project_3_landmark_detection/3. Landmark Detection and Tracking.ipynb

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    "# Project 3:  Implement SLAM \n",
    "\n",
    "---\n",
    "\n",
    "## Project Overview\n",
    "\n",
    "In this project, you'll implement SLAM for robot that moves and senses in a 2 dimensional, grid world!\n",
    "\n",
    "SLAM gives us a way to both localize a robot and build up a map of its environment as a robot moves and senses in real-time. This is an active area of research in the fields of robotics and autonomous systems. Since this localization and map-building relies on the visual sensing of landmarks, this is a computer vision problem. \n",
    "\n",
    "Using what you've learned about robot motion, representations of uncertainty in motion and sensing, and localization techniques, you will be tasked with defining a function, `slam`, which takes in six parameters as input and returns the vector `mu`. \n",
    "> `mu` contains the (x,y) coordinate locations of the robot as it moves, and the positions of landmarks that it senses in the world\n",
    "\n",
    "You can implement helper functions as you see fit, but your function must return `mu`. The vector, `mu`, should have (x, y) coordinates interlaced, for example, if there were 2 poses and 2 landmarks, `mu` will look like the following, where `P` is the robot position and `L` the landmark position:\n",
    "```\n",
    "mu =  matrix([[Px0],\n",
    "              [Py0],\n",
    "              [Px1],\n",
    "              [Py1],\n",
    "              [Lx0],\n",
    "              [Ly0],\n",
    "              [Lx1],\n",
    "              [Ly1]])\n",
    "```\n",
    "\n",
    "You can see that `mu` holds the poses first `(x0, y0), (x1, y1), ...,` then the landmark locations at the end of the matrix; we consider a `nx1` matrix to be a vector.\n",
    "\n",
    "## Generating an environment\n",
    "\n",
    "In a real SLAM problem, you may be given a map that contains information about landmark locations, and in this example, we will make our own data using the `make_data` function, which generates a world grid with landmarks in it and then generates data by placing a robot in that world and moving and sensing over some numer of time steps. The `make_data` function relies on a correct implementation of robot move/sense functions, which, at this point, should be complete and in the `robot_class.py` file. The data is collected as an instantiated robot moves and senses in a world. Your SLAM function will take in this data as input. So, let's first create this data and explore how it represents the movement and sensor measurements that our robot takes.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create the world\n",
    "\n",
    "Use the code below to generate a world of a specified size with randomly generated landmark locations. You can change these parameters and see how your implementation of SLAM responds! \n",
    "\n",
    "`data` holds the sensors measurements and motion of your robot over time. It stores the measurements as `data[i][0]` and the motion as `data[i][1]`.\n",
    "\n",
    "#### Helper functions\n",
    "\n",
    "You will be working with the `robot` class that may look familiar from the first notebook, \n",
    "\n",
    "In fact, in the `helpers.py` file, you can read the details of how data is made with the `make_data` function. It should look very similar to the robot move/sense cycle you've seen in the first notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "Landmarks:  [[19, 69], [46, 23], [21, 52], [98, 90], [88, 17]]\n",
      "Robot: [x=18.28922 y=10.59034]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from helpers import make_data\n",
    "\n",
    "# your implementation of slam should work with the following inputs\n",
    "# feel free to change these input values and see how it responds!\n",
    "\n",
    "# world parameters\n",
    "num_landmarks      = 5        # number of landmarks\n",
    "N                  = 20       # time steps\n",
    "world_size         = 100.0    # size of world (square)\n",
    "\n",
    "# robot parameters\n",
    "measurement_range  = 50.0     # range at which we can sense landmarks\n",
    "motion_noise       = 2.0      # noise in robot motion\n",
    "measurement_noise  = 2.0      # noise in the measurements\n",
    "distance           = 20.0     # distance by which robot (intends to) move each iteratation \n",
    "\n",
    "\n",
    "# make_data instantiates a robot, AND generates random landmarks for a given world size and number of landmarks\n",
