEeolIuoikr1q1Kqgw44YqDB4Mxx1nG2x/+aWtcvRy0c7Fj7Q0m0n0889WyDErK+yI9l3giUBEDgA+BG5U1Q25H87jKX8r8aSqg1W1mao2q5TkK6U2bbI6J1dfbcWvZs6EU04JOyrnXF5at4Znn4XPPoNbbw07mn0X6KwhESmJJYG3VHV4HodkADmr4lcHlgcZUzybO/fPPsf774cBA3xaqHPxrlcv+PFHm8XXuLHtcpZogpw1JMAQ4CdVfSKfw0YC3SOzh44H1qvq70HFFM/efNP2DVi71haLDRzoScC5RPHEE9Zy79XLpncnmiA/ak4EugFtRGRm5HaOiPQWkd2zb0cDi4FFwEvAtQHGE5e2b4drr7WriObNYcYMOPXUsKNyzu2NkiXh/ffh0ENtVt/KlWFHtHcC6xpS1W/Iewwg5zEK9Akqhni3bJnVCtq9Ovg//7FZCM65xFOpkhWoO/FE+7seN84SRCLwzoeQTJxoU0PnzYNhw2yRiicB5xJb06bw0kvw9deJNXjsiSDGVOG//4XTT4cKFeCHH6Bjx7Cjcs5FS9eutup40CDrLkoEnghiaOtWWyF80022CGXKFDjyyLCjcs5F2+OP2yY2PXtabaJ454kgRpYtg5NOgrfesqmhw4bZ6kTnXPLZbz9rDZQpYy3+TZvCjmjPPBHEwLff2sYxCxbY/gE+NTQJrVgBl11mJWKdw8rBvPuu7WFwzTXWLRyv/OMoYK+8YtNBDzrIuoLOOy/siFzUbd9ucwZfew3uuSfsaFwcadPGysO8+Sa8+mrY0eSvwEQgIqVFpJOIPCkiH4jI6yLyLxFpEIsAE1VWlm1e0bMnnHyyDQofdVTYUbmoU7Wi9N9/bwtB3n8ffk/JNZEuHwMHWkK47jqrHhCP9pgIRORu4FugJVYw7kXgfazE9EMiMlZEGgUdZKLZsMEGg594Aq6/HsaMgfLlw47KBeK//4WhQ+2y7+23bQ/D572auvtT8eI2NnjggXDRRbB5c9gR5UFV870B5xbw+KFAsz0dE+3bscceq/Hsl19UGzZULV5c9fnnw47GBWrkSNVixVQ7dlTNyrLvtWunWqmS6tat4cbm4s7Ysaoiqr17h/P+QLrm87m6xxaBqn5awOMrVTU9Wkkp0U2davWCfv3VWgHJso2dy8PkybaL+bHH2tjA7tH/vn1h1SobJXQuh9NPt+7iF16wvQziiegehrJF5BPyKAu9m6q2DyKoPWnWrJmmp8df7hkxwvYTPuww+PRTqJ97LzaXPBYsgBNOgHLl4LvvrMDMbqrQqJEtE58+HWSPVVZcitm+3fYZWb7cKpYedljs3ltEpqlqs7weK2iw+DHgcWAJsBUrDPcSsAmYE80gE9nTT9ukkYYNbWaQJ4Ek9scf0LattQA+++yvSQDsg/+GG2wjia++CidGF7dKlbLxgo0b4Yor4mdKaUFdQ1+p6ldAE1W9WFU/idwuAVrFJsT4lZ1tTb0bbrDB4QkT/v654JLImjVwxhlWWnLUKKhdO+/junaFypVtADle/tJd3GjQwGqLjR5tdYniQWHXEVQSkVq7vxCRmkBybxVWgO3b4dJLbWbQddfZlnVly4YdlQvMxo3WEli40PoBW7TI/9gyZeCOO6zy2BdfxC5GlzCuuw5OOw1uvtmqDoStsIngJmCiiEwUkYnABODGwKKKcxs2wLnn2njgQw/BU0/5fsJJbetWaNfO+vw/+MD+ggty1VW2qe3tt1vT0bkcRKw1kJVl29KG3XAsVCJQ1c+AOkDfyK2eqn4eZGDxasUK24lo4kSbPn7rrT4emNS2boUOHezq/o03LCEUxn772Srj6dOtuehcLjVr2oXkmDHw+uvhxrLHWUN/OVDkaKA+UHr391Q15uGHOWvol1+sizgjw/62zz47lDBcrGzbZklg7FirD9Cjx949PyvLZhBlZcGcOb7hhPub7Gxo3dpWHM+bB1WqBPdeRZk1tPsF7gKejtxOBR4BYj51NEz/+x+0amXjhGPHehJIetu22VSwsWNhyJC9TwJg/YX3329Vx+K50IwLTbFiVo9s61abeBJaHIU8rhNwGvCHql4ONAZKBRZVnJkxw0pI79xpMwJPPDHsiFygtmyxaWCffWYduZdfvu+vdf75dgUxYIDNOnIul7p1rYv5nXesyzkMhU0EW1U1G9glIgcBK4FaBTwnKUyZYgWjypaFSZOgceOwI3KB2rjRmntffmlX8T17Fu31RODZZ2HdOptJ5FwebrvN5hb06WMXnLFW2ESQLiLlsMVk04DpwA+BRRUnvvnGxgQOOcTGCuvUCTsiF6h16+DMM20Dibfesv0FoqFRI/sLf+EFmDYtOq/pkkqZMvDkkzZO8PTTsX//AgeLRUSA6qq6LPJ1GnCQqs4u4HmvAOcBK1X16DwePwUYga1aBhiuqvcWFHCsBou/+grOOQeOOALGjYNq1QJ/SxemFSvgrLPsL/G992x8IJrWrYN69WyqyHff+c5E7m9Ubb+SSZNsWCnaA8dFGiyOVK37OMfXSwtKAhFDgbYFHDNJVY+J3ApMArHy9deWBNLSrM/Ok0CSW7rU+vEXLrQVw9FOAmB1iR55xPoahwyJ/uu7hCdirYLt2+HOO2P73oW9LJksIs335oVV9Wsg4UbHJk2yJFCjBowfH9uiUC4E8+ZZEli92pp+Z54Z3Ht162a7FN18M/z2W3Dv4xJW7dpWtfjVV622YawUNhGcCnwvIj+LyGwR+VFECtMqKEhLEZklImP2tOOZiPQSkXQRSV+1alUU3jZv339v44SHH+5JICV8+60lgawsawa2bBns+xUrBi+/bKOBvXuHv5zUxaWBA6F0afj3v2P3noVNBGcD/wDaAO2wvv9CLrHM13Sghqo2xtYnfJzfgao6WFWbqWqzSpWCKXE0a5a1BKpUsSRQuXIgb+PixYgRViC+YkXrs2/YMDbvW7s2PPCAdUG9/XZs3tMllEMPhZtusl1PZ8yIzXsWtB/BAaq6aY8vsIdjIgPLo/IaLM7j2KXYbmer93RcEIPF8+fb6r799rOZQjVqRPXlXbwZPBiuucY2lfn0Uwjo4iJfWVm2MGX+fOua8qany2X9eptXcIPHbpcAABkwSURBVPzxVqU0GooyWDxCRB4XkdYisn+OF6wlIj1F5HMKHhDOL6jKkRlJiEiLSCyZ+/JaRfHrr3ZhCDZ13JNAEsvOtiJwV19tM4TGj499EgBbcfzKK7Z5ba9e3kXk/ubgg21twZgxNm4ZtIL2IzgN+BK4GpgrIutFJBN4E6gM9FDVYXk9V0TeAb4H6olIRiRx9BaR3Rs4dgLmiMgs4Cmgsxa28FGUrF1rlYU3brRqwXXrxvLdXUxt326DtQ8+aB++I0fCAQeEF8+RR1rFsZEj46covYsr111n3UQPPxz8exW66Fy8iFbX0LZtNkFkyhT4/HOrKOqSVGamTQmdNAn+8x+71IqHkrHZ2dYy+e476wz2KxGXy913WxHbBQuKvqC1yEXnkk12tl0cTppk5V89CSSx+fOto/WHH2xwdsCA+EgCYLOIhg61KSJdu4ZTW8DFtd69oWTJ4Fcbp2QiuP12GDYMHn8cLr447GhcYCZMsCmh69fbeECXLmFH9HfVqsGLL8LUqba1pXM5VK4MnTvbuoL164N7n5RLBG++aX1uvXtDv35hR+MC8+KL1vdXpYr1/51wQtgR5a9TJytu99BDvrWl+5u+fWHTJptfEJTC1Boqi60jOAJQ4FfgM1XdElxY+SvKGMGUKbaws2VL+3srWTLKwbnw7dplk7CfecYWhrzzDhx0UNhRFWzLFtsHedUqmDkz2B1KXMJp1QqWL7cqKPu6Le4+jxGISCfga6AF0A84EJsuOkNEAijIEpzffrPxwqpVbdtZTwJJKDPTloY/84zt8jFyZGIkAbA65++/b1PYLr3U1ho4F9G3LyxZYusQg1BQ19A9wMmqeiuwWlXvU9VewInAQ8GEFIypU2HHDvjkE1tM6pLMnDl2Rf3119aGfuyxfb90Ckv9+rZ3wYQJcN99YUfj4sgFF1gRzFmzgnn9gjZRFSA7cj9nH1LCXa6cf75tMJMoF4huL3z0kU0DO/BAqx9+/PFhR7TvLrvMzuHee+082u7Tek2XZEqUsEXoZcoE8/oFtQjuBr4WkXuBQ0XkdhF5DvgWGBBMSMHxJJBksrKsQtc//wkNGkB6emInAbCprc89Z7WPLrnESmQ7R3BJAApeWfw+Vnl0NvAEsB0YDzRX1eHBheVcAdautV08/vMfuPJK6xJKlo0jypaFDz+0BS+dOtnqR+cCVFDXEJGCcnmWkXAuFDNmQMeOkJFh00R79Qo7ouirXdtWO3boYNtcvvxy/CyEc0kn5dYRuAQ3dKitCdixw1oByZgEdmvf3rq+XnnF9jt2LiCeCFxi2LbNqoZefrktBJk+PfHHAwrjnntsPcQNN8SmDKVLSZ4IXPz7+WdrBQweDLfeaqsBDz007Khio3hxeOstK07fqZN1hzkXZZ4IXHz7+GPbQGbJElsg9tBDNpculZQrZ/8PW7bYhPKtW8OOyCUZTwQuPu3YATfeaB98depYV1C7ou6OmsDq17eWwbRpNksqwcrHu/jmicDFnyVLrLjKk09a3/g331jXSKpr3x7uv9/KacditxKXMlKsje3i3gcfwFVX2f3hw61F4P40YAD8+KPVUm/QILVbSS5qvEXg4sOWLTYr6KKLbBvHGTM8CeRFBIYMgaZNbeXxjz+GHZFLAp4IXPh+/NEKxu2eFTRpkncF7UnZsjBihNVWatcOVq4MOyKX4DwRuPCoWsno5s1h9WrbPPqhh7xGeGFUq2azqFautJbT9u1hR+QSmCcCF46VK+1q9vrr4bTTYPZs21HMFV6zZvDaa/Dddzau4jOJ3D4KLBGIyCsislJE5uTzuIjIUyKySERmi0jToGJxcebTT6265rhxNjNo1KjUWSAWbRdeaCWr33jDCvA5tw+CbBEMxXYzy8/ZQJ3IrRfwfICxuHiweTNce61VDa1c2ebE33CDF1MrqjvugK5d7d/33w87GpeAAksEqvo1sGYPh3QAXlczGSgnIr5Ra7KaMgWaNLHiaf37ww8/2PRHV3QiVp30xBOhRw/7v3ZuL4Q5RlANWJbj64zI9/5GRHqJSLqIpK9atSomwbko2bED7rzTPqS2b4fx420byVKlwo4suZQqZTu1Va1qC898Qxu3F8JMBHn1B+Q52qWqg1W1mao2q1SpUsBhuaj58Uc47jjbf/fSS21A+JRTwo4qeVWqZOMt27db99v69WFH5BJEmIkgAzg8x9fVgeUhxeKiadcuePBBKxa3fLkVTHvtNTj44LAjS35HHWUrsufPt8V5O3eGHZFLAGEmgpFA98jsoeOB9ar6e4jxuGiYM8f2C7j9dttda+5c+9fFTps2tnPbF1/Y9FyfVuoKEFitIRF5BzgFqCgiGcBdQEkAVX0BGA2cAywCtgCXBxWLi4GdO+HRR20jlYMPttkrF14YdlSp64orYNEia5nVrg033xx2RC6OBZYIVLVLAY8r0Ceo93cxNH069OwJM2dad8Qzz1h/tQvX/ffbpj633GIlOzp2DDsiF6d8ZbHbd1u3WjXMFi3gjz+sb/q99zwJxItixWyP55YtbZ2BTyt1+fBE4PbN+PHQqJHVBureHebN82qh8ahMGStQV7WqlfRYsiTsiFwc8kTg9k5mpvU/n3aaDUJ++SW88gqULx92ZC4/lSpZWY9du+Ccc2Dt2rAjcnHGE4ErHFXrZqhXD15/HW67zdYJtGkTdmSuMI480hac/fyzjRXs2BF2RC6OeCJwBZs3D049FS6/3BLBjBk2G6VMmbAjc3vj5JOt9TZhglcrdX/hicDlb9Mm+Ne/oHFjWxU8eLBtGtOwYdiRuX3VtatN8X39dVvx7Ry+Z7HLi6qtA7j5ZsjIsKmhDz7os4GSxb//DYsXw113Qa1alhxcSvMWgfur2bOtG6hzZ/vg/+47q2zpSSB5iFjrrk0bG/ifODHsiFzIPBE4s3o19OljpaLnzLFy0VOn2hx0l3z22w8+/NBWHV9wAfz0U9gRuRB5Ikh1O3bAf/8LdepYfZprroEFC+Dqq6F48bCjc0EqVw5Gj7YS1uecAytWhB2RC4knglSlaiuBGzSAm26y1cGzZll5iEMOCTs6FytpafDJJ5YE2reHLVvCjsiFwBNBKpo8GVq3tvnk++1ni40++8x3DEtVzZvDO+9YV2DXrpCVFXZELsY8EaSS+fPtw79lS1i40LqCZs2ybgHfNzi1degAgwbZorNbbgk7GhdjPn00Ffz6K9x7r60MLlPG7t90ExxwQNiRuXjSt69NKx00yKqVXn992BG5GPFEkMz++MPm/7/wgn3dpw8MHAiHHhpuXC5+PfEE/PIL3Hgj1Khh4wYu6XnXUDJasQL69bOrumefteqgCxfCk096EnB7Vrw4vPWWbTPapQukp4cdkYsBTwTJZPly6N/fEsCTT8LFF8P//gcvvQRHHBF2dC5R7L+/zSQ69FA47zxYujTsiFzAPBEkg6VLrdunVi1LABdeaAlg6FBbMOTc3jrsMFtjsH27l65OAZ4IEtns2XDppfZh/9JL0KOHLQZ77TVbIOZcURx1FHz8se19/M9/WlJwSckTQaJRhS++gLZtrSroyJE2sLd4sU0HrVUr7AhdMjn5ZHj1VatH1LOnl65OUj5rKFFs2WKDeE8+CXPnQpUq8MADVhLCdwdzQbr0UptJNHCgrUS+//6wI3JRFmiLQETaish8EVkkIrfl8fhlIrJKRGZGblcGGU9CWrLEFvhUrw69ekGJEtb1s3Qp3H67JwEXGwMG2GY2Dzxg3ZAuqQTWIhCR4sCzwBlABjBVREaq6rxch76nqtcFFUdC2rXLZm28+KJ1AxUrZn20118PrVr5KmAXeyLw3HOwbJm1QqtVs0FklxSCbBG0ABap6mJV3QG8C3QI8P0S3/z5thfw4YfbB/+cOXDnnXb1//77cNJJngRceEqUsN/Dxo1tZpqvMUgaQSaCasCyHF9nRL6XW0cRmS0iw0Tk8LxeSER6iUi6iKSvWrUqiFjDk5kJzz8PJ5xgG4w/9phVAv34Y0sAd99t3ULOxYMDD7QihYceCueea5MUXMILMhHkdemae8rBJ0CaqjYCxgGv5fVCqjpYVZuparNKybBT1saN8PbbVuirShW49lrYsAEeftia3iNG2GMlfCzfxaHKlWHMGNi5E84+2zY1cgktyE+aDCDnFX51YHnOA1Q1M8eXLwEPBxhPuNatg1GjbA+AMWNg2zbrZ73+eujWzZrb3u3jEsWRR9rU5dNPh3bt4MsvoWzZsKNy+yjIRDAVqCMiNYHfgM7AJTkPEJEqqvp75Mv2QHLtl7dokTWjR42yedi7dkHVqnDllVb+4YQTbCDYuUTUqpXtY9Cpk/0+f/SRt2ITVGA/NVXdJSLXAZ8DxYFXVHWuiNwLpKvqSOAGEWkP7ALWAJcFFU9MbNhgH/hjx9psnwUL7PtHHmllnzt2tE1A/MPfJYsLLrBd7a69Fnr3tqml3rJNOIGmb1UdDYzO9b07c9wfAAwIMoZAZWbabl9ffWW3adNsd6eyZW1FZp8+VrTLV/u6ZHbNNfDbb7bGoHJlX3CWgLwdV1hbt9puXtOm2bS577+36Z4AJUvCccfZ1M/TTrMun1Klwo3XuVi67z4rf/7AA1awzje1SSieCHLbvNm6dBYssAqec+bAjz9aPf/sbDumUiX74O/Rw7Z9bNHCB8pcahOxadCrV8MNN0DFirafgUsIqZMItm2zev2ZmXZbvRp+/91uv/1mc/aXLoWVK/98joh16zRqZINhTZrYhh3Vq3s/qHO5lShhg8dt29pmSOXL230XHXPmQL161gMRZamTCD76CC655O/f339/m8mTlmZz99PSoG5du9WpY3v8OucKp3RpWwdz6qm2Ov7zz21FvCuauXNtllbXrjY4H2WiCVZWtlmzZpq+L0vbly61GT0VKvx5q1LFVkr61b1z0bVqFbRuba3wCROgadOwI0pcf/xhXdE7dtjklBo19ullRGSaqjbL87GUSQTOudjKyLCr2M2bbVZd/fphR5R4Nm2CU06x8cqvvy5SQt1TIvAJ7c65YFSvbmtqSpSw2XS719W4wtm50wbcZ8yAd98NtFXlicA5F5w6daz8RFYWtGkDP/8cdkSJISvLZiWOGmVjAuedF+jbeSJwzgWrfn0YN87W4rRpY+N1Ln/Z2XD11TYD68EHbcFewDwROOeC16iRdRNt2GCr7r18dd5UoW9fGDIE/v1vW6QaA54InHOx0bQpjB9vA6CtW9siTfenrCyr1/TMM9C/P9xzT8ze2hOBcy52mjSx6aTbt1vL4KfkKji8z3butEV4gwfb/tCPPhrTae2eCJxzsdWoka3pyc62xWZTp4YdUbi2brWtP99+28YE/vOfmK9t8kTgnIu9Bg3g22/hoINsFfK4cWFHFI6VK+38R460LqEYjQnk5onAOReOf/zDkkGtWrb/8XvvhR1RbP30Exx/PMyeDR9+aGXrQ+KJwDkXnipVbNVxixbQubN1iyRYtYN9Mnq0lavfvNm6yS64INRwPBE458JVvrx1DV1yCQwcCD17Wl2dZJSVBXfdZS2gtDSYMsWSYMhSp/qocy5+lSoFb75pK5HvucfKUXzwgbUYksXKlbZa+LPP7N/nn4+b6sbeInDOxQcRuPtuW1E7Y4atO5g0KeyoouPTT6FhQ1tH8fzz8OqrcZMEwBOBcy7edO4MP/xgJeJPPRUeecS6VBLRpk1w7bVWK+iww2yb29694670vScC51z8adDA1hdccAHceqvVKPrll7Cj2jsjR1qdpeeft5XCU6daqyAOBZoIRKStiMwXkUUi8rcJsiJSSkTeizw+RUTSgozHOZdADj4Y3n8fhg61rqJGjeDll//cOzxeLV0KHTvajocHHwzffQePPWbjIHEqsEQgIsWBZ4GzgfpAFxHJvTNFT2CtqtYGBgEPBxWPcy4BidjA6qxZcMwxcNVVttnNrFlhR/Z3a9fCLbfYvsKjR9sq4enToWXLsCMrUJAtghbAIlVdrKo7gHeBDrmO6QC8Frk/DDhNJM46z5xz4atZ0+bbDx1qxeqOPdYWYC1fHnZklgDuvx9q14bHH7dpsAsX2irhADaaD0KQiaAasCzH1xmR7+V5jKruAtYDFXK/kIj0EpF0EUlftWpVQOE65+La7tbB/PlWr3/wYFudfPPNNjUz1pYtsw/7GjWsZHTLltaF9eqrtjtbAgkyEeR1ZZ97yWBhjkFVB6tqM1VtVqlSpagE55xLUIccAs8+awnh4oth0CA4/HDo1s02dw9yZfLOnfDJJzYLKC3NZjSdc44lgFGjoHHj4N47QEEmggzg8BxfVwdyt+P+/xgRKQEcDKwJMCbnXLKoVcu6in76yVoII0bYVXnDhrZ6d+bM6CSFDRvg44+tTPShh0L79jBtmpWL/vln20/4mGOK/j4hEg0oe0Y+2BcApwG/AVOBS1R1bo5j+gANVbW3iHQG/qmqF+3pdZs1a6bp6emBxOycS2CbNtnq5HfftYVo2dlQtaolh5YtbS+EtDRrPeTVd68Kq1dbS2PBAksk33xjA9PZ2VYKo317mxHUtm3C9P/vJiLTVLVZno8FlQgib3wO8F+gOPCKqj4gIvcC6ao6UkRKA28ATbCWQGdV3eMedp4InHMFWrnS5vFPmADffw9Llvz5WLFi1r1UurRN6VSF9eth3bq/LlwrW9aqg7ZqZZvonHRSwn345xRaIgiCJwLn3F774w+YN88WpS1daoli+3bYts0GocuVs1ulSlC3rk0BrVEDSiRPObY9JYLkOUvnnMtP5cp2c3nyEhPOOZfiPBE451yK80TgnHMpzhOBc86lOE8EzjmX4jwROOdcivNE4JxzKc4TgXPOpbiEW1ksIquAfd2zriKwOorhJAI/59Tg55wainLONVQ1z/LNCZcIikJE0vNbYp2s/JxTg59zagjqnL1ryDnnUpwnAuecS3GplggGhx1ACPycU4Ofc2oI5JxTaozAOefc36Vai8A551wungiccy7FJU0iEJG2IjJfRBaJyG15PF5KRN6LPD5FRNJyPDYg8v35InJWLOMuin09ZxFJE5GtIjIzcnsh1rHvq0Kcc2sRmS4iu0SkU67HeojIwsitR+yiLpoinnNWjp/zyNhFve8Kcb79RGSeiMwWkS9FpEaOx5L1Z7yncy76z1hVE/6G7Yn8M1AL2A+YBdTPdcy1wAuR+52B9yL360eOLwXUjLxO8bDPKeBzTgPmhH0OAZ1zGtAIeB3olOP7hwCLI/+Wj9wvH/Y5BXnOkcc2hX0OAZzvqUDZyP1rcvxeJ/PPOM9zjtbPOFlaBC2ARaq6WFV3AO8CHXId0wF4LXJ/GHCaiEjk+++q6nZVXQIsirxevCvKOSeqAs9ZVZeq6mwgO9dzzwLGquoaVV0LjAXaxiLoIirKOSeiwpzvBFXdEvlyMlA9cj+Zf8b5nXNUJEsiqAYsy/F1RuR7eR6jqruA9UCFQj43HhXlnAFqisgMEflKRE4KOtgoKcrPKpl/zntSWkTSRWSyiJwf3dACsbfn2xMYs4/PjRdFOWeIws84WTavz+sqN/e82PyOKcxz41FRzvl34AhVzRSRY4GPRaSBqm6IdpBRVpSfVTL/nPfkCFVdLiK1gPEi8qOq/hyl2IJQ6PMVka5AM+DkvX1unCnKOUMUfsbJ0iLIAA7P8XV1YHl+x4hICeBgYE0hnxuP9vmcI91gmQCqOg3rn6wbeMRFV5SfVTL/nPOlqssj/y4GJgJNohlcAAp1viJyOjAQaK+q2/fmuXGoKOccnZ9x2AMlURpsKYENDNXkz8GWBrmO6cNfB07fj9xvwF8HixeTGIPFRTnnSrvPERug+g04JOxzisY55zh2KH8fLF6CDSKWj9xP9nMuD5SK3K8ILCTXIGS83Qr5e90Eu3ipk+v7Sfsz3sM5R+VnHPp/QhT/M88BFkT+swZGvncvlj0BSgMfYIPBPwC1cjx3YOR584Gzwz6XoM8Z6AjMjfzCTQfahX0uUTzn5tgV1mYgE5ib47lXRP4vFgGXh30uQZ8zcALwY+Tn/CPQM+xzidL5jgNWADMjt5Ep8DPO85yj9TP2EhPOOZfikmWMwDnn3D7yROCccynOE4FzzqU4TwTOOZfiPBE451yK80TgXCGISDkRuXYPj5eJlOsovodjxolI+WAidG7feSJwrnDKYdVc83MFMFxVs/ZwzBsFvIZzofBE4FzhPAT8I1Lz/dE8Hr8UGAEgIlVE5OvIsXNyFPUbCXSJUbzOFZovKHOuECKb+oxS1aPzeGw/4FdVrRz5uj9QWlUfiHQVlVXVjZHHFgLHa6TWk3PxIFmqjzoXporAuhxfTwVeEZGSwMeqOjPHYyuBqlgpCOfigncNOVd0W7G6TgCo6tdAa6yY3xsi0j3HsaUjxzsXNzwROFc4G4ED83pAbTes4iJSGiCyn+xKVX0JGAI0jXxfgMrA0lgE7FxheSJwrhAiffrfRgZ/8xos/gJoFbl/CjBTRGZglV6fjHz/WGCy2m5xzsUNHyx2LgpEpAnQT1W77eGYJ7HywV/GLjLnCuYtAueiQFVnABP2tKAMmONJwMUjbxE451yK8xaBc86lOE8EzjmX4jwROOdcivNE4JxzKc4TgXPOpbj/A36yih9uBdaCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta1, origin_x, origin_y = gait2angle(0.11,0.19,-0.11,0.19,0,0.12,0.25,0.5,100,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gait origin is  5.442269728554689e-19 0.16713333333333336\n"
