dubins_2.0.ipynb

{
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  "metadata": {
    "colab": {
      "name": "TensorFlow with GPU",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 2",
      "name": "python2"
    }
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  "cells": [
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      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "[View in Colaboratory](https://colab.research.google.com/github/sharathsrini/Extended-Kalman-Filter-for-Sensor-Fusion/blob/master/dubins_2.0.ipynb)"
      ]
    },
    {
      "metadata": {
        "id": "Fhxs3TtAy8oF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 473
        },
        "outputId": "3f502fe5-29ae-4846-e468-3242e8ca6357"
      },
      "cell_type": "code",
      "source": [
        "import math\n",
        "\n",
        "\n",
        "def mod2pi(theta):\n",
        "    return theta - 2.0 * math.pi * math.floor(theta / 2.0 / math.pi)\n",
        "\n",
        "\n",
        "def pi_2_pi(angle):\n",
        "    return (angle + math.pi) % (2*math.pi) - math.pi\n",
        "\n",
        "\n",
        "def LSL(alpha, beta, d):\n",
        "    sa = math.sin(alpha)\n",
        "    sb = math.sin(beta)\n",
        "    ca = math.cos(alpha)\n",
        "    cb = math.cos(beta)\n",
        "    c_ab = math.cos(alpha - beta)\n",
        "\n",
        "    tmp0 = d + sa - sb\n",
        "\n",
        "    mode = [\"L\", \"S\", \"L\"]\n",
        "    p_squared = 2 + (d * d) - (2 * c_ab) + (2 * d * (sa - sb))\n",
        "    if p_squared < 0:\n",
        "        return None, None, None, mode\n",
        "    tmp1 = math.atan2((cb - ca), tmp0)\n",
        "    t = mod2pi(-alpha + tmp1)\n",
        "    p = math.sqrt(p_squared)\n",
        "    q = mod2pi(beta - tmp1)\n",
        "    #  print(math.degrees(t), p, math.degrees(q))\n",
        "\n",
        "    return t, p, q, mode\n",
        "\n",
        "\n",
        "def RSR(alpha, beta, d):\n",
        "    sa = math.sin(alpha)\n",
        "    sb = math.sin(beta)\n",
        "    ca = math.cos(alpha)\n",
        "    cb = math.cos(beta)\n",
        "    c_ab = math.cos(alpha - beta)\n",
        "\n",
        "    tmp0 = d - sa + sb\n",
        "    mode = [\"R\", \"S\", \"R\"]\n",
        "    p_squared = 2 + (d * d) - (2 * c_ab) + (2 * d * (sb - sa))\n",
        "    if p_squared < 0:\n",
        "        return None, None, None, mode\n",
        "    tmp1 = math.atan2((ca - cb), tmp0)\n",
        "    t = mod2pi(alpha - tmp1)\n",
        "    p = math.sqrt(p_squared)\n",
        "    q = mod2pi(-beta + tmp1)\n",
        "\n",
        "    return t, p, q, mode\n",
        "\n",
        "\n",
        "def LSR(alpha, beta, d):\n",
        "    sa = math.sin(alpha)\n",
        "    sb = math.sin(beta)\n",
        "    ca = math.cos(alpha)\n",
        "    cb = math.cos(beta)\n",
        "    c_ab = math.cos(alpha - beta)\n",
        "\n",
        "    p_squared = -2 + (d * d) + (2 * c_ab) + (2 * d * (sa + sb))\n",
        "    mode = [\"L\", \"S\", \"R\"]\n",
        "    if p_squared < 0:\n",
        "        return None, None, None, mode\n",
        "    p = math.sqrt(p_squared)\n",
        "    tmp2 = math.atan2((-ca - cb), (d + sa + sb)) - math.atan2(-2.0, p)\n",
        "    t = mod2pi(-alpha + tmp2)\n",
        "    q = mod2pi(-mod2pi(beta) + tmp2)\n",
        "\n",
        "    return t, p, q, mode\n",
        "\n",
        "\n",
        "def RSL(alpha, beta, d):\n",
        "    sa = math.sin(alpha)\n",
        "    sb = math.sin(beta)\n",
        "    ca = math.cos(alpha)\n",
        "    cb = math.cos(beta)\n",
        "    c_ab = math.cos(alpha - beta)\n",
        "\n",
        "    p_squared = (d * d) - 2 + (2 * c_ab) - (2 * d * (sa + sb))\n",
        "    mode = [\"R\", \"S\", \"L\"]\n",
        "    if p_squared < 0:\n",
        "        return None, None, None, mode\n",
        "    p = math.sqrt(p_squared)\n",
        "    tmp2 = math.atan2((ca + cb), (d - sa - sb)) - math.atan2(2.0, p)\n",
        "    t = mod2pi(alpha - tmp2)\n",