    "data = make_data(N, num_landmarks, world_size, measurement_range, motion_noise, measurement_noise, distance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A note on `make_data`\n",
    "\n",
    "The function above, `make_data`, takes in so many world and robot motion/sensor parameters because it is responsible for:\n",
    "1. Instantiating a robot (using the robot class)\n",
    "2. Creating a grid world with landmarks in it\n",
    "\n",
    "**This function also prints out the true location of landmarks and the *final* robot location, which you should refer back to when you test your implementation of SLAM.**\n",
    "\n",
    "The `data` this returns is an array that holds information about **robot sensor measurements** and **robot motion** `(dx, dy)` that is collected over a number of time steps, `N`. You will have to use *only* these readings about motion and measurements to track a robot over time and find the determine the location of the landmarks using SLAM. We only print out the true landmark locations for comparison, later.\n",
    "\n",
    "\n",
    "In `data` the measurement and motion data can be accessed from the first and second index in the columns of the data array. See the following code for an example, where `i` is the time step:\n",
    "```\n",
    "measurement = data[i][0]\n",
    "motion = data[i][1]\n",
    "```\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example measurements: \n",
      " [[0, -32.06613041368001, 17.789856607171608], [1, -3.9418164935965625, -25.141556006665155], [2, -28.037011415338654, 3.161247423682196], [3, 48.552431365975345, 40.21574865966725], [4, 37.850087729240975, -33.03337727463735]]\n",
      "\n",
      "\n",
      "Example motion: \n",
      " [-4.8892150196763104, -19.393183763667366]\n"
     ]
    }
   ],
   "source": [
    "# print out some stats about the data\n",
    "time_step = 0\n",
    "\n",
    "print('Example measurements: \\n', data[time_step][0])\n",
    "print('\\n')\n",
    "print('Example motion: \\n', data[time_step][1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Try changing the value of `time_step`, you should see that the list of measurements varies based on what in the world the robot sees after it moves. As you know from the first notebook, the robot can only sense so far and with a certain amount of accuracy in the measure of distance between its location and the location of landmarks. The motion of the robot always is a vector with two values: one for x and one for y displacement. This structure will be useful to keep in mind as you traverse this data in your implementation of slam."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialize Constraints\n",
    "\n",
    "One of the most challenging tasks here will be to create and modify the constraint matrix and vector: omega and xi. In the second notebook, you saw an example of how omega and xi could hold all the values the define the relationships between robot poses `xi` and landmark positions `Li` in a 1D world, as seen below, where omega is the blue matrix and xi is the pink vector.\n",
    "\n",
    "<img src='images/motion_constraint.png' width=50% height=50% />\n",
    "\n",
    "\n",
    "In *this* project, you are tasked with implementing constraints for a 2D world. We are referring to robot poses as `Px, Py` and landmark positions as `Lx, Ly`, and one way to approach this challenge is to add *both* x and y locations in the constraint matrices.\n",
    "\n",
    "<img src='images/constraints2D.png' width=50% height=50% />\n",
    "\n",
    "You may also choose to create two of each omega and xi (one for x and one for y positions)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Write a function that initializes omega and xi\n",
    "\n",
    "Complete the function `initialize_constraints` so that it returns `omega` and `xi` constraints for the starting position of the robot. Any values that we do not yet know should be initialized with the value `0`. You may assume that our robot starts out in exactly the middle of the world with 100% confidence (no motion or measurement noise at this point). The inputs `N` time steps, `num_landmarks`, and `world_size` should give you all the information you need to construct intial constraints of the correct size and starting values.\n",
    "\n",
    "*Depending on your approach you may choose to return one omega and one xi that hold all (x,y) positions *or* two of each (one for x values and one for y); choose whichever makes most sense to you!*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def initialize_constraints(N, num_landmarks, world_size):\n",
