COMPLETE HYBRID A STAR ALGORITHM - IN MOULDING V3.0

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        "[View in Colaboratory](https://colab.research.google.com/github/sharathsrini/Extended-Kalman-Filter-for-Sensor-Fusion/blob/master/COMPLETE%20HYBRID%20A%20STAR%20ALGORITHM%20-%20IN%20MOULDING%20V3.0)"
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      "source": [
        "############PROGRAM STARTS HERE ######################\n",
        "import numpy as np\n",
        "import math as MT\n",
        "from math import floor\n",
        "import matplotlib.pyplot as plt\n",
        "import time\n",
        "\n",
        "\n",
        "###CONSTANTS\n",
        "max_angle = 0.785398 #45Deg\n",
        "min_angle = -0.785398 #-45Deg\n",
        "free_space=0\n",
        "locked_space=1\n",
        "\n",
        "### HYPER PARAMETERS\n",
        "NUMBERS_OF_STEERS=4\n",
        "STEER_OFFSET=5.0*np.pi/180\n",
        "LENGTH=4.0\n",
        "NUM_THETA_CELLS =60\n",
        "\n",
        "### GRID MAKING \n",
        "grid_x_m = 50\n",
        "grid_y_m = 50\n",
        "\n",
        "### FOR CELL DIVISION\n",
        "coll_cell_side = 0.5\n",
        "grid_on_x = np.int( np.ceil(grid_x_m/coll_cell_side) )\n",
        "grid_on_y = np.int( np.ceil(grid_y_m/coll_cell_side) )\n",
        "\n",
        "### FIT ZEROS\n",
        "GRID_TEST = np.zeros((grid_on_x,grid_on_y),np.int)\n",
        "### INITIALIZE COST_MAPS AND ASTAR CLOSE MAPS\n",
        "closed_A_star=np.array([[free_space for x in range(grid_on_x)] for y in range(grid_on_y)])\n",
        "cost_map = np.array([[-1 for x in range(grid_on_x)] for y in range(grid_on_y)])\n",
        "policy_map = [[' ' for x in range(grid_on_x)] for y in range(grid_on_y)]\n",
        "\n",
        "### MOTION MATRIX FOR ASTAR\n",
        "motion_mat=np.array([[1,0],[-1,0],[0,-1],[0,1]])\n",
        "policy_mat=['>',]\n"
      ],
      "execution_count": 0,
      "outputs": []
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        "\n",
        "### STATE CLASS\n",
        "class state:\n",
        "  def __init__(self,x,y,theta,g,f,h,steer):\n",
        "    self.x=x\n",
        "    self.y=y\n",
        "    self.theta=theta\n",
        "    self.g=g\n",
        "    self.f=f\n",
        "    self.h=h\n",
        "    self.steer=steer\n",
        "    \n",
        " ## GOAL NODE        \n",
        "class goal:\n",
        "    def __init__(self, x, y):\n",
        "        self.x = x\n",
        "        self.y = y\n",
        "        \n",
        "        \n",
        "### INPUT VEHICLE CO-ORDINATES\n",
        "class vehicle_points():\n",
        "  def __init__(self,input_co_ordinates,center):\n",
        "    self.input_co_ordinates=input_co_ordinates\n",
        "    self.center=center\n",
        "    \n",
        "### PATH CLASS FOR TRACKING   \n",
        "class path():\n",
        "  def __init__(self,closed,came_from,final):\n",
        "    self.closed=closed\n",
        "    self.came_from=came_from\n",
        "    self.final=final\n",
        "    \n",
        "\n",
        "### AUGMENT DELTA +/- GIVEN OFFSET\n",
        "def delta_augmentation(delta, numbers, offset):\n",
        "    delta_list = []\n",
        "    delta_list.append(delta)\n",
        "    delta_calc_add=delta_calc_sub = delta\n",
        "    for i in range(0 ,numbers):\n",
        "        delta_calc_add += offset\n",
        "        delta_calc_sub -= offset\n",
        "        if delta_calc_add < max_angle:\n",
        "            delta_list.append(delta_calc_add)\n",
        "        if delta_calc_sub > min_angle:\n",
        "            delta_list.append(delta_calc_sub)\n",
        "    return delta_list\n",
        "  \n",
        "\n",
        "\n",
        "### NEW STATE TRANSITIONS\n",
        "def new_state_transition(current_state,goal,speed):\n",
        "    next_states = []\n",
        "    delta_angles = delta_augmentation( delta=current_state.steer, numbers=NUMBERS_OF_STEERS,offset=STEER_OFFSET)\n",
        "    DT=1.0/speed\n",
        "    for delta in delta_angles:\n",
        "        omega  = (speed / LENGTH) * np.tan(delta)\n",
        "        theta2 = normalize_theta(current_state.theta + (omega * DT))\n",
        "        dX = speed * np.cos(theta2) * DT\n",
        "        dY = speed * np.sin(theta2) * DT\n",
        "        #i=i+1\n",
        "        #print(i,[SPEED,np.cos(theta2),DT,omega,theta2,dX,dY])\n",
        "        x2     = current_state.x + dX\n",
        "        y2     = current_state.y + dY\n",
        "        g2     = current_state.g + np.sqrt(dX*dX + dY*dY)\n",
        "        arc_cost=arc_heuristic(goal.x-x2,goal.y-y2,theta2)         \n",
        "        #print(arc_cost)\n",
        "        h2     = euclidean_distance([x2,y2],[goal.x,goal.y])+arc_cost\n",
        "        if(cost_map[idx(x2)][idx(y2)]==-1):\n",
