JAD_simulation_p1.ipynb

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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import solve_ivp\n",
    "from scipy.interpolate import interp1d\n",
    "from bokeh.io import push_notebook, show, output_notebook\n",
    "from bokeh.plotting import figure \n",
    "from bokeh.layouts import row, column\n",
    "from ipywidgets import interact\n",
    "output_notebook()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Defining parameters\n",
    "k1 = 0.2  # 1/s   # put this to 0\n",
    "k2 = 0.6  # 1/s   #lambda # Add T which describes the delay\n",
    "vmax = 25.0  # m/s\n",
    "tdes = 1.0  # s\n",
    "hbuf = 1.06\n",
    "alpha_p = 0.4  # m/s^2\n",
    "vp = 15.0  # m/s\n",
    "tp = 10.0  # s\n",
    "d = 7.5 # m\n",
    "ts1 = 20.0  # s\n",
    "init_sep = (d + tdes * vmax) * hbuf\n",
    "timelist = []\n",
    "poslist = []\n",
    "tmax = 400\n",
    "num_cars = 200\n",
    "timesteps = 100\n",
    "car_pos = np.zeros(timesteps)\n",
    "init_car_pos = np.linspace(num_cars * init_sep, 0, num_cars) \n",
    "car_vel = np.zeros(timesteps)\n",
    "init_car_vel = np.empty(num_cars)\n",
    "init_car_vel.fill(vmax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Setup plots\n",
    "# Figure 1\n",
    "# p1 = figure(plot_width=500, plot_height=500, title='Time-Space Diagram without JAD',\n",
    "#            x_axis_label='Time', y_axis_label='Position')\n",
    "# r11 = p1.multi_line(timelist, poslist)\n",
    "p1 = figure(plot_width=500, plot_height=500, title='Time-Space Diagram without JAD',\n",
    "           x_axis_label='Position', y_axis_label='Time')\n",
    "r11 = p1.multi_line(poslist, timelist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# def RunJAD():\n",
    "def LeadingCar(t, y):\n",
    "    x, v = y\n",
    "    dydt = [v, a]\n",
    "    return dydt\n",
    "def FollowingCar(t, y):\n",
    "    x, v = y\n",
    "    dydt = [v, -(k2 + k1 * tdes) * v - k1 * x + vfront(t) * k2 + xfront(t) * k1 - k1 * d]  # solve this usinng a dde solver\n",
    "    return dydt\n",
    "def SolveCarFollow(a, t1, t2):\n",
    "    y0 = [init_car_pos[0], init_car_vel[0]]\n",
    "    sol = solve_ivp(LeadingCar, (t1, t2), y0, method='RK45', t_eval=timepoints)\n",
    "    global car_pos, car_vel\n",
    "    car_pos = np.copy(sol.y[0, :])\n",
    "    car_vel = np.copy(sol.y[1, :])\n",
    "    np.clip(car_vel, 0, vmax, out=car_vel)\n",
    "    init_car_pos[0] = car_pos[-1]\n",
    "    init_car_vel[0] = car_vel[-1]\n",
    "    timelist.append(sol.t)\n",
    "    poslist.append(car_pos)\n",
    "    for i in range(1, num_cars):\n",
    "        y0 = [init_car_pos[i], init_car_vel[i]]\n",
    "        global xfront, vfront\n",
    "        xfront = interp1d(timepoints, car_pos, bounds_error=False, fill_value='extrapolate')\n",
    "        vfront = interp1d(timepoints, car_vel, bounds_error=False, fill_value='extrapolate')\n",
    "        sol = solve_ivp(FollowingCar, (t1, t2), y0, method='RK45', t_eval=timepoints)\n",
    "        car_pos = np.copy(sol.y[0, :])\n",
    "        car_vel = np.copy(sol.y[1, :])\n",
    "        np.clip(car_vel, 0, vmax, out=car_vel)\n",
    "        init_car_pos[i] = car_pos[-1]\n",
    "        init_car_vel[i] = car_vel[-1]\n",
    "        if np.mod(i, 5) == 0:\n",
    "            timelist.append(sol.t)\n",
    "            poslist.append(car_pos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Constant velocity phase 1\n",
    "a = 0\n",
    "tl1 = 0\n",
    "tl2 = ts1\n",
    "timepoints = np.linspace(tl1, tl2, timesteps)\n",
    "xfront = interp1d(timepoints, car_pos)\n",
    "vfront = interp1d(timepoints, car_vel)\n",
    "SolveCarFollow(a, 0, ts1)\n",
    "\n",
    "# Constant deceleration phase\n",
    "a = -alpha_p\n",
    "tl3 = tl2 + (vp - vmax) / a\n",
    "timepoints = np.linspace(tl2, tl3, timesteps)\n",
    "SolveCarFollow(a, tl2, tl3)\n",
    "\n",
    "# Constant velocity phase 2\n",
    "a = 0\n",
    "tl4 = tl3 + tp\n",
    "timepoints = np.linspace(tl3, tl4, timesteps)\n",
    "SolveCarFollow(a, tl3, tl4)\n",
    "\n",
    "# Constant acceleration phase\n",
    "a = alpha_p\n",
    "tl5 = tl4 + (vmax - vp) / a\n",
    "timepoints = np.linspace(tl4, tl5, timesteps)\n",
    "SolveCarFollow(a, tl4, tl5)\n",
    "\n",
    "# Constant velocity phase 3\n",
    "a = 0\n",
    "tl6 = tmax\n",
    "timepoints = np.linspace(tl5, tl6, timesteps)\n",
    "SolveCarFollow(a, tl5, tl6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "r11.data_source.data['x'] = timelist\n",
    "r11.data_source.data['y'] = poslist\n",
    "push_notebook(handle=target1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
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1163\",\"type\":\"MultiLine\"}],\"root_ids\":[\"f693df34-0c29-4871-b50b-fdefe1dc6294\"]},\"title\":\"Bokeh Application\",\"version\":\"0.13.0\"}};\n",
       "  var render_items = [{\"docid\":\"a57cde99-5e25-4818-86a7-d8e682bd1cc2\",\"notebook_comms_target\":\"729184e1-9ddc-49a2-96ff-674ea2b33cd1\",\"roots\":{\"f693df34-0c29-4871-b50b-fdefe1dc6294\":\"2631854e-9285-4177-bee5-9ba6ae14754e\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\")\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "f693df34-0c29-4871-b50b-fdefe1dc6294"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "target1 = show(p1, notebook_handle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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