    "    ''' This function takes in a number of time steps N, number of landmarks, and a world_size,\n",
    "        and returns initialized constraint matrices, omega and xi.'''\n",
    "    \n",
    "    ## Recommended: Define and store the size (rows/cols) of the constraint matrix in a variable\n",
    "    dim = 2*N+2*num_landmarks\n",
    "    omega_shape = (dim ,dim )\n",
    "    xi_shape = (dim, 1)\n",
    "    ## Define the constraint matrix, Omega, with two initial \"strength\" values\n",
    "    ## for the initial x, y location of our robot\n",
    "    omega = np.zeros(omega_shape)\n",
    "    \n",
    "    omega[0,0] = 1.0\n",
    "    omega[1,1] = 1.0\n",
    "    \n",
    "    ## Define the constraint *vector*, xi\n",
    "    ## you can assume that the robot starts out in the middle of the world with 100% confidence\n",
    "    xi = np.zeros(xi_shape)\n",
    "    \n",
    "    xi[0,0] = world_size/2\n",
    "    xi[1,0] = world_size/2\n",
    "    \n",
    "    return omega, xi   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test as you go\n",
    "\n",
    "It's good practice to test out your code, as you go. Since `slam` relies on creating and updating constraint matrices, `omega` and `xi` to account for robot sensor measurements and motion, let's check that they initialize as expected for any given parameters.\n",
    "\n",
    "Below, you'll find some test code that allows you to visualize the results of your function `initialize_constraints`. We are using the [seaborn](https://seaborn.pydata.org/) library for visualization.\n",
    "\n",
    "**Please change the test values of N, landmarks, and world_size and see the results**. Be careful not to use these values as input into your final smal function.\n",
    "\n",
    "This code assumes that you have created one of each constraint: `omega` and `xi`, but you can change and add to this code, accordingly. The constraints should vary in size with the number of time steps and landmarks as these values affect the number of poses a robot will take `(Px0,Py0,...Pxn,Pyn)` and landmark locations `(Lx0,Ly0,...Lxn,Lyn)` whose relationships should be tracked in the constraint matrices. Recall that `omega` holds the weights of each variable and `xi` holds the value of the sum of these variables, as seen in Notebook 2. You'll need the `world_size` to determine the starting pose of the robot in the world and fill in the initial values for `xi`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import data viz resources\n",
    "import matplotlib.pyplot as plt\n",
    "from pandas import DataFrame\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define a small N and world_size (small for ease of visualization)\n",
    "N_test = 5\n",
    "num_landmarks_test = 2\n",
    "small_world = 10\n",
    "\n",
    "# initialize the constraints\n",
    "initial_omega, initial_xi = initialize_constraints(N_test, num_landmarks_test, small_world)"
   ]
  },
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   "execution_count": 6,
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      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a22e4a3c8>"
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     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
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\n",
      "text/plain": [
       "<Figure size 720x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define figure size\n",
    "plt.rcParams[\"figure.figsize\"] = (10,7)\n",
    "\n",
    "# display omega\n",
    "sns.heatmap(DataFrame(initial_omega), cmap='Blues', annot=True, linewidths=.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a2347b0f0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 72x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define  figure size\n",
    "plt.rcParams[\"figure.figsize\"] = (1,7)\n",
    "\n",
    "# display xi\n",
    "sns.heatmap(DataFrame(initial_xi), cmap='Oranges', annot=True, linewidths=.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## SLAM inputs \n",
    "\n",
    "In addition to `data`, your slam function will also take in:\n",
    "* N -   The number of time steps that a robot will be moving and sensing\n",
    "* num_landmarks - The number of landmarks in the world\n",
    "* world_size - The size (w/h) of your world\n",
    "* motion_noise - The noise associated with motion; the update confidence for motion should be `1.0/motion_noise`\n",
