S74_drone_perception.ipynb

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   "cell_type": "markdown",
   "id": "nrMMD-vw_zWz",
   "metadata": {},
   "source": [
    "# Visual SLAM"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5AH6FtPfaySi",
   "metadata": {
    "colab_type": "text",
    "tags": [
     "no-tex"
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   "source": [
    "<a href=\"https://colab.research.google.com/github/gtbook/robotics/blob/main/S74_drone_perception.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
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   "cell_type": "code",
   "execution_count": 1,
   "id": "fcMudhlbdd9w",
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install -q -U gtbook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "x_tMf-p9U_V9",
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import plotly.graph_objects as go\n",
    "try:\n",
    "    import google.colab\n",
    "except:\n",
    "    import plotly.io as pio\n",
    "    pio.renderers.default = \"png\"\n",
    "\n",
    "import gtsam\n",
    "from gtbook.display import show\n",
    "import gtsam.utils.plot as gtsam_plot"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "t8sxvGoMeUAP",
   "metadata": {},
   "source": [
    "```{index} perception; visual SLAM\n",
    "```\n",
    "\n",
    "> When we do SLAM with cameras, we call it visual SLAM."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b246cd0c",
   "metadata": {
    "tags": [
     "no-pdf"
    ]
   },
   "source": [
    "<img src=\"Figures7/S74-Autonomous_camera_drone-04.jpg\" alt=\"Splash image with strange drone presumably thinking about maps\" width=\"40%\" align=center style=\"vertical-align:middle;margin:10px 0px\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca30f321",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Visual SLAM is *almost* the same problem as the \"SLAM with Landmarks\" problem from Section 6.4, but we will now use 3D poses and 3D points, and we will use the inertial measurements from the IMU to inform us about the movement of the platform. This is a typical pipeline on drones, phones, etc., everything with an IMU. \n",
    "\n",
    "Many unmanned aerial vehicles use cameras as their main sensors in addition to inertial sensing, as they are an incredibly rich sensing modality, do not consume a whole lot of energy, and are quite small. Especially the latter two considerations are very important in the weight and energy constrained world of autonomous drones. Furthermore, in military applications there is another reason to favor cameras over active sensors like LIDAR: cameras do not *emit* energy and hence are stealthier.\n",
    "\n",
    "```{index} pair: structure from motion; SfM\n",
    "```\n",
    "Below we first introduce how we can estimate the trajectory of a drone using an inertial measurement unit or IMU, which we introduced in Section 7.2. Here we integrate IMU measurements over time to yield an estimate of the trajectory of the drone over time. Below that we discuss how we can build 3D maps from images alone (!), in a process called **structure from motion** or **SfM**. We then discuss Visual SLAM, which combines both IMU integration and SfM in a real-time, incremental pipeline. Implementing visual SLAM is beyond our scope, but it should be easy to imagine how inertial sensing and 3D reconstruction done together and in real-time is an incredible asset to autonomous flight."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "yWex_s-uwF_h",
   "metadata": {},
   "source": [
    "## Integrating the IMU\n",
    "\n",
    "We start off by encoding the information provided by the inertial measurement unit (IMU) in a factor graph.\n",
    "\n",