        "          h2+=100\n",
        "        else:\n",
        "          h2+=cost_map[idx(x2)][idx(y2)]\n",
        "        f2     = g2 + h2\n",
        "        new_state=state(x2,y2,theta2,g2,f2,h2,delta)\n",
        "        #jj=np.arctan2(goal.y-y2,goal.x-x2)\n",
        "        #print(['X: ',x2,'Y: ',y2,'ang_goal',normalize_theta(jj)*180/np.pi,'taken_angle',theta2*180/np.pi,'cost:',arc_cost])\n",
        "        next_states.append(new_state)\n",
        "    return next_states\n",
        "\n",
        "### TRANSFORM VEHICLE CO-ORDINATES \n",
        "def transform_vehicle_co_ordinates(vehicle_point_object, next_state, angle_of_rotation):\n",
        "    displaced_matrix = np.array([next_state[0]-vehicle_point_object.center[0],next_state[1]-vehicle_point_object.center[1]])\n",
        "    transformed_matrix=np.add(vehicle_point_object.input_co_ordinates,displaced_matrix)\n",
        "    return vehicle_points(rotate_vehicle_co_ordinates(vehicle_points(transformed_matrix,next_state),angle_of_rotation),next_state)\n",
        "  \n",
        "  \n",
        "### ROTATE VEHICLE CO-ORDINATES     \n",
        "def rotate_vehicle_co_ordinates(vehicle_point_object,angle_of_rotation):\n",
        "    rotation_matrix = np.array([[np.cos(angle_of_rotation), np.sin(angle_of_rotation)], \n",
        "                                [-np.sin(angle_of_rotation), np.cos(angle_of_rotation)]])\n",
        "    return np.add(vehicle_point_object.center,np.matmul(np.subtract(vehicle_point_object.input_co_ordinates,vehicle_point_object.center), rotation_matrix))\n",
        "  \n",
        "  \n",
        "### CHECK VEHICLE IN SAFE POSITION  \n",
        "def is_vehicle_in_safe_position(vehicle_point_object,grid):\n",
        "  for point in vehicle_point_object.input_co_ordinates:\n",
        "    if(is_within_grid( idx(point[0]),idx(point[1])) and  \n",
        "       (grid[idx(point[0])][idx(point[1])]==0)):\n",
        "      continue\n",
        "    else:\n",
        "      return False\n",
        "  return True\n",
        "\n",
        "### CHK A STAR VEHICLE:\n",
        "def A_vehicle_is_safe(vehicle_point_A,add_value,grid):\n",
        "  vp=vehicle_point_A.input_co_ordinates+add_value\n",
        "  for point in vp:\n",
        "    if(is_within_grid( idx(point[0]),idx(point[1])) and  \n",
        "       (grid[idx(point[0])][idx(point[1])]==0)):\n",
        "      continue\n",
        "    else:\n",
        "      #print('False',add_value)\n",
        "      return False\n",
        "  #('True',add_value)\n",
        "  return True\n",
        "    \n",
        "    \n",
        "\n",
        "### EUCLIDEAN DISTANCE\n",
        "def euclidean_distance(start_point,end_point):\n",
        "  return np.round(np.sqrt((end_point[0]-start_point[0])**2 +(end_point[1]-start_point[1])**2),4)\n",
        "\n",
        "### ARC HEURISTIC\n",
        "def arc_heuristic(x,y,theta_to_be_taken):\n",
        "  ang_rad=normalize_theta(np.arctan2(y,x))\n",
        "  diff=np.pi-abs(abs(theta_to_be_taken-ang_rad)-np.pi)\n",
        "  return diff\n",
        "  \n",
        "### NORMALIZE THETA\n",
        "def normalize_theta(theta):\n",
        "  if( theta<0 ):\n",
        "    theta +=( 2*np.pi )\n",
        "  elif( theta>2*np.pi ):\n",
        "    theta %=( 2*np.pi)\n",
        "  return theta\n",
        "\n",
        "### THETA TO STACK NUMBER\n",
        "def theta_to_stack_number(theta):\n",
        "  new = (theta+2*np.pi)%(2*np.pi)\n",
        "  stack_number = round(new*NUM_THETA_CELLS/2*np.pi)%NUM_THETA_CELLS\n",
        "  return int(stack_number)\n",
        "\n",
        "### FLOOR VALUE\n",
        "def idx(value):\n",
        "  return int(MT.floor(value))\n",
        "\n",
        "### CHECK WITHIN GRID  \n",
        "def is_within_grid(x,y):\n",
        "  return (x>=0 and x<grid_on_x and y>=0 and y<grid_on_y)\n",
        "\n",
        "### IS_GOAL_REACHED\n",
        "def is_goal_reached(start,goal):\n",
        "  result=False\n",
        "  if( idx(start[0]) == idx(goal[0]) and idx(start[1])==idx(goal[1])):\n",
        "    result=True\n",
        "  return result\n",
        "\n",
        "\n",
        "### A_STAR SEARCH\n",
        "def A_Star(current_state,goal,grid):\n",
        "  vehicle_point_A=vehicle_points(np.array([[0,2],[0,1],[0,-1],[0,-2],[1,0],[2,0],[-1,0],[-2,0]]),[0,0])\n",
        "  print(\"STARTED A*\")\n",
        "  open_list = []\n",
        "  open_list.append(current_state )\n",
        "  is_goal_attained=False\n",
        "  cost=0\n",
        "  heu=0\n",
        "  closed_A_star[current_state.x][current_state.y]=1\n",
        "  cost_map[current_state.x][current_state.y]=cost\n",
        "  \n",
        "  while(len(open_list)>0):\n",
        "    open_list.sort(key=lambda state_srt : float(state_srt.f))\n",
        "    old_state=open_list.pop(0)\n",