     ]
    },
    {
     "data": {
      "image/png": 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raPyyBFESIiPdJWJKCvz0k9fRGGPCwcSJcPBgyHVtzc0SREm57TaIirIur8aYgmV3bb3wQmhy7ESbocMSREk5+WTX5fWtt9ylozHG5GXGDDcxUCnWXCoKSxAlacAA1+V1/HivIzHGhCpVePZZOPvskOzampsliJJ0zjlw2WWuy2tGhtfRGGNC0fz5rnvrgAEh2bU1t9COLhwNGOCamN5+2+tIjDGh6NlnITraNUmHOEsQJa1TJ0hIgOeec5eSxhiT7bff3Hipu+5yddxCnCWIkiYCDzwAq1bBF194HY0xJpSMHg2VK7sEEQYsQQTD9dfDaae5S0ljjAE3h/2kSW5O+1NP9TqagFiCCIZKlVz5ja++gmXLvI7GGBMKXn7ZdV65/36vIwmYJYhg6dvX1Vh57jmvIzHGeC0jA158ES65BGJjvY4mYEFNECJyiYj8KiJrRGSgn/UdRGSpiGSKyLW5lncSkbRcjwwR6R7MWEtcrVpuQqGpU12td2NM+TV1Kmzd6u5PhpGgJQgRiQDGAZcCTYBeInLsmPKNQDIwJfdCVZ2rqgmqmgB0BvYDXwYr1qC57z5XAvzFF72OxBjjFVXXkhAfD126eB1NoQTzCqI1sEZV16nqIeBd4MrcG6jqelVdDmTls59rgc9VdX/wQg2SRo3gqqtc2+O+fV5HY4zxwpdfws8/uzFSIl5HUyjBTBCnA5tyPU/3LSusnsBUfytEpK+IpIpI6rZQrX/0wAOwc6frvWCMKX+eew7q1IFevbyOpNCCmSD8pcpCjRwTkTpAHDDL33pVnaCqiaqaWLt27SKEWAratYM2bdwfic04Z0z5smyZu4K4+27XuzHMBDNBpAP1cj2vCxT2bu31wIeqerjEovLCww/DunXw3nteR2KMKU1PPQXVq0O/fl5HUiSRQdz3YqCxiDQEfsc1Fd1QyH30Ah4p6cBKXbdurpDfyJHQo0fYtUOWlsOHD5Oenk6GFToMG1FRUdStW5eKFSt6HUroWbcOpk1zzcwhOmNcQYKWIFQ1U0T645qHIoDXVXWFiAwHUlV1poi0Aj4EagFXiMgwVY0FEJEY3BXIvGDFWGoqVHBXEbfeCrNmub7Q5jjp6elUr16dmJgYxJJoyFNVduzYQXp6Og0bNvQ6nNAzapSbbfK++7yOpMhEy0hBucTERE1NTfU6jLwdOgRnnOEeKSleRxOSVq1axTnnnGPJIYyoKr/88gvnnnuu16GElq1boUEDN9/0hAleR5MvEVmiqon+1tlI6tJSqZK71Jw3DxYt8jqakGXJIbzY7ysPzz/vPhQ++KDXkRSLJYjSdPvtcNJJ7l6EMaZs+vNPN2nYtddC48ZeR1MsliBKU7VqrojfzJmwYoXX0Rg/RowYQWxsLPHx8SQkJPD9998DMGbMGPbvD62xmkOHDmXUqFFeh2GO9fLLsHs3DDyuulDYsQRR2vr3hxNOgKef9joSc4xFixbx6aefsnTpUpYvX86cOXOoV8/11A7FBGFCUEaGm/Oha1do0cLraIrNEkRpO/lkV+l1yhTYsMHraEwuW7ZsITo6msqVKwMQHR3NaaedxtixY9m8eTOdOnWiU6dOAPTr14/ExERiY2MZMmRIzj5iYmIYMmQILVq0IC4ujl9++QWAvXv3cuuttxIXF0d8fDzvv/8+AF9++SVt27alRYsWXHfddezdu/e4uJKSkrjvvvto164dTZs25YcffshZt3LlSpKSkmjUqBFjx47NWd69e3datmxJbGwsE3w3SY8cOUJycjJNmzYlLi6O0aNHA7B27VouueQSWrZsSfv27XNiNkUwebK7QV0Grh4A1wuhLDxatmypYWPjRtXISNV77vE6kpCycuXKnO/vvVe1Y8eSfdx7b/7H37NnjzZr1kwbN26s/fr105SUlJx1DRo00G3btuU837Fjh6qqZmZmaseOHXXZsmU5240dO1ZVVceNG6e33Xabqqo+9NBDem+uAP744w/dtm2btm/fXvfu3auqqiNHjtRhw4YdF1fHjh319ttvV1XVefPmaWxsrKqqDhkyRNu2basZGRm6bds2Pemkk/TQoUNHxbd//36NjY3V7du3a2pqql544YU5+925c6eqqnbu3Fl/++03VVX97rvvtFOnTvmfqGPk/r2Va4cPqzZqpNq6tWpWltfRBAw37MDv+6pdQXihXj03q9TEiW6WKRMSqlWrxpIlS5gwYQK1a9emR48eTMqjhtb06dNp0aIFzZs3Z8WKFaxcuTJn3dVXXw1Ay5YtWb9+PQBz5szhb3/7W842tWrV4rvvvmPlypWcf/75JCQkMHnyZDbkcVXZy1fHp0OHDuzevZtdu3YBcNlll1G5cmWio6M55ZRT2Lp1KwBjx46lWbNmtGnThk2bNrF69WoaNWrEunXruPvuu/niiy+oUaMGe/fuZeHChVx33XUkJCRwxx13sGXLlmKdx3Lr/ffd4LiBA8vMYNhgjqQ2+XnoIXc5OnYsDB/udTQhZ8wYb44bERFBUlISSUlJxMXFMXnyZJKTk4/a5t///jejRo1i8eLF1KpVi+Tk5KNGf2c3UUVERJDpq7+lqsd1CVVVLrroIqZO9VuL8ijHvjb7efaxch8vJSWFOXPmsGjRIk444QSSkpLIyMigVq1aLFu2jFmzZjFu3DimT5/OmDFjOPHEE0lLSwv8JJnjqcKTT7qKCVdeWfD2YcKuILxy7rnQvTu88ILr8WA89+uvv7J69eqc52lpaTRo0ACA6tWrs2fPHgB2795N1apVqVmzJlu3buXzzz8vcN9du3blxVzzguzcuZM2bdrw7bffsmbNGgD279/Pb7/95vf106ZNA+Cbb76hZs2a1KxZM89j/fnnn9SqVYsTTjiBX375he+++w6A7du3k5WVxTXXXMNjjz3G0qVLqVGjBg0bNmTGjBmAS1rLbJrcwvv8c1eY76GHXOWEMqLs/CTh6NFHYdculySM5/bu3Uvv3r1p0qQJ8fHxrFy5kqFDhwLQt29fLr30Ujp16kSzZs1o3rw5sbGx9OnTh/PPP7/AfT/66KPs3LmTpk2b0qxZM+bOnUvt2rWZNGkSvXr1Ij4+njZt2uR5g7hWrVq0a9eOO++8k9deey3fY11yySVkZmYSHx/PP//5T9q0aQPA77//TlJSEgkJCSQnJ/Pkk08C8M477/Daa6/RrFkzYmNj+fjjjwtx1gyqMGwYxMS4puMyxEpteO2KK2DhQli/3lV9LMdWrVplJRv8SEpKYtSoUSQm+q2G4Lly/3vLrq82YQL89a9eR1NoVmojlA0eDH/8AePHex2JMaawsq8e6teH3r29jqbEWYLwWqtWcOmlrvKjnz7wxqSkpITs1UO599VXrrbaI4+E5YRABbEEEQr++U/X3fXll72OxBgTqOyrh9NPd6X8yyBLEKGgbVu46CJ45hmwcg7GhId58+Cbb9y4h1zdjcsSSxChYsgQ+O9/4ZVXvI7EGBOIYcOgTh1XpbmMsgQRKs4/Hzp3dkX8DhzwOhpjTH7mz3cTfz38MERFeR1N0FiCCCWDB8N//gOvvup1JOVWXuW+CzJ48GDmzJkT1NiSkpIIy67cZdFjj8Gpp7rCm2WYldoIJR07usfIka4/dRn+ZBKKcpf7rly5Mtu3b+fQoUMBvXa4lUspPxYuhDlz4NlnoUoVr6MJqqBeQYjIJSLyq4isEZHj6t+KSAcRWSoimSJy7THr6ovIlyKySkRWikhMMGMNGYMHw+bN8PrrXkdS7uRV7vuHH37IKcD38ccfU6VKFQ4dOkRGRgaNGjUCIDk5mffeew/Iu+T3tm3buOiii2jRogV33HEHDRo0YLufYo3VqlXjgQceoEWLFnTp0oVt27blrJsxYwatW7fmrLPOYsGCBQCsX7+e9u3b06JFC1q0aMHChQtzfp4OHTqQkJBA06ZNc7YPpMS4ycfw4VC7Ntxxh9eRBF3QriBEJAIYB1wEpAOLRWSmqq7MtdlGIBn4u59dvAmMUNXZIlINyApWrCGlUyd3P+LJJ6FPn/J7FXHffVDSBeQSEvKtAti1a1eGDx/OWWedxYUXXkiPHj3o2LEjLVq04McffwRgwYIFNG3alMWLF5OZmcl5553nd1/R0dEsXbqU8ePHM2rUKF599VWGDRtG586deeSRR/jiiy9y5mk41r59+2jRogXPPvssw4cPZ9iwYTl1nDIzM/nhhx/417/+xbBhw5gzZw6nnHIKs2fPJioqitWrV9OrVy9SU1OZMmUKF198MYMGDeLIkSPs37+f7du38/jjjzNnzhyqVq3KU089xXPPPcfgwYOLeXLLie++cyOnn3oKqlb1OpqgC2YTU2tgjaquAxCRd4ErgZwEoarrfeuOevMXkSZApKrO9m1Xfj7iiLjeERde6Ibu33OP1xGVG9nlvhcsWMDcuXPp0aMHI0eOJDk5mTPPPJNVq1bxww8/MGDAAObPn8+RI0do3769333lLvn9wQcfAK7Q3ocffgi4ekm1atXy+9oKFSrQo0cPAG666aacfR273+xS4ocPH6Z///6kpaURERGRU/CvVatW9OnTh8OHD9O9e3cSEhKYN29eTolxgEOHDtG2bdvinLby5dFH3dXDXXd5HUmpCGaCOB3YlOt5OuD/49bxzgJ2icgHQENgDjBQVY/k3khE+gJ9AerXr1/sgENGly7uSmLECLjttnLxSeU4HtX7zqvcd/v27fn888+pWLEiF154IcnJyRw5ciTPOaHzKvldFLlLffvb7+jRozn11FNZtmwZWVlZRPmuOjt06MD8+fP57LPPuPnmm3nwwQepVatWwCXGzTG+/tqNnB492s0vXw4E8x6EvxkzAv0PiQTa45qeWgGNcE1RR+9MdYKqJqpqYu3atYsaZ2gaMcKNi8g1jaQJrvzKfXfo0IExY8bQtm1bateuzY4dO/jll1+IjY0NeP8XXHAB06dPB9x9gJ07d/rdLisrK+d+xpQpU7jgggvy3e+ff/5JnTp1qFChAm+99RZHjrjPURs2bOCUU07hr3/9K7fddhtLly4tVIlxk4sqDBoEdevCnXd6HU2pCeYVRDpQL9fzusDmQrz2x1zNUx8BbYD86xyXJW3bwuWXu3ER/frBiSd6HVGZt3fvXu6++2527dpFZGQkZ555Zs59gvPOO4+tW7fSoUMHAOLj4znllFOOm8gnP0OGDKFXr15MmzaNjh07UqdOHar7qeBbtWpVVqxYQcuWLalZs2bOXBB5ueuuu7jmmmuYMWMGnTp1oqrvijMlJYVnnnmGihUrUq1aNd58882jSowfPHgQgMcff5yzzjor4J+jXPrsM3f/YcKEcnVfsMBy3yKSiPs0fxpwAPgZmKOqfxTwukjgN6AL8DuwGLhBVVf42XYS8Kmqvud7HgEsBS5U1W0i8gZu3tRxeR0vbMt95yctDZo3d+2ejz3mdTRBV9bLRh88eJCIiAgiIyNZtGgR/fr18zuTW7Vq1cKqZ1FZ/72RlQUtWrhimqtWQcWKXkdUoopU7ltEkkVkKfAIUAX4FfgvcAEwW0Qmi0ieDf+qmgn0B2YBq4DpqrpCRIaLSDffMVqJSDpwHfCKiKzwvfYIrnnpKxH5CddcNbGwP3jYS0iA66937fG5ujqa8LRx40ZatWpFs2bNuOeee5g4sfz9SYel995zs8UNG1bmkkNB8ryCEJG/Aa+rqt+6DyKSAJysql8FMb6AlckrCIBffoHYWNft89lnvY4mqMr8J9Eyqkz/3jIzoWlTiIx0SSIiwuuISlyRriBUdVxeycG3Pi1UkkOZds45cMstMG4cpKd7HY0x5ctbb8Gvv7om3jKYHApSYC8mEWkoIs+JyAciMjP7URrBGZ8hQ1w76OOPex2JMeXHwYOuWSkxEbp39zoaTwTSi+kjXO+hTygvo5lDTUyMq800YQI89BD4yjsYY4Lo1VdhwwZXgr8QvdXKkkDGQWSo6lhVnauq87IfQY/MHG3QINcOOnSo15EYU/bt3++u2Nu3h65dvY7GM4EkiOdFZIiItBWRFtmPoEdmjnbaaXD33fD227B8udfRlFnp6elceeWVNG7cmDPOOIN77703p6JrSkoKIsInn3ySs/3ll19OSkpKUGLZvHkz117ralimpaXxry63CJQAACAASURBVH/9K2fdzJkzGTlyZFCOa4Dnn3el90eMKLdXDxBYE1MccDPQmf81ManvuSlNAwfCxIlukpLPP/c6Gk8lPj6b7XuPL8UdXa0SqY9eVKR9qipXX301/fr14+OPP+bIkSP07duXQYMG8cwzzwBQt25dRowYwRVXXFGs+ANx2mmn5YyoTktLIzU1lf/7v/8DoFu3bnTr1i3oMZRL27a5YplXXOGuIMqxQK4grgIaqWpHVe3ke1hy8MJJJ7lBc1984erRl2P+kkN+ywPx9ddfExUVxa2+CegjIiIYPXo0r7/+Ovt9c4U3a9aMmjVrMnv27Hz3lZSUxH333Ue7du1o2rQpP/zwAwB//PEH3bt3Jz4+njZt2rDcdzU4b948EhISSEhIoHnz5uzZs4f169fTtGlTDh06xODBg5k2bRoJCQlMmzaNSZMm0b9/f8CV1OjSpQvx8fF06dKFjRs3Aq4E+T333EO7du1o1KhRTrIxBXjsMdfE9NRTXkfiuUASxDLA6jyEiv793U3rBx90PZtMickub5FbjRo1qF+/fk7tIoBHH32UxwPoUbZv3z4WLlzI+PHj6dOnD+DKbTRv3pzly5fzxBNPcMsttwAwatQoxo0bR1paGgsWLKBKroloKlWqxPDhw+nRowdpaWk5lV6z9e/fn1tuuYXly5dz4403ck+uCsBbtmzhm2++4dNPP2XgwOOmZDHHWr0aXnrJzTNdVsd2FEIgCeJU4BcRmWXdXENA5crwxBOuDMfbb3sdTZmiqn5rKx27PLvEd/YEPHnp1asX4Ar97d69m127dvHNN99w8803A9C5c2d27NjBn3/+yfnnn8+AAQMYO3ZsTi2oQC1atIgbbrgBgJtvvplvvvkmZ1337t2pUKECTZo0YevWrQHvs9x65BH3P2adQYDAEsQQXDPTE8CzuR7GKz16QMuWrrnpQJ5jGU0hxcbGHjfn8+7du9m0aRNnnHHGUcsHDRrEiBEj8t3fsclGRPyW/BYRBg4cyKuvvsqBAwdo06ZNzix0ReGvPDgUvdx4ubFoEbz/vrs6/8tfvI4mJORXi0kAcndtPbabq/j7uGWCr0IFGDUKNm2ycuAlqEuXLuzfv58333wTgCNHjvDAAw+QnJzMCSeccNS2Xbt2ZefOnSxbtizP/WVXYf3mm2+oWbMmNWvWpEOHDrzzzjuA6xUVHR1NjRo1WLt2LXFxcTz88MMkJiYelyCqV6/Onj17/B6nXbt2vPvuuwC88847BZYHN36owt//7hLDAw94HU3IyO8KYq6I3H1sQT4RqSQinUVkMtA7uOGZPCUluXLgTzwBfuY1Luuiq1Uq1PJAiAgffvghM2bMoHHjxpx11llERUXxxBNP+N1+0KBBpOdT/qRWrVq0a9eOO++8k9dec5Xqhw4dSmpqKvHx8QwcOJDJkycDMGbMGJo2bUqzZs2oUqUKl1566VH76tSpEytXrsy5SZ3b2LFjeeONN4iPj+ett97i+eefL/I5KLc+/BAWLnTzTZeTyYACkV+xviigD3Ajbla3XUAUEAF8CYxT1RKeNLjoymyxvvysXAlxce7GdRl4UyhLRd+SkpIYNWoUiYl+a6CVKWH/ezt82BXErFjRFeQrxP2fsiC/Yn15nglVzQDGA+NFpCIQDRxQ1V3BCdMUWpMmrrfF+PFuEN2ZZ3odkTHhZ8IE13vp00/LXXIoSEBTjqrqYVXdYskhBA0d6npd/OMfXkdicklJSSkXVw9hb/duV5AvKQl8gxDN/wRzTmpTGurUcTfXZsyAb7/1OhpjwssTT7iR0888U65LauTFEkRZ8OCDbjL1e+4B34T1xpgCrFkDo0dD796upLc5TiDzQfQXkVqlEYwpoqpV3SegpUvh9de9jsaY8DBgAFSq5OouGb8CuYL4C7BYRKaLyCU29iFE9ejhCov94x+wy24VGZOvL76ATz6BwYNdM63xq8AEoaqPAo1xkwYlA6tF5AkROSPfFwK+hPKriKwRkeMKwYhIBxFZKiKZInLtMeuOiEia72GlPQoi4rq67tjhbrqZIimo3HfNmjVziupdeOGFgBvbcPrpp+csD1bNIyv/XUIOHXJzvDduDPfe63U0IS3QXkwK/Mf3yARqAe+JyNN5vUZEIoBxwKVAE6CXiDQ5ZrONuKQzxc8uDqhqgu9hdY0D0bw59O0LL7zgxkiUdcunw+imMPRE93X59GLtLrvcd/fu3Vm9ejW//fYbe/fuZdCgQTnbtG/fnrS0NNLS0piTq6Lu/fffn7M8WG/Ux5b/zp0gunXrZsX4AvXii26e6dGjXROTyVMg9yDuEZElwNPAt0CcqvYDWgLX5PPS1sAaVV2nqoeAd4Erc2+gqutVdTk2lWnJefxxqF7dfUIqy7V3lk+HT+6BPzcB6r5+ck+xkkQg5b6Lysp/h4itW90V9qWXwmWXeR1NyAvkCiIauFpVL1bVGap6GEBVs4DL83nd6cCmXM/TfcsCFSUiqSLynYj4nTFcRPr6tkndtm1bIXZdhkVHu3+A2bNhZhlumftqOBw+plDh4QNueREFUu57wYIFOW/cuYv1jR49Omf5rFmz/O7fyn+HgH/8wxW4HD3a60jCQoHDBlV1cD7rVuXzUn83swvzkba+qm4WkUbA1yLyk6quPeb4E4AJ4EptFGLfZVu/fm506P33w8UXQ1SU1xGVvD/zqIGU1/IABFLuu3379nz66afHbXP//ffz97//Pd/951X++/333wf8l/++8cYbufrqq6lbt27AP8eiRYv44IMPAFf++6GHHspZV67Lf6emwhtvuGJ8Z5/tdTRhIZjjINKBerme1wU2B/piVd3s+7oOSAGal2RwZVrFiu6G9b//Dc8953U0wVEzjzfMvJYHoDDlvovCyn97KCvLjRM65RT45z+9jiZsBDNBLAYai0hDEakE9AQCavMQkVoiUtn3fTRwPlAO7rqWoC5d4Kqr3KTrmzYVvH246TIYKlY5elnFKm55UXdZiHLfRWHlvz30zjtuvocnn4QaNbyOJmwELUGoaibQH5gFrAKmq+oKERkuIt0ARKSViKQD1wGviMgK38vPBVJFZBkwFxipqpYgCuu559yN6rLYlS/+erhiLNSsB4j7esVYt7yIClvuu7Cs/LdH/vjDNSudd54bNW0Cp6pl4tGyZUs1fjz5pCqozpzpdSQFWrlypdchBE3Hjh118eLFXocRFCH/e/vrX1UjIlTT0ryOJCQBqZrH+6rVYirrHnjA1brv3x/27fM6GmNK17ffwsSJrtt3s2ZeRxN2LEGUdRUrwiuvwMaNNhG7h6z8twcOH4Y774R69exvv4gsQZQH55/vJhYaPdrNmGVMefDcc/Dzz27ktE0jWiSWIMqLp56CWrXcJ6osG7huyrh//9sNGO3eHbpZpZ6isvn1youTToJnn3W9OCZOhDvu8DqiIlNVftr+E5NWTGJB+gIOHjlI5YjKdKjbgeTYZJpGN/U74M2UE6runltEBIwd63U0Yc0SRHly880waRIMHOg+WZ16qtcRFdrhrMMMWjCIuZvmcujIIbJ8ZbwyjmQwZ8McFvy+gKS6SYxoP4KKFSp6HK3xxPvvw7/+5ZqY6tUreHuTJ2tiKk9E4KWXYP9+N1lKmFHVnOSQcSQjJzlkyyKLA5kHmLtpLoMWDCrSSOERI0YQGxtLfHw8CQkJfP/991x11VUkJCRw5plnHlXue+HChQBs27aNihUr8sorrxy1r5iYGOLi4oiPj6djx45s2LCBHTt25Lz+L3/5y1FlwrPLipek3GXAP/roI1bmqvI7ePDgoyrSlgm7d7txPwkJcPfdXkcT9qQo/0ShKDExUY8tk2DyMGQIDB/uJk25+GKvo8mxatUqzj333DzXL9+2nNu/vJ0DmQfy3CZblcgqvNb1NeJqxwV8/EWLFjFgwABSUlKoXLky27dv59ChQ5x22mmA64k0atSo42oxjR8/nqlTpxIREUFKSkrO8piYGFJTU4mOjmbIkCFs3ryZiRMn5qwfOnQo1apVK7CGU0lJTk7m8ssvz5lToqQU9HsrVf37w/jx8N130Lq119GEBRFZoqp+u9jZFUR59MgjcO658Ne/uk9cYWLyiskczDwY0LYHMw8yeeXkQu1/y5YtREdH59Qrio6OzkkO+Zk6dSrPPvss6enp/P777363adu2bZ7r8lKtWjUeeOABWrRoQZcuXciuWJyWlkabNm2Ij4/nqquuYufOnYAbQd2kSRPi4+Pp2bMnQE4Z8IULFzJz5kwefPBBEhISWLt2LcnJyTklv7/66iuaN29OXFwcffr04eBBd55jYmIYMmQILVq0IC4urlg1oYJu3jwYN87VXLLkUCIsQZRHUVFu7urff4cHH/