    "* measurement_noise - The noise associated with measurement/sensing; the update weight for measurement should be `1.0/measurement_noise`\n",
    "\n",
    "#### A note on noise\n",
    "\n",
    "Recall that `omega` holds the relative \"strengths\" or weights for each position variable, and you can update these weights by accessing the correct index in omega `omega[row][col]` and *adding/subtracting* `1.0/noise` where `noise` is measurement or motion noise. `Xi` holds actual position values, and so to update `xi` you'll do a similar addition process only using the actual value of a motion or measurement. So for a vector index `xi[row][0]` you will end up adding/subtracting one measurement or motion divided by their respective `noise`.\n",
    "\n",
    "### Implement Graph SLAM\n",
    "\n",
    "Follow the TODO's below to help you complete this slam implementation (these TODO's are in the recommended order), then test out your implementation! \n",
    "\n",
    "#### Updating with motion and measurements\n",
    "\n",
    "With a 2D omega and xi structure as shown above (in earlier cells), you'll have to be mindful about how you update the values in these constraint matrices to account for motion and measurement constraints in the x and y directions. Recall that the solution to these matrices (which holds all values for robot poses `P` and landmark locations `L`) is the vector, `mu`, which can be computed at the end of the construction of omega and xi as the inverse of omega times xi: $\\mu = \\Omega^{-1}\\xi$\n",
    "\n",
    "**You may also choose to return the values of `omega` and `xi` if you want to visualize their final state!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Complete the code to implement SLAM\n",
    "from numpy.linalg import inv\n",
    "from numpy.linalg import det\n",
    "## slam takes in 6 arguments and returns mu, \n",
    "## mu is the entire path traversed by a robot (all x,y poses) *and* all landmarks locations\n",
    "def slam(data, N, num_landmarks, world_size, motion_noise, measurement_noise):\n",
    "    \n",
    "    ## Use your initilization to create constraint matrices, omega and xi\n",
    "    \n",
    "    omega, xi = initialize_constraints(N, num_landmarks, world_size)\n",
    "    \n",
    "    ## Iterate through each time step in the data\n",
    "    ## get all the motion and measurement data as you iterate\n",
    "           \n",
    "    ## update the constraint matrix/vector to account for all *measurements*\n",
    "    ## this should be a series of additions that take into account the measurement noise                       \n",
    "    \n",
    "    ## update the constraint matrix/vector to account for all *motion* and motion noise\n",
    "    \n",
    "    for k, x in enumerate(data):\n",
    "        # robot pose index in omega\n",
    "        i_robot = k * 2\n",
    "        \n",
    "        measurment = x[0]\n",
    "        motion = x[1]\n",
    "\n",
    "        # update based on measurment\n",
    "        \n",
    "        for i in range(len(measurment)):\n",
    "\n",
    "            # landmark index in omega\n",
    "            i_landmark = 2 * (N + measurment[i][0])\n",
    "            \n",
    "            for j in range(2):\n",
    "                omega[i_landmark+j][i_landmark+j] += 1.0/measurement_noise\n",
    "                omega[i_robot+j][i_robot+j]       += 1.0/measurement_noise\n",
    "                omega[i_robot+j][i_landmark+j]    -= 1.0/measurement_noise     \n",
    "                omega[i_landmark+j][i_robot+j]    -= 1.0/measurement_noise\n",
    "                xi[i_landmark+j][0]               += measurment[i][1+j]/measurement_noise\n",
    "                xi[i_robot+j][0]                  -= measurment[i][1+j]/measurement_noise\n",
    "            \n",
    "        # update based on robot motion\n",
    "        \n",
    "        for j in range(4):    \n",
    "            omega[i_robot+j][i_robot+j] +=   1.0/motion_noise\n",
    "        for j in range(2):\n",
    "            omega[i_robot+j][i_robot+j+2] -= 1.0/motion_noise\n",
    "            omega[i_robot+j+2][i_robot+j] -= 1.0/motion_noise\n",
    "            xi[i_robot+j][0]              -= motion[j]/motion_noise\n",
    "            xi[i_robot+j+2][0]            += motion[j]/motion_noise\n",
    "            \n",
    "    ##  After iterating through all the data\n",
    "    ## Compute the best estimate of poses and landmark positions\n",
    "    ## using the formula, omega_inverse * Xi\n",
    "    \n",