    "As an example in code, below we define a scenario with forward velocity 2m/s, while pitching up\n",
    "with angular velocity 30 degree/sec (negative in FLU). We set up a simulation using a built-in GTSAM class called the `ScenarioRunner`. To use this class, we need to define four things:\n",
    "\n",
    "- a scenario: below we use a \"constant twist\" scenario, which is very much like the example in Section 7.2, a constant angular and linear velocity specified in the body frame\n",
    "- noise parameters for the gyroscope and accelerometer\n",
    "- the sample frequency, which we set at 10Hz\n",
    "- bias parameters, to simulate how a bias actually corrupts the IMU measurements\n",
    "\n",
    "We show how to create a `runner` with these parameters in Figure [1](#fig:scenario-runner)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e0615c59",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
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   "outputs": [],
   "source": [
    "#| caption: Creating a `ScenarioRunner` instance to simulate an IMU.\n",
    "#| label: fig:scenario-runner\n",
    "# Set up scenario with constant velocity model, both angular (W) and linear (V)\n",
    "wb = np.array([0, -np.radians(30), 0])\n",
    "vb = np.array([2, 0, 0])\n",
    "scenario = gtsam.ConstantTwistScenario(wb, vb)\n",
    "\n",
    "# Create noise parameters\n",
    "noise_parameters = gtsam.PreintegrationParams.MakeSharedU(9.8)\n",
    "kGyroSigma = np.radians(0.5) / 60  # 0.5 degree ARW\n",
    "kAccelSigma = 0.1 / 60  # 10 cm VRW\n",
    "I3 = np.identity(3, float)\n",
    "noise_parameters.setGyroscopeCovariance(kGyroSigma**2 * I3)\n",
    "noise_parameters.setAccelerometerCovariance(kAccelSigma**2 * I3)\n",
    "noise_parameters.setIntegrationCovariance(0.0000001**2 * I3) # ignore this for now\n",
    "\n",
    "# Set the sample time\n",
    "dt = 0.1 # 10 Hz\n",
    "\n",
    "# Create bias parameters\n",
    "accBias = np.array([0, 0.1, 0]) # bias in accelerometer\n",
    "gyroBias = np.array([0, 0, 0]) # bias in gyroscope\n",
    "bias = gtsam.imuBias.ConstantBias(accBias, gyroBias)\n",
    "\n",
    "# Instantiate IMU simulation class as `runner`\n",
    "runner = gtsam.ScenarioRunner(scenario, noise_parameters, dt, bias)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "v3Ya8OiuNNFC",
   "metadata": {},
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    "Our approach will be to use the `runner` class to generate noisy measurements, and then use GTSAM to optimize for the optimal trajectory given those measurements.\n",
    "With the `scenario` class, we can create some (good) initial values by calling the `scenario.navState` at $t=0$ as well as every 5 steps, which is twice per second, given our sampling time $dt=0.1$.\n",
    "This is done in the code from Figure [2](#fig:init-values)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "zM33lHV41VSQ",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adding initial state with position [0. 0. 0.]\n",
      "Adding navState 1 at t=0.5 with position [1.  0.  0.1]\n",
      "Adding navState 2 at t=1.0 with position [1.9 0.  0.5]\n",
      "Adding navState 3 at t=1.5 with position [2.7 0.  1.1]\n",
      "Adding navState 4 at t=2.0 with position [3.3 0.  1.9]\n",
      "Adding navState 5 at t=2.5 with position [3.7 0.  2.8]\n",
      "Adding navState 6 at t=3.0 with position [3.8 0.  3.8]\n"
     ]
    }
   ],
   "source": [
    "#| caption: Create initial values for visual SLAM, using the IMU simulation.\n",
    "#| label: fig:init-values\n",
    "# Define key naming scheme for GTSAM\n",
    "X = gtsam.symbol_shorthand.X # for poses\n",
    "V = gtsam.symbol_shorthand.V # for velocities\n",
    "B0 = gtsam.symbol('b', 0) # for bias\n",