        "    q = mod2pi(beta - tmp2)\n",
        "\n",
        "    return t, p, q, mode\n",
        "\n",
        "\n",
        "def RLR(alpha, beta, d):\n",
        "    sa = math.sin(alpha)\n",
        "    sb = math.sin(beta)\n",
        "    ca = math.cos(alpha)\n",
        "    cb = math.cos(beta)\n",
        "    c_ab = math.cos(alpha - beta)\n",
        "\n",
        "    mode = [\"R\", \"L\", \"R\"]\n",
        "    tmp_rlr = (6.0 - d * d + 2.0 * c_ab + 2.0 * d * (sa - sb)) / 8.0\n",
        "    if abs(tmp_rlr) > 1.0:\n",
        "        return None, None, None, mode\n",
        "\n",
        "    p = mod2pi(2 * math.pi - math.acos(tmp_rlr))\n",
        "    t = mod2pi(alpha - math.atan2(ca - cb, d - sa + sb) + mod2pi(p / 2.0))\n",
        "    q = mod2pi(alpha - beta - t + mod2pi(p))\n",
        "    return t, p, q, mode\n",
        "\n",
        "\n",
        "def LRL(alpha, beta, d):\n",
        "    sa = math.sin(alpha)\n",
        "    sb = math.sin(beta)\n",
        "    ca = math.cos(alpha)\n",
        "    cb = math.cos(beta)\n",
        "    c_ab = math.cos(alpha - beta)\n",
        "\n",
        "    mode = [\"L\", \"R\", \"L\"]\n",
        "    tmp_lrl = (6. - d * d + 2 * c_ab + 2 * d * (- sa + sb)) / 8.\n",
        "    if abs(tmp_lrl) > 1:\n",
        "        return None, None, None, mode\n",
        "    p = mod2pi(2 * math.pi - math.acos(tmp_lrl))\n",
        "    t = mod2pi(-alpha - math.atan2(ca - cb, d + sa - sb) + p / 2.)\n",
        "    q = mod2pi(mod2pi(beta) - alpha - t + mod2pi(p))\n",
        "\n",
        "    return t, p, q, mode\n",
        "\n",
        "\n",
        "def dubins_path_planning_from_origin(ex, ey, eyaw, c):\n",
        "    # nomalize\n",
        "    dx = ex\n",
        "    dy = ey\n",
        "    D = math.sqrt(dx ** 2.0 + dy ** 2.0)\n",
        "    d = D / c\n",
        "    #  print(dx, dy, D, d)\n",
        "\n",
        "    theta = mod2pi(math.atan2(dy, dx))\n",
        "    alpha = mod2pi(- theta)\n",
        "    beta = mod2pi(eyaw - theta)\n",
        "    #  print(theta, alpha, beta, d)\n",
        "\n",
        "    planners = [LSL, RSR, LSR, RSL, RLR, LRL]\n",
        "\n",
        "    bcost = float(\"inf\")\n",
        "    bt, bp, bq, bmode = None, None, None, None\n",
        "\n",
        "    for planner in planners:\n",
        "        t, p, q, mode = planner(alpha, beta, d)\n",
        "        if t is None:\n",
        "            #  print(\"\".join(mode) + \" cannot generate path\")\n",
        "            continue\n",
        "      \n",
        "        cost = (abs(t) + abs(p) + abs(q))\n",
        "        \n",
        "        if bcost > cost:\n",
        "            bt, bp, bq, bmode = t, p, q, mode\n",
        "            bcost = cost\n",
        "\n",
        "    #  print(bmode)\n",
        "    px, py, pyaw = generate_course([bt, bp, bq], bmode, c)\n",
        "\n",
        "    return px, py, pyaw, bmode, bcost\n",
        "\n",
        "\n",
        "def dubins_path_planning(sx, sy, syaw, ex, ey, eyaw, c):\n",
        "    ex = ex - sx\n",
        "    ey = ey - sy\n",
        "\n",
        "    lex = math.cos(syaw) * ex + math.sin(syaw) * ey\n",
        "    ley = - math.sin(syaw) * ex + math.cos(syaw) * ey\n",
        "    leyaw = eyaw - syaw\n",
        "\n",
        "    lpx, lpy, lpyaw, mode, clen = dubins_path_planning_from_origin(\n",
        "        lex, ley, leyaw, c)\n",
        "\n",
        "    px = [math.cos(-syaw) * x + math.sin(-syaw) *\n",
        "          y + sx for x, y in zip(lpx, lpy)]\n",
        "    py = [- math.sin(-syaw) * x + math.cos(-syaw) *\n",
        "          y + sy for x, y in zip(lpx, lpy)]\n",
        "    pyaw = [pi_2_pi(iyaw + syaw) for iyaw in lpyaw]\n",
        "    \n",
        "    return px, py, pyaw, mode, clen\n",
        "\n",
        "\n",
        "def generate_course(length, mode, c):\n",
        "\n",
        "    px = [0.0]\n",
        "    py = [0.0]\n",
        "    pyaw = [0.0]\n",
        "\n",
        "    for m, l in zip(mode, length):\n",
