MPC_New.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "from casadi import *\n",
    "import scipy.interpolate\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#state initilisation\n",
    "init_state= [0,0,0]\n",
    "goal_pose = [3,2,0]\n",
    "\n",
    "#robot paramertes\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#supplemntary model, but not used for the optimization problem...\n",
    "length= 1.2\n",
    "ds=0.1\n",
    "v= 2.77\n",
    "class model:\n",
    "    def __init__(self,x=0.0,y=0.0,theta=0.0,v=0):\n",
    "        self.x=x\n",
    "        self.y=y\n",
    "        self.theta=theta\n",
    "        self.v= v\n",
    "    \n",
    "    def pi_2_pi(angle):\n",
    "        return (angle + math.pi) % (2 * math.pi) - math.pi\n",
    "\n",
    "    def robot_model(state,v,delta,dt,L):\n",
    "        state.v=v\n",
    "        state.x = state.x + state.v * math.cos(state.theta) * dt\n",
    "        state.y = state.y + state.v * math.sin(state.theta) * dt\n",
    "        state.theta = state.theta + state.v / L * math.tan(delta) * dt\n",
    "        state.theta = model.pi_2_pi(state.theta)\n",
    "        \n",
    "        return state\n",
    "\n",
    "    def generate_trajectory(dis,km,kf):\n",
    "        print(dis)\n",
    "        sample= dis/ds\n",
    "        print(sample)\n",
    "        time= dis/v\n",
    "        dt=float(time/sample) \n",
    "        tk= np.array([0.0,time/2.0,time])\n",
    "        kk= np.array([0.0,km,kf])\n",
    "        t=np.arange(0.0,time,time/sample)\n",
    "        fkp= scipy.interpolate.interp1d(tk,kk,kind=\"quadratic\")\n",
    "        spline=[fkp(ti) for ti in t]\n",
    "        state=model()\n",
    "        x,y,theta= [state.x],[state.y],[state.theta]\n",
    "        \n",
    "        for i in spline:\n",
    "            model.robot_model(state,v,i,dt,length)\n",
    "            x.append(state.x)\n",
    "            y.append(state.y)\n",
    "            theta.append(state.theta)\n",
    "            \n",
    "        return x,y,theta \n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "kh=0.2\n",
    "kv=0.4\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "20.0\n",
      "3\n",
      "30.0\n",
      "4\n",
      "40.0\n",
      "5\n",
      "50.0\n",
      "6\n",
      "60.0\n",
      "7\n",
      "70.0\n",
      "8\n",
      "80.0\n",
      "9\n",
      "90.0\n"
     ]
    }
   ],
   "source": [
    "for i in range(2,10):\n",
    "    xc,yc,yawc=model.generate_trajectory(i,i/10,i/20)\n",
    "    #plt.plot(xc,yc)\n",
    "    #plt.show()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 792x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "yc 4.656120286831959\n",
      "zc 1.367852608487089\n",
      "[0.23566244626826888, 0.13564494926042842, 0.05495461851638979, 0.07479285110004295, 0.24097419676930723, 0.3004426935745126, 0.21584518858458634, 0.31482075874516235, 0.12082309257929635, 0.14061765386651284, 0.0968235175345459, 0.20430504645770184, 0.33830475196590387, 0.004262428481211655, 0.34680311279186926, 0.3703710350049014, 0.05533640254190036, 0.33278018815012955, 0.015212377083526896, 0.0251488313138839, 0.3788551265061801, 0.2949853529001348, 0.02961415740129643, 0.2944047341557507, 0.3161298790055465, 0.1345258644065082, 0.3635567321346209, 0.24506690669146902, 0.19155400056094232, 0.12512822753092762, 0.2273396124715076, 0.0539287165301745, 0.1716681163505693, 0.22941429645649022, 0.23949641361703275, 0.3529302643405477, 0.2660084018330284, 0.28437530418720725, 0.10636790287744735, 0.07285240513120775, 0.05616575749545958, 0.21734347513761887, 0.1429152351271545, 0.05803797087472376, 0.03971057229582012, 0.25364225020974407, 0.018057088201844883, 0.13887644997264736, 0.22845037752961847, 0.197050751669775, 0.25784479850382513, 0.05369923276048083, 0.21698904016108297, 0.3397884137731052, 0.34601541489478194, 7.360723350333665e-05, 0.036352247100239814, 0.050454909062294245, 0.35540017478188113, 0.012505616746082105, 0.316265706353245, 0.09024535818233469, 0.05314855682340043, 0.1580641636170133, 0.3977196118645364, 0.37625256647507865, 0.12977066787672875, 0.3668490125814973, 0.30802384235747843, 0.31589076778276826, 0.38937626909873124, 0.11381050401756121, 0.2697313947563361, 0.2093898671530309, 0.1472310216631872, 0.37288659337604024, 0.23538849080683752, 0.1681549627944322, 0.3201214762617441, 0.3238128890811706, 0.07090811415780789, 0.18438390506079905, 0.38544226648811997, 0.058669570301047275, 0.14422973115839044, 0.27595472328770704, 0.16262425155318586, 0.35737375826956863, 0.11454311507094378, 0.033612961481571314, 0.03555298333161918, 0.3265325900529218, 0.36800179050195947, 0.11042207004646767, 0.2070624838719368, 0.20761439263327508, 0.2196622436541017, 0.18890646860838756, 0.14773542159525688, 0.09100554506847787, 0.14807271744473513, 0.30639401470921457, 0.12770707139003737, 0.29141309395102993, 0.07265052618094003, 0.18311387558220274, 0.16306054592463146, 0.27274191854226665, 0.17421794658954048, 0.26272192867687044, 0.2318915076606074, 0.3907973578369869, 0.04820626616176682, 0.1564832931900556, 0.3612366104085961, 0.2638696257370335, 0.3754832120013451, 0.2516525789064628, 0.32902223961796506, 0.01525263618323507, 0.09387421064586343, 0.3660305770591652, 0.35795948510891507, 0.06998794869077037, 0.39218591231528616, 0.08364735238692358, 0.2626450220874103, 0.2891021334001918, 0.316392290559389, 0.36863277788404014, 0.24866615911404166, 0.08967522633075681, 0.24869911773808207, 0.30490482164072774, 0.12739306883852006, 0.29274458514781215, 0.12074275518604938, 0.31103644715501316, 0.12645054825225427, 0.33473222650733037, 0.018588027777794426, 0.23364966790429711, 0.3071487664073375, 0.20439995799326505, 0.14711169081852268, 0.27662574565955594, 0.3562609153016325, 0.1879076558939283, 0.05813289278856826, 0.2597700104264428, 0.22711181940223824, 0.2590855261841808, 0.258573351747732, 0.021537131549448408, 0.1626043021737021, 0.31980014598490175, 0.004071134068956495, 0.2969431232857043, 0.08293822273304752, 0.19799799885154612, 0.017801194377723827, 0.3455670724161542, 0.095141691281545, 0.01290083078493054, 0.35645147301596264, 0.3588543494014982, 0.34892213496873736, 0.03376335670542914, 0.14648911217145352, 0.2887120811816601, 0.3706572961575354, 0.18813362419441476, 0.2190681441869869, 0.2174163240361715, 0.05860995261042872, 0.10985975513380741, 0.29416713643128883, 0.15566426918956658, 0.20773855050265905, 0.13187893528700065, 0.17822228260486944, 0.007344207111784274, 0.010158671010726029, 0.22826690776108194, 0.21124380716390007, 0.31860761969705664, 0.18056216873685849, 0.20040197179586455, 0.05262611315808683, 0.03384383152795705, 0.3426362275038523, 0.14682421258616415, 0.13422300836438603, 0.34406413359508553, 0.039409524489761295, 0.11821502567768878, 0.09444396379737055, 0.354251733928347, 0.014587664992466866, 0.0760968267327983]\n",
      "val1 685.3993655131117\n"
     ]
    }
   ],
   "source": [
    "#This is the final model\n",
    "#Robot model working mechanism by changing the control inputs U (linear and angular velocity(v,ang))\n",
    "x_init=[0,0]\n",
    "x_dest=[20,4]\n",
    "dt=200\n",
    "v=0.2\n",
    "ang=[]\n",
    "#ang=0.023\n",
    "#ang= [0, 0.5, -0.5, 0.5, 0, 0,0, -1, 0.02 ,0]\n",
    "for i in range(0,dt):\n",
    "    o=np.random.uniform(0.0,0.4)\n",
    "    ang.append(o)\n",
    "\n",
    "L=1.2\n",
    "xc,yc,zc=[],[],[]\n",
    "x,y,theta=0,0,0\n",
    "fuel=[]\n",
    "temp=0\n",
    "val,val1=0,0\n",
    "#th=(v / L) * math.tan(ang)*20\n",
    "#x1=v*math.cos((v / L) * math.tan(ang)*20)*20\n",
    "#y1=v*math.sin((v / L) * math.tan(ang)*20)*20\n",
    "#print(\"x\",x1)\n",
    "#print(\"y\",y1)\n",
    "#print(\"th\",th)\n",
    "for i in range(0,dt):\n",
    "    x = x + v*math.cos(theta)*0.2\n",
    "    y = y + v*math.sin(theta)*0.2 \n",
    "    theta = theta + (v / L) * math.tan(ang[i])*0.2\n",
    "    xc.append(x)\n",
    "    yc.append(y)\n",
    "    zc.append(theta)\n",
    "    val1+=x\n",
    "    #val=sqrt((v**2*(xc[i]**2)+ang**2*(yc[i]**2)))\n",
    "    #val=(-0.0177*v**2+1.48*v+3.39)+(1.48*ang**2)\n",
    "    fuel.append(val)\n",
    "    temp+=val\n",
    "plt.show()\n",
    "plt.figure(figsize=(11, 7))\n",
    "plt.plot(xc,yc,4.5,4,\"o\")\n",
    "plt.show()\n",
    "print(\"xc\",xc)\n",
    "print(\"yc\",y)\n",
    "print(\"zc\",zc[-1])\n",
    "print(ang)\n",
    "print(\"val1\",val1)\n",
    "#print(\"xc\",xc)\n",
    "#print(\"yc\",yc)\n",
    "#print(\"zc\",zc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 637,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F:(x0[4],p[],lbx[4],ubx[4],lbg,ubg,lam_x0[4],lam_g0)->(x[4],f,g,lam_x[4],lam_g,lam_p[]) IpoptInterface\n"
     ]
    }
   ],
   "source": [
    "#creating the solver\n",
    "from casadi import *\n",
    "\n",
    "v = MX.sym('v')\n",
    "ang = MX.sym('ang')\n",
    "x=MX.sym('x')\n",
    "y=MX.sym('y')\n",
    "func=0\n",
    "g=0\n",
    "#optimization function\n",
    "for i in range(0,dt):    \n",
    "    #func=func+sqrt((v**2*(xc[i]**2)+ang**2*(yc[i]**2)))\n",
    "    #func=func+((-0.0177*v**2+1.48*v+3.39)+(1.48*ang**2))\n",
    "    func=func+((-0.0177*v**2+1.48*v+3.39)+(1.48*ang**2))*((sqrt(x_dest[1]-x)**2+sqrt(x_dest[0]-y)**2))\n",
    "                                                           \n",
    "#g=((x_dest[0]-xc[-1])-(x_dest[1]-yc[-1]))\n",
    "nlp= {}\n",
    "nlp['x']=vertcat(v,ang,x,y)\n",
    "nlp['f']=func\n",
    "nlp['g']=0\n",
    "#create solver instance\n",
    "F = nlpsol('F','ipopt',nlp);\n",
    "#print(nlp)\n",
    "#print(F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 627,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is Ipopt version 3.12.3, running with linear solver mumps.\n",
      "NOTE: Other linear solvers might be more efficient (see Ipopt documentation).\n",
      "\n",
      "Number of nonzeros in equality constraint Jacobian...:        0\n",
      "Number of nonzeros in inequality constraint Jacobian.:        0\n",