Q6moDNT59/XLNSXrLIYn76/ELtv2vXrmzatImzzjqLu+66i3nz5hX4mk2bNvGf//yH1q1bc/311x9X9iLbF198QffufqvW52nfvn20aNGCpUuX0rFjR4b5Zgq85ZZbeOqpp1i+fDlxcXE5y0eOHMmPP/7I8uXLefnll4/aV7t27ejWrRvPPPMMaWlpRxUfzMjIIDk5mWnTpvHTTz+RmZnJSy+9lLM+OjqapUuX0q9fP0aNGlWon6HU7NsHffrAGWe4+mOmRFiCKK/atHGjrCdMgDBphz54JLCrh2wZmRmF2r5atWosWbKECRMmULt2bXr06MGkSZPyfc27777L9de7+k89e/Zk6tSpR63v1KkTp5xyCnPmzOGGG24oVDwVKlTImevhpptu4ptvvuHPP/9k165ddOzYEYDevXszf75LhPHx8dx44428/fbbREYG3v/k119/pWHDhpx11lnH7RPg6quvBqBly5asX7++UD9DqfnHP2DdOvfBp2pVr6MpMyxBlGfDhrm6+LfdBnlUBg0llSMqF7xRLlGRhZ8HIyIigqSkJIYNG8aLL76YM1dDXqZOncqkSZOIiYmhW7duLFu2jNWrV+esnzt3Lhs2bCA2NpbBg4teaRaOLxd+rM8++4y//e1vLFmyhJYtW5KZmRnQfgu6D5nd5BYRERHwPkvV/PmuO+vdd0OHDl5HU6ZYgijPqlRxE6hs2gS5JpUJVR3qdqBCgH+yFahAh7qFe7P49ddfj3pzT0tLo0GDBvluv2/fPn7//XfWr1/P+vXreeSRR3JKbWerUqUKY8aM4c033+SPP/4IOJ6srKycewRTpkzhggsuoGbNmtSqVYsFCxYA8NZbb9GxY0eysrLYtGkTnTp14umnn2bXrl3s3bv3qP3lVSL8nHPOYf369Tmz5mXvMyzs3++alho2dKW8TYmyBFHetW3rury+/DJ89ZXX0eSrd2xvKkcGdhVRKaISvZsUrrTz3r176d27d86N3pUrVzI0nxo+U6dO5aqrrjpq2TXXXHNcMxNAnTp16NWrF+PGjQs4nqpVq+ZMg/r111/nXIFMnjyZBx98kPj4eNLS0hg8eDBHjhzhpptuIi4ujubNm3P//fdz4oknHrW/nj178swzz9C8eXPWrv3f5IxRUVG88cYbXHfddcTFxVGhQgXuvPPOgOP01KBBsHYtvPaaNS0FgXVzNW6O3oQEOHgQfvoJqlf3JIyCukuqKg/PfzhnHEReoiKi6FSvE091eCqsR1RXq1btuKuAUORZN9dvvnFNSv36ud5Lpkism6vJX5Uq7ubexo1ulHWIEhFGtB9Bp3qdqBJZ5bjmpgpUyEkOI9qPCOvkYAqQ3bTUoIGrM2aCwkptGOf8813N/NGj4ZproHNnryPyq2KFijzV4Sl+3v6zq8X0+wIyMjOIiow6qhZTWRAOVw+eefRRWL3aNYtapdagsQRh/ufxx10Nm1tugeXLXYG/UqaqBX7yFxHiasfxbNKzpRSVyYsnTdSzZ7sPMnfdFbIfZMoKa2Iy/3PCCTBlCvz3v9C3r6uKWYqioqLYsWOHN286ptBUlR07dhAVVfjuxEW2fburSHzuufDMM6V33HIqqFcQInIJ8DwQAbyqqiOPWd8BGAPEAz1V9b1j1tcAVgEfqmr/YMZqfFq0cFcSDz/susD26VNqh65bty7p6ek5JSVM6IuKiqJu3bqlczBVN/HVjh3uSveEE0rnuOVY0BKEiEQA44CLgHRgsYjMVNWVuTbbCCQDeVUrewwouN6BKVl//zvMmuVq2rRvD40bl8phK1asSMOGDUvlWCYMTZwIH3/s5jVJSPA6mnIhmE1MrYE1qrpOVQ8B7wJX5t5AVder6nI4vsCOiLQETgW+DGKMxp8KFWDyZKhUCW680c3ta4yXfvnFdaK46CL31ZSKYCaI04FNuZ6n+5YVSEQqAM8C+VaSE5G+IpIqIqnWLFHC6tZ1n9gWL7YJ3423Dh2CG25wTUqTJrkPMKZUBPNM++uKEujdx7uAf6nqpvw2UtUJqpqoqom1a9cudICmANdc4+o0PfmkK6VsjBcefRR+/NGNlg6g/LopOcG8SZ0O5J7vry6wOcDXtgXai8hdQDWgkojsVdXQHcVVVo0Z44qh3XwzLFsGtWp5HZEpT776yvVWuuMOuPLKgrc3JSqYVxCLgcYi0lBEKgE9gZmBvFBVb1TV+qoag7uB/aYlB49UqwbvvANbtrgeTdYF1ZSW//zHfTA5+2w3v7QpdUFLEKqaCfQHZuG6qk5X1RUiMlxEugGISCsRSQeuA14RkRXBiscUQ6tW7lPcRx9BqE4YY8qWzEzo2RN27YIZM6xLq0esWJ8JjCr06AEffABff211901wDRzoaiy9+aa7ijBBY8X6TPGJwKuvuikde/RwTU7GBMPMmS453HGHJQePWYIwgatRA95/H3bvdpf/oTi7mAlva9e6WmAtW7oOEsZTliBM4TRtCq+84no2DRrkdTSmLDlwAK691o1zeO89KM0aT8Yvq+ZqCu+mm+Dbb+Hpp92MdN27ex2RKQvuvhvS0uDTTyEmxutoDHYFYYpqzBhITHSVNX1zGRtTZK+/7gbCDRoEl13mdTTGxxKEKZrKlV33w8hIN4Dpzz+9jsiEq0WL3NwOXbrAsGFeR2NysQRhii4mxrUV//ab3bQ2RbNhg2uirFsXpk2DiAivIzK5WIIwxdOpE7z4InzxBTyYb21FY462Zw9ccQUcPOjuO5x8stcRmWPYTWpTfHfcAatWufsS557rZqMzJj9HjrjODitXusl/zjnH64iMH5YgTMkYNco1Nf3tb26CoU6dvI7IhLJ//MMNiHvxReja1etoTB6sicmUjMhImDoVzjrLlQlfvdrriEyomjTJdZG+6y73gcKELEsQpuTUrAmffOIGOl1+Oezc6XVEJtQsWOCaIC+80EZKhwFLEKZkNWrkCvr9+99w9dWQkeF1RCZU/PILXHUVNGwI06dDxYpeR2QKYAnClLwOHeCNNyAlxc1pfeSI1xEZr23a5O41REbCZ5/ZxFNhwhKECY4bb3RNCB98AP362URD5dmOHXDxxW4w5RdfwJlneh2RCZD1YjLBc++9sG0bjBgBtWu7r6Z82bvXlc5Ytw5mzYKEBK8jMoVgCcIE12OPuSTxxBMuSdx3n9cRmdJy6JCrzrp4sbuS7NjR64hMIVmCMMElAuPHu2aG+++H6Gg3QMqUbVlZkJzsrhpee83V6zJhxxKECb6ICHjnHdft9dZb3Q1Kq9hZdqm65sWpU93McH36eB2RKSK7SW1KR+XK8NFHrg36mmtceQVT9qjCgAFuhPTf/w4PPeR1RKYYgpogROQSEflVRNaIyEA/6zuIyFIRyRSRa3MtbyAiS0QkTURWiMidwYzTlJLq1V2TQ9Omrj/8p596HZEpSdlXDmPGuHtNTz/tdUSmmIKWIEQkAhgHXAo0AXqJSJNjNtsIJANTjlm+BWinqgnAecBAETktWLGaUnTSSTB7NjRr5gbSffyx1xGZkpCVBf37wwsvwAMPwHPPuftPJqwF8wqiNbBGVdep6iHgXeCoO1Wqul5VlwNZxyw/pKoHfU8rBzlOU9pq1YIvv4QWLVwvlw8+8DoiUxxZWa6u0vjxrknpmWcsOZQRwXzjPR3YlOt5um9ZQESknogs9+3jKVXd7GebviKSKiKp27ZtK3bAphSdeKJLEq1awfXXu9npTPjJynLl3l95xVVoHTnSkkMZEswE4e+vJODhtKq6SVXjgTOB3iJyqp9tJqhqoqom1q5duxihGk/UqOHuSbRpA716uV4vJnwcOQK33w6vvgr//Cc8/rglhzImmAkiHaiX63ld4LirgIL4rhxWAO1LKC4TSqpXd+UXzj//f+U5TOjbv9/dQ3rjDRg6FIYPt+RQBgUzQSwGGotIQxGpBPQEZgbyQhGpKyJVfN/XAs4Hfg1apMZb1aq5JNG9uxtMN2CAa7owoWnbNujc2ZV2f/FFGDLE64hMkAQtQahqJtAfmAWsAqar6goRGS4i3QBEpJWIpAPXAa+IyArfy88FvheRZcA8YJSq/hSsWE0IqFLF3Ye4+24YPRp69rRS4aFozRpo1w6WLXOdC2zCnzJNtIxU2UxMTNTU1FSvwzDFpQrPPgsPPgjt27vBdSed5HVUBuCHH9xEUFlZ7uqhbVuvIzIlQESWqGqiv3XWfdSEFhE3AnfqVPj+e7jgAtiwweuozCefQFKSaw5cuNCSQzlhCcKEpp49XQ+nzZuhdWuYN8/riMonVTciunt3iI2FRYvcvOOmXLAEYUJXUpL7tHriidCli2t6KiNNomFh925XN+vhh93XuXPh1ON6m5syzBKECW1Nmrj5BLp1c01P118Pe/Z4HVXZt2KFG8Q4c6YrmzFtmmteMuWKJQgT+mrUgPffd00dH3zgmpxWrfI6qrJr6lR3jnfvhq+/dl2PbYxDuWQJwoQHEdezac4cN/lQ69YwfbrXUZUthw65aqw33ODqZC1dCh06eB2V8ZAlCBNeOnVyb1xNm0KPHnDzzW4iIlM8aWmQmAhjx7pS3V9/DXXqeB2V8ZglCBN+6tZ1vZoGD3bNIU2bwuefex1VeDp82JXJaNXKjZCeOdMNVKxY0evITAiwBGHCU6VKMGyYGytRqxb83/+5wnG7d3sdWfhYscKNZxgyBK67Dn7+Ga64wuuoTAixBGHCW8uWsGQJDBzoCsfFxbn7FCZvmZnuhn+LFm4Q4nvvwZQpcPLJXkdmQowlCBP+KleGJ5+Eb791NZ0uush1h12/3uvIQs+cOdC8uRvbcMUV7irimmu8jsqEKEsQpuxo0wZ+/NE1PX36KZxzDgwaZOMmAFavdmNJLroI9u1z3YZnzIBTTvE6MhPCLEGYsqVKFXfz+rffXLv6E0+40hBvvFE+S4jv2uXmiI6NhZQUN+PbypVuLgcb22AKYAnClE1168Jbb8F330FMDPTp43rqfPRR+UgUu3fDqFHQuLHrldS7t0uaDz8MUVFeR2fChCUIU7add56r5/TOO268xFVXuU/Tkya5gWFlzX//65rVGjRwAwsTEtxN/IkT4S9/8To6E2YsQZiyT8SNDv7tNzduonJluPVWOOMM9+l6716vIyy+devc5D0NGrgb9l26uPkbZs92N6WNKQJLEKb8iIx0ZcR//NENrDvzTDe9af367s31u+/Cq1psRobronrlla4paeJEuOkm+OUXt7xVK68jNGHOZpQz5dt338Hzz7t7ExkZ7o32ppvco1Ejr6M7XlaW68771luuF9KuXa4kxi23uOlaTz/d6whNmMlvRjlLEMYA/Pmn6/r51luutw/A+efDZZdB585uQF5kZPGOoQrffOPexAuTfPbsgQUL4KuvXDXb9evhhBNcT6Sbb3bNSRERxYvNlFueJQgRuQR4HogAXlXVkces7wCMAeKBnqr6nm95AvASUAM4AoxQ1Wn5HcsShCkxGze6m9rvvgvLl7tlNWpAx47uzbhzZzj33MATxsGDbl9jxsCBA/D669CuXd7b79/vSoh8/bVLCj/8AEeOuPIiSUnu6uaqq2x+BlMiPEkQIhIB/AZcBKQDi4Feqroy1zYxuCTwd2BmrgRxFqCqulpETgOWAOeq6q68jmcJwgTF1q1uJrXsN+t169zySpVcc9Q55/zvcfbZbsa16tXdY8cOePlleOklaNbMVUm9+GJXIG/3bndlsHGju2eQ+5E9B3eFCq7Capcu7tGunRvnYUwJ8ipBtAWGqurFvuePAKjqk362nQR8mp0g/KxfBlyrqqvzOp4lCFMq1q93lWRXrvzfG/rate4Tvj+VKrmkERHxv6Rw+PDx251wwtHJplkzd8VSs2ZQfxxj8ksQxWxUzdfpwKZcz9OB8wq7ExFpDVQC1vpZ1xfoC1C/fv2iRWlMYcTEuEduhw65JPHrr+6qYc8el0A+/dR9X78+NGzo3uyzry5q1HBf69RxzVWnn+6uGIwJIcFMEP7G8RfqckVE6gBvAb1V9bjhr6o6AZgA7gqiKEEaU2yVKrk3+XPPPX5d9pSdGza4uZ0T/X5QMyYkBfMjSzpQL9fzusDmQF8sIjWAz4BHVfW7Eo7NmNLRubObAe+WW1z11N693U1rY8JAMBPEYqCxiDQUkUpAT2BmIC/0bf8h8KaqzghijMYEX0SEm8zot99c6QtLECZMBC1BqGom0B+YBawCpqvqChEZLiLdAESklYikA9cBr4jICt/Lrwc6AMkikuZ7JAQrVmNKRfXqrrmpRg2vIzEmIDZQzhhjyrH8ejFZtwljjDF+WYIwxhjjlyUIY4wxflmCMMYY41eZuUktItuADR4cOhrY7sFxQ5mdk+PZOTmenZPjeXFOGqhqbX8rykyC8IqIpObVA6C8snNyPDsnx7NzcrxQOyfWxGSMMcYvSxDGGGP8sgRRfBO8DiAE2Tk5np2T49k5OV5InRO7B2GMMcYvu4IwxhjjlyUIY4wxflmCKICInCQis0Vkte9rrTy2+0JEdonIp8csbygi3/teP81XyjzsFeK89PZts1pEeudaniIiv+aq1ntK6UVf84B2UwAABT1JREFUckTkEt/PsUZEBvpZX9n3e1/j+zuIybXuEd/yX0Xk4tKMO9iKel5EJEZEDuT6u3i5tGMPlgDOSQcRWSoimSJy7THr/P4fBZ2q2iOfB/A0MND3/UDgqTy26wJcgZtbO/fy6UBP3/cvA/28/plK67wAJwHrfF9r+b6v5VuXAiR6/XMU8xxE4KbCbYSbFncZ0OSYbe4CXvZ93xOY5vu+iW/7ykBD334ivP6ZQuC8xAA/e/0zeHROYoB44E3g2lzL8/w/CvbDriAKdiUw2ff9ZKC7v41U9StgT+5lIiJAZ+C9gl4fhgI5LxcDs1X1D1XdCcwGLiml+EpDa2CNqq5T1UPAu7jzklvu8/Qe0MX3d3El8K6qHlTVfwNrfPsrC4pzXsqqAs+Jqq5X1eXAsdMre/Z/ZAmiYKeq6hYA39fCNIWcDOxSN3kSuGlYTy/h+LwSyHk5HdiU6/mxP/8bvmaEf4bpm0NBP99R2/j+Dv7E/V0E8tpwVZzzAtBQRH4UkXki0j7YwZaS4vy+PftbiSyNg4Q6EZkD/MXPqkHF3bWfZWHTr7gEzkt+P/+Nqvq7iFQH3gduxl1ah5NAfr95bRPWfxsFKM552QLUV9UdItIS+EhEYlV1d0kHWcqK8/v27G/FEgSgqhfmtU5EtopIHVXdIiJ1gP8WYtfbgRNFJNL3KakusLmY4ZaaEjgv6UBSrud1cfceUNXffV/3iMgU3CV4uCWIdKBeruf+fr/Z26SLSCRQE/gjwNeGqyKfF3WN7gcBVHWJiKwFzgLCfbrI4vy+8/w/CjZrYirYTCC710Bv4ONAX+j7Y58LZPdIKNTrQ1wg52UW0FVEavl6OXUFZolIpIhEA4hIReBy4OdSiLmkLQYa+3qqVcLdbJ15zDa5z9O1wNe+v4uZQE9fb56GQGPgh1KKO9iKfF5EpLaIRACISCPceVlXSnEHUyDnJC9+/4+CFOfRvL67H+oPXLvoV8Bq39eTfMsTgVdzbbcA2AYcwGX8i33LG+H+8dcAM4DKXv9MpXxe+vh+9jXArb5lVYElwHJgBfA8YdqDB/g/4DdcD5VBvmXDgW6+76N8v/c1vr+DRrleO8j3ul+BS73+WULhvADX+P4mlgFLgSu8/llK8Zy08r137AN2ACtyvfa4/6PSeFipDWOMMX5ZE5Mxxhi/LEEYY4zxyxKEMcYYvyxBGGOM8csShDHGGL8sQRgTJCJSxVcuIqIQr+kvIrcGMy5jAmXdXI0JEhH5GxCpqs8X4jUnAN+qavPgRWZMYOwKwphCEpFWIrJcRKJEpKqIrBCRpn42vRHfCHMRSfJdTUwXkd9EZKSI3CgiP4jITyJyBoCq7gfWi0hZqexqwpjVYjKmkFR1sYjMBB4HqgBvq+pRpUJ85RQaqer6XIubAefiajGtw404by0i9wJ3A/f5tksF2lN2Sm+YMGUJwpiiGY6rr5MB3ONnfTT/39794kQMRHEc/75gEGA4BMEiUGDgHuwh8OvhCng4xIaEAyAQ3AKFIySbfYhWlOYlpGUnBPL9qHY6k477dfrnFd5GbU/Zl0jvi9Ct+vYX4HzQ7xU42upspRm8xSTNcwDsAft0dYXG3ov2j8H2ZrC/4evF2m4/XvpVBoQ0zy2wBO6Am/HB7P78tRMRVXh855C/Wd1W/4wBIU0UEQtgnZn3wDVwEhEXRdcVcDbjFKfAww+mKG2Fr7lKjUTEMXCVmZctx0ituIKQGsnMZ+BxyodydA+3l42mJE3iCkKSVHIFIUkqGRCSpJIBIUkqGRCSpJIBIUkqfQKYuaKT4zDm3gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta2, origin_x, origin_y = gait2angle(0.11,0.19,-0.11,0.19,0,0.12,0.25,0.5,100,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gait design and selection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Left leg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gait origin is  -0.017565095537107597 0.13955161251327014\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_on = 0.0271340208767868\n",
    "y_on = 0.150504090025698\n",
    "x_off = -0.0622642119510020\n",
    "y_off = 0.180845634937132\n",
    "\n",
    "x_sw = -0.0210965760128508\n",
    "y_sw = 0.0874034639992732\n",
    "\n",
    "LEFT_LEG = 0\n",
    "RIGHT_LEG = 1\n",
    "\n",
    "T            = 0.25        # seconds\n",
    "dutyfactor   = 0.5         # duty factor (higher means more )\n",
    "N            = 100         # no. of trajectory points\n",
    "leg_position = LEFT_LEG    # which leg?\n",
    "\n",
    "theta1, origin_x, origin_y = gait2angle(x_on, y_on, x_off, y_off, x_sw, y_sw, \\\n",
    "                    T, dutyfactor, N, leg_position)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gait origin is  0.017565095537107597 0.13955161251327014\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "leg_position = RIGHT_LEG    # which leg?\n",
    "\n",
    "theta2, origin_x, origin_y = gait2angle(x_on, y_on, x_off, y_off, x_sw, y_sw, \\\n",
    "                    T, dutyfactor, N, leg_position)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2 Precompute and interpolate the transform funtions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1 define trajectory parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gait origin is  -0.0125650955371076 0.1454251378418012\n",
      "gait origin is  0.0125650955371076 0.1454251378418012\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# y_shift = 0.02\n",
    "# x_pos = 0.07\n",
    "# x_on = 0.03\n",
    "# y_on = 0.2-y_shift\n",
    "# x_off = -0.07\n",
    "# y_off = 0.2-y_shift\n",
    "# x_sw = 0\n",
    "# y_sw = 0.08\n",
    "\n",
    "# y_origin = (y_off + y_sw)/2\n",
    "# x_origin = (x_on + x_off)/2\n",
    "\n",
    "trajectories = [\n",
    "    {'x_on': 0.0271340208767868,\n",
    "     'y_on': 0.150504090025698,\n",
    "     'x_off': -0.0622642119510020,\n",
    "     'y_off': 0.180845634937132,\n",
    "     'x_sw': -0.0210965760128508,\n",
    "     'y_sw': 0.0874034639992732,\n",
    "    },\n",
    "    {\n",
    "     'x_on': 0.0371340208767868,\n",
    "     'y_on': 0.150504090025698,\n",
    "     'x_off': -0.0622642119510020,\n",
    "     'y_off': 0.170845634937132,\n",
    "     'x_sw': -0.0210965760128508,\n",
    "     'y_sw': 0.0874034639992732,\n",
    "    },\n",
    "    {\n",
    "     'x_on': 0.0371340208767868,\n",
    "     'y_on': 0.160504090025698,\n",
    "     'x_off': -0.0622642119510020,\n",
    "     'y_off': 0.180845634937132,\n",