        "    if(goal.x==old_state.x and goal.y==old_state.y):\n",
        "      is_goal_attained=True\n",
        "      print(\"GOAL REACHED BY A*\")\n",
        "      return is_goal_attained\n",
        "    node=np.array([old_state.x,old_state.y])\n",
        "    for move in motion_mat:\n",
        "      nxt_node=node+move\n",
        "      if( is_within_grid(nxt_node[0],nxt_node[1])):\n",
        "        if(grid[nxt_node[0]][nxt_node[1]]==0 and closed_A_star[nxt_node[0]][nxt_node[1]]==0):\n",
        "          if(A_vehicle_is_safe(vehicle_point_A,np.array([nxt_node]),grid)):\n",
        "            g2=old_state.g+1\n",
        "            heu=euclidean_distance([nxt_node[0],nxt_node[1]],[goal.x,goal.y])\n",
        "            new_state=state(nxt_node[0],nxt_node[1],0,g2,g2+heu,heu,0)\n",
        "            open_list.append(new_state)\n",
        "            closed_A_star[nxt_node[0]][nxt_node[1]]=1\n",
        "            cost_map[nxt_node[0]][nxt_node[1]]=g2\n",
        "            #plt.plot([node[0],nxt_node[0]],[node[1],nxt_node[1]])\n",
        "  return is_goal_attained\n",
        "\n",
        "### SEARCH ALGORITHM\n",
        "def Hybrid_A_Star(grid,current_state,goal,vehicle_point_object,speed):\n",
        "  print(\"STARTED HYBRID A*\")\n",
        "  start_time = time.time()\n",
        "  closed = np.array([[[free_space for x in range(grid_on_x)] for y in range(grid_on_y)] for cell in range(NUM_THETA_CELLS)])\n",
        "  came_from = [[[free_space for x in range(grid_on_x)] for y in range(grid_on_y)] for cell in range(NUM_THETA_CELLS)]\n",
        "  is_goal_attained=False\n",
        "  stack_number=theta_to_stack_number(current_state.theta)\n",
        "  closed[stack_number][idx(current_state.x)][idx(current_state.y)]=1\n",
        "  came_from[stack_number][idx(current_state.x)][idx(current_state.y)]=current_state\n",
        "  total_closed=1\n",
        "  opened=[current_state]\n",
        "  \n",
        "  while (len(opened)>0):\n",
        "    opened.sort(key=lambda state_srt : float(state_srt.f))\n",
        "    state_now=opened.pop(0)\n",
        "    #print([state_now.x,state_now.y,state_now.theta*np.pi/180])\n",
        "    if(is_goal_reached([idx(state_now.x),idx(state_now.y)],[idx(goal.x),idx(goal.y)])):\n",
        "      is_goal_attained=True\n",
        "      print('GOAL REACHED BY HYBRID A*')\n",
        "      ret_path=path(closed,came_from,state_now)\n",
        "      end_time = time.time()\n",
        "      print(end_time - start_time)\n",
        "      return (is_goal_attained,ret_path)\n",
        "    \n",
        "    for evry_state in new_state_transition(state_now,goal,speed):\n",
        "      #print('Before',[evry_state.x,evry_state.y,evry_state.theta*np.pi/180])\n",
        "      if(not is_within_grid(idx(evry_state.x),idx(evry_state.y))):\n",
        "        continue\n",
        "      \n",
        "      stack_num=theta_to_stack_number(evry_state.theta)\n",
        "      #print([stack_num,idx(evry_state.x),idx(evry_state.y)])\n",
        "      if closed[stack_num][idx(evry_state.x)][idx(evry_state.y)]==0 and grid[idx(evry_state.x)][idx(evry_state.y)]==0:\n",
        "        new_vehicle_point_obj = transform_vehicle_co_ordinates(vehicle_point_object,[evry_state.x,evry_state.y],evry_state.theta)\n",
        "        #print(new_vehicle_point_obj.input_co_ordinates)\n",
        "        if(is_vehicle_in_safe_position(new_vehicle_point_obj,grid)):\n",
        "            opened.append(evry_state)\n",
        "            closed[stack_num][idx(evry_state.x)][idx(evry_state.y)]=1\n",
        "            came_from[stack_num][idx(evry_state.x)][idx(evry_state.y)]=state_now\n",
        "            total_closed+= 1\n",
        "            #print('After',[evry_state.x,evry_state.y,evry_state.theta*np.pi/180])\n",
        "            #plt.plot([state_now.x,evry_state.x],[state_now.y,evry_state.y])\n",
        "      #closed[stack_num][idx(evry_state.x)][idx(evry_state.y)]=1\n",
        "        #print('-------------')\n",
        "  print('No Valid path')\n",
        "  ret_path=path(closed,came_from,evry_state)\n",
        "  return (is_goal_attained,ret_path)\n",
        "\n",
        "\n",
        "\n",
        "### RECONSTRUCT PATH\n",
        "def reconstruct_path(came_from, start, final):\n",
        "    path                 = [(final)]\n",
        "    stack                = theta_to_stack_number(final.theta)\n",
        "    current              = came_from[stack][idx(final.x)][idx(final.y)]\n",
        "    stack                = theta_to_stack_number(current.theta)\n",
        "    while [idx(current.x), idx(current.y)] != [idx(start[0]), idx(start[1])] :\n",
        "        path.append(current)\n",
        "        current              = came_from[stack][idx(current.x)][idx(current.y)]\n",