      "Number of nonzeros in Lagrangian Hessian.............:        6\n",
      "\n",
      "Total number of variables............................:        4\n",
      "                     variables with only lower bounds:        0\n",
      "                variables with lower and upper bounds:        4\n",
      "                     variables with only upper bounds:        0\n",
      "Total number of equality constraints.................:        1\n",
      "Total number of inequality constraints...............:        0\n",
      "        inequality constraints with only lower bounds:        0\n",
      "   inequality constraints with lower and upper bounds:        0\n",
      "        inequality constraints with only upper bounds:        0\n",
      "\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "   0 1.7600097e+004 0.00e+000 5.50e+002  -1.0 0.00e+000    -  0.00e+000 0.00e+000   0\n",
      "   1 1.5702081e+004 0.00e+000 5.55e+002  -1.0 6.26e+000   2.0 2.35e-002 4.75e-002f  1\n",
      "   2 1.5677994e+004 0.00e+000 3.15e+002  -1.0 9.79e-001   1.5 4.92e-001 3.22e-003f  1\n",
      "   3 1.5637778e+004 0.00e+000 4.53e+001  -1.0 9.28e-001    -  1.00e+000 3.00e-002f  1\n",
      "   4 1.5635233e+004 0.00e+000 5.68e-004  -1.0 4.12e-003    -  1.00e+000 1.00e+000f  1\n",
      "   5 1.5631679e+004 0.00e+000 7.68e-006  -2.5 1.60e-003    -  1.00e+000 1.00e+000f  1\n",
      "   6 1.5631548e+004 0.00e+000 1.15e-007  -3.8 4.72e-005    -  1.00e+000 1.00e+000f  1\n",
      "   7 1.5631541e+004 0.00e+000 3.33e-010  -5.7 2.45e-006    -  1.00e+000 1.00e+000f  1\n",
      "   8 1.5631541e+004 0.00e+000 2.59e-012  -8.6 3.04e-008    -  1.00e+000 1.00e+000f  1\n",
      "\n",
      "Number of Iterations....: 8\n",
      "\n",
      "                                   (scaled)                 (unscaled)\n",
      "Objective...............:  1.3329849359342438e+003   1.5631541107918771e+004\n",
      "Dual infeasibility......:  2.5894780200475074e-012   3.0366083687251420e-011\n",
      "Constraint violation....:  0.0000000000000000e+000   0.0000000000000000e+000\n",
      "Complementarity.........:  2.5062496572333210e-009   2.9390087980471045e-008\n",
      "Overall NLP error.......:  2.5062496572333210e-009   2.9390087980471045e-008\n",
      "\n",
      "\n",
      "Number of objective function evaluations             = 9\n",
      "Number of objective gradient evaluations             = 9\n",
      "Number of equality constraint evaluations            = 9\n",
      "Number of inequality constraint evaluations          = 0\n",
      "Number of equality constraint Jacobian evaluations   = 9\n",
      "Number of inequality constraint Jacobian evaluations = 0\n",
      "Number of Lagrangian Hessian evaluations             = 8\n",
      "Total CPU secs in IPOPT (w/o function evaluations)   =      0.006\n",
      "Total CPU secs in NLP function evaluations           =      0.007\n",
      "\n",
      "EXIT: Optimal Solution Found.\n",
      "           F  :   t_proc      (avg)   t_wall      (avg)    n_eval\n",
      "       nlp_f  |        0 (       0)        0 (       0)         9\n",
      "       nlp_g  |        0 (       0)        0 (       0)         9\n",
      "  nlp_grad_f  |   4.00ms (400.00us)   3.97ms (397.10us)        10\n",
      "  nlp_hess_l  |   4.00ms (500.00us)   3.99ms (498.50us)         8\n",
      "   nlp_jac_g  |        0 (       0)        0 (       0)        10\n",
      "       total  |  15.00ms ( 15.00ms)  14.96ms ( 14.96ms)         1\n",
      "solved output [0.1, 0.1, 1, 1]\n",
      "solved function output 15631.5\n",
      "<function nlpsol_out at 0x000001BEC5F83E50>\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"
    }
   ],
   "source": [
    "#running the solver in loop\n",
    "for i in range(0,1):\n",
    "# Solve the problem using a guess\n",
    "    solver=F(x0=[0.4,0.023,15,5],lbx=0.1,ubx=1.0,ubg=0.00, lbg=0)\n",
    "    out=[]\n",
    "    out.append(solver[\"x\"])\n",
    "    print(\"solved output\",solver[\"x\"])\n",
    "    print(\"solved function output\",solver[\"f\"])\n",
    "    print(nlpsol_out)\n",
    "    v=out[0][0]\n",
    "    ang=out[0][1]\n",
    "    xc,yc,zc=[],[],[]\n",
    "    x,y,theta=0,0,0\n",
    "    fuel=[]\n",
    "    temp=0\n",
    "    val=0\n",
    "    for i in range(0,dt):\n",
    "        x = x + v*math.cos(theta)*0.2\n",
    "        y = y + v*math.sin(theta)*0.2 \n",
    "        theta = theta + (v / L) * math.tan(ang)*0.2\n",
    "        xc.append(x)\n",
    "        yc.append(y)\n",
    "        zc.append(theta)\n",
    "        #val=sqrt((v**2*(xc[i]**2)+ang**2*(yc[i]**2)))\n",
    "        #fuel.append(val)\n",
    "        #temp+=val\n",
    "    #print(xc[-1],yc[-1])\n",
    "    #plt.plot(fuel)\n",
    "    #plt.show()\n",
    "    plt.plot(xc,yc)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 457,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1becdd60c10>]"
      ]
     },
     "execution_count": 457,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LiViUg8e72deuqRBE3o+78+Cq5JDKy8+bFHQ5gIJesnTyF7LqkBV5X2uaD7Fpz+jd+DsbCnrJSiKWmvNGHbIi7+uhVduSQyoX58+0Xgp6ycqEyjJi4ytoUtCLDGr34U6efauVZZfOZFxZcdDlnKSgl6wNdMiKSGZBz1I5GAW9ZC0Ri/LuvmOc6NVUCCJnSh9SOWNi8EMq0ynoJWvxWJTefufdtuNBlyKSd368fjeH82hIZToFvWQtUacOWZFMkjf+3k68Ln+GVKZT0EvW5kypoqykSL+QFTnD6m0Hk0MqA56lcjAKeslaSXER82qrNbmZyBkeWtXMhMpSbsmjIZXpFPQyJPG6qJpuRNIkh1TuZdmvzMqrIZXpFPQyJIlYlP3HNBWCyIB/eXk7AMsvnxVwJYNT0MuQqENW5JSunj5WrtnBdQvq8m5IZToFvQxJPDZwExIFvcjJIZUB3vg7Gwp6GZJJVWXURstp0i9kpcC5Ow++1Ey8LsJlc/JvSGU6Bb0MWbwuykY13UiBe3XbQZr2tvPJPJqlcjAKehmygakQunv7gy5FJDAPvZTfQyrTKehlyBKxCD19ztb9x4IuRSQQuw518NzG5JDKitL8HFKZLuugN7NiM1tnZk+l1heb2Stmtt7MGs3s0kGOazazNwb2y1XhEpyTNyFR840UqH95JTmk8hNX5NcslYMZyhX9XcCmtPW/Af7C3RcD/zO1Ppir3H2xuzcMvUTJN+dNraKsuEgdslKQOrv7eGzNTn7jA3VMnzAu6HKyklXQm9kM4EbggbTNDkRTy+OBltyWJvmqtLiIC2qq1SErBenULJX1QZeStZIs97sXuBuIpG37HPCsmf0dyRPGlYMc68BzZubAt939/kw7mdkKYAXArFn5+wszSUrEovxiy76gyxAZVclZKptJxKJcmudDKtOd9YrezG4C2tx97RlP/RHweXefCXwe+M4gL7HE3S8GbgDuNLMPZdrJ3e939wZ3b5g6dWr2fwIJRCIWYV/7CfYf01QIUjhe2ZoaUpmns1QOJpummyXAzWbWDKwErjazh4HbgR+m9vk+kLEz1t1bUo9twBOD7Sdjy0CHrNrppZA8tGobEytLuXnxtKBLGZKzBr27f9ndZ7h7PbAMeMHdl5Nsk//11G5XA1vOPNbMqswsMrAMXAe8maPaJUCJWLIVT1MhSKHYdaiD5ze2suzSsTGkMl22bfSZ/CFwn5mVAF2k2tfNbBrwgLsvBWqBJ1JfcUqAR9z9meGVLPlgcnU5UyPlulm4FIx/eWU7ZsbyPLvxdzaGFPTu/iLwYmr5l8AlGfZpAZamlrcCi4ZbpOSneF1EY+mlIHR297Fy9U5+4wO1Y2ZIZTr9MlbO2YJYlHfajtHTp6kQJNx+tH43Rzrz88bf2VDQyzmLxyJ09/Wzdd/xoEsRGTHuzkMvNbMgFuVX6icGXc45UdDLOTs58kYdshJiL289wObW9ry98Xc2FPRyzs6fWk1psalDVkLtoZeax+SQynQKejlnZSVFnD+1Wh2yElo7D3bw75tauW0MDqlMp6CXYVkQi6rpRkLr4TE8pDKdgl6GJR6L0Hr0BAePdwddikhOdXT38ujqHVz/gTqmjcEhlekU9DIsp6ZC0FW9hMuP1rVwtKuX28fQLJWDUdDLsCRiqZuQ7FWHrIRHcpbKbWN6SGU6Bb0My9RIOVOqy9QhK6Hy8rsHeLv1GHeMgRt/Z0NBL8MWr1OHrITLQ6uamVRVxs2Lxu6QynQKehm2RCzC263H6NVUCBICp4ZUzhzTQyrTKehl2OJ1Ubp7+9m2X1MhyNg3lmepHMxwpikWAU7vkJ1bGznL3iJJOw508CdPvMGsyZVcMmsiDfUTmTWpMtA28Y7uXlamhlTGxo/tIZXpFPQybOfXVFFSZDTtORqaNk0ZWT19/Xxm5Tre3tvOhp2HeeTVHQBMqS7nktkTuGT2RC6ZPYmF06OUl4xe88kT63ZztKuXO5bUj9p7jgYFvQxbeUmxpkKQIbn3399mw87D/J/fvYgbFsbY0tbO2u2HWNt8iLU7DvHsW61AcpqND04fnwr+iVw8eyJTqstHpCZ357urmvnAtCgNs8f+kMp0CnrJiUQswqvbDgZdhowBq97dzzdffJePN8zgpg8mvwHG66LE66L83mXJdvG29i5e236YtdsPsnb7IR58qZlv/2IrAHOmVHFxqqnnktkTuWBqNUVFw2/uGRhS+bf/5YOhGFKZTkEvORGPRfnR+hYOd3QzobIs6HIkTx063s0XHtvAnMlV/PlvfmDQ/WoiFVy/sI7rF9YB0NXTx5u7j9C4/RBrtx/ixc1t/OC1XQBEK0q4ePZEGlJX/ItnTqCybOjR9mBqSOVvhrD5UUEvORGvS3bCbtrTzhXnTw64GslH7s49P3ydA8dP8H9/fwlV5dnHT0VpMQ31k2ion3TytZoPdNDYfJDXdhyisfkQL27eB0BxkbEgFj3Z3HPJ7IlnnatmYEjlnR++IDRDKtMp6CUnFsRO3YREQS+ZPLJ6B8++1cqfLI1z4Yzxw3otM2POlCrmTKni1oaZABzp6OG1nal2/u2HeGzNTh5a1QzAtPEVJ6/6L5k9iUQsQknxqdHl/+/lZorM+L3LZw2rrnyloJecmBopZ1KVpkKQzLa0tvPVpzbya3On8F9/9bwReY/xlaVcNb+Gq+bXAMmRPU172mlMtfOv3X6Ip17fA8C40mIWz5xAQ/1EFs2YwGNrdnL9wnANqUyXddCbWTHQCOx295vMbDHwLaAC6AX+u7uvznDc9cB9QDHwgLv/dS4Kl/xiZiRiEZo0uZmcoaunj888uo7KshK+fuuinHScZqO0uIgLZ4znwhnj+eSS5E29Ww530rj9EK9tP0Tj9oN888V36et3AO4IwSyVgxnKFf1dwCYgmlr/G+Av3P3fzGxpav3D6QekTg7fAK4FdgFrzOxJd9843MIl/8Trojz8ynb6+p3iUfrHLPnva8800bS3ne/c3kBNtCLQWqZNGMfNE8ad/L3H8RO9bNh1mKOdvaEbUpkuqykQzGwGcCPwQNpm51TojwdaMhx6KfCOu291925gJXDLuZcr+SxeF+GEpkKQND9vauPBl5q548p6rknUBl3Oe1SVl3Dl+VO4fmFd6IZUpsv2iv5e4G4g/fftnwOeNbO/I3nCuDLDcdOBnWnru4DLMr2Bma0AVgDMmhXODpGwS6R1yF5QUx1wNRK0tvYuvvT9DcyvjXDPDfGgyyloZ72iN7ObgDZ3X3vGU38EfN7dZwKfB76T6fAM2zzT+7j7/e7e4O4NU6dOPVtZkocuqKmmuMjUISv09ztffHwDx0708o+/e1EohyyOJdlc0S8Bbk61w1cAUTN7GPhNku32AN/n9GadAbuAmWnrM8jcxCMhUFFazHlTqmjaow7ZQvfPL23jP7fs56sfXcg8TXQXuLNe0bv7l919hrvXA8uAF9x9OcnA/vXUblcDWzIcvgaYa2ZzzKwsdfyTOalc8lIiFtXImwL35u4jfO2ZJj6SqGX5ZWqGzQfDmY/+D4Gvm9kG4H+Ral83s2lm9jSAu/cCnwaeJTli53F3f2t4JUs+i8ci7D7cyZGOnqBLkQB0dPfy2ZXrmFRVxt+EcM6YsWpIP5hy9xeBF1PLvwQuybBPC7A0bf1p4OnhFCljR3qH7GXn6ReyhearT21k2/7jPPypy5hUpTmP8oXuMCU5lagbCHo13xSap9/Yw6Ord/LfPnQ+Sy6YEnQ5kkZBLzlVGy1nQmWpRt4UmJbDndzzg9dZNGM8X7xuXtDlyBkU9JJTZkaiLsomXdEXjL5+53OPrae337lv2UWUFitW8o3+j0jOxWMRNu89enIOEQm3b/78HVZvO8hXbllI/ZSqoMuRDBT0knOJuihdPf1sP6CpEMJu7fZD3PuzLdy8aBofu3h60OXIIBT0knOnRt6o+SbMjnb1cNfKdcTGV/CXv7VQQynzmIJecm5ubTVFhjpkQ8zd+bMfvcmeI13ct2wx0YrSoEuS96Ggl5yrKC3mvKnVbNJUCKH1xLrd/Hh9C3ddM5dLZk8Kuhw5CwW9jIh4XYSmvbqiD6PtB47zZz96k0vrJ3HnVRcEXY5kQUEvIyIRi7LrUCdHuzQVQpj09PXz2ZXrKS4y/n7ZYt1gZoxQ0MuISMSSMxZuVodsqPz982+zYedh/vpjH2T6hHDeXzWMFPQyIuKpqRDUIRseq97dzz/9x7v8TsNMll4YC7ocGQIFvYyI2PgKohUl6pANiUPHu/nCYxuYM7mKP795QdDlyBAp6GVEmFlqbnpd0Y917s7/+MHrHDh+gn+47SIqy4Y06a3kAQW9jJhELMrmve30ayqEMe2R1Tt4bmMrd/9GnIXTxwddjpwDBb2MmEQsQkd3HzsOdgRdipyjLa3tfPWpjfza3Cl86lfnBF2OnCMFvYyYeN2pm5DI2NPV08dnHl1HVVkJX//4Ioo0lHLMUtDLiJlXG6HIYKM6ZMekrz3TRNPedv721g9SE6kIuhwZBgW9jJhxZcXUT6miSUMsx5yfN7Xx4EvN3HFlPVfHa4MuR4ZJ3ecyohJ1UdY0H+Snr++hbnw5NZEKaqLllJcUB12aDKKtvYsvfX8D8boI99wQD7ocyQEFvYyoK86fzE/f2MOdj7x22vaJlaXURiuoiVZQGymnNlpB7fi05WgFU6rLKNHdikZVf7/zxcc3cOxEL4+uuJyKUp2QwyDroDezYqAR2O3uN5nZY8D81NMTgMPuvjjDcc1AO9AH9Lp7wzBrljFk+eWzWXphjNajXbQe7aLt6An2ppZbj56grb2LzXuPsq/9BGeOwjSDKdXl1EbLqY0MnAgqkuvR5DeD2mgFkyrL1FGYI//80jb+c8t+vvrRhcyrjQRdjuTIUK7o7wI2AVEAd/+dgSfM7OvAkfc59ip3339OFcqYN6mqjElVZSdvSJJJX79z4NgJWo+eSJ4E2pMngtYjyeWWI12s33mYA8e733NsSZFREymnJlpBXTR5IqhJfSsYOCnURiqIjivRzTHex5u7