    "     'x_sw': -0.0210965760128508,\n",
    "     'y_sw': 0.0974034639992732,\n",
    "    }]\n",
    "\n",
    "trajectory = \"3\"\n",
    "traj = trajectories[int(trajectory)-1]\n",
    "# load trajectory parameters (on, off and swing points)\n",
    "x_on = traj['x_on']\n",
    "y_on = traj['y_on']\n",
    "x_off = traj['x_off']\n",
    "y_off = traj['y_off']\n",
    "x_sw = traj['x_sw']\n",
    "y_sw = traj['y_sw']\n",
    "\n",
    "LEFT_LEG = 0\n",
    "RIGHT_LEG = 1\n",
    "\n",
    "\n",
    "T          = 0.25 # seconds\n",
    "dutyfactor = 0.5 # dutyfactor\n",
    "N          = 100 # number of trajectory points\n",
    "\n",
    "# calculate the gait/trajectory's origin (using left leg always!)\n",
    "_, origin_x, origin_y, allpts = gait2angle(x_on, y_on, x_off, y_off, x_sw, y_sw, \\\n",
    "                    T, dutyfactor, N, LEFT_LEG)\n",
    "\n",
    "_, a, b, allpts_R = gait2angle(x_on, y_on, x_off, y_off, x_sw, y_sw, \\\n",
    "                    T, dutyfactor, N, RIGHT_LEG)\n",
    "\n",
    "x_origin = origin_x\n",
    "y_origin = origin_y\n",
    "\n",
    "psi_left = sp.atan2((y_off-y_origin),(x_off-x_origin))\n",
    "psi_right = sp.atan2((y_on-y_origin),(x_on-x_origin))\n",
    "\n",
    "x = np.array([x_on-x_origin,x_off-x_origin])\n",
    "y = np.array([y_on-y_origin,y_off-y_origin])\n",
    "z_st = np.polyfit(x, y, deg = 1)\n",
    "poly_st = np.poly1d(z_st)\n",
    "y_st = z_st[1]\n",
    "\n",
    "x = np.array([x_off-x_origin,x_sw-x_origin,x_on-x_origin])\n",
    "y = np.array([y_off-y_origin,y_sw-y_origin,y_on-y_origin])\n",
    "z_sw = np.polyfit(x, y, deg = 2)\n",
    "poly_sw = np.poly1d(z_sw)\n",
    "# y_sw = z_sw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 define ψ to motor angle function & get current ψ function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ψ to motor angle function for left odrive\n",
    "def psi2angleL(psi,x_on=x_on,y_on=y_on,x_off=x_off,y_off=y_off,x_sw=x_sw,y_sw=y_sw,x_origin=x_origin,y_origin=y_origin):\n",
    "\n",
    "    #whether psi matches the swing or stance\n",
    "    if psi_right<psi<psi_left:\n",
    "        #calculate the x,y position related to psi\n",
    "        if psi == sp.pi/2 or psi == np.pi/2:\n",
    "            cal_x = 0\n",
    "        else:\n",
    "            x = sp.symbols('x')\n",
    "            cal_x = y_st/sp.tan(psi)\n",
    "        cal_y = y_st\n",
    "    else:\n",
    "        x = sp.symbols('x')\n",
    "        cal_x = sp.solve(sp.tan(psi) - poly_sw(x)/x,x)\n",
    "        if psi == sp.pi/2*3 or psi == np.pi/2*3:\n",
    "            cal_x = 0 \n",
    "        elif sp.pi/2<psi<sp.pi/2*3:\n",
    "            if cal_x[0]<0:\n",
    "                cal_x = cal_x[0]\n",
    "            else:\n",
    "                cal_x = cal_x[1]\n",
    "        elif psi>sp.pi/2*3 or psi<sp.pi/2:\n",
    "            if cal_x[0]>=0:\n",
    "                cal_x = cal_x[0]\n",
    "            else:\n",
    "                cal_x = cal_x[1]\n",
    "        cal_y = poly_sw(cal_x)\n",
    "    \n",
    "    cal_x = cal_x + x_origin\n",
    "    cal_y = cal_y + y_origin\n",
    "        \n",
    "    theta_motor = fsolve(lambda x: IK_constraint_eqn(x, cal_x, cal_y, l1, l2,w), (0,np.pi))    \n",
    "    \n",
    "    return(theta_motor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ψ to motor angle function for right odrive\n",
    "def psi2angleR(psi,x_on=x_on,y_on=y_on,x_off=x_off,y_off=y_off,x_sw=x_sw,y_sw=y_sw,x_origin=x_origin,y_origin=y_origin):\n",
    "\n",
    "    #whether psi matches the swing or stance\n",
    "    if psi_right<psi<psi_left:\n",
    "        #calculate the x,y position related to psi\n",
    "        if psi == sp.pi/2 or psi == np.pi/2:\n",
    "            cal_x = 0\n",
    "        else:\n",
    "            x = sp.symbols('x')\n",
    "            cal_x = sp.solve(sp.tan(psi) - poly_st(x)/x,x)[0]\n",
    "        cal_y = poly_st(cal_x)\n",
    "    else:\n",
    "        x = sp.symbols('x')\n",
    "        cal_x = sp.solve(sp.tan(psi) - poly_sw(x)/x,x)\n",
    "        if psi == sp.pi/2*3 or psi == np.pi/2*3:\n",
    "            cal_x = 0 \n",
    "        elif sp.pi/2<psi<sp.pi/2*3:\n",
    "            if cal_x[0]<0:\n",
    "                cal_x = cal_x[0]\n",
    "            else:\n",
    "                cal_x = cal_x[1]\n",
    "        elif psi>sp.pi/2*3 or psi<sp.pi/2:\n",
    "            if cal_x[0]>=0:\n",
    "                cal_x = cal_x[0]\n",
    "            else:\n",
    "                cal_x = cal_x[1]\n",
    "        else:\n",
    "            cal_x = 0 \n",
    "        cal_y = poly_sw(cal_x)\n",
    "    \n",
    "    cal_x = -(cal_x + x_origin)\n",
    "    cal_y = cal_y + y_origin\n",
    "        \n",
    "    theta_motor = fsolve(lambda x: IK_constraint_eqn(x, cal_x, cal_y, l1, l2,w), (0,np.pi))    \n",
    "    \n",
    "    return(theta_motor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3 precompute the function (input is motor_θ and output are x and y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_int = 100\n",
    "thetaL_int, thetaR_int = np.mgrid[0:2*np.pi+2*np.pi/N_int:2*np.pi/N_int, -np.pi:np.pi+2*np.pi/N_int:2*np.pi/N_int]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [],
   "source": [
    "#%%time\n",
    "#generate points for the Right leg    \n",
    "x_L = np.zeros((N_int+1,N_int+1))\n",
    "y_L = np.zeros((N_int+1,N_int+1))\n",
    "a = 0\n",
    "\n",
    "for i in np.arange(0,2*np.pi+2*np.pi/N_int,2*np.pi/N_int):\n",
    "    b = 0\n",
    "    for j in np.arange(-np.pi,np.pi+2*np.pi/N_int,2*np.pi/N_int):\n",
    "        # [x,y] = FK_fast.subs([(thetaL_sym, i), (thetaR_sym, j)])\n",
    "        [x,y] = FK_lambda(j, i)\n",
    "        x = x-x_origin\n",
    "        y = y-y_origin\n",
    "        x_L[a,b] = x\n",
    "        y_L[a,b] = y\n",
    "        b = b+1\n",
    "    a = a+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.save('x_L_traj{}.npy'.format(trajectory), x_L)\n",
    "np.save('y_L_traj{}.npy'.format(trajectory), y_L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_L = np.load('x_L_traj{}.npy'.format(trajectory))\n",
    "y_L = np.load('y_L_traj{}.npy'.format(trajectory))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [],
   "source": [
    "#%%time\n",
    "tck_getxL = interpolate.bisplrep(thetaL_int, thetaR_int, x_L,s=0.01)\n",
    "tck_getyL = interpolate.bisplrep(thetaL_int, thetaR_int, y_L,s=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %%time\n",
    "# #generate points for the Right leg    \n",
    "x_R = np.zeros((N_int+1,N_int+1))\n",
    "y_R = np.zeros((N_int+1,N_int+1))\n",
    "a = 0\n",
    "for i in np.arange(0,2*np.pi+2*np.pi/N_int,2*np.pi/N_int):\n",
    "    b = 0\n",
    "    for j in np.arange(-np.pi,np.pi+2*np.pi/N_int,2*np.pi/N_int):\n",
    "        #[x,y] = FK_fast.subs([(thetaL_sym, i), (thetaR_sym, j)])\n",
    "        [x,y] = FK_lambda(j,i)\n",
    "        x = -(x-x_origin)\n",
    "        y = y-y_origin\n",
    "        x_R[a,b] = x\n",
    "        y_R[a,b] = y\n",
    "        b = b+1\n",
    "    a = a+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.save('x_R_traj{}.npy'.format(trajectory),x_R)\n",
    "np.save('y_R_traj{}.npy'.format(trajectory),y_R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_R = np.load('x_R_traj{}.npy'.format(trajectory))\n",
    "y_R = np.load('y_R_traj{}.npy'.format(trajectory))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [],
   "source": [
    "#%%time\n",
    "tck_getxR = interpolate.bisplrep(thetaL_int, thetaR_int, x_R,s=0.01)\n",
    "tck_getyR = interpolate.bisplrep(thetaL_int, thetaR_int, y_R,s=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [],
   "source": [
    "def xy2psi(x,y):\n",
    "    if x>0 and y>=0:\n",
    "        real_psi = sp.atan(y/x)\n",
    "    elif x>0 and y<0:\n",
    "        real_psi = sp.atan(y/x) + 2*sp.pi\n",
    "    elif x<0:\n",
    "        real_psi = sp.atan(y/x) + sp.pi\n",
    "    elif x==0 and y>0:\n",
    "        real_psi = sp.pi/2\n",
    "    else:\n",
    "        real_psi = sp.pi/2*3\n",
    "    return(real_psi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.4 precompute the function (input is ψ and output is motor_θ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_int = 50\n",
    "psi_int = np.arange(0,2*np.pi+np.pi/N_int*2,np.pi/N_int*2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %%time\n",
    "# # use interpolation to genetate funcition to match psi and motor thetas\n",
    "\n",
    "#generate points for the Left leg\n",
    "j = 0\n",
    "theta_intL = np.zeros((N_int+1,2))\n",
    "for i in psi_int:\n",
    "    theta_intL[j] = psi2angleL(i)\n",
    "    j = j+1\n",
    "    \n",
    "#generate points for the Right leg    \n",
    "j = 0\n",
    "theta_intR = np.zeros((N_int+1,2))\n",
    "for i in psi_int:\n",
    "    theta_intR[j] = psi2angleR(i)\n",
    "    j = j+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.save('theta_intL_traj{}.npy'.format(trajectory),theta_intL)\n",
    "np.save('theta_intR_traj{}.npy'.format(trajectory),theta_intR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_intL = np.load('theta_intL_traj{}.npy'.format(trajectory))\n",
    "theta_intR = np.load('theta_intR_traj{}.npy'.format(trajectory))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [],
   "source": [
    "#%%time\n",
    "tck_L0=interpolate.splrep(psi_int,theta_intL[:,0])\n",
    "tck_L1=interpolate.splrep(psi_int,theta_intL[:,1])\n",
    "tck_R0=interpolate.splrep(psi_int,theta_intR[:,0])\n",
    "tck_R1=interpolate.splrep(psi_int,theta_intR[:,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.5 define phase change function for CPG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [],
   "source": [
    "# consider right leg moves faster than left leg \n",
    "# psi from psi_right(o,pi/2) to psi_left(pi/2,pi) to psi_right(2*pi,5/2*pi)\n",
    "psi_st = np.float64(np.array([psi_right,psi_left]))\n",
    "delta_st = np.float64(np.array([psi_left-psi_right,sp.pi*2-(psi_left-psi_right)]))\n",
    "z = np.polyfit(psi_st, delta_st, deg = 1)\n",
    "poly_delta_st = np.poly1d(z)\n",
    "\n",
    "psi_sw = np.float64(np.array([psi_left,psi_right+sp.pi*2]))\n",
    "delta_sw = np.float64(np.array([sp.pi*2-(psi_left-psi_right),psi_left-psi_right]))\n",
    "z = np.polyfit(psi_sw, delta_sw, deg = 1)\n",
    "poly_delta_sw = np.poly1d(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3 Ready to use Odrive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "\n",
    "import odrive\n",
    "import odrive.utils\n",
    "import odrive.enums"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.1 Connect to ODrive"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Connect to odrv0, calibrate,  dump errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 606,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Connected!\n",
      "Odrive serial 35696338546763\n",
      "Motor 0 calibrated: False\n",
      "Motor 1 calibrated: False\n"
     ]
    }
   ],
   "source": [
    "odrv0 = odrive.find_any(serial_number = '20773394304B', timeout = 30)\n",
    "if odrv0 is not None:\n",
    "    print('Connected!')\n",