        "        stack                = theta_to_stack_number(current.theta)\n",
        "    return path\n",
        "\n",
        "\n",
        "###DISPLAY PATH\n",
        "def show_path(path, start, goal,vehicle_pt_obj_act):\n",
        "  X=[start[0]]\n",
        "  Y=[start[1]]\n",
        "  Theta=[]\n",
        "  path.reverse()\n",
        "  X     += [p.x for p in path]\n",
        "  Y     += [p.y for p in path]\n",
        "  Theta+=[p.theta for p in path]\n",
        "  for i in range(len(X)-1):\n",
        "    Xj=[]\n",
        "    Yj=[]\n",
        "    vehicle_pt_obj_now=transform_vehicle_co_ordinates(vehicle_pt_obj_act,[X[i],Y[i]], Theta[i])\n",
        "    rev=vehicle_pt_obj_now.input_co_ordinates\n",
        "    revI=rev[:4]\n",
        "    revL=rev[4:]\n",
        "    revF=np.concatenate([revI,revL[::-1]])\n",
        "    l=np.append(revF,[revF[0]],axis=0)\n",
        "    #print(l)\n",
        "    for i in l:\n",
        "      Xj.append(i[0])\n",
        "      Yj.append(i[1])\n",
        "    plt.plot(Xj,Yj)\n",
        "  print([p.steer*180/np.pi for p in path])\n",
        "  plt.plot(X,Y, color='black')\n",
        "  plt.scatter([start[0]], [start[1]], color='blue')\n",
        "  plt.scatter([goal[0]], [goal[1]], color='red')\n",
        "  plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
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      "metadata": {
        "id": "2exSViITSeqc",
        "colab_type": "code",
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      "cell_type": "code",
      "source": [
        "### PUT OBSTACLES:\n",
        "def put_obstacles(X_list,Y_list,grid):\n",
        "    if(len(X_list)>0):\n",
        "      for i in  X_list:\n",
        "        x_XO=[]\n",
        "        x_YO=[]\n",
        "        for k in range(i[1],i[2]):\n",
        "          x_XO.append(i[0])\n",
        "          x_YO.append(k)\n",
        "          grid[i[0]][k]=1\n",
        "        plt.scatter(x_XO,x_YO)\n",
        "    if(len(Y_list)>0):\n",
        "      for i in Y_list:\n",
        "        y_XO=[]\n",
        "        y_YO=[]\n",
        "        for k in range(i[1],i[2]):\n",
        "          y_XO.append(i[0])\n",
        "          y_YO.append(k)\n",
        "          grid[k][i[0]]=1\n",
        "        plt.scatter(y_YO,y_XO)\n",
        "  "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "ZOneuDF-KiZN",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 347
        },
        "outputId": "5aff0112-5493-423a-88b0-d12e102968da"
      },
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import math\n",
        "# Vehicle parameter\n",
        "W = 2.5 #[m] width of vehicle\n",
        "LF = 3.7 #[m] distance from rear to vehicle front end of vehicle\n",
        "LB = 1.0 #[m] distance from rear to vehicle back end of vehicle\n",
        "TR = 0.5 # Tyre radius [m] for plot\n",
        "TW = 1.2 # Tyre width [m] for plot\n",
        "MAX_STEER = 0.6 #[rad] maximum steering angle\n",
        "WB = 2.7  #[m] wheel base: rear to front steer\n",
        "\n",
        "def plot_car(x, y, yaw, steer, retrun_car = False):\n",
        "    car_color = \"-k\"\n",
        "\n",
        "    LENGTH = LB+LF\n",
        "\n",
        "    car_OutLine = np.array([[-LB, (LENGTH - LB), (LENGTH - LB), (-LB), (-LB)],\n",
        "                             [W / 2, W / 2, - W / 2, - W / 2, W / 2]])\n",
        "\n",
        "\n",
        "    rr_wheel = np.array([[TR, - TR, - TR, TR, TR],\n",
        "                         [-W / 12.0 + TW, - W / 12.0 + TW, W / 12.0 + TW, W / 12.0 + TW, - W / 12.0 + TW]])\n",
        "\n",
        "    rl_wheel = np.array([[TR, - TR, - TR, TR, TR],\n",
        "                         [-W / 12.0 - TW, - W / 12.0 - TW, W / 12.0 - TW, W / 12.0 - TW, - W / 12.0 - TW]])\n",
        "\n",
        "    fr_wheel = np.array([[TR, - TR, - TR, TR, TR],\n",
        "                         [- W / 12.0 + TW, - W / 12.0 + TW, W / 12.0 + TW, W / 12.0 + TW, - W / 12.0 + TW]])\n",
        "\n",
        "    fl_wheel = np.array([[TR, - TR, - TR, TR, TR],\n",
        "                         [-W / 12.0 - TW, - W / 12.0 - TW, W / 12.0 - TW, W / 12.0 - TW, - W / 12.0 - TW]])\n",
        "\n",
        "    Rot1 = np.array([[math.cos(yaw), math.sin(yaw)],\n",
        "                    [-math.sin(yaw), math.cos(yaw)]])\n",
        "    Rot2 = np.array([[math.cos(steer), -math.sin(steer)],\n",
        "                     [math.sin(steer), math.cos(steer)]])\n",
        "\n",
        "\n",
        "    fr_wheel = np.dot(fr_wheel.T, Rot2).T\n",
        "    fl_wheel = np.dot(fl_wheel.T, Rot2).T\n",
        "    fr_wheel[0,:] += WB\n",
        "    fl_wheel[0,:] += WB\n",
        "    fr_wheel = np.dot(fr_wheel.T, Rot1).T\n",
        "    fl_wheel = np.dot(fl_wheel.T, Rot1).T\n",
        "\n",
        "    car_OutLine = np.dot(car_OutLine.T, Rot1)\n",
        "\n",