    "\n",
    "# Create values and add initial state\n",
    "values = gtsam.Values()\n",
    "state = scenario.navState(0)\n",
    "print(f\"Adding initial state with position {np.round(state.pose().translation(),1)}\")\n",
    "values.insert(X(0), state.pose())\n",
    "values.insert(V(0), state.velocity())\n",
    "\n",
    "i, T = 0, 3.5 # run scenario at 10Hz for 3.5 seconds, adding state every 5th iteration\n",
    "for j, t in enumerate(np.arange(0, T, dt)):\n",
    "    if j>0 and j % 5 == 0:\n",
    "        # create IMU factor\n",
    "        i += 1\n",
    "        state = scenario.navState(t)\n",
    "        print(f\"Adding navState {i} at t={t} with position {np.round(state.pose().translation(),1)}\")\n",
    "        values.insert(X(i), state.pose().retract(np.random.normal(scale=0.1, size=(6,))))\n",
    "        values.insert(V(i), state.velocity() + np.random.normal(scale=0.1, size=(3,)))\n",
    "\n",
    "# Add bias, as we will need it below\n",
    "values.insert(B0, bias)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "toqDZq6Pu99t",
   "metadata": {},
   "source": [
    "```{index} IMU preintegration\n",
    "```\n",
    "In Figure [3](#fig:imu-graph) we create the most complicated factor graph of the entire book, as it involves a factor that is connected to no less than five unknowns at every step. GTSAM contains a powerful, state of the art factor called the `ImuFactor` that allows us to accumulate IMU measurements and periodically add the resulting relative pose information to the graph. This process is called **IMU preintegration** and is used in many state-of-the-art navigation systems.\n",
    "\n",
    "In code, this accumulation of (high-rate) IMU measurements is done in a class called `PreintegratedImuMeasurements`, abbreviated \"PIM\", which is done at 10Hz.\n",
    "Every 5 steps we add an `ImuFactor` that is connected to two successive poses with keys `X(i)` and `X(i+1)` and their corresponding velocities with keys `V(i)` and `V(i+1)`, as well as the (single) bias unknown with key `B(0)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ed36f3f8",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
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   },
   "outputs": [],
   "source": [
    "#| caption: Create a graph with IMU factors using the `ScenarioRunner` instance.\n",
    "#| label: fig:imu-graph\n",
    "# Create graph\n",
    "imu_graph = gtsam.NonlinearFactorGraph()\n",
    "Iso = gtsam.noiseModel.Isotropic\n",
    "state = scenario.navState(0)\n",
    "imu_graph.addPriorPose3(X(0), state.pose(), Iso.Sigma(6, 0.1))\n",
    "imu_graph.addPriorVector(V(0), state.velocity(), Iso.Sigma(3, 0.1))\n",
    "imu_graph.addPriorConstantBias(B0, bias, Iso.Sigma(6, 0.1))\n",
    "\n",
    "i, T = 0, 3.5 # run scenario at 10Hz for 3.5 seconds, adding state every 5th iteration\n",
    "pim = gtsam.PreintegratedImuMeasurements(noise_parameters, bias)\n",
    "for j, t in enumerate(np.arange(0, T, dt)):\n",
    "    measuredOmega = runner.measuredAngularVelocity(t)\n",
    "    measuredAcc = runner.measuredSpecificForce(t)\n",
    "    pim.integrateMeasurement(measuredAcc, measuredOmega, dt)\n",
    "    if j>0 and j % 5 == 0:\n",
    "        # create IMU factor\n",
    "        factor = gtsam.ImuFactor(X(i), V(i), X(i + 1), V(i + 1), B0, pim)\n",
    "        imu_graph.push_back(factor)\n",
    "        i += 1\n",
    "        pim.resetIntegration()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "SHGX6Q8qOG3t",
   "metadata": {},
   "source": [
    "In Figure [4](#fig:imu_graph) we display the resulting factor graph. The figure shows (a bit messily) that the IMUFactors tie together the `Pose3` states $x_k$, the velocities $v_k$ and the unknown IMU biases $b_0$."