    "    print('Odrive serial {}'.format(odrv0.serial_number))\n",
    "    \n",
    "    m0 = odrv0.axis0.motor.is_calibrated\n",
    "    m1 = odrv0.axis1.motor.is_calibrated\n",
    "    \n",
    "    print('Motor 0 calibrated: {}'.format(m0))\n",
    "    print('Motor 1 calibrated: {}'.format(m1))    \n",
    "    \n",
    "else:\n",
    "    print('Not connected')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t Odrv 0_Motor 0 calibration result: True \r\n",
      " \t Odrv 0_Motor 1 calibration result: True\n",
      "odrv0 errors\n"
     ]
    }
   ],
   "source": [
    "print('\\t Odrv 0_Motor 0 calibration result: {} \\r\\n'.format(odrv0.axis0.motor.is_calibrated), \n",
    "      '\\t Odrv 0_Motor 1 calibration result: {}'.format(odrv0.axis1.motor.is_calibrated))\n",
    "\n",
    "print('odrv0 errors')\n",
    "# odrive.utils.dump_errors(odrv0, True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "curr_limit_all = 3 # amperes\n",
    "odrv0.axis0.motor.config.current_lim = curr_limit_all\n",
    "odrv0.axis1.motor.config.current_lim = curr_limit_all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 607,
   "metadata": {},
   "outputs": [],
   "source": [
    "odrv0.axis0.requested_state = odrive.enums.AXIS_STATE_FULL_CALIBRATION_SEQUENCE\n",
    "odrv0.axis1.requested_state = odrive.enums.AXIS_STATE_FULL_CALIBRATION_SEQUENCE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 469,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "odrv0 errors\n",
      "axis0\n",
      "  axis: \u001b[92;1mno error\u001b[0m\n",
      "  motor: \u001b[92;1mno error\u001b[0m\n",
      "  encoder: \u001b[92;1mno error\u001b[0m\n",
      "  controller: \u001b[92;1mno error\u001b[0m\n",
      "axis1\n",
      "  axis: \u001b[92;1mno error\u001b[0m\n",
      "  motor: \u001b[92;1mno error\u001b[0m\n",
      "  encoder: \u001b[92;1mno error\u001b[0m\n",
      "  controller: \u001b[92;1mno error\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "print('odrv0 errors')\n",
    "odrive.utils.dump_errors(odrv0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%qtconsole"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "del odrv0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "odrv0.axis0.requested_state = odrive.enums.AXIS_STATE_CLOSED_LOOP_CONTROL\n",
    "odrv0.axis1.requested_state = odrive.enums.AXIS_STATE_CLOSED_LOOP_CONTROL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'RemoteObject' object has no attribute 'axis0'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-68-eb6b1c3e4dba>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0modrv0\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maxis0\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrequested_state\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0modrive\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0menums\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mAXIS_STATE_IDLE\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0modrv0\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maxis1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrequested_state\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0modrive\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0menums\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mAXIS_STATE_IDLE\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Downloads/ODrive/Firmware/fibre/python/fibre/remote_object.py\u001b[0m in \u001b[0;36m__getattribute__\u001b[0;34m(self, name)\u001b[0m\n\u001b[1;32m    243\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mattr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    244\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 245\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mobject\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__getattribute__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    246\u001b[0m             \u001b[0;31m#raise AttributeError(\"Attribute {} not found\".format(name))\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    247\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'RemoteObject' object has no attribute 'axis0'"
     ]
    }
   ],
   "source": [
    "odrv0.axis0.requested_state = odrive.enums.AXIS_STATE_IDLE\n",
    "odrv0.axis1.requested_state = odrive.enums.AXIS_STATE_IDLE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Connect to odrv1, calibrate,  dump errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 427,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Connected!\n",
      "Odrive serial 53331572306485\n",
      "Motor 0 calibrated: True\n",
      "Motor 1 calibrated: True\n"
     ]
    }
   ],
   "source": [
    "odrv1 = odrive.find_any(serial_number = '3081396C3235', timeout = 20)\n",
    "if odrv1 is not None:\n",
    "    print('Connected!')\n",
    "    print('Odrive serial {}'.format(odrv1.serial_number))\n",
    "    \n",
    "    m0 = odrv1.axis0.motor.is_calibrated\n",
    "    m1 = odrv1.axis1.motor.is_calibrated\n",
    "    \n",
    "    print('Motor 0 calibrated: {}'.format(m0))\n",
    "    print('Motor 1 calibrated: {}'.format(m1))    \n",
    "    \n",
    "else:\n",
    "    print('Not connected')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t Odrv 1_Motor 0 calibration result: True \r\n",
      " \t Odrv 1_Motor 1 calibration result: True\n"
     ]
    }
   ],
   "source": [
    "print('\\t Odrv 1_Motor 0 calibration result: {} \\r\\n'.format(odrv1.axis0.motor.is_calibrated), \n",
    "      '\\t Odrv 1_Motor 1 calibration result: {}'.format(odrv1.axis1.motor.is_calibrated))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "curr_limit_all = 20 # amperes\n",
    "odrv1.axis0.motor.config.current_lim = curr_limit_all\n",
    "odrv1.axis1.motor.config.current_lim = curr_limit_all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 418,
   "metadata": {},
   "outputs": [],
   "source": [
    "odrv1.axis0.requested_state = odrive.enums.AXIS_STATE_FULL_CALIBRATION_SEQUENCE\n",
    "odrv1.axis1.requested_state = odrive.enums.AXIS_STATE_FULL_CALIBRATION_SEQUENCE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 419,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "odrv1 errors\n",
      "axis0\n",
      "  axis: \u001b[92;1mno error\u001b[0m\n",
      "  motor: \u001b[92;1mno error\u001b[0m\n",
      "  encoder: \u001b[92;1mno error\u001b[0m\n",
      "  controller: \u001b[92;1mno error\u001b[0m\n",
      "axis1\n",
      "  axis: \u001b[92;1mno error\u001b[0m\n",
      "  motor: \u001b[92;1mno error\u001b[0m\n",
      "  encoder: \u001b[92;1mno error\u001b[0m\n",
      "  controller: \u001b[92;1mno error\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "print('odrv1 errors')\n",
    "odrive.utils.dump_errors(odrv1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Connect to both odrv0 and odrv1, calibrate,  dump errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Connected!\n",
      "Odrive serial 35696338546763\n",
      "Motor 0 calibrated: False\n",
      "Motor 1 calibrated: False\n",
      "Connected!\n",
      "Odrive serial 53331572306485\n",
      "Motor 0 calibrated: False\n",
      "Motor 1 calibrated: True\n"
     ]
    }
   ],
   "source": [
    "odrv0 = odrive.find_any(serial_number = '20773394304B', timeout = 20)\n",
    "odrv1 = odrive.find_any(serial_number = '3081396C3235', timeout = 20)\n",
    "if odrv0 is not None:\n",
    "    print('Connected!')\n",
    "    print('Odrive serial {}'.format(odrv0.serial_number))\n",
    "    \n",
    "    m0 = odrv0.axis0.motor.is_calibrated\n",
    "    m1 = odrv0.axis1.motor.is_calibrated\n",
    "    \n",
    "    print('Motor 0 calibrated: {}'.format(m0))\n",
    "    print('Motor 1 calibrated: {}'.format(m1))    \n",
    "    \n",
    "else:\n",
    "    print('Not connected')\n",
    "\n",
    "if odrv1 is not None:\n",
    "    print('Connected!')\n",
    "    print('Odrive serial {}'.format(odrv1.serial_number))\n",
    "    \n",
    "    m0 = odrv1.axis0.motor.is_calibrated\n",
    "    m1 = odrv1.axis1.motor.is_calibrated\n",
    "    \n",
    "    print('Motor 0 calibrated: {}'.format(m0))\n",
    "    print('Motor 1 calibrated: {}'.format(m1))    \n",
    "    \n",
    "else:\n",
    "    print('Not connected')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2 preparation before moving motor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 608,
   "metadata": {},
   "outputs": [],
   "source": [
    "odrv0.axis0.requested_state = odrive.enums.AXIS_STATE_IDLE\n",
    "odrv0.axis1.requested_state = odrive.enums.AXIS_STATE_IDLE\n",
    "odrv1.axis0.requested_state = odrive.enums.AXIS_STATE_IDLE\n",
    "odrv1.axis1.requested_state = odrive.enums.AXIS_STATE_IDLE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 609,
   "metadata": {},
   "outputs": [],
   "source": [
    "curr_limit_all = 15 # amperes\n",
    "odrv0.axis0.motor.config.current_lim = curr_limit_all\n",
    "odrv0.axis1.motor.config.current_lim = curr_limit_all\n",
    "odrv1.axis0.motor.config.current_lim = curr_limit_all\n",
    "odrv1.axis1.motor.config.current_lim = curr_limit_all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 610,
   "metadata": {},
   "outputs": [],
   "source": [
    "odrv0.axis0.controller.config.vel_limit = 2000000 # encoder counts/sec\n",
    "odrv0.axis1.controller.config.vel_limit = 2000000 # encoder counts/sec\n",
    "odrv1.axis0.controller.config.vel_limit = 2000000 # encoder counts/sec\n",
    "odrv1.axis1.controller.config.vel_limit = 2000000 # encoder counts/sec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calibrate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t Odrv 1_Motor 0 calibration result: True \r\n",
      " \t Odrv 1_Motor 1 calibration result: True\n",
      "\t Odrv 0_Motor 0 calibration result: True \r\n",
      " \t Odrv 0_Motor 1 calibration result: True\n"
     ]
    }
   ],
   "source": [
    "# calibrate odrv0\n",
    "odrv0.axis0.requested_state = odrive.enums.AXIS_STATE_FULL_CALIBRATION_SEQUENCE\n",
    "odrv0.axis1.requested_state = odrive.enums.AXIS_STATE_FULL_CALIBRATION_SEQUENCE\n",
    "\n",
    "# calibrate odrv1\n",
    "odrv1.axis0.requested_state = odrive.enums.AXIS_STATE_FULL_CALIBRATION_SEQUENCE\n",
    "odrv1.axis1.requested_state = odrive.enums.AXIS_STATE_FULL_CALIBRATION_SEQUENCE\n",
    "\n",
    "# wait for calibration to take place and then check if calibrated\n",
    "time.sleep(15)\n",
    "print('\\t Odrv 1_Motor 0 calibration result: {} \\r\\n'.format(odrv1.axis0.motor.is_calibrated), \n",
    "      '\\t Odrv 1_Motor 1 calibration result: {}'.format(odrv1.axis1.motor.is_calibrated))\n",
    "\n",
    "print('\\t Odrv 0_Motor 0 calibration result: {} \\r\\n'.format(odrv0.axis0.motor.is_calibrated), \n",
    "      '\\t Odrv 0_Motor 1 calibration result: {}'.format(odrv0.axis1.motor.is_calibrated))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 611,
   "metadata": {},
   "outputs": [],
   "source": [
    "odrv0.axis0.controller.error=0\n",
    "odrv0.axis0.motor.error=0\n",
    "odrv0.axis0.encoder.error=0\n",
    "odrv0.axis0.error=0\n",
    "\n",
    "odrv0.axis1.controller.error=0\n",
    "odrv0.axis1.motor.error=0\n",
    "odrv0.axis1.encoder.error=0\n",
    "odrv0.axis1.error=0\n",
    "\n",
    "odrv1.axis0.controller.error=0\n",