    "    mu = np.dot(inv(omega),xi)\n",
    "    return mu, omega, xi # return `mu`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu,omega,xi = slam(data, N, num_landmarks, world_size, motion_noise, measurement_noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a2353c898>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x1224 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define figure size\n",
    "plt.rcParams[\"figure.figsize\"] = (20,17)\n",
    "\n",
    "# display omega\n",
    "sns.heatmap(DataFrame(omega), cmap='Blues', annot=True, linewidths=.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a2470e860>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 72x1224 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define  figure size\n",
    "plt.rcParams[\"figure.figsize\"] = (1,17)\n",
    "\n",
    "# display xi\n",
    "sns.heatmap(DataFrame(xi), cmap='Oranges', annot=True, linewidths=.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Helper functions\n",
    "\n",
    "To check that your implementation of SLAM works for various inputs, we have provided two helper functions that will help display the estimated pose and landmark locations that your function has produced. First, given a result `mu` and number of time steps, `N`, we define a function that extracts the poses and landmarks locations and returns those as their own, separate lists. \n",
    "\n",
    "Then, we define a function that nicely print out these lists; both of these we will call, in the next step.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# a helper function that creates a list of poses and of landmarks for ease of printing\n",
    "# this only works for the suggested constraint architecture of interlaced x,y poses\n",
    "def get_poses_landmarks(mu, N):\n",
    "    # create a list of poses\n",
    "    poses = []\n",
    "    for i in range(N):\n",
    "        poses.append((mu[2*i].item(), mu[2*i+1].item()))\n",
    "\n",
    "    # create a list of landmarks\n",
    "    landmarks = []\n",
    "    for i in range(num_landmarks):\n",
    "        landmarks.append((mu[2*(N+i)].item(), mu[2*(N+i)+1].item()))\n",
    "\n",
    "    # return completed lists\n",
    "    return poses, landmarks\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_all(poses, landmarks):\n",
    "    print('\\n')\n",
    "    print('Estimated Poses:')\n",
    "    for i in range(len(poses)):\n",
    "        print('['+', '.join('%.3f'%p for p in poses[i])+']')\n",
    "    print('\\n')\n",
    "    print('Estimated Landmarks:')\n",
    "    for i in range(len(landmarks)):\n",
    "        print('['+', '.join('%.3f'%l for l in landmarks[i])+']')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run SLAM\n",
    "\n",
    "Once you've completed your implementation of `slam`, see what `mu` it returns for different world sizes and different landmarks!\n",
    "\n",
    "### What to Expect\n",
    "\n",
    "The `data` that is generated is random, but you did specify the number, `N`, or time steps that the robot was expected to move and the `num_landmarks` in the world (which your implementation of `slam` should see and estimate a position for. Your robot should also start with an estimated pose in the very center of your square world, whose size is defined by `world_size`.\n",
    "\n",
    "With these values in mind, you should expect to see a result that displays two lists:\n",
    "1. **Estimated poses**, a list of (x, y) pairs that is exactly `N` in length since this is how many motions your robot has taken. The very first pose should be the center of your world, i.e. `[50.000, 50.000]` for a world that is 100.0 in square size.\n",
    "2. **Estimated landmarks**, a list of landmark positions (x, y) that is exactly `num_landmarks` in length. \n",
    "\n",
    "#### Landmark Locations\n",
    "\n",
    "If you refer back to the printout of *exact* landmark locations when this data was created, you should see values that are very similar to those coordinates, but not quite (since `slam` must account for noise in motion and measurement)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Estimated Poses:\n",
      "[50.000, 50.000]\n",
      "[43.620, 32.493]\n",
      "[38.442, 13.535]\n",
      "[19.481, 8.629]\n",
      "[0.412, 2.997]\n",
      "[12.256, 16.915]\n",
      "[26.611, 32.922]\n",
      "[39.724, 48.166]\n",
      "[52.453, 63.691]\n",
      "[64.805, 78.659]\n",
      "[78.620, 92.591]\n",
      "[98.193, 94.095]\n",
      "[78.287, 90.536]\n",
      "[59.808, 85.575]\n",