j/C1Z5q4dkEtyy+bFXQ5kkNZBb2ZzQBuBP4K+MIZzxnwceDqnFcnBaO4yKhJNeVcyOA/yunu7WffsROpbwddp04Mqcd39x1j1bv7OdrV+55jiwwqy0oYV1ZMZVkx40qL05ZLqBxYTj2XXE7bfpb9x3IzU0d3L59duY5JVWV87WMf1AkxZLK9or8XuBvI9F3u14BWd98yyLEOPGdmDnzb3e/PtJOZrQBWAMyapasJyayspIjpE8addebEzu4+2trTTwRdHO7ooaO7j86eXjq6++jo7qOrJ/l48Hgnnd3J7Z3dfXT09A355uZlxUWnTgRnnixKT22fNmEcc2uqmVcbYeakyryY6vcrP9nItv3H+d6nLmNSVVnQ5UiOnTXozewmoM3d15rZhzPschvw6Pu8xBJ3bzGzGuB5M2ty91+cuVPqBHA/QENDg34zL8MyrqyY2ZOrmD256pxfo7u3PxX6p04AnakTw8BJIf1kcdr2nj66UtuOdPaw90jnyX0OpjU/VZQWcUEq9JP/JZenTxg3alfVT7+xh5VrdvJHHz6fKy+YMirvKaMrmyv6JcDNZrYUqACiZvawuy83sxLgt4FLBjvY3VtSj21m9gRwKfCeoBfJN2UlRZSVFDGe3N4P9diJXra0trOl9Rhvt7azubWdVe8c4Iev7T65T1VZMXPTgn/gv9poeU5PAC2HO7nnB6+zaMZ4vnDtvJy9ruSXswa9u38Z+DJA6or+S+6+PPX0R4Amd9+V6VgzqwKK3L09tXwd8JUc1C0yZlWXl3DRrIlcNGviaduPdPSwpS0Z/AMngRea2ni88dQ/r2hFSTL06yLMG/gmUBdhSnX5kOvo63c+99h6+vqd+5ZdROkY7mOQ9zfccfTLOKPZxsymAQ+4+1KgFngidQVSAjzi7s8M8z1FQml8ZSkN9ZNoqD/9ZtsHjp3g7dZjyZPA3uRJ4Kev7+GRzlO3aZxUVXby6n9ubYT5qW8DEyoHb2//5s/fYfW2g3z91kXUTzn3Ji7Jf+aef83hDQ0N3tjYGHQZInnL3dnXnjwBJL8BnPomcOzEqRFHNZHyVPhXMz91EphXW83brcf4+Ldf5sYLY9y3bLFG2YSAma0d7HdK+mWsyBhkdmo46q/OPdWB6u7sOdJ1Kvz3Jr8JPLp6B109/Sf3KysuIja+gr/8rYUK+QKgoBcJETNj2oRxTJswjqvm15zc3t/v7DrUyebWdt5ubad5/3Fuv7KeaEVuO5olPynoRQpAUZExa3IlsyZXcu0CzUZZaNTNLiIScgp6EZGQU9CLiIScgl5EJOQU9CIiIaegFxEJOQW9iEjIKehFREIuL+e6MbN9wPZzPHwKoNsWJumzOJ0+j9Pp8zglDJ/FbHefmumJvAz64TCzRt2APEmfxen0eZxOn8cpYf8s1HQjIhJyCnoRkZALY9BnvPl4gdJncTp9HqfT53FKqD+L0LXRi4jI6cJ4RS8iImkU9CIiIReaoDez681ss5m9Y2b3BF1PkMxsppn93Mw2mdlbZnZX0DUFzcyKzWydmT0VdC1BM7MJZvavZtaU+jtyRdA1BcnMPp/6d/KmmT1qZhVB15RroQh6MysGvgHcACwAbjOzBcFWFahe4IvungAuB+4s8M8D4C5gU9BF5In7gGfcPQ4sooA/FzObDnwWaHD3hUAxsCzYqnIvFEEPXAq84+5b3b0bWAncEnBNgXH3Pe7+Wmq5neQ/5OnBVhUcM5sB3Ag8EHQtQTOzKPAh4DsA7t7t7ocDLSp4JcA4MysBKoGWgOvJubAE/XRgZ9r6Lgo42NKZWT1wEfBqwKUE6V7gbqA/4DrywXnAPuDBVFPWA2ZWFXRRQXH33cDfATuAPcARd38u2KpyLyxBbxm2Ffy4UTOrBn4AfM7djwZdTxDM7Cagzd3XBl1LnigBLgb+yd0vAo4DBdunZWYTSX77nwNMA6rMbHmwVeVeWIJ+FzAzbX0GIfz6NRRmVkoy5L/n7j8Mup4ALQFuNrNmkk16V5vZw8GWFKhdwC53H/iG968kg79QfQTY5u773L0H+CFwZcA15VxYgn4NMNfM5phZGcnOlCcDrikwZmYk22A3ufv/DrqeILn7l919hrvXk/x78YK7h+6KLVvuvhfYaWbzU5uuATYGWFLQdgCXm1ll6t/NNYSwc7ok6AJywd17zezTwLMke83/2d3fCrisIC0BPgG8YWbrU9v+xN2fDq4kySOfAb6XuijaCnwy4HoC4+6vmtm/Aq+RHK22jhBOh6ApEEREQi4sTTciIjIIBb2ISMgp6EVEQk5BLyIScgp6EZGQU9CLiIScgl5EJOT+PyfJV3xygS5SAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "loss=[5.0661393e+001,5.0661393e+001 ,5.0655255e+001,4.7563294e+001,4.7506171e+001 ,4.7482457e+001 ,4.7387446e+001 ,4.8165258e+001 ,4.8037306e+001 ,4.9342843e+001] \n",
    "plt.plot(loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**create constraints and initilize optimization variables**\n",
    "\n",
    "1. Here the constraints are bounday conditions around the magins(inequality constraint)\n",
    "2. waypoints are(equality constraint)\n",
    "3. Destination(equality constraint)\n",
    "4. Obstacles(inequality constraint)\n",
    "\n",
    "\n",
    "**The optimization varilables are control inputs**\n",
    "\n",
    "1. U1= Linear Velocity \n",
    "2. U2= Angular Velocity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Main function to iterate over the solver**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 685,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'x': MX(x), 'f': MX(sqrt((sq((x-100))+x))), 'g': 0}\n"
     ]
    }
   ],
   "source": [
    "x=MX.sym('x')\n",
    "func= sqrt((x-100)**2+(sqrt(x)-0)**2)                                                      \n",
    "nlp= {}\n",
    "nlp['x']=vertcat(x)\n",
    "nlp['f']=func\n",
    "nlp['g']=0\n",
    "#create solver instance\n",
    "F = nlpsol('F','ipopt',nlp);\n",
    "print(nlp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#simple point solver (learning example)\n",
    "solver=F(x0=0)\n",
    "out=[]\n",
    "out.append(solver[\"x\"])\n",
    "print(\"solved output\",solver[\"x\"])\n",
    "print(\"solved function output\",solver[\"f\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y=[]\n",
    "for i in range(0,20):\n",
    "    y.append(sqrt(i))\n",
    "plt.plot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'x': MX(ang), 'f': MX(sqrt((sq(((10*(0.4*cos((10*(0.333333*tan(ang))))))-3))+sq(((10*(0.4*sin((10*(0.333333*tan(ang))))))-3))))), 'g': 0}\n"
     ]
    }
   ],
   "source": [
    "#minimize the distance by varying the velocity and time\n",
    "from casadi import *\n",
    "import math\n",
    "dest=[3,3]\n",
    "v=MX.sym('v')\n",
    "t=MX.sym('t')\n",
    "ang=MX.sym('ang')\n",
    "t=10\n",
    "func=0\n",
    "g=0\n",
    "dt=100\n",
    "func1,func2=0,0\n",
    "#func = sqrt((((v*math.cos(0.1)*t)-dest[0])**2)+((v*math.sin(0.1)*t)-dest[1])**2)+(-0.0177*v**2+1.48*v+3.39)\n",
    "func = sqrt((((0.4*cos((0.4/1.2)*tan(ang)*t)*t)-dest[0])**2)+((0.4*sin((0.4/1.2)*tan(ang)*t)*t)-dest[1])**2)\n",
    "#new function\n",
    "'''\n",
    "for _ in range(0,100):\n",
    "    theta= theta+ (0.4/1.2)*tan(ang)*t/100\n",
    "    func1 = func1+ (0.4*cos(theta)*t/100)\n",
    "    func2= func2+ (0.4*sin(theta)*t/100)\n",
    "func= sqrt((((func1-dest[0])**2)+(func2-dest[1])**2))\n",
    "'''\n",
    "nlp= {}\n",
    "nlp['x']=vertcat(ang)\n",
    "#nlp['x']=vertcat(v,t) \n",
    "nlp['f']=func\n",
    "nlp['g']=0\n",
    "opts= {}\n",
    "opts[\"ipopt.max_iter\"]=5000\n",
    "#create solver instance\n",
    "F = nlpsol('F','ipopt',nlp,opts);\n",
    "print(nlp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is Ipopt version 3.12.3, running with linear solver mumps.\n",
      "NOTE: Other linear solvers might be more efficient (see Ipopt documentation).\n",
      "\n",
      "Number of nonzeros in equality constraint Jacobian...:        0\n",
      "Number of nonzeros in inequality constraint Jacobian.:        0\n",
      "Number of nonzeros in Lagrangian Hessian.............:        1\n",
      "\n",
      "Total number of variables............................:        1\n",
      "                     variables with only lower bounds:        0\n",
      "                variables with lower and upper bounds:        1\n",
      "                     variables with only upper bounds:        0\n",
      "Total number of equality constraints.................:        0\n",
      "Total number of inequality constraints...............:        1\n",
      "        inequality constraints with only lower bounds:        0\n",
      "   inequality constraints with lower and upper bounds:        0\n",
      "        inequality constraints with only upper bounds:        0\n",
      "\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "   0 5.3548836e-001 0.00e+000 1.27e+001  -1.0 0.00e+000    -  0.00e+000 0.00e+000   0\n",
      "   1 7.5466252e-001 0.00e+000 4.11e+000  -1.0 6.68e-002    -  1.00e+000 2.50e-001f  3\n",
      "   2 6.4287021e-001 0.00e+000 6.61e-002  -1.0 8.42e-003    -  1.00e+000 1.00e+000f  1\n",
      "   3 5.2452609e-001 0.00e+000 1.65e-001  -2.5 9.15e-003    -  9.73e-001 1.00e+000f  1\n",
      "   4 5.1569126e-001 0.00e+000 1.54e-003  -2.5 7.00e-004    -  1.00e+000 1.00e+000f  1\n",
      "   5 5.1288385e-001 0.00e+000 1.64e-004  -3.8 2.23e-004    -  1.00e+000 1.00e+000f  1\n",
      "   6 5.1272759e-001 0.00e+000 5.16e-007  -5.7 1.24e-005    -  1.00e+000 1.00e+000f  1\n",
      "   7 5.1272572e-001 0.00e+000 7.37e-011  -8.6 1.48e-007    -  1.00e+000 1.00e+000f  1\n",
      "\n",
      "Number of Iterations....: 7\n",
      "\n",
      "                                   (scaled)                 (unscaled)\n",
      "Objective...............:  5.1272572441424957e-001   5.1272572441424957e-001\n",
      "Dual infeasibility......:  7.3747230544540798e-011   7.3747230544540798e-011\n",
      "Constraint violation....:  0.0000000000000000e+000   0.0000000000000000e+000\n",
      "Complementarity.........:  2.5093151701989290e-009   2.5093151701989290e-009\n",
      "Overall NLP error.......:  2.5093151701989290e-009   2.5093151701989290e-009\n",
      "\n",
      "\n",
      "Number of objective function evaluations             = 14\n",
      "Number of objective gradient evaluations             = 8\n",
      "Number of equality constraint evaluations            = 0\n",
      "Number of inequality constraint evaluations          = 14\n",
      "Number of equality constraint Jacobian evaluations   = 0\n",
      "Number of inequality constraint Jacobian evaluations = 8\n",
      "Number of Lagrangian Hessian evaluations             = 7\n",
      "Total CPU secs in IPOPT (w/o function evaluations)   =      0.012\n",
      "Total CPU secs in NLP function evaluations           =      0.000\n",
      "\n",
      "EXIT: Optimal Solution Found.\n",
      "           F  :   t_proc      (avg)   t_wall      (avg)    n_eval\n",
      "       nlp_f  |        0 (       0)        0 (       0)        14\n",
      "       nlp_g  |        0 (       0)        0 (       0)        14\n",
      "  nlp_grad_f  |        0 (       0)        0 (       0)         9\n",
      "  nlp_hess_l  |        0 (       0)        0 (       0)         7\n",
      "   nlp_jac_g  |        0 (       0)        0 (       0)         9\n",
      "       total  |  12.00ms ( 12.00ms)  12.40ms ( 12.40ms)         1\n",
      "solved output [DM(0.2)]\n",
      "solved function output 0.512726\n"
     ]
    }
   ],
   "source": [
    "lbx=[0.02]\n",
    "ubx=[0.2]\n",
    "#solver=F(x0=[0.1,2],lbx=lbx,ubx=ubx)\n",
    "solver=F(x0=[0.2],lbx=lbx,ubx=ubx)\n",
    "out=[]\n",
    "out.append(solver[\"x\"])\n",
    "print(\"solved output\",out)\n",
    "print(\"solved function output\",solver[\"f\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time 20\n",
      "velocity 0.4\n",
      "angle 0.02\n",
      "7.976664987835587 0.5272961558667796\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x16121205100>,\n",
       " <matplotlib.lines.Line2D at 0x16121205400>]"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "#t=out[0][0]\n",
    "ang=out[0][0]\n",
    "#ang=out[0][2]\n",
    "v=0.4\n",
    "t=20\n",
    "print(\"time\",t)\n",
    "print(\"velocity\",v)\n",
