Steering-Solution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the previous notebook you simulated the Dubin's Car model by choosing random steering angles. Typically there is a target location the vehicle is progressing to, thus choosing control inputs that which move closer to the target would be ideal.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams['figure.figsize'] = 12, 12"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dubin's car simulation from the previous notebook."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement a function called `steer()`, which takes as inputs two states `x1` and `x2` and returns a control input (steering angle) that \"tries\" to make progress from `x1` to `x2`. This method should consist roughly of the following:\n",
    "\n",
    "1. Get a sense of where `x2` is relative to the state of `x1` by calculating the orientation difference between the current orientation, $\\theta$, and the direction toward `x2`.\n",
    "2. Generate a random steering angle by sampling from a gaussian that is centered roughly on some direction that will move you from `x1` to `x2`.\n",
    "3. Clip the angle if it is outside the range allowed by `MAX_STEERING_ANGLE`.\n",
    "\n",
    "This might all sound a little fuzzy, but that's the idea here! We're just going to try some guessing and see if we can find a simple method for making progress from `x1` to `x2`.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# limit the steering angle range\n",
    "MAX_STEERING_ANGLE = np.deg2rad(30)\n",
    "# Set the width of the Gaussian we'll draw angles from\n",
    "ANGLE_STDDEV = np.deg2rad(3)\n",
    "\n",
    "# NOTE TO THE READER:\n",
    "# This steer() function is not meant to be a particularly clever\n",
    "# method of steering from x1 to x2.  Rather this is just a way \n",
    "# of guessing which way we might steer in order to make rough\n",
    "# progress toward x2. We'll get to better steering later!\n",
    "\n",
    "def steer(x1, x2):\n",
    "    theta = x1[2]\n",
    "    \n",
    "    # calculate angle difference between the direction toward x2\n",
    "    # and our current orientation\n",
    "    angle = np.arctan2(x2[1] - x1[1], x2[0] - x1[0]) - theta\n",
    "    \n",
    "    # Now we'll just do something rather naive and assume that if we know the \n",
    "    # direction of x2, we'll set the steering angle roughly in that direction\n",
    "    # sample angle from a gaussian centered around the direction toward x2\n",
    "    angle = np.random.normal(angle, ANGLE_STDDEV)\n",
    "    \n",
    "    # clip angle value between min and max\n",
    "    angle = np.clip(angle, -MAX_STEERING_ANGLE, MAX_STEERING_ANGLE)\n",
    "                \n",
    "    return angle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modification of the Dubin's car simulation from the previous notebook. Instead of running the simulation for a single timestep the simulation is run from time 0 to time `T` with timesteps of size `dt`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate(state, angle, v, dt):\n",
    "    x = state[0]\n",
    "    y = state[1]\n",
    "    theta = state[2]    \n",
    "    \n",
    "    nx = x + v*np.cos(theta)*dt\n",
    "    ny = y + v*np.sin(theta)*dt\n",
    "    ntheta = theta + v*np.tan(angle)*dt\n",
    "    \n",
    "    return [nx, ny, ntheta]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initially, we place the car at the center of the coordinate system (0, 0) and give heading of $0$ which is facing in the positive direction along the $x$ axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 51, 3)\n"
     ]
    }
   ],
   "source": [
    "dt = 0.2\n",
    "T = 10\n",
    "\n",
    "start = [0, 0, 0]\n",
    "goal = [10, 0, 0]\n",
    "\n",
    "angles = [steer(start, goal) for _ in range(100)]\n",
    "lines = []\n",
    "\n",
    "for angle in angles:\n",
    "    line = [start]\n",
    "    state = np.copy(start)\n",
    "    v = np.random.uniform(0, 1)\n",
    "    for _ in np.arange(0, T, dt):\n",
    "        state = simulate(state, angle, v, dt)\n",
    "        line.append(state)\n",
    "    lines.append(line)\n",
    "    \n",
    "lines = np.array(lines)\n",
    "print(lines.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's visualize the path! It should be a smooth path from the start location to the goal location."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff627687630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(lines.shape[0]):\n",
    "    plt.plot(lines[i, :, 0], lines[i, :, 1], 'b-')\n",
    "plt.plot(start[0], start[1], 'bo')\n",
    "plt.plot(goal[0], goal[1], 'ro')\n",
    "plt.axis('equal')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ok so that kind of works! You could tighten up the allowable standard deviation of the Gaussian to aim more directly at `x2`, but things break down when `x2` is at any appreciable angle off center (try changing the y-coordinate of the `goal` location and you'll see what I mean). So in short, this is not a great solution! Can you figure out a better way to steer?**"
   ]
  },
  {
   "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}