        "    rr_wheel = np.dot(rr_wheel.T, Rot1).T\n",
        "    rl_wheel = np.dot(rl_wheel.T, Rot1).T\n",
        "\n",
        "    car_OutLine = car_OutLine.T\n",
        "    car_OutLine[0,:] += x\n",
        "    car_OutLine[1,:] += y\n",
        "    fr_wheel[0, :] += x\n",
        "    fr_wheel[1, :] += y\n",
        "    rr_wheel[0, :] += x\n",
        "    rr_wheel[1, :] += y\n",
        "    fl_wheel[0, :] += x\n",
        "    fl_wheel[1, :] += y\n",
        "    rl_wheel[0, :] += x\n",
        "    rl_wheel[1, :] += y\n",
        "\n",
        "    if retrun_car == False:\n",
        "        plt.plot(x, y, \"*\")\n",
        "        plt.plot(fr_wheel[0, :], fr_wheel[1, :], car_color)\n",
        "        plt.plot(rr_wheel[0, :], rr_wheel[1, :], car_color)\n",
        "        plt.plot(fl_wheel[0, :], fl_wheel[1, :], car_color)\n",
        "        plt.plot(rl_wheel[0, :], rl_wheel[1, :], car_color)\n",
        "        plt.plot(car_OutLine[0, :], car_OutLine[1, :], car_color)\n",
        "    else:\n",
        "        return car_OutLine[0, :], car_OutLine[1, :]\n",
        "\n",
        "plot_car(0.0, 0.0, np.pi, 0.0, retrun_car = False)\n"
      ],
      "execution_count": 109,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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BADCGOAMAYAxxBgDAGOIMAIAxxBkAAGOIMwAAxhBnAACMIc4AABhDnAEAMIY4AwBgDHEG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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f1232237d10>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "GnQoKc-BeRXn",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def show_animation(path, start, goal,vehicle_pt_obj_act):\n",
        "  x =[]\n",
        "  y = []\n",
        "  yaw = []\n",
        "  steer = []\n",
        "  path.reverse()\n",
        "  x     += [p.x for p in path]\n",
        "  y     += [p.y for p in path]\n",
        "  yaw += [p.theta for p in path]\n",
        " \n",
        "  steer =[p.steer*180/np.pi for p in path]\n",
        "  print(type(steer[0]))\n",
        "  \n",
        "  for ii in range(0,len(x),5):\n",
        "      plt.cla()\n",
        "      plt.plot(x, y, \"-r\", label=\"Hybrid A* path\")\n",
        "\n",
        "\n",
        "      plot_car(x[ii], y[ii], yaw[ii], steer[ii])\n",
        "      plt.grid(True)\n",
        "      plt.axis(\"equal\")\n",
        "      plt.pause(0.01)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "ZbpDvcJDRw3I",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "START=[40,45]\n",
        "SPEED=60\n",
        "goal_node = goal( 4,3)\n",
        "present_heading=(np.pi/2)\n",
        "vehicle_pt_obj_actual = vehicle_points( np.array([[0.5,0.5],[0.5,1.5],[0.5,2.5],[0.5,3.5],[1.5,0.5],[1.5,1.5],[1.5,2.5],[1.5,3.5]]),[0,2] )\n",
        "vehicle_pt_obj=transform_vehicle_co_ordinates(vehicle_pt_obj_actual,START,present_heading)\n",
        "#print(vehicle_pt_obj.input_co_ordinates)\n",
        "current_state = state(vehicle_pt_obj.center[0], vehicle_pt_obj.center[1], present_heading, 0.0, 0.0, 0.0,0.0)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "vJQLZcriX_il",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 5069
        },
        "outputId": "91a02610-10bd-4812-f538-421ac7eca3f5"
      },
      "cell_type": "code",
      "source": [
        "put_obstacles([[15,0,30],[26,0,30],[27,0,25],[60,15,35]],[],GRID_TEST)\n",
        "if(A_Star(state(goal_node.x,goal_node.y,0,0,0,0,0),goal(START[0],START[1]),GRID_TEST)):\n",
        "  process_further,ret_val=Hybrid_A_Star(GRID_TEST,current_state,goal_node,vehicle_pt_obj,SPEED)\n",
        "  if(process_further):\n",
        "    show_animation(reconstruct_path(ret_val.came_from,START,ret_val.final),START,[goal_node.x,goal_node.y],vehicle_pt_obj_actual)\n",
        "  else:\n",
        "    print(\"GOAL CANT BE REACHED!!\")\n",
        "else:\n",
        "  print(\"GOAL CANT BE REACHED!!\")\n"
      ],
      "execution_count": 112,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "STARTED A*\n",
            "GOAL REACHED BY A*\n",
            "STARTED HYBRID A*\n",
            "GOAL REACHED BY HYBRID A*\n",
            "0.895781040192\n",