    "print(\"angle\",ang)\n",
    "#print(ang)\n",
    "xc,yc=[],[]\n",
    "theta=0.0\n",
    "#ang=0.1\n",
    "x1,x2=0,0\n",
    "t=t/100\n",
    "for i in range(0,100):\n",
    "    x1=x1+v*math.cos(theta)*t\n",
    "    x2=x2+v*math.sin(theta)*t\n",
    "    theta = theta + (v / 1.2) * math.tan(ang)*t\n",
    "    xc.append(x1)\n",
    "    yc.append(x2)\n",
    "print(x1,x2)\n",
    "plt.figure(figsize=(10, 5))\n",
    "plt.plot(xc,yc,dest[0],dest[1],\"o\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13ff1ff27f0>]"
      ]
     },
     "execution_count": 282,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    " cost=[3.3099703e+001,\n",
    "    3.1484916e+001 ,\n",
    "    1.7774696e+001 ,\n",
    "    1.3164476e+001,\n",
    "    1.1309515e+001 ,\n",
    "    1.0286753e+001,\n",
    "    9.5050779e+000 ,\n",
    "    8.7115020e+000,\n",
    "    8.3286052e+000 ,\n",
    "    7.8670146e+000,\n",
    "   7.4222025e+000 ,\n",
    "   7.1945799e+000,\n",
    "   6.8714011e+000 ,\n",
    "  6.7117983e+000 ,\n",
    "   6.4199344e+000,\n",
    "   6.3441764e+000 ,\n",
    "   6.3402380e+000 ,\n",
    "   6.1372877e+000 ,\n",
    "   5.9515466e+000 ,\n",
    "   5.8014162e+000, \n",
    "   5.7958203e+000, \n",
    "   5.5985301e+000,\n",
    "   5.5147993e+000 ,\n",
    "   5.4537076e+000 ,\n",
    "   5.3693894e+000 ,\n",
    "   5.2996137e+000,\n",
    "   5.2274934e+000 ,\n",
    "   5.2038087e+000 ,\n",
    " 5.1099343e+000,\n",
    " 5.0969828e+000,\n",
    "4.4690714e+000 ,\n",
    "4.4690695e+000 ,\n",
    "   4.4690695e+000]\n",
    "\n",
    "plt.plot(cost)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from casadi import *\n",
    "from numpy import *\n",
    "%matplotlib inline\n",
    "#import matplotlib\n",
    "#matplotlib.use('TkAgg')\n",
    "import matplotlib.pyplot as plt\n",
    "class Iteration_Callback(Callback):\n",
    "    def __init__(self, name, nx, ng, opts={}):\n",
    "        Callback.__init__(self)\n",
    "\n",
    "        self.nx = nx\n",
    "        self.ng = ng\n",
    "\n",
    "        self.x_sols = []\n",
    "        self.f_sols = []\n",
    "        self.g_sols = []\n",
    "        self.lam_x_sols = []\n",
    "        self.lam_g_sols = []\n",
    "        self.lam_p_sols = []\n",
    "        '''\n",
    "        #for plotting the graph in realtime\n",
    "        self.fig= plt.figure()\n",
    "        self.ax1= self.fig.add_subplot(1,2,1)\n",
    "        self.ax2= self.fig.add_subplot(2,2,1)\n",
    "        self.fig.show()\n",
    "        '''\n",
    "        # Initialize internal objects\n",
    "        self.construct(name, opts)\n",
    "\n",
    "    def get_n_in(self): return nlpsol_n_out()\n",
    "    def get_n_out(self): return 1\n",
    "    def get_name_in(self, i): return nlpsol_out(i)\n",
    "    def get_name_out(self, i): return \"ret\"\n",
    "\n",
    "    def get_sparsity_in(self, i):\n",
    "        n = nlpsol_out(i)\n",
    "        if n == 'f':\n",
    "            return Sparsity.scalar()\n",
    "        elif n in ('x', 'lam_x'):\n",
    "            return Sparsity.dense(self.nx)\n",
    "        elif n in ('g', 'lam_g'):\n",
    "            return Sparsity.dense(self.ng)\n",
    "        else:\n",
    "            return Sparsity(0, 0)\n",
    "\n",
    "    def eval(self, arg):\n",
    "        \n",
    "        darg = {}\n",
    "        for (i, s) in enumerate(nlpsol_out()): darg[s] = arg[i]\n",
    "        x_sol = [float(elem) for elem in darg['x'].full()]\n",
    "        \n",
    "        self.x_sols.append(x_sol)\n",
    "        self.f_sols.append(darg['f'].full()[0][0])\n",
    "        self.g_sols.append(darg['g'].full()[0][0])\n",
    "        self.lam_x_sols.append(darg['lam_x'].full())\n",
    "        self.lam_g_sols.append(darg['lam_g'].full())\n",
    "        self.lam_p_sols.append(darg['lam_p'].full())\n",
    "        #print(\"solution\",self.f_sols)\n",
    "        '''\n",
    "        #for plotting the graph in realtime\n",
    "        self.ax1.plot(self.x_sols)\n",
    "        self.ax2.plot(self.f_sols)\n",
    "        self.fig.canvas.draw()\n",
    "        self.fig.canvas.flush_events()\n",
    "        plt.show()\n",
    "        '''\n",
    "        plt.plot(self.f_sols,color='C0')\n",
    "        #plt.plot(self.g_sols,color='C0')\n",
    "        #print(self.g_sols)\n",
    "        return[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ang_0, ang_1, ang_2, ang_3, ang_4, ang_5, ang_6, ang_7, ang_8, ang_9]\n",
      "@1=1.2, @2=(((v/@1)*tan(ang_0))*t), @3=(@2+(((v/@1)*tan(ang_1))*t)), @4=(@3+(((v/@1)*tan(ang_2))*t)), @5=(@4+(((v/@1)*tan(ang_3))*t)), @6=(@5+(((v/@1)*tan(ang_4))*t)), @7=(@6+(((v/@1)*tan(ang_5))*t)), @8=(@7+(((v/@1)*tan(ang_6))*t)), @9=(@8+(((v/@1)*tan(ang_7))*t)), @10=(@9+(((v/@1)*tan(ang_8))*t)), @11=-0.0177, @12=1.48, @13=3.39, ((sqrt(((0.0045+sq((((((((((((v*t)+((v*cos(@2))*t))+((v*cos(@3))*t))+((v*cos(@4))*t))+((v*cos(@5))*t))+((v*cos(@6))*t))+((v*cos(@7))*t))+((v*cos(@8))*t))+((v*cos(@9))*t))+((v*cos(@10))*t))-3)))+sq((((((((((((v*sin(@2))*t)+((v*sin(@3))*t))+((v*sin(@4))*t))+((v*sin(@5))*t))+((v*sin(@6))*t))+((v*sin(@7))*t))+((v*sin(@8))*t))+((v*sin(@9))*t))+((v*sin(@10))*t))-1))))+((@10+(((v/@1)*tan(ang_9))*t))-0.785398))+((((((((((((@11*sq(v))+(@12*v))+@13)+(((@11*sq(v))+(@12*v))+@13))+(((@11*sq(v))+(@12*v))+@13))+(((@11*sq(v))+(@12*v))+@13))+(((@11*sq(v))+(@12*v))+@13))+(((@11*sq(v))+(@12*v))+@13))+(((@11*sq(v))+(@12*v))+@13))+(((@11*sq(v))+(@12*v))+@13))+(((@11*sq(v))+(@12*v))+@13))+(((@11*sq(v))+(@12*v))+@13)))\n",
      "0\n",
      "F:(x0[12],p[],lbx[12],ubx[12],lbg,ubg,lam_x0[12],lam_g0)->(x[12],f,g,lam_x[12],lam_g,lam_p[]) IpoptInterface\n"
     ]
    }
   ],
   "source": [
    "from casadi import *\n",
    "import math\n",
    "dest=[3,1]\n",
    "#way=[3,0]\n",
    "t=SX.sym('t')\n",
    "v=SX.sym('v')\n",
    "dt= 10\n",
    "rob_rad=0.1\n",
    "obs_rad=0.1\n",
    "ang=SX.sym(\"ang\",dt)\n",
    "#v=SX.sym(\"v\")\n",
    "#t=SX.sym(\"t\")\n",
    "print(ang)\n",
    "func,func1,func2=0,0,0\n",
    "g=0\n",
    "theta=0\n",
    "fuel_cost=0\n",
    "coff=0.0045\n",
    "for i in range(0,dt):\n",
    "        func1=func1+v*cos(theta)*t\n",
    "        func2=func2+v*sin(theta)*t\n",
    "        theta=theta + (v / 1.2)*tan(ang[i])*t\n",
    "        fuel_cost=fuel_cost+(-0.0177*v**2+1.48*v+3.39)\n",
    "        #if i==dt/2:\n",
    "            #func_con=(sqrt(coff+(func1-way[0])**2+(func2-way[1])**2))\n",
    "        if i==dt-1:\n",
    "            func=(sqrt(coff+(func1-dest[0])**2+(func2-dest[1])**2))+fuel_cost\n",
    "            #g=sqrt((func1-way[0])**2+(func2-way[1])**2)-(rob_rad+obs_rad)\n",
    "            #g=func_con\n",
    "            print(func)     \n",
    "            print(g)\n",
    "nlp= {}\n",
    "nlp['x']=vertcat(ang,v,t)\n",
    "nlp['f']=func\n",
    "nlp['g']=0\n",
    "mycallback = Iteration_Callback('mycallback',(dt+2), 1)\n",
    "opts = {}\n",
    "opts['iteration_callback'] = mycallback\n",
    "opts['ipopt.tol'] = 1e-8\n",
    "opts[\"ipopt.max_iter\"]=5000\n",
    "#create solver instance\n",
    "F = nlpsol('F','ipopt',nlp,opts);\n",
    "print(F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.2, 0.2]\n",
      "\n",
      "******************************************************************************\n",
      "This program contains Ipopt, a library for large-scale nonlinear optimization.\n",
      " Ipopt is released as open source code under the Eclipse Public License (EPL).\n",
      "         For more information visit http://projects.coin-or.org/Ipopt\n",
      "******************************************************************************\n",
      "\n",
      "This is Ipopt version 3.12.3, running with linear solver mumps.\n",
      "NOTE: Other linear solvers might be more efficient (see Ipopt documentation).\n",
      "\n",
      "Number of nonzeros in equality constraint Jacobian...:        0\n",
      "Number of nonzeros in inequality constraint Jacobian.:        0\n",
      "Number of nonzeros in Lagrangian Hessian.............:       66\n",
      "\n",
      "Total number of variables............................:       12\n",
      "                     variables with only lower bounds:        0\n",
      "                variables with lower and upper bounds:       12\n",
      "                     variables with only upper bounds:        0\n",
      "Total number of equality constraints.................:        1\n",
      "Total number of inequality constraints...............:        0\n",
      "        inequality constraints with only lower bounds:        0\n",
      "   inequality constraints with lower and upper bounds:        0\n",
      "        inequality constraints with only upper bounds:        0\n",
      "\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "   0 3.9638875e+001 0.00e+000 1.29e+001  -1.0 0.00e+000    -  0.00e+000 0.00e+000   0\n",
      "   1 3.8142970e+001 0.00e+000 1.16e+001  -1.0 1.15e-001   2.0 9.82e-001 1.00e+000f  1\n",
      "   2 3.7327998e+001 0.00e+000 7.23e+000  -1.0 2.23e-001   1.5 1.00e+000 2.87e-001f  1\n",
      "   3 3.7437955e+001 0.00e+000 1.70e+000  -1.0 2.88e-001    -  6.15e-001 1.00e+000f  1\n",
      "   4 3.7347675e+001 0.00e+000 4.87e-001  -1.0 4.39e-002   1.0 1.00e+000 1.00e+000f  1\n",
      "   5 3.7125706e+001 0.00e+000 4.35e+000  -1.7 7.90e-001    -  4.23e-001 1.00e+000f  1\n",
      "   6 3.7103696e+001 0.00e+000 3.09e-001  -1.7 8.34e-002   0.6 1.00e+000 1.00e+000f  1\n",
      "   7 3.6256644e+001 0.00e+000 7.69e+000  -1.7 8.60e-001   0.1 1.44e-001 1.00e+000f  1\n",
      "   8 3.6095462e+001 0.00e+000 7.43e+000  -1.7 3.14e-001   1.4 1.00e+000 6.25e-002f  5\n",
      "   9 3.6051118e+001 0.00e+000 3.55e+001  -1.7 1.45e+001    -  1.48e-001 1.09e-002f  5\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  10 3.6037677e+001 0.00e+000 1.09e+001  -1.7 1.36e-001   0.9 1.00e+000 1.00e+000f  1\n",
      "  11 3.5805715e+001 0.00e+000 1.37e+001  -1.7 4.08e-001   1.4 2.11e-001 6.25e-002f  5\n",