      "[39.677, 80.646]\n",
      "[20.112, 75.987]\n",
      "[1.829, 69.525]\n",
      "[7.355, 49.093]\n",
      "[11.378, 28.081]\n",
      "[16.576, 8.768]\n",
      "\n",
      "\n",
      "Estimated Landmarks:\n",
      "[18.603, 68.721]\n",
      "[46.370, 23.408]\n",
      "[21.258, 51.804]\n",
      "[99.035, 90.061]\n",
      "[88.582, 17.112]\n"
     ]
    }
   ],
   "source": [
    "# call your implementation of slam, passing in the necessary parameters\n",
    "mu,_,_ = slam(data, N, num_landmarks, world_size, motion_noise, measurement_noise)\n",
    "\n",
    "# print out the resulting landmarks and poses\n",
    "if(mu is not None):\n",
    "    # get the lists of poses and landmarks\n",
    "    # and print them out\n",
    "    poses, landmarks = get_poses_landmarks(mu, N)\n",
    "    print_all(poses, landmarks)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize the constructed world\n",
    "\n",
    "Finally, using the `display_world` code from the `helpers.py` file (which was also used in the first notebook), we can actually visualize what you have coded with `slam`: the final position of the robot and the positon of landmarks, created from only motion and measurement data!\n",
    "\n",
    "**Note that these should be very similar to the printed *true* landmark locations and final pose from our call to `make_data` early in this notebook.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last pose:  (16.57562398727231, 8.768048368239292)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# import the helper function\n",
    "from helpers import display_world\n",
    "\n",
    "# Display the final world!\n",
    "\n",
    "# define figure size\n",
    "plt.rcParams[\"figure.figsize\"] = (20,20)\n",
    "\n",
    "# check if poses has been created\n",
    "if 'poses' in locals():\n",
    "    # print out the last pose\n",
    "    print('Last pose: ', poses[-1])\n",
    "    # display the last position of the robot *and* the landmark positions\n",
    "    display_world(int(world_size), poses[-1], landmarks)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question: How far away is your final pose (as estimated by `slam`) compared to the *true* final pose? Why do you think these poses are different?\n",
    "\n",
    "You can find the true value of the final pose in one of the first cells where `make_data` was called. You may also want to look at the true landmark locations and compare them to those that were estimated by `slam`. Ask yourself: what do you think would happen if we moved and sensed more (increased N)? Or if we had lower/higher noise parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer**: Estimated last pose: ($x_1, y_1$)=(16.57562398727231, 8.768048368239292), True last pose: ($x_2,y_2$)=(18.28922, 10.59034). The distance between the two points: $D=\\sqrt{(x_2-_x1)^2+(y_2-y_1)^2}=\\sqrt{(18.28922-16.57562)^2+(10.59034-8.768048)^2}\\approx 2.5$\n",
    "\n",
    "The poses are different because of the movement and measurement noise, so the estimate will have some uncertainty. With better sensors and less noise in the measurements, we can get a better estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing\n",
    "\n",
    "To confirm that your slam code works before submitting your project, it is suggested that you run it on some test data and cases. A few such cases have been provided for you, in the cells below. When you are ready, uncomment the test cases in the next cells (there are two test cases, total); your output should be **close-to or exactly** identical to the given results. If there are minor discrepancies it could be a matter of floating point accuracy or in the calculation of the inverse matrix.\n",
    "\n",
    "### Submit your project\n",
    "\n",
    "If you pass these tests, it is a good indication that your project will pass all the specifications in the project rubric. Follow the submission instructions to officially submit!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Estimated Poses:\n",
      "[50.000, 50.000]\n",
      "[37.973, 33.652]\n",
      "[26.185, 18.155]\n",
      "[13.745, 2.116]\n",
      "[28.097, 16.783]\n",
      "[42.384, 30.902]\n",
      "[55.831, 44.497]\n",
      "[70.857, 59.699]\n",
      "[85.697, 75.543]\n",
      "[74.011, 92.434]\n",
      "[53.544, 96.454]\n",
      "[34.525, 100.080]\n",
      "[48.623, 83.953]\n",
      "[60.197, 68.107]\n",
      "[73.778, 52.935]\n",
      "[87.132, 38.538]\n",
      "[80.303, 20.508]\n",
      "[72.798, 2.945]\n",
      "[55.245, 13.255]\n",