            "<type 'float'>\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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kOal8JeqsG9YD6Dq+IpK0VL4Sdda1awhZLPjPOtvsKCIiplD5SnT5/djWfU6g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\nRK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f1232068850>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3ZtOmTQCsWbOmxr3jcHbBBRewevVqAD7//HNSU1NJTEy0OFXg9ezZ\ns3rOSP+ZFRcXM23aNBYuXEj9+vWB6Jlv06ZNLF68GDjykUhZWVnUzAYwc+ZM/vnPf/LSSy8xcOBA\nhg4dGjXzvfbaazz77LMAFBYWsn//fgYMGBAVswFceOGFbNiwAb/fT1FRUcB/N3VXo59Yu3Ytzz77\nLN988w0NGzYkJSWFxYsXk5uby8MPP4zf7+ess87igQcesDpqrcyYMYNNmzZhs9mYMGECHTt2tDpS\nrWzbto2pU6eSl5eHw+GgUaNGzJgxg7Fjx1JRUUGTJk14/PHHcTqdVkf9TVauXMmcOXNo1apV9bYp\nU6Ywfvz4iJ/P4/Hw4IMPkp+fj8fjYdiwYXTq1IkxY8ZE/Gz/a86cOTRt2pQLL7wwKuYrKSlh5MiR\nHD58mKqqKoYNG8bpp58eFbMdtWLFiuozmu+88046d+4csPlUviIiIiGmw84iIiIhpvIVEREJMZWv\niIhIiKl8RUREQkzlKyIiEmIqXxERkRBT+YqIiISYyldERCTE/j9sQYW7qo+DogAAAABJRU5ErkJg\ngg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f1234816510>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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SMCpiCQ6VlTj2fI23Y2fd7EFEwoqKWIKC4+uvsHk8eLRbWkTCjIpYgoIj+8Tx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\nqYhFREQMUhGLiIgY9P9GQMYjQp6nVgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f12320da9d0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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EwkuFLJbiyNmF4XIRaNzU7CgiImGlQhbrMAwcu3cTuLgZuFxmpxERCSsVsliG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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f1234998990>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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HPGLECFauXElGRgYHDx7kuuuuC0UuEbGAw4cPMXHieOLi4pg+fQ42m+2Ebdx/X0ncu29T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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f12347f6590>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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dTE4iIhJdKmSxFGfBiSOs27c3OYmISHSpkMVSHAU7MFwugq3amB1FRCSqVMhi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\nHAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f1232389510>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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xFGfOqSOszz/f5CQiIuGlQhZLceTswnC58DdpZnYUEZGwUiGLdRgGjuxs/M1b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\nTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f123256a810>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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SHbMTiUQNFbKIlIt5+03cH62h5MqrKb3uBrPjiEQVFbKIAGA7kk/iI5Mw4uIonDEXbDaz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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f1232680090>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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DpCl3YauqonzWXIzkFmYnEokZKmQRqRX3ymrcb6+n6pJLqf7p5WbHEYkpKmQRAcB2pJSk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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f123253cf10>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Ro0epXbt26eM6derExFxnOJ1OEhMTz9rm8/lKTwfFyusI4HA48Hg8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\nEQv4fxWNCc95dSAQAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f1234974410>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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D1+UffUopoM+QRSQ+qJAlbD7+eCMAgUAAOL5YXZs/xWYYR86w/oFjRW4YBnDy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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f1234853490>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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GDFavXk3r1q254oorwhpSIkdBwfFC/uabA5x7br+ax5/vKOFfr27lizZnAjD/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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f1232229850>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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IiLVUvmIa9+efAipfERGVr5jG8+knGH6/3vMVEdtT+Yo5AgFc678iPOAEcLms\nTiMiYimVr5jC/cUaHNEoNScMtDqKiIjlVL5iCvf6dQBE+h1ncRIREeupfMUU9TdUyO1jcRIREeup\nfMUUrg3FAER6aVlJERHdzVxaRCgU4p13/kX79ln06pVLenrGIc+7iouItm+P0S7TooQiIvFD5Sst\nIj//Be68c3z94w4djiE3tze9euWS270HJ236ml4nnEhqNIrTqQMuImJvKl9pEWvXfg7Ab34zhj17\ndlNSUsx77/2b997793cf9OnH+Hvk0LNnLrm5ufTq1Zvc3N706NGT3r37kpSUZFF6ERFzqXyl2ZYv\nf5tly5bicDi4/PKrGDLkDAAqKyvZuHEDm/JfYMszf2LtcQNYBxQXr2fNms9+8HV27TpocnIREWuo\nfKXZ7rvvLrZv/waAUaNGsmTJK5x99jmkpKQwYMDx/PStpaQAB6bcS/XPzyMajfLNN1spKSli9eoP\nmT17urUDiIiYTG++SbPU1NSwYUMJAJmZ7QF+cPh43Zb9rDm2P+FetctKOp1OunTpSmZme6LRKADX\nXnuDialFRKyl8pVm2bJlE+FwGID09HQAevU6dO3ml7w9eeH0y4h26XrI9quuymPOnJkALF78ZzZu\nLDEhsYiI9VS+0izFxcX1fw4EKklPzyA7OxuAdZv3MeOvH/NF226s7XQcM5Z8xrrN+wDYv38f27dv\nIzOz9tKjmpoaAoEq8wcQEbGAyleapfjblasAdu/eTW5uLg6HA4C+Xdty5aB29c9f/os+9O3aFoCS\nktrSTktLr3++R4+eZkQWEbGcyleaZcaMh+v/HIlEfnDIefXHX3PZyiVczBZWr9tVv72ufCsrK3E4\nHHTu3AW/329OaBERi6l8pVlycjod8njAgOMPedz5wA7yVi7hol7J5LRPqd9et8e8d+8eDMMgV/f4\nFREbUflKs7z//mo8Hg/HHdefV175B1dddd0hz5/+zScARHJ7c0rf7Prtf/rTvNrtkQiAyldEbEXX\n+UqzbNmyiZqaGvr3P54zzjjzB8+7i769m1HP3EO215VunT59+sUupIhInNGerzRL3dnOP7bn6iop\nIpLTCVJTD9m+dWsZ119/EwBXXnkNF100OrZBRUTiiMpXmqXuvdvvn2gFQEUFru3biHxvrxdqF+Ko\nqKgA4JZbxulkKxGxFZWvNEtJSW35Hm7P1/3tohmR3offKy4uLsLj8dClS7eY5RMRiUcqX2mW4uIi\n3G433bp1/8Fzrm/3isO9frjnaxgGJSXFdO/eA4/HE/OcIiLxROUrR622QIvo1q37YQu0rnwjhzkk\nXVZWxoED++l5mEPSIiKJTuUG1u4SAAAL80lEQVQrR2337t3s37//8O/3Aq5vF9KIHOaQ9JEOV4uI\nJDqVrxyV0tJSzj77dADWr1/Hyy+/+IOPcRcXYfhTiHbM+cFz352opT1fEbEfla8clcLC/6O0dCcA\nX3+9gWnTHjz0AyIRXBtLat/v/Xat5/+kPV8RsTMtsiFHpaho/SGPjz228yGPnVu34AiFfnDIeefO\nHYwfP5YvvlgLQDh86GIbIiJ2oD1fOSp1e651vv++r/vb579fvkuX/i/Ll7/Nrl2lADzwwD0xTCki\nEp9UvnJUiouLcTgc9bcEzM099L1b17crX4W/V751pV1328GsrGxEROxG5StNFo1GWbPmMwzDoE2b\nNsAP37utP9P5e3vEdSdaGYYB6IQrEbEnla802TffbP3Bn79/2NlVvB7D6STSvcch20tKiklPz6h/\nrBOuRMSOVL7SZJ07dyE9vfZwc0ZGG047bcihJ1yFw3g+/5RIn77g89VvDgQCbN26hYyM78pXe74i\nYkcqX2kyh8PBLbfcCsBTTy3gtdf+icvlqn/e/eVaHIEANSf/9JDP++ijDzEMg61bt9RvU/mKiB3p\nUiM5KnUFeuON15Kbm0uvXr3Jze1Nr1696f/5JxwP1Jxy6iGf8/179vbt2482bdqaFVlEJG6ofOWo\nXH75VRw4cICSkiLWrPmcjz/+6JDnXUC32dPJfeP//Ucx57Ju3dcMGnQc3bp1Z9myd6wJLyJisUaV\nb1FREWPHjuXqq6/m8ssvZ8eOHUycOJFIJEJWVhazZs3C6/XGOqvEkZNPPpVFi54HIBwOs2XLJoqL\niykuLmLro9NZHwrx5cEDbPjnG8AbP/j8Pn366mdGRGyrwfINBAI89NBDDB48uH7bvHnzyMvLY8SI\nEcyZM4eCggLy8vJiGlTil9vtpkePXvTo0YvzBg6i/YP3Ejr3PA4szmfPnj2UlBRRUlJbzCUlRXzz\nzVYuvHC01bFFRCzTYPl6vV4WLFjAggUL6rcVFhbywAMPADBs2DAWLlyo8hUAPJ99DED4xJNwOBy0\nb9+e9u3bc9ppQyxOJiISPxosX7fbjdt96IdVVVXVHzLMzMykrKwsNumk1XF/+gkA4YEnWpxERCR+\nNfuEq7qVio6kbVs/brerwY8zW1ZWmtURTGParF+tASDj7KFgwd+vXtPEY5c5QbPayVGVr9/vJxgM\n4vP5KC0tJTv7yOvz7tsXOKpwsZSVlUZZWbnVMUxh2qyGQeaqDzE6HcteRzKY/Per1zTx2GVO0KyJ\n6Ei/YBzVIhtDhgxh6dKlACxbtoyhQ4ceXTJJKM4d23GW7SJ8gg45i4gcSYN7vmvXrmXGjBls27YN\nt9vN0qVLmT17NpMnTyY/P5+cnBxGjRplRlaJc+4vv71Hb/8BFicREYlvDZZv//79Wbx48Q+2L1q0\nKCaBpPVybt4EQKRHT2uDiIjEOa3tLC3GtWkTAJGu3SzNISIS71S+0mJcdXu+3Xoc+QNFRGxO5Sst\nxrV5E9HUNIx27ayOIiIS11S+0jIMo7Z8u3YDh8PqNCIicU3lKy3CsXcvjkAlkc5drI4iIhL3VL7S\nIlzbvwEg2qmTxUlEROKfyldahHP7dgAiOcdanEREJP6pfKVFOLd9u+ebk2NxEhGR+KfylRbh2lG7\n5xvtpD1fEZGGqHylRdTt+UY6as9XRKQhKl9pEa6tWzCcTqIqXxGRBql8pUU4N28iemxn8HqtjiIi\nEvdUvtJ8VVW4du7Qms4iIo2k8pVmc23dAuiGCiIijaXylWZzbdoIqHxFRBpL5SvNVnc3o6jKV0Sk\nUVS+0mzObdsAiBzb2eIkIiKtg8pXms1Zv66zFtgQEWkMla80m2v7dgyXi2h2B6ujiIi0CipfaTbn\n9m1Ej+kILpfVUUREWgWVrzRPJIJz5w6tbCUi0gQqX2kW565SHOEwEb3fKyLSaCpfaRbn5s2ALjMS\nEWkKla80i2vz14AW2BARaQqVrzSLa5PKV0SkqVS+0ix1q1upfEVEGk/lK83i2rwJw+3WAhsiIk2g\n8pVmcW7ZTDTnWHC7rY4iItJqqHzl6FVX49xVSuRY7fWKiDSFyleOmrN0Jw7DIJrTyeooIiKtispX\njlrd3YxUviIiTaPylaPm+vZuRhGVr4hIk6h85ag5t28HtOcrItJUKl85atGsLAy/n/CA462OIiLS\nqqh85aiFxuSxu3irrvEVEWkila80j8djdQIRkVZH5SsiImIyla+IiIjJVL4iIiImU/mKiIiYTOUr\nIiJiMpWviIiIyVS+IiIiJlP5ioiImEzlKyIiYjKVr4iIiMlUviIiIiZzGIZhWB1CRETETrTnKyIi\nYjKVr4iIiMlUviIiIiZT+YqIiJhM5SsiImIyla+IiIjJ3FYHMNuqVasYP34806ZNY9iwYQCsW7eO\n+++/H4A+ffrwwAMPWJiw5UybNo3PPvsMh8PBlClTOP74462O1KKKiooYO3YsV199NZdffjk7duxg\n4sSJRCIRsrKymDVrFl6v1+qYLWLmzJl89NFHhMNhbrrpJgYMGJBws1ZVVTF58mT27NlDKBRi7Nix\n9O3bN+Hm/E/BYJDzzz+fsWPHMnjw4ISctbCwkPHjx5ObmwtA7969uf766xNy1qaw1Z7vli1bWLRo\nEYMGDTpk+9SpU5kyZQpLliyhoqKCd955x6KELWfVqlVs3ryZ/Px8pk6dytSpU62O1KICgQAPPfQQ\ngwcPrt82b9488vLyeOGFF+jatSsFBQUWJmw5H3zwAcXFxeTn5/Pss88ybdq0hJx1+fLl9O/fn+ef\nf565c+cyffr0hJzzPz311FNkZGQAifvzC3DqqaeyePFiFi9ezL333pvQszaWrco3KyuLJ554grS0\ntPpt1dXVbNu2rX6vcNiwYaxcudKqiC1m5cqVnHPOOQD07NmTAwcOUFFRYXGqluP1elmwYAHZ2dn1\n2woLCxk+fDiQOK8jwCmnnMJjjz0GQHp6OlVVVQk568iRI7nhhhsA2LFjBx06dEjIOets2LCBkpIS\nzjrrLCBxf34Px06z/hhblW9ycjIul+uQbfv27SM9Pb3+cWZmJmVlZWZHa3G7d++mbdu29Y/btWuX\nEHPVcbvd+Hy+Q7ZVVVXVH7pKlNcRwOVy4ff7ASgoKODMM89M2FkBLr30Uu68806mTJmS0HPOmDGD\nyZMn1z9O5FlLSkq4+eabueyyy3j//fcTetbGStj3fF966SVeeumlQ7bdeuutDB069Iifl6irbSbq\nXD8mEed96623KCgoYOHChZx77rn12xNt1iVLlvDVV18xYcKEQ2ZLpDlfffVVBg4cSOfOnQ/7fCLN\n2q1bN8aNG8eIESPYunUrV155JZFIpP75RJq1KRK2fEePHs3o0aMb/Lh27dqxf//++selpaWHHMps\nrbKzs9m9e3f94127dpGVlWVhotjz+/0Eg0F8Pl/CvI513n33XebPn8+zzz5LWlpaQs66du1aMjMz\n6dixI/369SMSiZCSkpJwcwK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            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f1232612950>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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zrl8HgK9zV5OTiIiYQ+UrYefcuhkA/3nnm5xERMQcKl8JO0e+HqggItFN5Sth\n58jPw9+kKcTHmx1FRMQUKl8JK1vxIRx7CvC31l6viEQvla+EVdUhZ93fKyJRTOUrYVW1prPO94pI\nFFP5Slgd3fP1t21nchIREfOofCWsnEf2fH16mpGIRDGVr4SVIz+XQJ26GKmpZkcRETGNylfCx+fD\nsX0b/jZtwGYzO42IiGlUvhI2jp3fYqusxK9DziIS5VS+EjaOvCO3GekeXxGJcipfCZuq24y05ysi\nUU7lK2HjyD9SvlpgQ0SinMpXwsaZl4vhcOBv3sLsKCIiplL5SngYBo68rYeL1+UyO42IiKlUvhIW\ntv37sR84oEPOIiKofCVMnPla01lE5CiVr4TF0SudfVrTWURE5Svh8dNtRtrzFRFR+UpYVN1mpPIV\nEVH5Sng483IJNEzBqN/A7CgiIqZT+Uroeb3Yd+7ApyudRUQAla+EgWP7NmyGoUPOIiJHqHwl5LSs\npIjI8VS+EnLOPJWviMixVL4SclX3+GqBDRERQOUrYeDYlo8RG0ugSVOzo4iIRASVr4RWIIAzLxd/\ny1bgcJidRkQkIqh8JaQcuVuxlZXi69TF7CgiIhFD5SshFbMqB4DKbr82OYmISORQ+UpIqXxFRH7J\naXYAqd02bPiKp556lObNW9K16wV06XIB7dq1JyYmBgDn6pUEkurgb9fe5KQiIpGjRuWbm5vL4MGD\nuf322xk4cCAFBQWMHDkSv99PSkoKkydPxuVyhTqrRKA335zLsmWfsWzZZ7z22uFtbreb88/vRNf2\nHeiVn0eXbt05B9DlViIih1VbvmVlZTz99NP06NGjatv06dPJzMykb9++TJ06laysLDIzM0MaVCKP\n3+9n7dovcTgcvPvuh3z99Sa++mod69atZf36taxZs4pZAKtWEt+qMR07dq7aO+7a9UJatWqN3a4z\nHyISfar9P5/L5WLmzJmkpqZWbcvJyaFPnz4AZGRkkJ2dHbqEEpEMw6B374tZs2YVMTExfPDBv/nD\nH25lypTpfPLJcrZv/56lA2/jb8AfemfQrFkLVq9eycsvv8C99/6ZSy65iHPOqceAATeYPYqISNhV\nW75OpxO3233cNo/HU3WYOTk5mcLCwtCkk4i1a9dOcnO3AlBeXs7zz0+joOD7qs+73W4u3reXwcC0\nv81k2bJstm//nn/96