      "  12 3.5535117e+001 0.00e+000 2.15e+001  -1.7 1.70e+001    -  1.49e-001 6.32e-002f  2\n",
      "  13 3.5531113e+001 0.00e+000 5.00e+001  -1.7 1.05e+000   0.9 2.18e-001 2.59e-002f  6\n",
      "  14 3.5389234e+001 0.00e+000 2.26e+001  -1.7 7.57e-001   0.4 1.00e+000 1.22e-001f  3\n",
      "  15 3.5197018e+001 0.00e+000 4.71e+000  -1.7 5.35e+000  -0.1 1.04e-001 1.38e-002f  5\n",
      "  16 3.5121267e+001 0.00e+000 3.72e+001  -1.7 2.79e+000    -  1.00e+000 5.00e-001f  2\n",
      "  17 3.5044107e+001 0.00e+000 6.41e+001  -1.7 1.42e+000   0.4 1.09e-001 3.34e-002f  5\n",
      "  18 3.4983295e+001 0.00e+000 3.92e+001  -1.7 1.03e+000  -0.1 1.00e+000 2.03e-001f  3\n",
      "  19 3.4970871e+001 0.00e+000 6.81e+001  -1.7 3.64e+000  -0.6 3.13e-001 5.38e-002f  4\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  20 3.4921422e+001 0.00e+000 4.32e+001  -1.7 9.70e-001  -0.2 1.00e+000 2.17e-001f  3\n",
      "  21 3.9203351e+001 0.00e+000 1.08e+002  -1.7 5.90e+001    -  6.25e-002 5.72e-002w  1\n",
      "  22 3.5490220e+001 0.00e+000 7.90e+001  -1.7 1.54e-001   3.0 1.00e+000 3.67e-001w  1\n",
      "  23 4.6066390e+001 0.00e+000 7.36e+001  -1.7 1.30e-001   2.5 7.46e-003 1.00e+000w  1\n",
      "  24 3.4855811e+001 0.00e+000 7.31e+001  -1.7 4.41e-001   2.9 6.25e-002 7.15e-003f  3\n",
      "  25 3.4761377e+001 0.00e+000 4.15e+001  -1.7 1.75e-002   2.4 1.00e+000 2.50e-001f  3\n",
      "  26 3.4748385e+001 0.00e+000 7.56e+001  -1.7 1.36e+000    -  1.00e+000 5.00e-001f  2\n",
      "  27 3.4649745e+001 0.00e+000 2.37e+001  -1.7 9.68e-003   2.0 1.00e+000 2.50e-001f  3\n",
      "  28 3.4572610e+001 0.00e+000 5.55e+001  -1.7 1.37e+000    -  1.00e+000 1.00e+000f  1\n",
      "  29 3.4521866e+001 0.00e+000 6.73e+001  -1.7 1.27e+000    -  1.00e+000 5.00e-001f  2\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  30 3.4504104e+001 0.00e+000 3.91e+001  -1.7 2.03e-003   1.5 1.00e+000 1.00e+000f  1\n",
      "  31 3.4435335e+001 0.00e+000 3.24e+001  -1.7 1.25e+000    -  1.00e+000 1.00e+000f  1\n",
      "  32 3.4387707e+001 0.00e+000 6.37e+001  -1.7 1.49e+000    -  1.00e+000 1.00e+000f  1\n",
      "  33 3.4344492e+001 0.00e+000 4.71e+001  -1.7 1.08e+000    -  1.00e+000 1.00e+000f  1\n",
      "  34 3.4338849e+001 0.00e+000 4.56e+000  -1.7 2.22e-003   1.0 1.00e+000 1.00e+000f  1\n",
      "  35 3.4310933e+001 0.00e+000 6.19e+001  -1.7 2.83e+000    -  1.00e+000 4.61e-001f  2\n",
      "  36 3.4291424e+001 0.00e+000 1.86e+001  -1.7 6.39e-001    -  1.00e+000 1.00e+000f  1\n",
      "  37 3.4282847e+001 0.00e+000 1.36e+000  -1.7 7.32e-001    -  1.00e+000 5.00e-001f  2\n",
      "  38 3.4282709e+001 0.00e+000 7.72e-004  -1.7 1.50e-003    -  1.00e+000 1.00e+000f  1\n",
      "  39 3.4264578e+001 0.00e+000 2.75e+001  -3.8 9.19e-001    -  9.49e-001 1.00e+000f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  40 3.4263167e+001 0.00e+000 9.77e-001  -3.8 7.97e-002    -  1.00e+000 1.00e+000f  1\n",
      "  41 3.4263161e+001 0.00e+000 5.67e-004  -3.8 3.14e-003    -  1.00e+000 1.00e+000f  1\n",
      "  42 3.4263013e+001 0.00e+000 1.91e-003  -5.7 8.10e-003    -  1.00e+000 1.00e+000f  1\n",
      "  43 3.4263013e+001 0.00e+000 8.60e-007  -5.7 1.50e-004    -  1.00e+000 1.00e+000f  1\n",
      "  44 3.4263011e+001 0.00e+000 2.95e-007  -8.6 1.01e-004    -  1.00e+000 1.00e+000f  1\n",
      "  45 3.4263011e+001 0.00e+000 6.35e-010  -8.6 4.33e-006    -  1.00e+000 1.00e+000f  1\n",
      "\n",
      "Number of Iterations....: 45\n",
      "\n",
      "                                   (scaled)                 (unscaled)\n",
      "Objective...............:  3.4263011093901696e+001   3.4263011093901696e+001\n",
      "Dual infeasibility......:  6.3511529508366746e-010   6.3511529508366746e-010\n",
      "Constraint violation....:  0.0000000000000000e+000   0.0000000000000000e+000\n",
      "Complementarity.........:  2.5059035755928752e-009   2.5059035755928752e-009\n",
      "Overall NLP error.......:  2.5059035755928752e-009   2.5059035755928752e-009\n",
      "\n",
      "\n",
      "Number of objective function evaluations             = 165\n",
      "Number of objective gradient evaluations             = 46\n",
      "Number of equality constraint evaluations            = 165\n",
      "Number of inequality constraint evaluations          = 0\n",
      "Number of equality constraint Jacobian evaluations   = 46\n",
      "Number of inequality constraint Jacobian evaluations = 0\n",
      "Number of Lagrangian Hessian evaluations             = 45\n",
      "Total CPU secs in IPOPT (w/o function evaluations)   =      0.204\n",
      "Total CPU secs in NLP function evaluations           =      0.000\n",
      "\n",
      "EXIT: Optimal Solution Found.\n",
      "           F  :   t_proc      (avg)   t_wall      (avg)    n_eval\n",
      "callback_fun  | 145.00ms (  3.15ms) 145.29ms (  3.16ms)        46\n",
      "       nlp_f  |        0 (       0)        0 (       0)       165\n",
      "       nlp_g  |        0 (       0)        0 (       0)       165\n",
      "  nlp_grad_f  |        0 (       0)        0 (       0)        47\n",
      "  nlp_hess_l  |        0 (       0)        0 (       0)        45\n",
      "   nlp_jac_g  |        0 (       0)        0 (       0)        47\n",
      "       total  | 250.00ms (250.00ms) 249.47ms (249.47ms)         1\n",
      "solved output [DM([0.259422, 0.259515, 0.259602, 0.259682, 0.259754, 0.25982, 0.259877, 0.259927, 0.259968, 0.26, 0.02, 16.1501])]\n",
      "solved function output 34.263\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"
    }
   ],
   "source": [
    "#solver=F(x0=[0.1,2],lbx=lbx,ubx=ubx)\n",
    "x0=[]\n",
    "lbx=[]\n",
    "ubx=[]\n",
    "# the loop for setting angle\n",
    "for i in range(0,dt):\n",
    "    x0.append(0.02)\n",
    "    lbx.append(0.02)\n",
    "    #ubx.append(0.2)  #previous value\n",
    "    ubx.append(0.5)\n",
    "# the loop for setting velocity  \n",
    "for i in range(0,1):\n",
    "    x0.append(0.2)\n",
    "    lbx.append(0.02)\n",
    "    ubx.append(2)\n",
    "# the loop for setting sample time \n",
    "for i in range(0,1):\n",
    "    x0.append(0.2)\n",
    "    lbx.append(0.02)\n",
    "    #ubx.append(2) #previous value\n",
    "    ubx.append(35)\n",
    "print(x0)\n",
    "solver=F(x0=x0,lbx=lbx,ubx=ubx,lbg=0,ubg=0)\n",
    "out=[]\n",
    "out.append(solver[\"x\"])\n",
    "print(\"solved output\",out)\n",
    "print(\"solved function output\",solver[\"f\"])\n",
    "plt.legend([\"Cost\"])\n",
    "plt.xlabel(\"Iterations\")\n",
    "plt.ylabel(\"Cost Value\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "angle [DM(0.259422), DM(0.259515), DM(0.259602), DM(0.259682), DM(0.259754), DM(0.25982), DM(0.259877), DM(0.259927), DM(0.259968), DM(0.26)]\n",
      "3 1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Y Coordinates')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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anYe4e2oy59SvzttD4n2mR9HS8GYiSARai0hz9wPgm4G5RdbZClwCICINgbZAmhdjMsYYj20/kMXQd5dSo1ow793Zwy9aCBXHa91Qq2qeiIwGvgKCgMmqmioio9zLJwD/B0wRkVW4qpLGqOpeb8VkjDGeOnA0hzsmL+VoTj4fjepNk/Awp0PyGq+OR6CqXwBfFJk3odDnHcBl3ozBGGNKKzs3nxHvJbE14yhTh/eo9GMOny2/GJjGGGPKS36Bcv+M5SRv3c9rt8T5dB9CnrIuJowxxk1VGTs3la/X7OKJqzpwZZfGTodUISwRGGOM2xuLfuX9JVu4+8IWDDsvcIa/tURgjDHAh0nbeOGrdVwX24QxlwdWK3ZLBMaYgLdo3W4e/XgV57eK4F83dvX53kRLyxKBMSagrdh2gHunLaNtw1q8eVscVYMDr1gMvDM2xhi3LRmZ3DklkXo1qjLlzgRqhfrnC2NnYonAGBOQ9h45xpDJSylQ5b07e9Cglm+ON1we7D0CY0zAyTyWx51TEtl1KJvpd/WiZWRNp0NylN0RGGMCSm5+AX+cvozV2w/y2i1xxMXUdTokx9kdgTEmYKgqf/14FYvW7eG5gZ3p16Gh0yFVCnZHYIwJGOPmr+ej5HQeuKQ1t/SIcTqcSsMSgTEmIHywZAvjF27k5oSm/Klfa6fDqVQsERhj/N5Xqb/xxKeruaRdA565rpNfDTNZHiwRGGP8WtLmfdw/YzldosMZf2s3goOs2CvKvhFjjN/auPsww99Lokl4GJOHJlC9qrWPKY4lAmOMX9p1KJs7JicSElSFqXf2oF6Nqk6HVGlZIjDG+J1D2bncMXkpB47mMGVYAk3rVXc6pErN7pOMMX7lWF4+d09NZuPuI7w7LIFOUXWcDqnSs0RgjPEbBQXKQ7NW8FNaBi/d1JULWkc6HZJPOGPVkIi0FJFq7s99ROR+EQn3emTGGFNK//hiLfNW7uTRAe24vlu00+H4DE+eEcwG8kWkFfAO0ByY7tWojDGmlCZ9n8ak/21iaO9m3H1hC6fD8SmeJIICVc0DrgdeVtU/A4ExorMxxifMXbGDZz5fyxWdG/H4VR3shbFS8iQR5IrILcAdwDz3vMAcvcEYU+n8uHEvD81KoWfzeoz7QyxBATbMZHnwJBEMA84FnlXVTSLSHPjAu2EZY8yZrdlxiJHvJ9M8ogYTh8QTGhLkdEg+6YythlR1jYiMAWLc05uA570dmDHGlCR9/1GGvruUWqHBvHdnD+qEWUVFWXnSauhqIAX4r3s6VkTmejkuY4w5rb1HjnHH5KVk5+bz3p09aFwnzOmQfJonVUNjgR7AAQBVTcHVcsgYYyrcbwezuemtn9h+IIu3h8TTpmEtp0PyeZ68UJanqgeLPIVXL8VjjDGntW3fUW6dtIT9mblMvbMnPZrXczokv+BJIlgtIrcCQSLSGrgf+NG7YRljzMk27j7CbZN+Jjsvn2kjetK1abjTIfkNT6qG7gM6AsdwvUh2EHjAk52LyOUisk5ENorIo6dZp4+IpIhIqoh852ngxpjAkbrjIDe99RN5BcrMkb0sCZQzT+4IrlTVx4DHjs8QkUHAhyVtJCJBwOvApUA6kCgic1V1TaF1woE3gMtVdauINCj9KRhj/NmyrfsZOnkpNasF88GInrSIrOl0SH7HkzuCv3o4r6gewEZVTVPVHGAmcG2RdW4FPlbVrQCqutuD/RpjAsSPv+7ltkk/U69GVWaNOteSgJec9o5ARAYAVwBRIvJqoUW1gTwP9h0FbCs0nQ70LLJOGyBERBYBtYBXVHVqMbGMBEYCxMTEeHBoY4yv+/aX3Yz6IJlz6lfng+E9aVA71OmQ/FZJVUM7gCTgGiC50PzDwJ892Hdx73kXbW0UDHQHLgHCgJ9EZImqrj9pI9WJwESA+Ph4a7FkjJ/7YtVOHpi5nLaNajH1zp42upiXnTYRqOoKYIWITFfV3DLsOx1oWmg6GldyKbrOXlXNBDJFZDHQFViPMSYgfZSczl8+WkFcTF0mD0ugdqi9MextnjwjaCYiH4nIGhFJO/7nwXaJQGsRaS4iVYGbgaJvJH8KXCAiwSJSHVfV0dpSnYExxm+8/9NmHv5wBb1bRjB1eA9LAhXEk1ZD7wJPAi8BfXF1QnfG7v1UNU9ERgNfAUHAZFVNFZFR7uUTVHWtiPwXWAkUAJNUdXXZTsUY48smfPcrz3/5C/3aN+S1W7tZB3IVSFRLrnIXkWRV7S4iq1S1s3ve96p6QYVEWER8fLwmJSU5cWhjjBeoKuPmr2f8wo1c3bUJ4/7QlZAgTyorTGm4y/L44pZ5ckeQLSJVgA3uX/jbAWvvb4w5a6rK/81by+QfNnFzQlOevb6zjSfgAE/S7p+A6ri6lugO3I5rkBpjjCmz/ALlrx+vYvIPmxh2XjOeG2hJwCmejEeQ6P54BNfzAWOMOSu5+QU8NGsFc1fs4L6LW/HgpW1seEkHnTERiEgb4BHgnMLrq+rFXozLGOOnsnPzuW/Gcuav2cWYy9txT5+WTocU8Dx5RvAhMAF4G8j3bjjGGH92NCePu99P5vsNe3n62o4MObeZ0yEZPB+P4E2vR2KM8WuHsnMZPiWR5C37eeHGLgyKb3rmjUyF8CQRfCYi9wKf4OqKGgBV3ee1qIwxfmVfZg53TF7K2p2HGH9LHFd2aex0SKYQTxLB8RZCjxSap0CL8g/HGONvdh/K5rZ3fmZzxlEmDunOxe0aOh2SKcKTVkM2PrExpkzS9x/ltkk/s/vwMaYMS6B3ywinQzLFKKkb6otVdaGIDCxuuap+7L2wjDG+btPeTAa/vYTDx/J4f3hPup9T1+mQzGmUdEdwEbAQuLqYZQpYIjDGFOuX3w5x26SlFKgy465edIqq43RIpgQldUP9pPtfe4nMGOOxlekHGDJ5KdWCqzBzRC9aNajldEjmDEqqGnqwpA1VdVz5h2OM8WVLN+3jzimJhFcPYfqIXsTUr+50SMYDJVUNHU/jbYEEfh9L4GpgsTeDMsb4nsXr9zDy/SSahIcxbURPGtcJczok46GSqoaeAhCRr4E4VT3snh6L621jY4wB4KvU37hv+nJaNqjJ+8N7EFGzmtMhmVLw5D2CGCCn0HQO0Mwr0RhjfM6nKdt5cNYKOkfV4b1hPahT3UYV8zWeJIL3gaUi8gmu1kLXA+95NSpjjE+YsXQrf/tkFT2b12PSHQnUrOZJkWIqmxKvmrj6hZ0KfAkcH5FsmKou93ZgxpjKbdL3aTzz+Vr6tI1kwm3dbWhJH1ZiIlBVFZE5qtodWFZBMRljKrG8/AJe+Godby1OY0CnRrxyczeqBtvQkr7Mk/u4JSKSUGiAGmNMgNqfmcN9M5bzv417ua1XDGOv7kiwjS/s8zxJBH2BUSKyGcgEBNfNQhdvBmaMqVxWbz/IqA+S2X3oGP+6oQt/SLBupP2FJ4lggNejMMZUap8sT+fR2auoV6Mqs0adS2zTcKdDMuXIk95Ht4hIV35/WPy9qq7wbljGmMogN7+Af3yxlnd/2EzP5vV4fXCcvSPgh85YuSciDwDTgAbuvw9E5D5vB2aMcdbeI8e4bdLPvPvDZoad14wPRvS0JOCnPKkaGg70VNVMABH5J/ATMN6bgRljnLNi2wFGfZDMvswcXrqpK9d3i3Y6JONFniQC4eRB6/Pd84wxfmhW4jb+/ulqImtWY/Y9va0L6QDgSSJ4F/jZ/WaxANcC73g1KmNMhcvJK+Dpeal8sGQr57eK4NVbulGvRlWnwzIVwJOHxeNEZBFwvnuWvVlsjJ/ZfSibe6YtI3nLfu6+qAWPXNbW3g8IIJ52DJKPq58hBQq8F44xpqIlb9nPPR8kczg7j9du7cZVXZo4HZKpYKVpNRSBtRoyxm+oKtN+3sLNE38irGoQn/yxtyWBAGWthowJQNm5+Tz5aSr/SdpGn7aRvHJTN+s+OoB5UglY5lZDInK5iKwTkY0i8mgJ6yWISL6I3OjJfo0xZbfzYBY3TVzCf5K2cd/FrXjnjgRLAgGutK2GAK7Dg1ZDIhIEvA5cCqQDiSIyV1XXFLPeP4GvShG3MaYMfk7L4I/Tl5GdW8Bbt3enf8dGTodkKoHSthoSPG811APYqKppACIyE1fT0zVF1rsPmI1rXGRjjBeoKlN+3Myzn68lpn51Zo7sTqsGtc68oQkIp00EIpIARKjql6q6DPd4BCJyjYhUUdXkM+w7CthWaDod6FnkGFG4Rjy7mBISgYiMBEYCxMTEnOGwxpjCsnPz+dvHq/h4+Xb6tW/IuJu6UjvUqoLM70p6RvACsLaY+Wvcy86kuOcIWmT6ZWCMquYXs+7vG6lOVNV4VY2PjIz04NDGGIBt+45yw5s/8knKdh68tA0Tb+9uScCcoqSqofqqurnoTFXdKCL1Pdh3OlC4w/JoYEeRdeKBma4RMYkArhCRPFWd48H+jTEl+GHjXkZPX0ZegfLOHfFc3K6h0yGZSqqkRBBWwrIaHuw7EWgtIs2B7cDNwK2FV1DV5sc/i8gUYJ4lAWPOjqoy6ftNPPflWlpG1mTikHiaR3jyv6wJVCUlggUi8izwd1U9UaUjIk8BC8+0Y1XNE5HRuFoDBQGTVTVVREa5l084u9CNMUUdzcljzOxVfLZiB1d0bsQLN3alRjVPOxAwgUoKlfEnLxCpAUzC1fonxT27K5AEjFDVIxURYFHx8fGalJTkxKGNqdS2ZGRy9/vJrN91mEf6t2PURS1wV7sag4gkq2p8cctO+1PB/SbxLSLSAujonp16vDmoMabyWLRuN/fPWI6IMGVYDy5sY40qjOc8eY8gDbDC35hKSFV5Y9Gv/PvrdbRrVJu3butOTP3qTodlfIxVHhrjo44cy+PhWSv4b+pvXBvbhOcHdiGsapDTYRkfVNILZV8A9xbXhNQY46xf9xzh7veT2bQ3k79f2Z7h5ze35wGmzEq6I5gCfC0i7wH/UtXcignJGFOSr1N/46FZKwgJrsL7w3vQu2WE0yEZH1fSw+JZIvI58ASQJCLvU2hQGlUdVwHxGWPc9mXm8PRnqcxJ2UHnqDpMuL07UeElve5jjGfO9IwgF8gEqgG1sNHJjKlwqspnK3cydm4qh7Nz+VO/1tzbpxVVg20oSVM+SnpGcDkwDpgLxKnq0QqLyhgDwG8Hs/n7nNUsWLuLrk3D+dcNXWjbyHoNNeWrpDuCx4BBqppaUcEYY1xUlZmJ2/jH52vJLSjg71e2Z9h5zQmqYg+ETfkr6RnBBRUZiDHGZUtGJo/OXsVPaRmc26I+z9/QmXPqW19BxnvsPQJjKon8AuXdHzbx76/XEVKlCs8N7MzNCU2tWajxOksExlQC6347zF9mr2TFtgP0a9+AZ67rTKM6oU6HZQKEJQJjHJSTV8Abizby+rcbqR0awvhbunFVl8Z2F2AqlCUCYxySsu0AYz5aybpdh7kutglPXN2RejWqOh2WCUCWCIypYFk5+bz49Tom/7CJhrVDmTzURg8zzrJEYEwF+vHXvTw6exVb9x1lcM8YHh3Qjlo2hrBxmCUCYyrAwaxcnv9yLTOWbqNZ/erMHNmLXi08GfrbGO+zRGCMl81fs4u/z1nFnsPHuPuiFvy5XxtCQ6y7aFN5WCIwxkv2HjnG2LmpzFu5k3aNavH2kHi6RIc7HZYxp7BEYEw5U1U+TdnBU5+lknksn4cubcPdF7W0TuJMpWWJwJhytONAFo99sopv1+2hW4yrk7jWDa2TOFO5WSIwphwUFCjTlm7ln1/+Qn6B8sRVHbijdzPrJM74BEsExpylTXszGTN7JUs37eP8VhE8N7AzTevZAPLGd1giMKaM8vILmPS/Tbw0fz1Vg6vwrxu6MCg+2rqHMD7HEoExZbBmxyHGzF7Jqu0HuaxDQ/7vuk40rG2dxBnfZInAmFI4lpfPaws38uaiXwmvHsIbg+MY0KmR3QUYn2aJwBgPJW/Zz5jZK9m4+wgD46J4/MoO1LVO4owfsERgzBls3H2EV77ZwLyVO2hSJ4wpwxLo07aB02EZU24sERhzGpv3ZvLqNxuYk7Kd0JAg7rmoJff2bUXNava/jfEv9l+0MUWk7z/K+G828tGydIKrCMPPb87dF7UkomY1p0Mzxiu8mghE5HLgFSAImKSqzxdZPhgY4548Atyjqiu8GZMxp/PbwWxe+3YD/0nchiDc3usc7u3TkgbWGsj4Oa8lAhEJAl4HLgXSgUQRmauqawqttgm4SFX3i8gAYCLQ01sxGVOc3YezeXPRr0z7eSuqyh/imzL64lY0rhPmdGjGVAhv3hH0ADaqahqAiMwErgVOJAJV/bHQ+kuAaC/GY8xJMo4c463FaUz9aTO5+coNcVHcd3FreyvYBBxvJoIoYFuh6XRK/rU/HPiyuAUiMhIYCRATE1Ne8ZkAdeBoDm9/n8a7P2wmOzef62KjuP+S1jSLqOF0aMY4wpuJoLg3bLTYFUX64koE5xe3XFUn4qo2Ij4+vth9GHMmh7Jzeef7TUz+3yYOH8vjqi6N+VO/1rRqYL2DmsDmzUSQDjQtNB0N7Ci6koh0ASYBA1Q1w4vxmACVeSyPKT9uZuLiNA5m5dK/Y0P+fGkb2jWq7XRoxlQK3kwEiUBrEWkObAduBm4tvIKIxAAfA7er6novxmICUFZOPu8v2cyE79LYl5nDJe0a8OdL29Apqo7ToRlTqXgtEahqnoiMBr7C1Xx0sqqmisgo9/IJwBNAfeANd18teaoa762YTGDIzs1nxtKtvLHoV/YcPsYFrSN48NI2dIup63RoxlRKoupbVe7x8fGalJTkdBimEsrJK+A/Sdt4feFGfjuUTa8W9XjosrYkNKvndGjGOE5Ekk/3Q9veLDY+Lze/gI+XpfPqNxvZfiCL+HPqMu6mrvRuGeF0aMb4BEsExmflFyifpmznlW82sCXjKF2j6/CPgZ25sHWEdQttTClYIjA+p6BAmbdqJy8vWE/ankw6NK7NpCHxXNK+gSUAY8rAEoHxGarKV6m/8dL8DazbdZi2DWsx4bY4LuvQiCo2SLwxZWaJwFR6qso3a3fz0oL1pO44RIvIGrx6Szeu6tzYEoAx5cASgam0VJXFG/Yybv56Vmw7wDn1qzPuD125pmsTgoOqOB2eMX7DEoGpdPYcPsac5dv5MHkb63cdISo8jH/e0JmBcdGEWAIwptxZIjCVQk5eAd+u282HSeksWrebvAKlW0w4zw90JYCqwZYAjPEWSwTGUWt3HuLDpHQ+TdlORmYOkbWqMfyC5gzqHm2dwRlTQSwRmAp34GgOn6bs4MPkbazefoiQIKFf+4YMio/mwtaRVv9vTAWzRGAqRH6BsnjDHj5KSmf+ml3k5BfQoXFtnry6A9fGRlGvRlWnQzQmYFkiMF6VtucIHyan8/GydHYdOkbd6iHc2jOGQfHRdGxivYAaUxlYIjDl7nB2Lp+v3MmHyekkb9lPUBWhT5tInrommovbNbQHv8ZUMpYITLkoKFCWpGXwYXI6X67eSXZuAa0a1OSvA9pxfbcoGtQOdTpEY8xpWCIwZ2XbvqN8lJzO7GXppO/PolZoMAPjohnUPZrYpuHW948xPsASgSm1rJx8vly9kw+T0vkpLQMROK9lBI/0b0v/jo0IDQlyOkRjTClYIjAeUVWWbd3Ph0npzFu5kyPH8oipV50HL23DDd2jiQoPczpEY0wZWSIwJfrtYDazl6UzOzmdtL2ZVK8axBWdGzOoezQJzepZp2/G+AFLBOYUx/Lymb9mFx8mpfP9hj0UKPRoVo9RfVpyRefG1Kxm/9kY40/s/2gDwJFjeSRt3sfCX3bzacoODmbl0rhOKPf2acWN3aNpFlHD6RCNMV5iiSBAHS/4l6TtY0laBqu2HyS/QKkaXIX+HRsxqHs057WKIMiqfozxe5YIAsTpCv6QICG2aTj39mlJrxb1iYupS1hVa/VjTCCxROCnrOA3xnjKEoGfsILfGFNWlgh8lBX8xpjyYonAR1jBb4zxFksElVRJBX/X6HDuuchd8J8TTvWqdhmNMWVnJUglkXksj6Qt+1mSlsGStAxWplvBb4ypGFaiVDBVZV9mDun7s0jfn8XqHQet4DfGOMpKmHKmqmScKOiPkr4/i+2FPqfvzyIrN//E+lbwG2OcZiVOKakqe4/knFSwnyjwD7g+Z+cWnLRNePUQouuG0TKyJhe2iSS6bhjRdasTXTeMZvVr2MNdY4yjvJoIRORy4BUgCJikqs8XWS7u5VcAR4GhqrrMmzGdiaqy58ixUwr545+378/iWN7JBX3d6iFE161O6wY16ds2kqhwd0FfL4yo8DBqhYY4dDbGGHNmXksEIhIEvA5cCqQDiSIyV1XXFFptANDa/dcTeNP9r9cUFBQu6E8t5NMPZJFTpKCvV6Mq0XXDaNeoFv3aN3QX9K7CPqpumPXGaYzxad4swXoAG1U1DUBEZgLXAoUTwbXAVFVVYImIhItIY1XdWd7BfPvLbp6et4bt+7PIyT+5oK/vLujbN67NpR0aEl03jKjjBX14GDWsoDfG+DFvlnBRwLZC0+mc+mu/uHWigJMSgYiMBEYCxMTElCmYujWq0qFJbS7r2NBVbeP+VR9VN8wezhpjApo3S8Di+i/WMqyDqk4EJgLEx8efstwTsU3Def3WuLJsaowxfq2KF/edDjQtNB0N7CjDOsYYY7zIm4kgEWgtIs1FpCpwMzC3yDpzgSHi0gs46I3nA8YYY07Pa1VDqponIqOBr3A1H52sqqkiMsq9fALwBa6moxtxNR8d5q14jDHGFM+rT0lV9QtchX3heRMKfVbgj96MwRhjTMm8WTVkjDHGB1giMMaYAGeJwBhjApwlAmOMCXDiel7rO0RkD7DF6TgKiQD2Oh2EF/n7+YGdo7+wcyzZOaoaWdwCn0sElY2IJKlqvNNxeIu/nx/YOfoLO8eys6ohY4wJcJYIjDEmwFkiOHsTnQ7Ay/z9/MDO0V/YOZaRPSMwxpgAZ3cExhgT4CwRGGNMgLNE4AERuVxE1onIRhF5tJjlfUTkoIikuP+ecCLOsyEik0Vkt4isPs1yEZFX3d/BShHxqVF+PDg/f7iGTUXkWxFZKyKpIvJAMev4+nX05Bx9+lqKSKiILBWRFe5zfKqYdcr3Oqqq/ZXwh6sL7V+BFkBVYAXQocg6fYB5Tsd6lud5IRAHrD7N8iuAL3GNKtcL+NnpmMv5/PzhGjYG4tyfawHri/lv1devoyfn6NPX0n1taro/hwA/A728eR3tjuDMegAbVTVNVXOAmcC1DsdU7lR1MbCvhFWuBaaqyxIgXEQaV0x0Z8+D8/N5qrpTVZe5Px8G1uIaA7wwX7+OnpyjT3NfmyPuyRD3X9FWPeV6HS0RnFkUsK3QdDrF/4d3rvtW7ksR6VgxoVUoT78HX+Y311BEmgHdcP2aLMxvrmMJ5wg+fi1FJEhEUoDdwHxV9ep19OrANH5CiplXNDsvw9WPxxERuQKYA7T2dmAVzJPvwZf5zTUUkZrAbOBPqnqo6OJiNvG563iGc/T5a6mq+UCsiIQDn4hIJ1Ut/HyrXK+j3RGcWTrQtNB0NLCj8Aqqeuj4rZy6RmULEZGIiguxQpzxe/Bl/nINRSQEVwE5TVU/LmYVn7+OZzpHf7mWAKp6AFgEXF5kUbleR0sEZ5YItBaR5iJSFbgZmFt4BRFpJCLi/twD1/eaUeGRetdcYIi7tUIv4KCq7nQ6qPLiD9fQHf87wFpVHXea1Xz6Onpyjr5+LUUk0n0ngIiEAf2AX4qsVq7X0aqGzkBV80RkNPAVrhZEk1U1VURGuZdPAG4E7hGRPCALuFndj/Z9hYjMwNXaIkJE0oEncT2kOn6OX+BqqbAROAoMcybSsvHg/Hz+GgLnAbcDq9z1ywB/A2LAP64jnp2jr1/LxsB7IhKEK4nNUtV5Rcqccr2O1sWEMcYEOKsaMsaYAGeJwBhjApwlAmOMCXCWCIwxJsBZIjDGmABnicD4PHePlJtEpJ57uq57+pxi1m0kIjNF5FcRWSMiX4hIGy/ENEVEbnR/niQiHcq4nz4i0rt8ozPmZJYIjM9T1W3Am8Dz7lnPAxNVdUvh9dwvGX0CLFLVlqraAVcb9IZnc3x3e++S4huhqmvKuPs+gCUC41WWCIy/eAnoJSJ/As4HXixmnb5ArvuFHABUNUVVv3e/ofmCiKwWkVUichOc6Pe9uPl9xNUv/nRcLzeJiLzmvsv4HGhw/BgiskhE4t2fj4jIs+4O0ZaISEP3/KtF5GcRWS4iC0Skobg6VRsF/Flc/epf4H7rdLaIJLr/znNvf5H83v/+chGpVe7fsPFb9max8QuqmisijwD/BS5zdxleVCcg+TS7GAjEAl2BCCBRRBbj+jVe3HxwdVHeSVU3ichAoC3QGdcdxhpgcjHHqQEsUdXHRORfwF3AM8D/cPU5ryIyAviLqj4kIhOAI6r6bwB34nlJVf8nIjG43nhvDzwM/FFVfxBXh2zZHnxtxgCWCIx/GQDsxFXgzy/ltucDM9y9Pu4Ske+AhBLmHwKWquom9/YXFlpvh4gsPM1xcoB57s/JwKXuz9HAf8TVp3xVYFMx24Kr35kO7q50AGq7f/3/AIwTkWnAx6qaXsrzNwHMqoaMXxCRWFyFai9cVSnFDdKRCnQ/3S5KOR8gs8i0J/215Bbq9yaf33+MjQdeU9XOwN1A6Gm2rwKcq6qx7r8oVT2sqs8DI4AwYImItPMgFmMASwTGD7gfAr+Jq2/6rcALwL+LWXUhUE1E7iq0bYKIXAQsBm4S14Agkbh+4S8tYX5Ri4Gb3es1xvU8ojTqANvdn+8oNP8wriEZj/saGF0o/lj3vy1VdZWq/hNIAiwRGI9ZIjD+4C5gq6oerw56A2jnLuBPcP8Svx641N18NBUYi6sf90+AlbjGpF6Iq47+txLmF/UJsAFYhSspfVfKcxgLfCgi3wN7C83/DLj++MNi4H4gXlwDlq/B9TAZ4E/uB9orcPW4+WUpj28CmPU+aowxAc7uCIwxJsBZIjDGmABnicAYYwKcJQJjjAlwlgiMMSbAWSIwxpgAZ4nAGGMC3P8DIHCQdSC2bHIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "ang=[]\n",
    "v=[]\n",
    "t=[]\n",
    "for i in range(0,dt):\n",
    "    ang.append(out[0][i])\n",
    "print(\"angle\",ang)\n",
    "v.append(out[0][10])\n",
    "t.append(out[0][11])\n",
    "xc,yc=[],[]\n",
    "theta=0.0\n",
    "x1,x2=0,0\n",
    "for i in range(0,dt):\n",
    "    x1=x1+v[0]*math.cos(theta)*t[0]\n",
    "    x2=x2+v[0]*math.sin(theta)*t[0]\n",
    "    theta = theta + (v[0] / 1.2) * math.tan(ang[i])*t[0]\n",
    "    xc.append(x1)\n",
    "    yc.append(x2)\n",
    "print(x1,x2)\n",
    "#plt.figure(figsize=(6, 4))\n",
    "plt.plot(xc,yc,dest[0],dest[1],\"o\")\n",
    "plt.legend([\"Trajectory\",\"Destination\"])\n",
    "plt.xlabel(\"X Coordinates\")\n",
    "plt.ylabel(\"Y Coordinates\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Cost Value')"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "cost1=[]\n",
    "cost1=[5.1407028e+000,4.8279191e+000 ,\n",
    "    3.2988949e+000, \n",
    "    2.8788262e+000 ,\n",
    "    2.3243103e+000 ,\n",
    "    2.0325987e+000 ,\n",
    "    1.7099310e+000 ,\n",
    "   1.4452566e+000 ,\n",
    "    1.3194831e+000 ,\n",
    "    1.2617696e+000 ,\n",
    "  1.2360491e+000, 1.2009504e+000, \n",
    "   1.1934256e+000 ,\n",
    "   1.1910525e+000 ,\n",
    "   1.1910547e+000 ,\n",
    "   1.1908748e+000 ,\n",
    "   1.1908742e+000 ]\n",
    "plt.plot(cost1)\n",
    "plt.legend([\"Cost\"])\n",
    "plt.xlabel(\"Iterations\")\n",
    "plt.ylabel(\"Cost Value\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 629,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.821345956502425\n",
      "3.821345956502425\n"
     ]
    }
   ],
   "source": [
    "xv=0\n",
    "x=[]\n",
    "v=0.4\n",
    "a=0.3\n",
    "out1=(v*cos(a))+(v*cos(a))+(v*cos(a))+(v*cos(a))+(v*cos(a))+(v*cos(a))+(v*cos(a))+(v*cos(a))+(v*cos(a))+(v*cos(a))\n",
    "for i in range(0,10):\n",
    "    xv=xv+v*cos(a)\n",
    "    x.append(xv)\n",
    "print(xv)\n",
    "print(out1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S:(x0[3],p[],lbx[3],ubx[3],lbg,ubg,lam_x0[3],lam_g0)->(x[3],f,g,lam_x[3],lam_g,lam_p[]) IpoptInterface\n"