   ]
  },
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   "cell_type": "code",
   "execution_count": 6,
   "id": "78794d08",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
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      "text/plain": [
       "<gtbook.display.show at 0x115d675b0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "#| caption: A (somewhat messy) factor graph for the IMU preintegration problem.\n",
    "#| label: fig:imu_graph\n",
    "position_hints = {'u': 2, 'x': 1, 'z': 0}\n",
    "position_hints.update({'v':2})\n",
    "show(imu_graph, gtsam.Values(), hints=position_hints)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7dd5960",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We can optimize even *without* any external measurements, but unless you pay for a very expensive IMU, your estimate will drift very rapidly. The result of this IMU-only optimization is shown in Figure [5](#fig:imu_result)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6d75b7d4",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial error: 22971318.12067142\n",
      "final error: 3.169445405134413e-23\n"
     ]
    }
   ],
   "source": [
    "print(f\"initial error: {imu_graph.error(values)}\")\n",
    "lm = gtsam.LevenbergMarquardtOptimizer(imu_graph, values)\n",
    "imu_result = lm.optimize()\n",
    "print(f\"final error: {imu_graph.error(imu_result)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ed87f830",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| caption: Result of the IMU preintegration optimization.\n",
    "#| label: fig:imu_result\n",
    "i = 0\n",
    "while imu_result.exists(X(i)):\n",
    "    gtsam_plot.plot_pose3(1, imu_result.atPose3(X(i)), 1)\n",
    "    i += 1\n",
    "plt.title(\"imu_result\")\n",
    "gtsam.utils.plot.set_axes_equal(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fLu2jCSUceNo",
   "metadata": {},
   "source": [
    "## Incorporating Visual Measurements\n",
    "\n",
    "> Structure from Motion is 3D reconstruction from images.\n",
    "\n",
    "In this section we provide an introduction to reconstructing a 3D environment from camera images over time, which allows for planning and obstacle avoidance, which we discuss in more detail in the next section. However, mapping the environment is, in and of itself, a useful capability in many applications. In some industrial and military applications, the map *is* the product of interest. In this section we discuss 3D reconstruction as a *batch* process, done after the drone has collected images."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a8e2d5d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<figure id=\"fig:Balbianello\">\n",
    "<img src=\"https://github.com/gtbook/robotics/blob/main/Figures7/Balbianello.jpg?raw=1\" alt=\"Balbianello\">\n",
    "<figcaption>Five images of the \"Balbianello\" villa on lake Como, taken from a moving boat. </figcaption>\n",
    "</figure>\n",
    "\n",
    "Structure from Motion, or SfM, is the problem of computing the 3D structure of a scene from multiple images, either taken from different cameras, or taken at different times as the camera moves in the environment. In Figure [6](#fig:Balbianello) we show one such image sequence, five images of the \"Balbianello\" villa in Italy, situated on lake Como."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9715f32",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "```{index} bundle adjustment\n",
    "```\n",
    "SfM is almost the same problem as Visual SLAM, but typically there is no odometry information to relate\n",
    "different camera views. The resulting optimization problem is sometimes called **bundle adjustment**. \n",
    "The most difficult problems associated with SfM are feature detection, data association, and initializing the optimization.\n",
    "\n",
    "Below we load the Balbianello data from a file and create a factor graph, as well as an initial estimate. A lot of work is done in the code snippet below! The particular file format, which stems from the \"Bundler\" library, is transformed into a data structure `sfm_data`. The method `sfmFactorGraph` then creates a factor graph with *all* the projection factors derived from the close to 1500 visual measurements. The `initialCamerasAndPointsEstimate` method next instantiates a `Values` object with initial estimates for all the cameras and the points, extracted from the Bundler file. We then print the initial error and see that it has a value of $126.9$, which is normalized with respect to 1-pixel standard deviation given in the noise model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ff7d45ce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial error: 126.9\n"
     ]
    }
   ],
   "source": [
    "filename = gtsam.findExampleDataFile(\"Balbianello.out\")\n",
    "sfm_data = gtsam.SfmData.FromBundlerFile(filename)\n",
    "model = gtsam.noiseModel.Isotropic.Sigma(2, 1.0)  # one pixel in u and v\n",
    "graph = sfm_data.sfmFactorGraph(model)\n",
    "initial = gtsam.initialCamerasAndPointsEstimate(sfm_data)\n",
    "print(f\"initial error: {graph.error(initial):.1f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "of7GXisLxRd1",
   "metadata": {},
   "source": [
    "The code above already did most of the heavy lifting that was so cumbersome and manual in earlier sections of this book, but it does not yet optimize! We once again use the Levenberg-Marquardt non-linear optimizer below, which is now performing *structure from motion*: we optimize for both the unknown camera poses (intrinsic camera calibration is assumed known here) and the unknown 3D points in the scene:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "704cbe24",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "final error: 125.5\n"