      "[37.416, 22.317]\n",
      "\n",
      "\n",
      "Estimated Landmarks:\n",
      "[82.956, 13.539]\n",
      "[70.495, 74.141]\n",
      "[36.740, 61.281]\n",
      "[18.698, 66.060]\n",
      "[20.635, 16.875]\n"
     ]
    }
   ],
   "source": [
    "# Here is the data and estimated outputs for test case 1\n",
    "\n",
    "test_data1 = [[[[1, 19.457599255548065, 23.8387362100849], [2, -13.195807561967236, 11.708840328458608], [3, -30.0954905279171, 15.387879242505843]], [-12.2607279422326, -15.801093326936487]], [[[2, -0.4659930049620491, 28.088559771215664], [4, -17.866382374890936, -16.384904503932]], [-12.2607279422326, -15.801093326936487]], [[[4, -6.202512900833806, -1.823403210274639]], [-12.2607279422326, -15.801093326936487]], [[[4, 7.412136480918645, 15.388585962142429]], [14.008259661173426, 14.274756084260822]], [[[4, -7.526138813444998, -0.4563942429717849]], [14.008259661173426, 14.274756084260822]], [[[2, -6.299793150150058, 29.047830407717623], [4, -21.93551130411791, -13.21956810989039]], [14.008259661173426, 14.274756084260822]], [[[1, 15.796300959032276, 30.65769689694247], [2, -18.64370821983482, 17.380022987031367]], [14.008259661173426, 14.274756084260822]], [[[1, 0.40311325410337906, 14.169429532679855], [2, -35.069349468466235, 2.4945558982439957]], [14.008259661173426, 14.274756084260822]], [[[1, -16.71340983241936, -2.777000269543834]], [-11.006096015782283, 16.699276945166858]], [[[1, -3.611096830835776, -17.954019226763958]], [-19.693482634035977, 3.488085684573048]], [[[1, 18.398273354362416, -22.705102332550947]], [-19.693482634035977, 3.488085684573048]], [[[2, 2.789312482883833, -39.73720193121324]], [12.849049222879723, -15.326510824972983]], [[[1, 21.26897046581808, -10.121029799040915], [2, -11.917698965880655, -23.17711662602097], [3, -31.81167947898398, -16.7985673023331]], [12.849049222879723, -15.326510824972983]], [[[1, 10.48157743234859, 5.692957082575485], [2, -22.31488473554935, -5.389184118551409], [3, -40.81803984305378, -2.4703329790238118]], [12.849049222879723, -15.326510824972983]], [[[0, 10.591050242096598, -39.2051798967113], [1, -3.5675572049297553, 22.849456408289125], [2, -38.39251065320351, 7.288990306029511]], [12.849049222879723, -15.326510824972983]], [[[0, -3.6225556479370766, -25.58006865235512]], [-7.8874682868419965, -18.379005523261092]], [[[0, 1.9784503557879374, -6.5025974151499]], [-7.8874682868419965, -18.379005523261092]], [[[0, 10.050665232782423, 11.026385307998742]], [-17.82919359778298, 9.062000642947142]], [[[0, 26.526838150174818, -0.22563393232425621], [4, -33.70303936886652, 2.880339841013677]], [-17.82919359778298, 9.062000642947142]]]\n",
    "\n",
    "##  Test Case 1\n",
    "##\n",
    "# Estimated Pose(s):\n",
    "#     [50.000, 50.000]\n",
    "#     [37.858, 33.921]\n",
    "#     [25.905, 18.268]\n",
    "#     [13.524, 2.224]\n",
    "#     [27.912, 16.886]\n",
    "#     [42.250, 30.994]\n",
    "#     [55.992, 44.886]\n",
    "#     [70.749, 59.867]\n",
    "#     [85.371, 75.230]\n",
    "#     [73.831, 92.354]\n",
    "#     [53.406, 96.465]\n",
    "#     [34.370, 100.134]\n",
    "#     [48.346, 83.952]\n",
    "#     [60.494, 68.338]\n",
    "#     [73.648, 53.082]\n",
    "#     [86.733, 38.197]\n",
    "#     [79.983, 20.324]\n",
    "#     [72.515, 2.837]\n",
    "#     [54.993, 13.221]\n",
    "#     [37.164, 22.283]\n",
    "\n",
    "\n",
    "# Estimated Landmarks:\n",
    "#     [82.679, 13.435]\n",
    "#     [70.417, 74.203]\n",
    "#     [36.688, 61.431]\n",
    "#     [18.705, 66.136]\n",
    "#     [20.437, 16.983]\n",
    "\n",
    "\n",
    "### Uncomment the following three lines for test case 1 and compare the output to the values above ###\n",
    "\n",
    "mu_1,_,_ = slam(test_data1, 20, 5, 100.0, 2.0, 2.0)\n",
    "poses, landmarks = get_poses_landmarks(mu_1, 20)\n",
    "print_all(poses, landmarks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Estimated Poses:\n",
      "[50.000, 50.000]\n",
      "[69.181, 45.665]\n",
      "[87.743, 39.703]\n",
      "[76.270, 56.311]\n",
      "[64.317, 72.176]\n",
      "[52.257, 88.154]\n",
      "[44.059, 69.401]\n",
      "[37.002, 49.918]\n",
      "[30.924, 30.955]\n",
      "[23.508, 11.419]\n",
      "[34.180, 27.133]\n",
      "[44.155, 43.846]\n",
      "[54.806, 60.920]\n",
      "[65.698, 78.546]\n",
      "[77.468, 95.626]\n",
      "[96.802, 98.821]\n",
      "[75.957, 99.971]\n",
      "[70.200, 81.181]\n",
      "[64.054, 61.723]\n",
      "[58.107, 42.628]\n",
      "\n",
      "\n",
      "Estimated Landmarks:\n",