     ]
    }
   ],
   "source": [
    "x = SX.sym('x'); y = SX.sym('y'); z = SX.sym('z')\n",
    "nlp = {'x':vertcat(x,y,z), 'f':x**2+100*z**2, 'g':z+(1-x)**2-y}\n",
    "S = nlpsol('S', 'ipopt', nlp)\n",
    "print(S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is Ipopt version 3.12.3, running with linear solver mumps.\n",
      "NOTE: Other linear solvers might be more efficient (see Ipopt documentation).\n",
      "\n",
      "Number of nonzeros in equality constraint Jacobian...:        3\n",
      "Number of nonzeros in inequality constraint Jacobian.:        0\n",
      "Number of nonzeros in Lagrangian Hessian.............:        2\n",
      "\n",
      "Total number of variables............................:        3\n",
      "                     variables with only lower bounds:        0\n",
      "                variables with lower and upper bounds:        0\n",
      "                     variables with only upper bounds:        0\n",
      "Total number of equality constraints.................:        1\n",
      "Total number of inequality constraints...............:        0\n",
      "        inequality constraints with only lower bounds:        0\n",
      "   inequality constraints with lower and upper bounds:        0\n",
      "        inequality constraints with only upper bounds:        0\n",
      "\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "   0 6.2500000e+001 0.00e+000 9.00e+001  -1.0 0.00e+000    -  0.00e+000 0.00e+000   0\n",
      "   1 1.8457621e+001 1.48e-002 4.10e+001  -1.0 4.10e-001   2.0 1.00e+000 1.00e+000f  1\n",
      "   2 7.8031530e+000 3.84e-003 8.76e+000  -1.0 2.63e-001   1.5 1.00e+000 1.00e+000f  1\n",
      "   3 7.1678278e+000 9.42e-005 1.04e+000  -1.0 9.32e-002   1.0 1.00e+000 1.00e+000f  1\n",
      "   4 6.7419924e+000 6.18e-003 9.95e-001  -1.0 2.69e-001   0.6 1.00e+000 1.00e+000f  1\n",
      "   5 5.4363330e+000 7.03e-002 1.04e+000  -1.7 8.40e-001   0.1 1.00e+000 1.00e+000f  1\n",
      "   6 1.2144815e+000 1.52e+000 1.32e+000  -1.7 3.21e+000  -0.4 1.00e+000 1.00e+000f  1\n",
      "   7 1.0214718e+000 2.51e-001 1.17e+001  -1.7 1.33e+000   0.9 1.00e+000 1.00e+000h  1\n",
      "   8 3.1864085e-001 1.04e-003 7.53e-001  -1.7 3.58e-001    -  1.00e+000 1.00e+000f  1\n",
      "   9 0.0000000e+000 3.19e-001 0.00e+000  -1.7 5.64e-001    -  1.00e+000 1.00e+000f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  10 0.0000000e+000 0.00e+000 0.00e+000  -1.7 3.19e-001    -  1.00e+000 1.00e+000h  1\n",
      "\n",
      "Number of Iterations....: 10\n",
      "\n",
      "                                   (scaled)                 (unscaled)\n",
      "Objective...............:  0.0000000000000000e+000   0.0000000000000000e+000\n",
      "Dual infeasibility......:  0.0000000000000000e+000   0.0000000000000000e+000\n",
      "Constraint violation....:  0.0000000000000000e+000   0.0000000000000000e+000\n",
      "Complementarity.........:  0.0000000000000000e+000   0.0000000000000000e+000\n",
      "Overall NLP error.......:  0.0000000000000000e+000   0.0000000000000000e+000\n",
      "\n",
      "\n",
      "Number of objective function evaluations             = 11\n",
      "Number of objective gradient evaluations             = 11\n",
      "Number of equality constraint evaluations            = 11\n",
      "Number of inequality constraint evaluations          = 0\n",
      "Number of equality constraint Jacobian evaluations   = 11\n",
      "Number of inequality constraint Jacobian evaluations = 0\n",
      "Number of Lagrangian Hessian evaluations             = 10\n",
      "Total CPU secs in IPOPT (w/o function evaluations)   =      0.042\n",
      "Total CPU secs in NLP function evaluations           =      0.000\n",
      "\n",
      "EXIT: Optimal Solution Found.\n",
      "           S  :   t_proc      (avg)   t_wall      (avg)    n_eval\n",
      "       nlp_f  |        0 (       0)        0 (       0)        11\n",
      "       nlp_g  |        0 (       0)        0 (       0)        11\n",
      "  nlp_grad_f  |        0 (       0)        0 (       0)        12\n",
      "  nlp_hess_l  |        0 (       0)        0 (       0)        10\n",
      "   nlp_jac_g  |        0 (       0)        0 (       0)        12\n",
      "       total  |  50.00ms ( 50.00ms)  49.87ms ( 49.87ms)         1\n",
      "x_opt:  [0, 1, 0]\n"
     ]
    }
   ],
   "source": [
    "r = S(x0=[2.5,3.0,0.75],lbg=0, ubg=0)\n",
    "x_opt = r['x']\n",
    "print('x_opt: ', x_opt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 10))\n",
    "plt.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x16de9cb34c0>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "#generate trajectory between 2 points\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy\n",
    "x=[0,2,2,4]\n",
    "y=[0,0,2,2]\n",
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.0, 0.0], [0.2, 0.0], [0.4, 0.0], [0.6000000000000001, 0.0], [0.8, 0.0], [1.0, 0.0], [1.2000000000000002, 0.0], [1.4000000000000001, 0.0], [1.6, 0.0], [1.8, 0.0], [2.0, 0.0], [2.0, 0.0], [2.0, 0.2], [2.0, 0.4], [2.0, 0.6000000000000001], [2.0, 0.8], [2.0, 1.0], [2.0, 1.2000000000000002], [2.0, 1.4000000000000001], [2.0, 1.6], [2.0, 1.8], [2.0, 2.0], [2.0, 2.0], [2.2, 2.0], [2.4, 2.0], [2.6, 2.0], [2.8, 2.0], [3.0, 2.0], [3.2, 2.0], [3.4000000000000004, 2.0], [3.6, 2.0], [3.8, 2.0], [4.0, 2.0]]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "def getEquidistantPoints(p1, p2, parts):\n",
    "    return zip(numpy.linspace(p1[0], p2[0], parts+1),\n",
    "               list(numpy.linspace(p1[1], p2[1], parts+1)))\n",
    "val=[]\n",
    "val.append(list(getEquidistantPoints((0,0), (2,0), 10)))\n",
    "val.append(list(getEquidistantPoints((2,0), (2,2), 10)))\n",
    "val.append(list(getEquidistantPoints((2,2), (4,2), 10)))\n",
    "out=[]\n",
    "for i in range(0,len(val)):\n",
    "    for k in range(0, len(val[i])):\n",
    "        out.append(list(val[i][k]))\n",
    "print(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.0, 0.0], [0.07692307692307693, 0.15384615384615385], [0.15384615384615385, 0.3076923076923077], [0.23076923076923078, 0.46153846153846156], [0.3076923076923077, 0.6153846153846154], [0.38461538461538464, 0.7692307692307693], [0.46153846153846156, 0.9230769230769231], [0.5384615384615385, 1.076923076923077], [0.6153846153846154, 1.2307692307692308], [0.6923076923076923, 1.3846153846153846], [0.7692307692307693, 1.5384615384615385], [0.8461538461538463, 1.6923076923076925], [0.9230769230769231, 1.8461538461538463], [1.0, 2.0], [1.076923076923077, 1.8461538461538458], [1.153846153846154, 1.692307692307692], [1.2307692307692308, 1.5384615384615383], [1.3076923076923077, 1.3846153846153846], [1.3846153846153846, 1.2307692307692308], [1.4615384615384617, 1.0769230769230766], [1.5384615384615385, 0.9230769230769229], [1.6153846153846154, 0.7692307692307692], [1.6923076923076925, 0.6153846153846149], [1.7692307692307694, 0.4615384615384611], [1.8461538461538463, 0.3076923076923074], [1.9230769230769231, 0.15384615384615374], [2.0, 0.0], [2.076923076923077, 0.1538461538461543], [2.153846153846154, 0.3076923076923086], [2.230769230769231, 0.4615384615384617], [2.307692307692308, 0.615384615384616], [2.3846153846153846, 0.7692307692307692], [2.4615384615384617, 0.9230769230769235], [2.5384615384615388, 1.0769230769230778], [2.6153846153846154, 1.2307692307692308], [2.6923076923076925, 1.3846153846153852], [2.769230769230769, 1.5384615384615383], [2.8461538461538463, 1.6923076923076925], [2.9230769230769234, 1.846153846153847], [3.0, 2.0]]\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"
    }
   ],
   "source": [
    "#sawtooth wavefrom\n",
    "from scipy import signal\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "t = np.linspace(0, 3, 40)\n",
    "triangle = signal.sawtooth(2 * np.pi *0.5* t, 0.5)\n",
    "plt.plot(t, triangle+1)\n",
    "li=[]\n",
    "t=list(t)\n",
    "for i in range(0,len(t)):\n",
    "    li.append([t[i],triangle[i]+1])\n",
    "print(li)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import csv \n",
    "Details = ['Name', 'class', 'passoutYear', 'subject']  \n",
    "row1 =  [1, 2, 3, 1]\n",
    "row2= ['john', '3rd', '2022', 'M2']\n",
    "row3=['kushi', '4th', '2021', 'M4']\n",
    "val=np.array([row1,row2,row3])\n",
    "with open('student.csv', 'w') as f: \n",
    "    write = csv.writer(f) \n",
    "    write.writerow(Details) \n",
    "    write.writerows(val) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [],
   "source": [
    "filename1=\"C:\\\\Users\\\\Prakash\\\\Desktop\\\\UDRI_project_path_planning\\\\case_2_angle\\\\case_2_angle\\\\case_3\\\\case2_3_pid.csv\"\n",
    "filename2=\"C:\\\\Users\\\\Prakash\\\\Desktop\\\\UDRI_project_path_planning\\\\case_2_angle\\\\case_2_angle\\\\case_3\\\\case2_3_angle.csv\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [
    {
     "ename": "FileNotFoundError",