        "        pd = 0.0\n",
        "        if m is \"S\":\n",
        "            d = 1.0 / c\n",
        "        else:  # turning couse\n",
        "            d = math.radians(3.0)\n",
        "\n",
        "        while pd < abs(l - d):\n",
        "            #  print(pd, l)\n",
        "            px.append(px[-1] + d * c * math.cos(pyaw[-1]))\n",
        "            py.append(py[-1] + d * c * math.sin(pyaw[-1]))\n",
        "\n",
        "            if m is \"L\":  # left turn\n",
        "                pyaw.append(pyaw[-1] + d)\n",
        "            elif m is \"S\":  # Straight\n",
        "                pyaw.append(pyaw[-1])\n",
        "            elif m is \"R\":  # right turn\n",
        "                pyaw.append(pyaw[-1] - d)\n",
        "            pd += d\n",
        "        else:\n",
        "            d = l - pd\n",
        "            px.append(px[-1] + d * c * math.cos(pyaw[-1]))\n",
        "            py.append(py[-1] + d * c * math.sin(pyaw[-1]))\n",
        "\n",
        "            if m is \"L\":  # left turn\n",
        "                pyaw.append(pyaw[-1] + d)\n",
        "            elif m is \"S\":  # Straight\n",
        "                pyaw.append(pyaw[-1])\n",
        "            elif m is \"R\":  # right turn\n",
        "                pyaw.append(pyaw[-1] - d)\n",
        "            pd += d\n",
        "\n",
        "    return px, py, pyaw\n",
        "\n",
        "\n",
        "def marker(x, y, yaw, length=1.0, width=0.5, fc=\"r\", ec=\"k\"):\n",
        "    u\"\"\"\n",
        "    Plot arrow\n",
        "    \"\"\"\n",
        "    import matplotlib.pyplot as plt\n",
        "\n",
        "    if not isinstance(x, float):\n",
        "        for (ix, iy, iyaw) in zip(x, y, yaw):\n",
        "            marker(ix, iy, iyaw)\n",
        "    else:\n",
        "        plt.arrow(x, y, length * math.cos(yaw), length * math.sin(yaw),\n",
        "                  fc=fc, ec=ec, head_width=width, head_length=width)\n",
        "        plt.plot(x, y)\n",
        "\n",
        "\n",
        "if __name__ == '__main__':\n",
        "    import time\n",
        "    start = time.time()\n",
        "    print(\"Dubins path planner sample start!!\")\n",
        "    import matplotlib.pyplot as plt\n",
        "\n",
        "    start_x = 0.0  # [m]\n",
        "    start_y = 0.0  # [m]\n",
        "    start_yaw = math.radians(180.0)  # [rad]\n",
        "\n",
        "    end_x = 20.0  # [m]\n",
        "    end_y = 0.0  # [m]\n",
        "    end_yaw = math.radians(180.0)  # [rad]\n",
        "\n",
        "    curvature = 1.0\n",
        "\n",
        "    px, py, pyaw, mode, clen = dubins_path_planning(start_x, start_y, start_yaw,\n",
        "                                                    end_x, end_y, end_yaw, curvature)\n",
        "    print(\"px:\",px)\n",
        "    print(\"py:\",py)\n",
        "    print(\"pyaw:\",pyaw)\n",
        "    print(\"clen:\",clen)\n",
        "        \n",
        "        \n",
        "\n",
        "    print(-start + time.time())\n",
        "    plt.plot(px, py, label=\"final course \" + \"\".join(mode))\n",
        "\n",
        "    # plotting\n",
        "    marker(start_x, start_y, start_yaw)\n",
        "    marker(end_x, end_y, end_yaw)\n",
        "\n",
        "    \n",
        "\n",
        "    plt.legend()\n",
        "    plt.grid(True)\n",
        "    plt.axis(\"equal\")\n",
        "    plt.show()"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Dubins path planner sample start!!\n",
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          "name": "stdout"
        },
        {
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Qulm9zgYAqN75IlzfQiwW9WjfQint4rQtPVdvrkqXY12mMrIKNHZEdzUN8+951xaPoVPF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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fa0cf7392d0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "TQuIMYawLvSe",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}