      "[76.779, 42.887]\n",
      "[85.065, 77.438]\n",
      "[13.548, 95.652]\n",
      "[59.449, 39.595]\n",
      "[69.263, 94.240]\n"
     ]
    }
   ],
   "source": [
    "# Here is the data and estimated outputs for test case 2\n",
    "\n",
    "test_data2 = [[[[0, 26.543274387283322, -6.262538160312672], [3, 9.937396825799755, -9.128540360867689]], [18.92765331253674, -6.460955043986683]], [[[0, 7.706544739722961, -3.758467215445748], [1, 17.03954411948937, 31.705489938553438], [3, -11.61731288777497, -6.64964096716416]], [18.92765331253674, -6.460955043986683]], [[[0, -12.35130507136378, 2.585119104239249], [1, -2.563534536165313, 38.22159657838369], [3, -26.961236804740935, -0.4802312626141525]], [-11.167066095509824, 16.592065417497455]], [[[0, 1.4138633151721272, -13.912454837810632], [1, 8.087721200818589, 20.51845934354381], [3, -17.091723454402302, -16.521500551709707], [4, -7.414211721400232, 38.09191602674439]], [-11.167066095509824, 16.592065417497455]], [[[0, 12.886743222179561, -28.703968411636318], [1, 21.660953298391387, 3.4912891084614914], [3, -6.401401414569506, -32.321583037341625], [4, 5.034079343639034, 23.102207946092893]], [-11.167066095509824, 16.592065417497455]], [[[1, 31.126317672358578, -10.036784369535214], [2, -38.70878528420893, 7.4987265861424595], [4, 17.977218575473767, 6.150889254289742]], [-6.595520680493778, -18.88118393939265]], [[[1, 41.82460922922086, 7.847527392202475], [3, 15.711709540417502, -30.34633659912818]], [-6.595520680493778, -18.88118393939265]], [[[0, 40.18454208294434, -6.710999804403755], [3, 23.019508919299156, -10.12110867290604]], [-6.595520680493778, -18.88118393939265]], [[[3, 27.18579315312821, 8.067219022708391]], [-6.595520680493778, -18.88118393939265]], [[], [11.492663265706092, 16.36822198838621]], [[[3, 24.57154567653098, 13.461499960708197]], [11.492663265706092, 16.36822198838621]], [[[0, 31.61945290413707, 0.4272295085799329], [3, 16.97392299158991, -5.274596836133088]], [11.492663265706092, 16.36822198838621]], [[[0, 22.407381798735177, -18.03500068379259], [1, 29.642444125196995, 17.3794951934614], [3, 4.7969752441371645, -21.07505361639969], [4, 14.726069092569372, 32.75999422300078]], [11.492663265706092, 16.36822198838621]], [[[0, 10.705527984670137, -34.589764174299596], [1, 18.58772336795603, -0.20109708164787765], [3, -4.839806195049413, -39.92208742305105], [4, 4.18824810165454, 14.146847823548889]], [11.492663265706092, 16.36822198838621]], [[[1, 5.878492140223764, -19.955352450942357], [4, -7.059505455306587, -0.9740849280550585]], [19.628527845173146, 3.83678180657467]], [[[1, -11.150789592446378, -22.736641053247872], [4, -28.832815721158255, -3.9462962046291388]], [-19.841703647091965, 2.5113335861604362]], [[[1, 8.64427397916182, -20.286336970889053], [4, -5.036917727942285, -6.311739993868336]], [-5.946642674882207, -19.09548221169787]], [[[0, 7.151866679283043, -39.56103232616369], [1, 16.01535401373368, -3.780995345194027], [4, -3.04801331832137, 13.697362774960865]], [-5.946642674882207, -19.09548221169787]], [[[0, 12.872879480504395, -19.707592098123207], [1, 22.236710716903136, 16.331770792606406], [3, -4.841206109583004, -21.24604435851242], [4, 4.27111163223552, 32.25309748614184]], [-5.946642674882207, -19.09548221169787]]] \n",
    "\n",
    "\n",
    "##  Test Case 2\n",
    "##\n",
    "# Estimated Pose(s):\n",
    "#     [50.000, 50.000]\n",
    "#     [69.035, 45.061]\n",
    "#     [87.655, 38.971]\n",
    "#     [76.084, 55.541]\n",
    "#     [64.283, 71.684]\n",
    "#     [52.396, 87.887]\n",
    "#     [44.674, 68.948]\n",
    "#     [37.532, 49.680]\n",
    "#     [31.392, 30.893]\n",
    "#     [24.796, 12.012]\n",
    "#     [33.641, 26.440]\n",
    "#     [43.858, 43.560]\n",
    "#     [54.735, 60.659]\n",
    "#     [65.884, 77.791]\n",
    "#     [77.413, 94.554]\n",
    "#     [96.740, 98.020]\n",
    "#     [76.149, 99.586]\n",
    "#     [70.211, 80.580]\n",
    "#     [64.130, 61.270]\n",
    "#     [58.183, 42.175]\n",
    "\n",
    "\n",
    "# Estimated Landmarks:\n",
    "#     [76.777, 42.415]\n",
    "#     [85.109, 76.850]\n",
    "#     [13.687, 95.386]\n",
    "#     [59.488, 39.149]\n",
    "#     [69.283, 93.654]\n",
    "\n",
    "\n",
    "### Uncomment the following three lines for test case 2 and compare to the values above ###\n",
    "\n",
    "mu_2,_,_ = slam(test_data2, 20, 5, 100.0, 2.0, 2.0)\n",
    "poses, landmarks = get_poses_landmarks(mu_2, 20)\n",
    "print_all(poses, landmarks)"
   ]
  }
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