     "evalue": "[Errno 2] No such file or directory: 'C:\\\\Users\\\\Prakash\\\\Desktop\\\\UDRI_project_path_planning\\\\case_2_angle\\\\case_2_angle\\\\case_3\\\\case2_3_angle.csv'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mFileNotFoundError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-211-1df919d83617>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mpandas\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mpd\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mref_traj\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mread_csv\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfilename2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m \u001b[0mref_x\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mref_traj\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"x_coord\"\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mref_y\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mref_traj\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"y_coord\"\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pandas\\io\\parsers.py\u001b[0m in \u001b[0;36mread_csv\u001b[1;34m(filepath_or_buffer, sep, delimiter, header, names, index_col, usecols, squeeze, prefix, mangle_dupe_cols, dtype, engine, converters, true_values, false_values, skipinitialspace, skiprows, skipfooter, nrows, na_values, keep_default_na, na_filter, verbose, skip_blank_lines, parse_dates, infer_datetime_format, keep_date_col, date_parser, dayfirst, cache_dates, iterator, chunksize, compression, thousands, decimal, lineterminator, quotechar, quoting, doublequote, escapechar, comment, encoding, dialect, error_bad_lines, warn_bad_lines, delim_whitespace, low_memory, memory_map, float_precision, storage_options)\u001b[0m\n\u001b[0;32m    608\u001b[0m     \u001b[0mkwds\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkwds_defaults\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    609\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 610\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0m_read\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfilepath_or_buffer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkwds\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    611\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    612\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pandas\\io\\parsers.py\u001b[0m in \u001b[0;36m_read\u001b[1;34m(filepath_or_buffer, kwds)\u001b[0m\n\u001b[0;32m    460\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    461\u001b[0m     \u001b[1;31m# Create the parser.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 462\u001b[1;33m     \u001b[0mparser\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mTextFileReader\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfilepath_or_buffer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    463\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    464\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mchunksize\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0miterator\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pandas\\io\\parsers.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, f, engine, **kwds)\u001b[0m\n\u001b[0;32m    817\u001b[0m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0moptions\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"has_index_names\"\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mkwds\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"has_index_names\"\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    818\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 819\u001b[1;33m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_engine\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_make_engine\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mengine\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    820\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    821\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mclose\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pandas\\io\\parsers.py\u001b[0m in \u001b[0;36m_make_engine\u001b[1;34m(self, engine)\u001b[0m\n\u001b[0;32m   1048\u001b[0m             )\n\u001b[0;32m   1049\u001b[0m         \u001b[1;31m# error: Too many arguments for \"ParserBase\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1050\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mmapping\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mengine\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0moptions\u001b[0m\u001b[1;33m)\u001b[0m  \u001b[1;31m# type: ignore[call-arg]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1051\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1052\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m_failover_to_python\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pandas\\io\\parsers.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, src, **kwds)\u001b[0m\n\u001b[0;32m   1865\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1866\u001b[0m         \u001b[1;31m# open handles\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1867\u001b[1;33m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_open_handles\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msrc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkwds\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1868\u001b[0m         \u001b[1;32massert\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mhandles\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1869\u001b[0m         \u001b[1;32mfor\u001b[0m \u001b[0mkey\u001b[0m \u001b[1;32min\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;34m\"storage_options\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"encoding\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"memory_map\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"compression\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pandas\\io\\parsers.py\u001b[0m in \u001b[0;36m_open_handles\u001b[1;34m(self, src, kwds)\u001b[0m\n\u001b[0;32m   1360\u001b[0m         \u001b[0mLet\u001b[0m \u001b[0mthe\u001b[0m \u001b[0mreaders\u001b[0m \u001b[0mopen\u001b[0m \u001b[0mIOHanldes\u001b[0m \u001b[0mafter\u001b[0m \u001b[0mthey\u001b[0m \u001b[0mare\u001b[0m \u001b[0mdone\u001b[0m \u001b[1;32mwith\u001b[0m \u001b[0mtheir\u001b[0m \u001b[0mpotential\u001b[0m \u001b[0mraises\u001b[0m\u001b[1;33m.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1361\u001b[0m         \"\"\"\n\u001b[1;32m-> 1362\u001b[1;33m         self.handles = get_handle(\n\u001b[0m\u001b[0;32m   1363\u001b[0m             \u001b[0msrc\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1364\u001b[0m             \u001b[1;34m\"r\"\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\pandas\\io\\common.py\u001b[0m in \u001b[0;36mget_handle\u001b[1;34m(path_or_buf, mode, encoding, compression, memory_map, is_text, errors, storage_options)\u001b[0m\n\u001b[0;32m    640\u001b[0m                 \u001b[0merrors\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;34m\"replace\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    641\u001b[0m             \u001b[1;31m# Encoding\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 642\u001b[1;33m             handle = open(\n\u001b[0m\u001b[0;32m    643\u001b[0m                 \u001b[0mhandle\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    644\u001b[0m                 \u001b[0mioargs\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmode\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mFileNotFoundError\u001b[0m: [Errno 2] No such file or directory: 'C:\\\\Users\\\\Prakash\\\\Desktop\\\\UDRI_project_path_planning\\\\case_2_angle\\\\case_2_angle\\\\case_3\\\\case2_3_angle.csv'"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "ref_traj = pd.read_csv(filename2)\n",
    "ref_x=ref_traj[\"x_coord\"]\n",
    "ref_y=ref_traj[\"y_coord\"]\n",
    "plt.plot(ref_x,ref_y)\n",
    "plt.plot(4,2,\"o\")\n",
    "plt.legend([\"Trajectory\",\"Destination\"])\n",
    "plt.xlabel(\"X Coordinates\")\n",
    "plt.ylabel(\"Y Coordinates\")\n",
    "plt.savefig(\"trajectory.png\",dpi=150)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0017637864170204688\n",
      "['0.15706529748201403', '0.40905335247574687', '0.6644001014263838', '0.9170714195456944', '1.1729723312767504', '1.4256086409413218', '1.6804272832650844', '1.9363161985940018', '2.186176828255273', '2.433740480950465', '2.670707986996013', '2.9010363500564718', '3.113991921079745', '3.307613193867218', '3.482257310453496', '3.635896020719732', '3.7630706068860387', '3.8597672864325627', '3.932267710992598', '3.9730410387171466']\n"
     ]
    }
   ],
   "source": [
    "#Reading the PID CSV files\n",
    "out=[]\n",
    "with open(filename1, 'r') as csvfile:\n",
    "    csvreader = csv.reader(csvfile)\n",
    "    for row in csvreader:\n",
    "        out.append(row)\n",
    "#print(out)\n",
    "print(float(out[2][1]))\n",
    "print(out[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "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": [
    "#Super imposing trajectories\n",
    "x=[float(out[1][i]) for i in range(0,len(out[1]))]\n",
    "y=[float(out[2][j]) for j in range(0,len(out[1]))]\n",
    "plt.plot(x,y)\n",
    "plt.plot(ref_x,ref_y)\n",
    "plt.plot(4,2,\"o\")\n",
    "plt.legend([\"Reference Trajectory\",\"Traced Trajectory\",\"Destination\"])\n",
    "plt.xlabel(\"X Coordinates\")\n",
    "plt.ylabel(\"Y Coordinates\")\n",
    "plt.savefig(\"trajectory_1_impose.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Linear Velocity in m/s')"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "#plotting the linear velocity\n",
    "velocity_lin=[float(out[5][i]) for i in range(0,len(out[5]))]\n",
    "plt.plot(velocity_lin)\n",
    "plt.legend([\"Linear Velocity\"])\n",
    "plt.xlabel(\"Time in ms\")\n",
    "plt.ylabel(\"Linear Velocity in m/s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [],
   "source": [
    "yaw=[float(out[3][i]) for i in range(0,len(out[3]))]\n",
    "theta=[float(out[4][j]) for j in range(0,len(out[4]))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "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"
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Yaw')"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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.plot(yaw)\n",
    "plt.figure\n",
    "plt.plot(theta)\n",
    "plt.legend([\"Theta\"])\n",
    "plt.xlabel(\"loop\")\n",
    "plt.ylabel(\"Theta\")\n",
    "plt.show()\n",
    "plt.figure\n",
    "plt.plot(yaw)\n",
    "plt.legend([\"Yaw\"])\n",
    "plt.xlabel(\"Time in ms\")\n",
    "plt.ylabel(\"Yaw\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Angular Velocity in m/s')"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "ang_velocity=[float(out[6][j]) for j in range(0,len(out[6]))]\n",
    "plt.plot(ang_velocity)\n",
    "plt.legend([\"Angular Velocity\"])\n",
    "plt.xlabel(\"Time in ms\")\n",
    "plt.ylabel(\"Angular Velocity in m/s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}