    "odrv1.axis0.motor.error=0\n",
    "odrv1.axis0.encoder.error=0\n",
    "odrv1.axis0.error=0\n",
    "\n",
    "odrv1.axis1.controller.error=0\n",
    "odrv1.axis1.motor.error=0\n",
    "odrv1.axis1.encoder.error=0\n",
    "odrv1.axis1.error=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 612,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "odrv0 errors\n",
      "axis0\n",
      "  axis: \u001b[92;1mno error\u001b[0m\n",
      "  motor: \u001b[92;1mno error\u001b[0m\n",
      "  encoder: \u001b[92;1mno error\u001b[0m\n",
      "  controller: \u001b[92;1mno error\u001b[0m\n",
      "axis1\n",
      "  axis: \u001b[92;1mno error\u001b[0m\n",
      "  motor: \u001b[92;1mno error\u001b[0m\n",
      "  encoder: \u001b[92;1mno error\u001b[0m\n",
      "  controller: \u001b[92;1mno error\u001b[0m\n",
      "\n",
      "odrv1 errors\n",
      "axis0\n",
      "  axis: \u001b[92;1mno error\u001b[0m\n",
      "  motor: \u001b[92;1mno error\u001b[0m\n",
      "  encoder: \u001b[92;1mno error\u001b[0m\n",
      "  controller: \u001b[92;1mno error\u001b[0m\n",
      "axis1\n",
      "  axis: \u001b[92;1mno error\u001b[0m\n",
      "  motor: \u001b[92;1mno error\u001b[0m\n",
      "  encoder: \u001b[92;1mno error\u001b[0m\n",
      "  controller: \u001b[92;1mno error\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "print('odrv0 errors')\n",
    "odrive.utils.dump_errors(odrv0)\n",
    "print('\\nodrv1 errors')\n",
    "odrive.utils.dump_errors(odrv1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Put the legs on NOW! (before running more code below)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 613,
   "metadata": {},
   "outputs": [],
   "source": [
    "odrv0.axis0.requested_state = odrive.enums.AXIS_STATE_CLOSED_LOOP_CONTROL\n",
    "odrv0.axis1.requested_state = odrive.enums.AXIS_STATE_CLOSED_LOOP_CONTROL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 614,
   "metadata": {},
   "outputs": [],
   "source": [
    "odrv1.axis0.requested_state = odrive.enums.AXIS_STATE_CLOSED_LOOP_CONTROL\n",
    "odrv1.axis1.requested_state = odrive.enums.AXIS_STATE_CLOSED_LOOP_CONTROL"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### define angle to position function & position to angle function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 615,
   "metadata": {},
   "outputs": [],
   "source": [
    "motor_cpr0 = (odrv0.axis0.encoder.config.cpr,odrv0.axis1.encoder.config.cpr)\n",
    "pos_zero0 = ([odrv0.axis0.encoder.pos_estimate,odrv0.axis1.encoder.pos_estimate])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 616,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get motor parameters\n",
    "motor_cpr1 = (odrv1.axis0.encoder.config.cpr,odrv1.axis1.encoder.config.cpr)\n",
    "pos_zero1 = ([odrv1.axis0.encoder.pos_estimate,odrv1.axis1.encoder.pos_estimate])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 617,
   "metadata": {},
   "outputs": [],
   "source": [
    "def angle2posL(theta, pos_zero = pos_zero0, motor_cpr = motor_cpr0, zero_theta = (0,np.pi)):\n",
    "    pos = np.zeros(shape=(1,2))\n",
    "    pos[0,0] = -(theta[0] - zero_theta[0])/(2*np.pi)*motor_cpr[0] + pos_zero[0]\n",
    "    pos[0,1] = -(theta[1] - zero_theta[1])/(2*np.pi)*motor_cpr[1] + pos_zero[1]    \n",
    "    return (pos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 618,
   "metadata": {},
   "outputs": [],
   "source": [
    "# angle to position for 2 odrives\n",
    "def angle2posR(theta, pos_zero = pos_zero1, motor_cpr = motor_cpr1, zero_theta = (0,np.pi)):\n",
    "    pos = np.zeros(shape=(1,2))\n",
    "    pos[0,0] = -(theta[0] - zero_theta[0])/(2*np.pi)*motor_cpr[0] + pos_zero[0]\n",
    "    pos[0,1] = -(theta[1] - zero_theta[1])/(2*np.pi)*motor_cpr[1] + pos_zero[1]    \n",
    "    return (pos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 619,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pos2angleL(pos, motor_cpr = motor_cpr0, pos_zero = pos_zero0, zero_theta = (0,np.pi)):\n",
    "    angle = np.zeros(shape=(1,2))\n",
    "    angle[0,0] = -2*np.pi*(pos[0] - pos_zero[0])/motor_cpr[0]+zero_theta[0]\n",
    "    angle[0,1] = -2*np.pi*(pos[1] - pos_zero[1])/motor_cpr[1]+zero_theta[1]\n",
    "    return (angle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 620,
   "metadata": {},
   "outputs": [],
   "source": [
    "# position to angle for 2 odrives\n",
    "def pos2angleR(pos, motor_cpr = motor_cpr1, pos_zero = pos_zero1, zero_theta = (0,np.pi)):\n",
    "    angle = np.zeros(shape=(1,2))\n",
    "    angle[0,0] = -2*np.pi*(pos[0] - pos_zero[0])/motor_cpr[0]+zero_theta[0]\n",
    "    angle[0,1] = -2*np.pi*(pos[1] - pos_zero[1])/motor_cpr[1]+zero_theta[1]\n",
    "    return (angle)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.3 Get legs on and start moving motors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### move legs to start points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 621,
   "metadata": {},
   "outputs": [],
   "source": [
    "odrv0.axis0.requested_state = odrive.enums.AXIS_STATE_CLOSED_LOOP_CONTROL\n",
    "odrv0.axis1.requested_state = odrive.enums.AXIS_STATE_CLOSED_LOOP_CONTROL\n",
    "odrv1.axis0.requested_state = odrive.enums.AXIS_STATE_CLOSED_LOOP_CONTROL\n",
    "odrv1.axis1.requested_state = odrive.enums.AXIS_STATE_CLOSED_LOOP_CONTROL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 622,
   "metadata": {},
   "outputs": [],
   "source": [
    "posgain = 60\n",
    "odrv0.axis0.controller.config.pos_gain = posgain\n",
    "odrv0.axis1.controller.config.pos_gain = posgain\n",
    "odrv1.axis0.controller.config.pos_gain = posgain\n",
    "odrv1.axis1.controller.config.pos_gain = posgain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 623,
   "metadata": {},
   "outputs": [],
   "source": [
    "# move left leg to on_point; ritht leg to off_point\n",
    "theta_startL = fsolve(lambda x: IK_constraint_eqn(x, x_on, y_on, l1, l2,w), (0,np.pi))\n",
    "# OFF position\n",
    "# theta_startR = fsolve(lambda x: IK_constraint_eqn(x, -x_off, y_off, l1, l2, w), (0,np.pi))\n",
    "# ON position to show CPG being able to maintain phase difference\n",
    "theta_startR = fsolve(lambda x: IK_constraint_eqn(x, -x_on, y_on, l1, l2, w), (0,np.pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 624,
   "metadata": {},
   "outputs": [],
   "source": [
    "odrv0.axis0.controller.pos_setpoint = angle2posL(theta_startL)[0,0]\n",
    "odrv0.axis1.controller.pos_setpoint = angle2posL(theta_startL)[0,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 625,
   "metadata": {},
   "outputs": [],
   "source": [
    "odrv1.axis0.controller.pos_setpoint = angle2posR(theta_startR)[0,0]\n",
    "odrv1.axis1.controller.pos_setpoint = angle2posR(theta_startR)[0,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### move motors using CPG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getNewCoordinates(gaitOrigin, x, y):\n",
    "    # get point from leg coordinate system\n",
    "    # change it's values to new coordinate system\n",
    "    newX = x - gaitOrigin[0]\n",
    "    newY = y - gaitOrigin[1]\n",
    "    newCoordinates = np.array([newX, newY])\n",
    "    return newCoordinates\n",
    "\n",
    "def getNewCoordinatesR(gaitOrigin, x, y):\n",
    "    # get point from leg coordinate system\n",
    "    # change it's values to new coordinate system\n",
    "    newX = -(x - gaitOrigin[0])\n",
    "    newY = y - gaitOrigin[1]\n",
    "    newCoordinates = np.array([newX, newY])\n",
    "    return newCoordinates\n",
    "\n",
    "def getNewPolarCoordinates(gaitCartesianCoord):\n",
    "    radial_len = np.sqrt(gaitCartesianCoord[0]**2 + gaitCartesianCoord[1]**2)\n",
    "    beta = np.arctan2(gaitCartesianCoord[1], gaitCartesianCoord[0])\n",
    "    polar = np.array([radial_len, beta])\n",
    "    return polar\n",
    "\n",
    "def getWorldCoord(gaitOrigin, x, y):\n",
    "    worldX = x + gaitOrigin[0]\n",
    "    worldY = y + gaitOrigin[1]\n",
    "    worldCoordinates = np.array([worldX, worldY])\n",
    "    return worldCoordinates\n",
    "\n",
    "def closestPolarPointInTrajectory(phi, targetPolarTraj, length, startidx): # should take actual position and command list(x,y) coordinates\n",
    "    # in nutshell I am finding nearest point in the trajectory\n",
    "    traj_np = np.array(targetPolarTraj).reshape((-1,2))\n",
    "    error = np.square(traj_np[:,1]-phi)\n",
    "    minerr_idx = np.argmin(error)\n",
    "    # print('min at idx', startidx + minerr_idx)\n",
    "    return targetPolarTraj[minerr_idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"\\n# PRECOMPUTE forward kinematics and save to disk\\nstart_thetaL = 0 # 0\\nend_thetaL = (2*np.pi*1000 + 1)/2 # 6284/2 = 3142\\npossible_thetaL = np.arange(start_thetaL, end_thetaL, 1) # in miliradians\\n\\n# 0.0732437783436377 to 0.24719020748058496\\nstart_thetaR = 0 # 0\\nend_thetaR = (2*np.pi*1000 + 1)/2 # 6284/2 = 3142\\npossible_thetaR = np.arange(start_thetaR, end_thetaR, 1) # in miliradians (radian * 1000)\\n\\n# make cache\\nfk_map = np.zeros((possible_thetaL.shape[0], possible_thetaR.shape[0], 2))\\n\\ndef get_thetaL_idx(thetaL, start_thetaL):\\n    return int(thetaL - int(start_thetaL))\\n\\ndef get_thetaR_idx(thetaR, start_thetaR):\\n    return int(thetaR - int(start_thetaR))\\n\\ndone = 1\\n\\nfor thetaL in possible_thetaL:\\n    for thetaR in possible_thetaR:\\n        done = done +1\\n        if done % 30000 == 0:\\n            print(thetaL, thetaR)\\n        thetaL_idx = get_thetaL_idx(thetaL, start_thetaL)\\n        thetaR_idx = get_thetaR_idx(thetaR, start_thetaR)\\n        \\n        M = frwd_kinmtcs_lambda((thetaR*2)/1000, (thetaL*2)/1000)\\n        x, y = sym_to_np(M).reshape((1,2))[0]\\n        \\n        fk_map[thetaL_idx, thetaR_idx, 0] = x\\n        fk_map[thetaL_idx, thetaR_idx, 1] = y\\n\\nnp.save('fk_map.npy', fk_map)\\n\""
      ]
     },
     "execution_count": 250,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "# PRECOMPUTE forward kinematics and save to disk\n",
    "start_thetaL = 0 # 0\n",
    "end_thetaL = (2*np.pi*1000 + 1)/2 # 6284/2 = 3142\n",
    "possible_thetaL = np.arange(start_thetaL, end_thetaL, 1) # in miliradians\n",
    "\n",
    "# 0.0732437783436377 to 0.24719020748058496\n",
    "start_thetaR = 0 # 0\n",
    "end_thetaR = (2*np.pi*1000 + 1)/2 # 6284/2 = 3142\n",
    "possible_thetaR = np.arange(start_thetaR, end_thetaR, 1) # in miliradians (radian * 1000)\n",
    "\n",
    "# make cache\n",
    "fk_map = np.zeros((possible_thetaL.shape[0], possible_thetaR.shape[0], 2))\n",
    "\n",
    "def get_thetaL_idx(thetaL, start_thetaL):\n",
    "    return int(thetaL - int(start_thetaL))\n",
    "\n",
    "def get_thetaR_idx(thetaR, start_thetaR):\n",
    "    return int(thetaR - int(start_thetaR))\n",
    "\n",
    "done = 1\n",
    "\n",
    "for thetaL in possible_thetaL:\n",
    "    for thetaR in possible_thetaR:\n",
    "        done = done +1\n",
    "        if done % 30000 == 0:\n",
    "            print(thetaL, thetaR)\n",
    "        thetaL_idx = get_thetaL_idx(thetaL, start_thetaL)\n",
    "        thetaR_idx = get_thetaR_idx(thetaR, start_thetaR)\n",
    "        \n",
    "        M = frwd_kinmtcs_lambda((thetaR*2)/1000, (thetaL*2)/1000)\n",