     ]
    }
   ],
   "source": [
    "lm = gtsam.LevenbergMarquardtOptimizer(graph, initial)\n",
    "result = lm.optimize()\n",
    "print(f\"final error: {graph.error(result):.1f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24491487",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The final error is not much smaller than the initial error, which tells us that the initial estimate was already very good. It is quite fortunate to have found that initial estimate in the file, because in many cases initializing a structure from motion problem can be quite a difficult undertaking. When we are flying a drone, we can build up an estimate of the 3D environment gradually, and hence an initial estimate is always available to use from the previous time step. However, we will not discuss this more in depth here.\n",
    "\n",
    "The result of SfM is a sparse point cloud and a set of well-determined camera poses, which can be \"densified\" using multi-view stereo techniques. This is out of scope of this book, however, and below we simply extract the 3D points and display them in 3D with `plotly`, in Figure [7](#fig:sfm_result)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8fa3f485",
   "metadata": {},
   "outputs": [],
   "source": [
    "structure = gtsam.utilities.extractPoint3(result)\n",
    "valid = structure[:,2] > -5.0\n",
    "bRc = sfm_data.camera(0).pose().rotation()\n",
    "wRc = gtsam.Rot3([1,0,0],[0,0,-1],[0,1,0]) # make camera point to world y\n",
    "wRb = wRc.compose(bRc.inverse())\n",
    "structure = (wRb.matrix() @ structure.T).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "PpnillzmGvEG",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| caption: Structure from motion result as a sparse 3D point cloud.\n",
    "#| label: fig:sfm_result\n",
    "fig = go.Figure()\n",
    "fig.add_trace(go.Scatter3d(x=structure[valid,0],y=structure[valid,1],z=structure[valid,2],\n",
    "    mode=\"markers\", marker=dict(size=2, color=\"blue\"), showlegend= False))\n",
    "fig.update_layout(margin=dict(l=0, r=0, t=0, b=0))\n",
    "fig.update_yaxes(scaleanchor = \"x\", scaleratio = 1); fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "-ly4-3iUOEY-",
   "metadata": {},
   "source": [
    "## Visual SLAM\n",
    "\n",
    "> Visual SLAM is based on Structure from Motion.\n",
    "\n",
    "Visual SLAM combines both IMU integration and SfM in a real-time, incremental pipeline. Typically, The drone starts with no pre-built map, opens its eyes as it were, and starts building a 3D map of the environment incrementally. Initial estimates for the camera positions are given by integrating the IMU forward. New landmarks are added incrementally as the drone progresses throughout the environment. Fast, incremental optimization techniques can be used to keep the computation under control, but discussing these is out of scope for an introductory textbook. Suffice to say that, modulo a *lot* of engineering efforts, this process can be made to work incredibly well. When done well, this provides a superpower to autonomous drones, allowing them to map their environment in real time and enabling obstacle avoidance and planning in hitherto unknown environments.\n",
    "\n",
    "Visual SLAM from images and IMU integration compliment each other perfectly. The IMU excels at dealing with high frequency motion like vibrations, which is common on drones. However, it suffers from drift: the inertial measurement units available for consumer drones can drift away from the true trajectory quite rapidly. High quality IMUs are typically very expensive and only available in high-end applications. In fact, this technology is so sensitive that even *disclosing* the accuracy of military-grade IMUs is a crime in many countries. Visual SLAM, on the other hand, is not great at dealing with high frequency motions, but does not suffer from drift as much, especially in environments where many loop closures can be made. It is only in very long, open-ended trajectories that drift again becomes a problem."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "RgOtNYYqEBEt",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77ROd0ZMWxgH",
   "metadata": {},
   "source": [
    "Above we introduced Visual SLAM as an extension of SLAM with landmarks and its critical integration with an IMU integration process. We discussed how the latter can be done with factor graphs, and while these are some of the most complex factor graphs we have encountered, the principle stays the same. Structure from motion was introduced as a method for constructing 3D maps from images, and while we did not go into too much detail about the specific factors, the same optimization pattern can be found at its center. Visual SLAM was then introduced, at a high level, as a combination of IMU integration and SfM."
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "include_colab_link": true,
   "name": "S74_drone_perception.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "gtbook",
   "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": "3.9.19"
  },
  "latex_metadata": {
   "affiliation": "Georgia Institute of Technology",
   "author": "Frank Dellaert and Seth Hutchinson",
   "title": "Introduction to Robotics"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}