yPGjZtEq1atAfjyy9VmxBcRMdVZX3BlGEa1X1O/fjxOZ2Sf8UtJSTI7QlgE\na85ly7ZU/TktLY2SkhK6du1QdRh5Q/4P7NlbRqdzz6Xh+a2OfGUSzZqlkZ6eTEnJAcaNG8dzzz0X\nsv/20fKeQvTMGi1zgma1ujP/KUU1AAAMHElEQVQq3/j4eLxeL263m7179x53SPpEiorKzihcuKSk\nJFFYWGx2jJAL5pyff/7fqj/v2bOHnj0vZf/+0qptr72zlpi2V/JEyQoOHfMzt2/Pp0ePX1X9pS0r\naxF9+/42KJmOFS3vKUTPrNEyJ2hWqzjVXyrO6GqXnj17snjxYgCWLFlCr169ziyZ1Frr1q0FwHFk\nycjOnbsCsGVHERP/8SVb95axsUlHHj3vJrbsKKp63cqVORiGgdsdB8CKFV+EObmIiPmq3fPduHEj\nEydOZPfu3TidThYvXswzzzzD6NGjWbBgAenp6fTv3z8cWSVCGIbB8uVLAUhJSWXPngK6dr0AgPbN\n6pMUH8Ojs1YCcHuHWFKa1a967fr1h0u7vNwLQJcuXcOYXEQkMlRbvh07dmTu3Lm/2D5nzpyQBJLI\nt2/fvqo/79lTAFBVvgCrtuzj98VfE7PxK7LP+zPXHfPadevW4nA48Pv9AHTpcgEiItFGN1nKaUtL\nSyMj4/CtZs2bt+Dqq6+jefOWVZ9vnJLIzZve5+YVC2jUolHVdp/Px6ZNG0hJSava1rXrheELLiIS\nIbS8pJyRc889/GzeWbNep9PPnljUrX0qjh3fEkhvTLdOjau2r1+/Fq/Xy549P92SpMPOIhKNtOcr\nZ2T9+rXExsbSrl2HX36yvBz797vxN2t+3Oa1a9cc93FqahrnnNMIEZFoo/KV01ZeXs7mzZs4//yO\nJ1zT27FrJzbD+EX53nnnIF59dR42m420tHP4618nhCmxiEhkUfnKadu8eROVlZUnvFhq7949DBr5\nAG8AlY3P/cXn69Wrh2EY/O53/0v//r8LQ1oRkcij8pXTdvQe3xNdLDV27JO89Z/PuQXo+Y/XWbLk\ng+NWQVu/ft2R1+oqZxGJXipfOW1H79U9urDGUbm5W1m48E3aNUjmNmDznj0MHHgT11xzJdnZXxx5\n7ZeAbjESkeim8pXTtm7dWtxuN+3atT9ue27uVgKBANuKfsQNLHx2Bn37XsOqVTlcf31f5sx5hXXr\n1lK3bj2aN29hTngRkQig8pXT4vF42LLlazp27IzTefydaldffS2zZr1OS3ccLwG3jH6Q1q3b8Jvf\nXAFAZWUF27dvo0uXC7DZbCakFxGJDCpfOS2bNm3A7/ef8JytzWbj2mv7s/7cc3k5Lo76DZKZMeNZ\nPv30YwDatGkH6N5eERGVr5yWoxdMnfScrWEQu/s7bm/VhuzsLxk0aAgAw4YNZ+PGDYAuthIRUfnK\naTl6sdXJloW07duHrayMQPMWxMXF8dRT49i37xBjxjxW9VpdbCUi0U7lK6dl/fq1xMcn0Lp1mxN+\n3rHjW4BfLLABhy/UatCgAU2aNA1hQhGRyKfylRorLS1l69YtdOrUueo5vj/n2PEN8MvyLSr6kZ07\nv9XFViIiqHzlNGzcuIFAIHDKc7Yn2/PV4hoiIj9R+UqN1WSBjJOX79HzvXqEoIiIyldq7NhlJb/7\nbhc7d+74xdfYd38HQOBn6zr/9Frt+YqIqHylxr766vCh44UL59G798V069aZYcPuZfeRwgWwf7+b\nQMMUiI097rXr16+lYcMUGjVKD2tmEZFIpPKVGmvRoiUA06ZNobi4GMMwmDdvLr/6VUeuvfYq3nt3\nEYd2f4f/Z3u9hYWFfPfdLrp21cVWIiIAzuq/ROSw11+fT0HB91x88YV4vR7atm3H7t27KS0tIScn\nm5ycbO4AWuZtpfOfb6dz5wvo2vUCfvihEND9vSIiR6l8pcZsNhvp6Y25//4HeO65KeTmbqVt23b8\n8Y93snr1Kt5+eyFO4IDfz6JF77Bo0TvHvf5kC3OIiEQbla+ctuHDR3PzzQOZMmUi8+bN5aGHRlR9\nbhQwavhDbO1/A+vXr2XdurWsX7+W8vJyeva8xLzQIiIRROUrZ6Rx43OZOnUG99xzHxMm/JX33lsE\nwHAg0KIFzZo1p1mz5lx33W/NDSoiEoF0wZWclTZt2jJr1uvMnbuARf9zNfWAwAmWlhQRkZ+ofCUo\nrrqqL//j9wEnXtdZRER+ovKVoHHs+JZA3XoY9eqbHUVEJKKpfCU4AgEcO3fgb97C7CQiIhFP5StB\nYS/ch83rJaDHBYqIVEvlK0Fh/343wC9WtxIRkV9S+UpQ2HcfLt9A48YmJxERiXwqXwkKR8GRPd90\nla+ISHVUvhIUVXu+Kl8RkWqpfCUo7AUqXxGRmlL5SlAEUlLxN21OIO0cs6OIiEQ8la8ERenTE/hx\nxZfgcJgdRUQk4ql8JThsNnDqOR0iIjWh8hUREQkzla+IiEiYqXxFRETCTOUrIiISZipfERGRMFP5\nioiIhJnKV0REJMxUviIiImGm8hUREQkzla+IiEiYqXxFRETCzGYYhmF2CBERkWiiPV8REZEwU/mK\niIiEmcpXREQkzFS+IiIiYabyFRERCTOVr4iISJg5zQ5gppUrVzJ06FDGjRtHRkYGAFu2bOGJJ54A\noF27djz55JMmJgyecePGsX79emw2G2PGjKFz585mRwqq3NxcBg8ezO23387AgQMpKChg5MiR+P1+\nUlJSmDx5Mi6Xy+yYQTFp0iTWrFmDz+fj7rvvplOnTpab1ePxMHr0aPbv3095eTmDBw+mffv2lpvz\nWF6vl2uuuYbBgwfTo0cPy82ak5PD0KFDadOmDQBt27blzjvvtNycNRW1e747d+5kzpw5XHjhhcdt\nHzt2LGPGjGH+/PmUlJSwbNkykxIGz8qVK9mxYwcLFixg7NixjB071uxIQVVWVsbTTz9Njx49qrZN\nnz6dzMxM5s2bR7NmzcjKyjIxYfCsWLGCvLw8FixYwCuvvMK4ceMsOetnn31Gx44deeONN5g2bRoT\nJkyw5JzHeuGFF6hbty5g3d/f7t27M3fuXObOncujjz5q2TlrImrLNyUlheeff56kpKSqbRUVFeze\nvbtqrzAjI4Ps7GyzIgZNdnY2V1xxBQCtWrXi4MGDlJSUmJwqeFwuFzNnziQ1NbVqW05ODn369AGs\n8z4CdOvWjeeeew6AOnXq4PF4LDlrv379uOuuuwAoKCggLS3NknMetW3bNvLz87n88ssB6/7+/ly0\nzHkiUVu+cXFxOByO47YVFRVRp06dqo+Tk5MpLCwMd7Sg++GHH6hfv37Vxw0aNLDEXEc5nU7cbvdx\n2zweT9XhK6u8jwAOh4P4+HgAsrKyuOyyyyw7K8CAAQMYPnw4Y8aMsfScEydOZPTo0VUfW3XW/Px8\nBg0axM0338wXX3xh2TlrIirO+b711lu89dZbx22777776NWr1ylfZ9WVN60618lYcd6PP/6YrKws\nZs+ezZVXXlm13Wqzzp8/n82bNzNixIjjZrPSnIsWLaJr1640adLkhJ+3yqzNmzdnyJAh9O3bl127\ndnHrrbfi9/urPm+VOWsqKsr3xhtv5MYbb6z26xo0aMCBAweqPt67d+9xhzJrq9TUVH744Yeqj/ft\n20dKSoqJiUIvPj4er9eL2+22zPt41PLly3nxxRd55ZVXSEpKsuSsGzduJDk5mUaNGtGhQwf8fj8J\nCQmWmxNg6dKl7Nq1i6VLl7Jnzx5cLpcl39O0tDT69esHQNOmTWnYsCEbNmyw3Jw1FbWHnU8kJiaG\nli1bsnr1agCWLFlS7d5xbXDJJZewePFiADZt2kRqaiqJiYkmpwqtnj17Vs1slfcRoLi4mEmTJvHS\nSy9Rr149wJqzrl69mtmzZwOHT5uUlZVZck6AadOm8fbbb7Nw4UJuvPFGBg8ebMlZ3333XWbNmgVA\nYWEh+/fv54YbbrDcnDUVtU81Wrp0KbNmzWL79u00aNCAlJQUZs+eTX5+Po899hiBQIAuXbrw0EMP\nmR01KJ555hlWr16NzWbj8ccfp3379mZHCpqNGzcyceJEdu/ejdPpJC0tjWeeeYbRo0dTXl5Oeno6\n48ePJyYmxuyoZ23BggXMmDGDFi1aVG2bMGECjzzyiKVm9Xq9PPzwwxQUFOD1ehkyZAgdO3Zk1KhR\nlprz52bMmEHjxo259NJLLTdrSUkJw4cP59ChQ1RWVjJkyBA6dOhguTlrKmrLV0RExCw67CwiIhJm\nKl8REZEwU/mKiIiEmcpXREQkzFS+IiIiYabyFRERCTOVr4iISJipfEVERMLs/wOhg6SER+7D5gAA\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f1231f81910>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AhHRDBRFpJVS+Ypy7aDuWN4Vwp2zTUUREokLlK2aFw7g+LSbYsxc4HKbTiIhE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\nERGJsv8P6Eq1PMVrg7EAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f12348e55d0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "ngCLXNAp0EBq",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        ""
      ]
    }
  ]
}