    "        x, y = sym_to_np(M).reshape((1,2))[0]\n",
    "        \n",
    "        fk_map[thetaL_idx, thetaR_idx, 0] = x\n",
    "        fk_map[thetaL_idx, thetaR_idx, 1] = y\n",
    "\n",
    "np.save('fk_map.npy', fk_map)\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 390,
   "metadata": {},
   "outputs": [],
   "source": [
    "# cell loads cached FK map\n",
    "start_thetaL = 0 # 0\n",
    "start_thetaR = 0 # 0\n",
    "\n",
    "def get_thetaL_idx(thetaL, start_thetaL):\n",
    "    return int(thetaL - int(start_thetaL))\n",
    "\n",
    "def get_thetaR_idx(thetaR, start_thetaR):\n",
    "    return int(thetaR - int(start_thetaR))\n",
    "\n",
    "fk_map = np.load('fk_map.npy')\n",
    "\n",
    "def get_fk(thetaL, thetaR):\n",
    "    thetaL_idx = get_thetaL_idx((thetaL*1000)/2, start_thetaL)\n",
    "    thetaR_idx = get_thetaR_idx((thetaR*1000)/2, start_thetaR)\n",
    "    return fk_map[thetaL_idx,thetaR_idx,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 391,
   "metadata": {},
   "outputs": [],
   "source": [
    "# cell loads cached IK map\n",
    "start_x = 0.220*1000 # -220\n",
    "start_y = 0.070*1000 # 70\n",
    "\n",
    "def get_x_idx(x, start_x):\n",
    "    return int(x - int(start_x))\n",
    "\n",
    "def get_y_idx(y, start_y):\n",
    "    return int(y - int(start_y))\n",
    "\n",
    "ik_map = np.load('ik_map.npy')\n",
    "def get_ik(world_x, world_y):\n",
    "    x_idx = get_x_idx(world_x*1000, start_x)\n",
    "    y_idx = get_y_idx(world_y*1000, start_y)\n",
    "    return ik_map[x_idx,y_idx,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 392,
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate gait trajectory points \n",
    "# (in polar coordinate system) for both legs\n",
    "\n",
    "allpts_gait = []\n",
    "allpts_gait_polar_L = []\n",
    "allpts_gait_polar_R = []\n",
    "gaitOrigin = (x_origin, y_origin)\n",
    "gaitOrigin_R = (-x_origin, y_origin)\n",
    "zero_pi_add_val_L = 0\n",
    "zero_pi_add_val_R = 0\n",
    "zero_min_pi_add_val = 2*np.pi\n",
    "prev = 0\n",
    "\n",
    "for idx, val in enumerate(allpts):\n",
    "    x, y = val\n",
    "    x_gait, y_gait = getNewCoordinates(gaitOrigin, x, y)\n",
    "    x_gait_R, y_gait_R = getNewCoordinates(gaitOrigin_R, -x, y)\n",
    "    polar_gait_L = getNewPolarCoordinates(np.array([x_gait, y_gait]))\n",
    "    polar_gait_R = getNewPolarCoordinates(np.array([x_gait_R, y_gait_R]))\n",
    "    if polar_gait_L[1] > 0 and polar_gait_L[1] < np.pi:\n",
    "        if prev == 1:\n",
    "            zero_min_pi_add_val += 2*np.pi\n",
    "        prev = 0\n",
    "        polar_gait_L[1] += zero_pi_add_val_L\n",
    "    else:\n",
    "        if prev == 0:\n",
    "            zero_pi_add_val_L += 2*np.pi\n",
    "        prev = 1\n",
    "        polar_gait_L[1] += zero_min_pi_add_val\n",
    "    \n",
    "    if polar_gait_R[1] > 0 and polar_gait_R[1] < np.pi:\n",
    "        if prev == 1:\n",
    "            zero_min_pi_add_val += 2*np.pi\n",
    "        prev = 0\n",
    "        polar_gait_R[1] += zero_pi_add_val_R\n",
    "    else:\n",
    "        if prev == 0:\n",
    "            zero_pi_add_val_R += 2*np.pi\n",
    "        prev = 1\n",
    "        polar_gait_R[1] += zero_min_pi_add_val\n",
    "    polar_gait_L[1] = polar_gait_L[1] % (2*np.pi)\n",
    "    polar_gait_R[1] = (np.pi-polar_gait_R[1]) % (2*np.pi)\n",
    "    \n",
    "    allpts_gait.append((x_gait, y_gait))\n",
    "    allpts_gait_polar_L.append((polar_gait_L[0], polar_gait_L[1]))\n",
    "    allpts_gait_polar_R.append((polar_gait_R[0], polar_gait_R[1]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 393,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nreal_pos_R = (odrv1.axis0.encoder.pos_estimate,odrv1.axis1.encoder.pos_estimate)\\nreal_angle_R = pos2angleR(real_pos_R)\\n\\nx_R, y_R = get_fk(real_angle_R[0,1], real_angle_R[0,0])\\n\\nx_R_gait, y_R_gait = getNewCoordinatesR(gaitOrigin, x_R, y_R)\\n\\nright_leg_curr_phase = np.float(xy2psi(x_R_gait, y_R_gait))\\n\\nx_L, y_L = get_fk(real_angle_L[0,1], real_angle_L[0,0])\\nx_R, y_R = get_fk(real_angle_R[0,1], real_angle_R[0,0])\\n\\nx_L_gait, y_L_gait = getNewCoordinates(gaitOrigin, x_L, y_L)\\n\\nright_leg_curr_phase = np.float(xy2psi(xR,yR))\\n\\nprint(xR, yR)\\nprint(right_leg_curr_phase)\\n\\nradial_gait, theta_gait = closestPolarPointInTrajectory(\\n                                            (right_leg_curr_phase) % (2*np.pi),\\n                                            allpts_gait_polar_R,\\n                                            len(allpts_gait_polar_R),\\n                                            0)\\n    \\nx_gait, y_gait = radial_gait*np.cos(theta_gait), radial_gait*np.sin(theta_gait)\\nx_world, y_world = getWorldCoord(gaitOrigin_R, x_gait, y_gait)\\n\\nprint(x_world, y_world)\\n\\nplt.scatter(*zip(*allpts_R))\\nplt.plot(x_world, y_world, \\'o\\', c=\\'g\\', markersize=14, label=\"Current position\")\\n# plt.plot(nextPtX_world, nextPtY_world, \\'o\\', markersize=10, label=\"NEXT position\")\\nplt.title(\\'Current and next position (right leg)\\')\\nplt.xlabel(\\'x\\')\\nplt.ylabel(\\'y\\')\\nplt.legend()\\nplt.show()\\n'"
      ]
     },
     "execution_count": 393,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# DEBUG CELL\n",
    "# plots current phase of right leg\n",
    "\"\"\"\n",
    "real_pos_R = (odrv1.axis0.encoder.pos_estimate,odrv1.axis1.encoder.pos_estimate)\n",
    "real_angle_R = pos2angleR(real_pos_R)\n",
    "\n",
    "x_R, y_R = get_fk(real_angle_R[0,1], real_angle_R[0,0])\n",
    "\n",
    "x_R_gait, y_R_gait = getNewCoordinatesR(gaitOrigin, x_R, y_R)\n",
    "\n",
    "right_leg_curr_phase = np.float(xy2psi(x_R_gait, y_R_gait))\n",
    "\n",
    "x_L, y_L = get_fk(real_angle_L[0,1], real_angle_L[0,0])\n",
    "x_R, y_R = get_fk(real_angle_R[0,1], real_angle_R[0,0])\n",
    "\n",
    "x_L_gait, y_L_gait = getNewCoordinates(gaitOrigin, x_L, y_L)\n",
    "\n",
    "right_leg_curr_phase = np.float(xy2psi(xR,yR))\n",
    "\n",
    "print(xR, yR)\n",
    "print(right_leg_curr_phase)\n",
    "\n",
    "radial_gait, theta_gait = closestPolarPointInTrajectory(\n",
    "                                            (right_leg_curr_phase) % (2*np.pi),\n",
    "                                            allpts_gait_polar_R,\n",
    "                                            len(allpts_gait_polar_R),\n",
    "                                            0)\n",
    "    \n",
    "x_gait, y_gait = radial_gait*np.cos(theta_gait), radial_gait*np.sin(theta_gait)\n",
    "x_world, y_world = getWorldCoord(gaitOrigin_R, x_gait, y_gait)\n",
    "\n",
    "print(x_world, y_world)\n",
    "\n",
    "plt.scatter(*zip(*allpts_R))\n",
    "plt.plot(x_world, y_world, 'o', c='g', markersize=14, label=\"Current position\")\n",
    "# plt.plot(nextPtX_world, nextPtY_world, 'o', markersize=10, label=\"NEXT position\")\n",
    "plt.title('Current and next position (right leg)')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 626,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "0.01339101791381836\n",
      "0.011842966079711914\n",
      "0.01147603988647461\n",
      "0.011970281600952148\n",
      "0.012094974517822266\n",
      "0.011527299880981445\n",
      "0.012543439865112305\n",
      "0.012518882751464844\n",
      "0.012528181076049805\n",
      "0.010454893112182617\n",
      "0.012915372848510742\n",
      "0.012999296188354492\n",
      "0.012906551361083984\n",
      "0.011065006256103516\n",
      "0.011324644088745117\n",
      "0.012478113174438477\n",
      "0.011744022369384766\n",
      "0.011681795120239258\n",
      "0.01287388801574707\n",
      "0.011059284210205078\n",
      "0.011329174041748047\n",
      "0.015322685241699219\n",
      "0.017094135284423828\n",
      "0.01386880874633789\n",
      "0.019330978393554688\n",
      "0.020049333572387695\n",
      "0.018954753875732422\n",
      "0.0197751522064209\n",
      "0.02156352996826172\n",
      "0.019937515258789062\n",
      "0.018720388412475586\n",
      "0.020517587661743164\n",
      "0.01885223388671875\n",
      "0.01932692527770996\n",
      "0.020207643508911133\n",
      "0.02062845230102539\n"
     ]
    }
   ],
   "source": [
    "from time import sleep\n",
    "# aL, aR represent to the angles related to the supposed coordinate system\n",
    "w_speed = 6*(2*np.pi)\n",
    "A_L = 9*(w_speed/8)\n",
    "A_R = 9*(w_speed/8)\n",
    "delta_t = 0.005\n",
    "\n",
    "start = time.time()\n",
    "t_curr = 0\n",
    "\n",
    "# get the initial point\n",
    "real_pos_L = (odrv0.axis0.encoder.pos_estimate,odrv0.axis1.encoder.pos_estimate)\n",
    "real_pos_R = (odrv1.axis0.encoder.pos_estimate,odrv1.axis1.encoder.pos_estimate)\n",
    "    \n",
    "real_angle_L = pos2angleL(real_pos_L)\n",
    "real_angle_R = pos2angleR(real_pos_R)\n",
    "\n",
    "x_L, y_L = get_fk(real_angle_L[0,1], real_angle_L[0,0])\n",
    "x_R, y_R = get_fk(real_angle_R[0,1], real_angle_R[0,0])\n",
    "\n",
    "x_L_gait, y_L_gait = getNewCoordinates(gaitOrigin, x_L, y_L)\n",
    "x_R_gait, y_R_gait = getNewCoordinates(gaitOrigin_R, x_R, y_R)\n",
    "\n",
    "# next phase that the leg will go to\n",
    "left_leg_nxt_phase = np.float(xy2psi(x_L_gait, y_L_gait))\n",
    "right_leg_nxt_phase = np.float(xy2psi(x_R_gait, y_R_gait))\n",
    "\n",
    "\n",
    "error_angle_list = []\n",
    "\n",
    "theta_list_L = []\n",
    "theta_list_R = []\n",
    "\n",
    "phase_L = []\n",
    "phase_R = []\n",
    "\n",
    "phase_inrange_L = []\n",
    "phase_inrange_R = []\n",
    "\n",
    "t_start = 0\n",
    "t_end = delta_t\n",
    "\n",
    "#start moving\n",
    "while(t_curr < 20):\n",
    "    delta_t = t_end - t_start\n",
    "    print(delta_t)\n",
    "    t_start = time.time()\n",
    "    t_curr = (time.time() - start)\n",
    "    \n",
    "    real_pos_L = (odrv0.axis0.encoder.pos_estimate,odrv0.axis1.encoder.pos_estimate)\n",
    "    real_pos_R = (odrv1.axis0.encoder.pos_estimate,odrv1.axis1.encoder.pos_estimate)\n",
    "    \n",
    "    real_angle_L = pos2angleL(real_pos_L)\n",
    "    real_angle_R = pos2angleR(real_pos_R)\n",
    "    \n",
    "    theta_list_L.append((t_curr, real_angle_L[0,1], real_angle_L[0,0]))\n",
    "    theta_list_R.append((t_curr, real_angle_R[0,1], real_angle_R[0,0]))\n",
    "    \n",
    "    x_L, y_L = get_fk(real_angle_L[0,1], real_angle_L[0,0])\n",
    "    x_R, y_R = get_fk(real_angle_R[0,1], real_angle_R[0,0])\n",
    "\n",
    "    x_L_gait, y_L_gait = getNewCoordinates(gaitOrigin, x_L, y_L)\n",
    "    x_R_gait, y_R_gait = getNewCoordinatesR(gaitOrigin, x_R, y_R)\n",
    "    \n",
    "    left_leg_curr_phase = np.float(xy2psi(x_L_gait, y_L_gait))\n",
    "    right_leg_curr_phase = np.float(xy2psi(x_R_gait, y_R_gait))\n",
    "    \n",
    "    phase_L.append((t_curr, left_leg_curr_phase))\n",
    "    phase_R.append((t_curr, right_leg_curr_phase))\n",
    "    \n",
    "    if psi_right<=left_leg_curr_phase<=psi_left:\n",
    "        delta_psi = poly_delta_st(left_leg_curr_phase)\n",
    "    elif left_leg_curr_phase>psi_left:\n",
    "        delta_psi = poly_delta_sw(left_leg_curr_phase)\n",
    "    else:\n",
    "        delta_psi = poly_delta_sw(left_leg_curr_phase+2*np.pi)\n",
    "    \n",
    "    # CPG coupling\n",
    "    phase_diff_bw_legs = right_leg_curr_phase-left_leg_curr_phase\n",
    "    left_leg_nxt_phase = left_leg_curr_phase + delta_t * (w_speed + \n",
    "                                         (A_L * np.sin(phase_diff_bw_legs - delta_psi)))\n",
    "    right_leg_nxt_phase = right_leg_curr_phase + delta_t * (w_speed + \n",
    "                                        (A_R * np.sin(delta_psi - phase_diff_bw_legs)))\n",
    "    \n",
    "    error = phase_diff_bw_legs - delta_psi\n",
    "    if error < -(3*np.pi)/2:\n",
    "        error = error + 2*np.pi\n",
    "    error_angle_list.append((t_curr, error))\n",
    "    \n",
    "    \n",
    "    left_leg_nxt_phase_inrange = left_leg_nxt_phase % (2*np.pi)\n",
    "    right_leg_nxt_phase_inrange = right_leg_nxt_phase % (2*np.pi)\n",
    "    \n",
    "    phase_inrange_L.append((t_curr, left_leg_nxt_phase_inrange))\n",
    "    phase_inrange_R.append((t_curr, right_leg_nxt_phase_inrange))\n",
    "    \n",
    "    # find motor angles for left leg\n",
    "    leftLegNextPtRadial_gait, leftLegNextPtTheta_gait = closestPolarPointInTrajectory(\n",
    "                                            left_leg_nxt_phase_inrange,\n",
    "                                            allpts_gait_polar_L,\n",
    "                                            len(allpts_gait_polar_L),\n",
    "                                            0)\n",
    "    \n",
    "    left_nextPtX_gait, left_nextPtY_gait = \\\n",
    "                                    leftLegNextPtRadial_gait*np.cos(leftLegNextPtTheta_gait), \\\n",
    "                                    leftLegNextPtRadial_gait*np.sin(leftLegNextPtTheta_gait)\n",
    "    left_nextPtX_world, left_nextPtY_world = getWorldCoord(gaitOrigin, \\\n",
    "                                                           left_nextPtX_gait, left_nextPtY_gait)\n",
    "    \n",
    "    left_leg_thetaL, left_leg_thetaR = get_ik(left_nextPtX_world, left_nextPtY_world)\n",
    "    \n",
    "    motor_theta_L = (left_leg_thetaR, left_leg_thetaL)\n",
    "    \n",
    "    # find motor angles for right leg\n",
    "    rightLegNextPtRadial_gait, rightLegNextPtTheta_gait = closestPolarPointInTrajectory(\n",
    "                                            right_leg_nxt_phase_inrange,\n",
    "                                            allpts_gait_polar_R,\n",
    "                                            len(allpts_gait_polar_R),\n",
    "                                            0)\n",
    "    \n",
    "    nextPtX_gait, nextPtY_gait = rightLegNextPtRadial_gait*np.cos(rightLegNextPtTheta_gait), \\\n",
    "                                    rightLegNextPtRadial_gait*np.sin(rightLegNextPtTheta_gait)\n",
    "    nextPtX_world, nextPtY_world = getWorldCoord(gaitOrigin_R, nextPtX_gait, nextPtY_gait)\n",
    "    \n",
    "    right_leg_thetaL, right_leg_thetaR = get_ik(-nextPtX_world, nextPtY_world)\n",
    "    \n",
    "    ######################################\n",
    "    # DEBUGGING CODE: START\n",
    "    # uncomment to plot current position of right left\n",
    "    # v/s its next position on its trajectory\n",
    "    # find current position of right leg \n",
    "#     radial_gait, theta_gait = closestPolarPointInTrajectory(\n",
    "#                                             right_leg_curr_phase % (2*np.pi),\n",
    "#                                             allpts_gait_polar_R,\n",
    "#                                             len(allpts_gait_polar_R),\n",
    "#                                             0)\n",
    "    \n",
    "#     x_gait, y_gait = radial_gait*np.cos(theta_gait), radial_gait*np.sin(theta_gait)\n",
    "#     x_world, y_world = getWorldCoord(gaitOrigin_R, x_gait, y_gait)\n",
    "    # PLOT current v/s next position for right leg\n",
    "#     plt.scatter(*zip(*allpts_R))\n",
    "#     plt.plot(x_world, y_world, 's', c='g', markersize=14, label=\"Current position\")\n",
    "#     plt.plot(nextPtX_world, nextPtY_world, 'o', c='r', markersize=10, label=\"NEXT position\")\n",
    "#     plt.title('Current and next position (right leg)')\n",
    "#     plt.xlabel('x')\n",
    "#     plt.ylabel('y')\n",
    "#     plt.legend()\n",
    "#     plt.show()\n",
    "    #\n",
    "    # DEBUGGING CODE: END\n",
    "    #######################################\n",
    "    \n",
    "    \n",
    "    motor_theta_R = (right_leg_thetaR, right_leg_thetaL)\n",
    "    \n",
    "    # move legs to new position\n",
    "    odrv0.axis0.controller.pos_setpoint = angle2posL(motor_theta_L)[0,0]\n",
    "    odrv0.axis1.controller.pos_setpoint = angle2posL(motor_theta_L)[0,1]\n",
    "    odrv1.axis0.controller.pos_setpoint = angle2posR(motor_theta_R)[0,0]\n",
    "    odrv1.axis1.controller.pos_setpoint = angle2posR(motor_theta_R)[0,1]\n",
    "    t_end = time.time()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 627,
   "metadata": {},
   "outputs": [],
   "source": [
    "odrv0.axis0.requested_state = odrive.enums.AXIS_STATE_IDLE\n",
    "odrv0.axis1.requested_state = odrive.enums.AXIS_STATE_IDLE\n",
    "odrv1.axis0.requested_state = odrive.enums.AXIS_STATE_IDLE\n",
    "odrv1.axis1.requested_state = odrive.enums.AXIS_STATE_IDLE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 628,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(*zip(*error_angle_list))\n",
    "plt.title('Error vs time')\n",
    "plt.xlabel('time (sec)')\n",
    "plt.ylabel('Error angle')\n",
    "plt.show()\n",
    "# plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 629,
   "metadata": {},
   "outputs": [],
   "source": [
    "# theta_list_L = []\n",
    "# theta_list_R = []\n",
    "\n",
    "# phase_L = []\n",
    "# phase_R = []\n",
    "\n",
    "# phase_inrange_L = []\n",
    "# phase_inrange_R = []\n",
    "\n",
    "\n",
    "np.save('theta_list_L_9wby8_holdleg.npy', theta_list_L)\n",
    "np.save('theta_list_R_9wby8_holdleg.npy', theta_list_R)\n",
    "np.save('phase_L_9wby8_holdleg.npy', phase_L)\n",
    "np.save('phase_R_9wby8_holdleg.npy', phase_R)\n",
    "np.save('phase_inrange_L_9wby8_holdleg.npy', phase_inrange_L)\n",
    "np.save('phase_inrange_R_9wby8_holdleg.npy', phase_inrange_R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 630,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.save('error_angle_list_coupis_9wby8_holdleg.npy', error_angle_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 0 => error_angle_list_coupis_0.npy\n",
    "# "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 339,
   "metadata": {},
   "outputs": [],
   "source": [
    "# error_angle_list_coupis_0 = error_angle_list\n",
    "# np.save('error_angle_list_coupis_0.npy', error_angle_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "metadata": {},
   "outputs": [],
   "source": [
    "# error_angle_list_coupis_35 = error_angle_list\n",
    "np.save('error_angle_list_coupis_35.npy', error_angle_list_coupis_35)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(*zip(*error_angle_list_coupis_35))\n",
    "plt.title('Error vs time')\n",
    "plt.xlabel('time (sec)')\n",
    "plt.ylabel('Error angle')\n",
    "plt.show()\n",
    "# plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "odrv0.axis0.controller.error=0\n",
    "odrv0.axis0.motor.error=0\n",
    "odrv0.axis0.encoder.error=0\n",
    "odrv0.axis0.error=0\n",
    "\n",
    "odrv0.axis1.controller.error=0\n",
    "odrv0.axis1.motor.error=0\n",
    "odrv0.axis1.encoder.error=0\n",
    "odrv0.axis1.error=0\n",
    "\n",
    "odrv1.axis0.controller.error=0\n",
    "odrv1.axis0.motor.error=0\n",
    "odrv1.axis0.encoder.error=0\n",
    "odrv1.axis0.error=0\n",
    "\n",
    "odrv1.axis1.controller.error=0\n",
    "odrv1.axis1.motor.error=0\n",
    "odrv1.axis1.encoder.error=0\n",
    "odrv1.axis1.error=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%qtconsole"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "# aL, aR represent to the angles related to the supposed coordinate system\n",
    "w_speed = 10\n",
    "A_L = 0\n",
    "A_R = 0\n",
    "delta_t = 0.005\n",
    "\n",
    "start = time.time()\n",
    "t_curr = 0\n",
    "\n",
    "#get the initial point\n",
    "real_pos_L = (odrv0.axis0.encoder.pos_estimate,odrv0.axis1.encoder.pos_estimate)\n",
    "real_pos_R = (odrv1.axis0.encoder.pos_estimate,odrv1.axis1.encoder.pos_estimate)\n",
    "    \n",
    "real_angle_L = pos2angleL(real_pos_L)\n",
    "real_angle_R = pos2angleR(real_pos_R)\n",
    "\n",
    "xL = interpolate.bisplev(real_angle_L[0,1],real_angle_L[0,0], tck_getxL)\n",
    "yL = interpolate.bisplev(real_angle_L[0,1],real_angle_L[0,0], tck_getyL)\n",
    "xR = interpolate.bisplev(real_angle_R[0,1],real_angle_R[0,0], tck_getxR)\n",
    "yR = interpolate.bisplev(real_angle_R[0,1],real_angle_R[0,0], tck_getyR)\n",
    "\n",
    "aL0 = xy2psi(xL,yL)\n",
    "aR0 = xy2psi(xR,yR)\n",
    "\n",
    "#start moving\n",
    "while(t_curr < 60):\n",
    "    t_curr = (time.time() - start)\n",
    "    \n",
    "    real_pos_L = (odrv0.axis0.encoder.pos_estimate,odrv0.axis1.encoder.pos_estimate)\n",
    "    real_pos_R = (odrv1.axis0.encoder.pos_estimate,odrv1.axis1.encoder.pos_estimate)\n",
    "    \n",
    "    real_angle_L = pos2angleL(real_pos_L)\n",
    "    real_angle_R = pos2angleR(real_pos_R)\n",
    "    \n",
    "    xL = interpolate.bisplev(real_angle_L[0,1],real_angle_L[0,0], tck_getxL)\n",
    "    yL = interpolate.bisplev(real_angle_L[0,1],real_angle_L[0,0], tck_getyL)\n",
    "    xR = interpolate.bisplev(real_angle_R[0,1],real_angle_R[0,0], tck_getxR)\n",
    "    yR = interpolate.bisplev(real_angle_R[0,1],real_angle_R[0,0], tck_getyR)\n",
    "#     print('xL, yL is ({},{})'.format(xL, yL))\n",
    "#     print('xR, yR is ({},{})'.format(xR, yR))\n",
    "    \n",
    "    aL = xy2psi(xL,yL)\n",
    "    aR = xy2psi(xR,yR)\n",
    "    \n",
    "    if psi_right<=aL<=psi_left:\n",
    "        delta_psi = poly_delta_st(aL)\n",
    "    elif aL>psi_left:\n",
    "        delta_psi = poly_delta_sw(aL)\n",
    "    else:\n",
    "        delta_psi = poly_delta_sw(aL+2*np.pi)\n",
    "    \n",
    "#     if aL>aR:\n",
    "#         aR = aR + sp.pi*2\n",
    "#     print('aL is {}, aR is {}'.format(np.float(aL), np.float(aR)))\n",
    "\n",
    "    aL0 = aL0 + delta_t*(w_speed+A_L*sp.sin(((aR-aL)-delta_psi)))\n",
    "    aR0 = aR0 + delta_t*(w_speed+A_R*sp.sin((delta_psi-(aR-aL))))\n",
    "    \n",
    "    aL1 = aL0 % (sp.pi*2)\n",
    "    aR1 = aR0 % (sp.pi*2)\n",
    "    \n",
    "    motor_theta_L = (interpolate.splev(np.float(aL1),tck_L0),interpolate.splev(np.float(aL1),tck_L1))\n",
    "    motor_theta_R = (interpolate.splev(np.float(aR1),tck_R0),interpolate.splev(np.float(aR1),tck_R1))\n",
    "    \n",
    "    odrv0.axis0.controller.pos_setpoint = angle2posL(motor_theta_L)[0,0]\n",
    "    odrv0.axis1.controller.pos_setpoint = angle2posL(motor_theta_L)[0,1]\n",
    "    odrv1.axis0.controller.pos_setpoint = angle2posR(motor_theta_R)[0,0]\n",
    "    odrv1.axis1.controller.pos_setpoint = angle2posR(motor_theta_R)[0,1]\n",
    "\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
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