gtsam/python/gtsam/examples/EKF_SLAM.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "title-cell-fls",
   "metadata": {},
   "source": [
    "# EKF-SLAM (using Incremental Fixed-Lag Smoother)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "copyright-cell-fls",
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "source": [
    "GTSAM Copyright 2010-2023, Georgia Tech Research Corporation,\n",
    "Atlanta, Georgia 30332-0415\n",
    "All Rights Reserved\n",
    "Authors: Frank Dellaert, et al. (see THANKS for the full author list)\n",
    "\n",
    "See LICENSE for the license information"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "colab-button-cell-fls",
   "metadata": {},
   "source": [
    "<a href=\"https://colab.research.google.com/github/borglab/gtsam/blob/develop/python/examples/EKF_SLAM.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "intro-fls-short",
   "metadata": {},
   "source": [
    "This notebook demonstrates 2D Simultaneous Localization and Mapping (SLAM) using an EKF, although it is implemented using GTSAM's `IncrementalFixedLagSmoother`, just using a lag of 1.\n",
    "\n",
    "**Scenario:** A robot moves in a circular path, receiving noisy odometry and bearing-range measurements to landmarks.\n",
    "\n",
    "**Approach:** We use a fixed-lag smoother which maintains and optimizes only a recent window of variables (defined by the `SMOOTHER_LAG`). Variables older than the lag are marginalized out, keeping the computational cost bounded, making it suitable for online applications. By default we set the lag to *1* here, which makes this an extended Kalman filter. But **feel free to change the lag and see the fixed-lag smoother results**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "setup-imports-fls",
   "metadata": {},
   "source": [
    "## 1. Setup and Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "install-code-fls",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Install GTSAM and Plotly from pip if running in Google Colab\n",
    "try:\n",
    "    import google.colab\n",
    "    %pip install --quiet gtsam-develop plotly\n",
    "except ImportError:\n",
    "    pass # Not in Colab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "imports-code-fls",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from tqdm.notebook import tqdm # Progress bar\n",
    "import math\n",
    "\n",
    "import gtsam\n",
    "from gtsam.symbol_shorthand import X, L # Symbols for poses and landmarks\n",
    "\n",
    "# Import the IncrementalFixedLagSmoother\n",
    "from gtsam import IncrementalFixedLagSmoother\n",
    "\n",
    "# Helper modules\n",
    "import simulation\n",
    "from gtsam_plotly import SlamFrameData, create_slam_animation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "params-fls",
   "metadata": {},
   "source": [
    "## 2. Simulation and Smoother Parameters\n",
    "\n",
    "Define parameters for the simulation environment, robot motion, noise models, and the fixed-lag smoother."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "params-code-fls",
   "metadata": {},
   "outputs": [],
   "source": [
    "# World parameters\n",
    "NUM_LANDMARKS = 15\n",
    "WORLD_SIZE = 10.0 # Environment bounds [-WORLD_SIZE/2, WORLD_SIZE/2]\n",
    "\n",
    "# Robot parameters\n",
    "ROBOT_RADIUS = 3.0\n",
    "ROBOT_ANGULAR_VEL = np.deg2rad(20.0) # Radians per step\n",
    "NUM_STEPS = 50\n",
    "DT = 1.0 # Time step duration\n",
    "\n",
    "# Noise parameters (GTSAM Noise Models)\n",
    "PRIOR_NOISE = gtsam.noiseModel.Diagonal.Sigmas(np.array([0.1, 0.1, np.deg2rad(1.0)]))\n",
    "ODOMETRY_NOISE = gtsam.noiseModel.Diagonal.Sigmas(np.array([0.1, 0.05, np.deg2rad(2.0)]))\n",
    "MEASUREMENT_NOISE = gtsam.noiseModel.Diagonal.Sigmas(np.array([np.deg2rad(2.0), 0.2]))\n",
    "\n",
    "# Sensor parameters\n",
    "MAX_SENSOR_RANGE = 5.0\n",
    "\n",
    "# --- Fixed-Lag Smoother Parameters ---\n",
    "# Define the length of the smoothing window in seconds.\n",
    "# A lag of 1*DT (e.g., 1.0 second) means the smoother maintains the state\n",
    "# estimate for the current time step only, behaving like a filter.\n",
    "# Larger lags incorporate more past information for smoothing.\n",
    "SMOOTHER_LAG = 0.99 * DT\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ground-truth-fls",
   "metadata": {},
   "source": [
    "## 3. Generate Ground Truth Data\n",
    "\n",
    "Create the true environment, robot path, and simulate noisy sensor readings using the `simulation` module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ground-truth-call-fls",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulation Generated: 15 landmarks.\n",
      "Simulation Generated: 51 ground truth poses and 50 odometry measurements.\n",
      "Simulation Generated: 210 bearing-range measurements.\n"
     ]
    }
   ],
   "source": [
    "landmarks_gt_dict, poses_gt, odometry_measurements, measurements_sim, landmarks_gt_array = \\\n",
    "    simulation.generate_simulation_data(\n",
    "        num_landmarks=NUM_LANDMARKS,\n",
    "        world_size=WORLD_SIZE,\n",
    "        robot_radius=ROBOT_RADIUS,\n",
    "        robot_angular_vel=ROBOT_ANGULAR_VEL,\n",
    "        num_steps=NUM_STEPS,\n",
    "        dt=DT,\n",
    "        odometry_noise_model=ODOMETRY_NOISE,\n",
    "        measurement_noise_model=MEASUREMENT_NOISE,\n",
    "        max_sensor_range=MAX_SENSOR_RANGE,\n",
    "        X=X, # Pass symbol functions\n",
    "        L=L\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "smoother-impl",
   "metadata": {},
   "source": [
    "## 4. Fixed-Lag Smoother SLAM Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "smoother-init",
   "metadata": {},
   "source": [
    "### Initialize Smoother and Helper Functions\n",
    "\n",
    "We create the `IncrementalFixedLagSmoother` with the specified lag. We also initialize the first state (pose X(0) at time 0.0) and add it to the smoother using its `update` method. The `update` method requires factors, initial values (theta), and timestamps for the *new* variables being added."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "smoother-init-code",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initializing IncrementalFixedLagSmoother with lag = 0.99 seconds...\n",
      "Performing initial smoother update...\n",
      "Initial update complete.\n"
     ]
    }
   ],
   "source": [
    "# Helper for graphviz visualization\n",
    "WRITER = gtsam.GraphvizFormatting()\n",
    "WRITER.binaryEdges = True\n",
    "\n",
    "def make_dot(graph, estimate):\n",
    "    # Visualize the factor graph currently managed by the smoother\n",
    "    WRITER.boxes = {key for key in estimate.keys() if gtsam.symbolChr(key) == ord('l')}\n",
    "    return graph.dot(estimate, writer=WRITER)\n",
    "\n",
    "# --- Smoother Initialization ---\n",
    "print(f\"Initializing IncrementalFixedLagSmoother with lag = {SMOOTHER_LAG} seconds...\")\n",
    "# Use ISAM2 parameters if specific settings are needed, otherwise defaults are used.\n",
    "isam2_params = gtsam.ISAM2Params()\n",
    "smoother = IncrementalFixedLagSmoother(SMOOTHER_LAG, isam2_params)\n",
    "\n",
    "# Variables to store results for animation\n",
    "history = []\n",
    "\n",
    "# --- Initial Step (k=0) ---\n",
    "initial_pose_key = X(0)\n",
    "initial_time = 0.0\n",
    "initial_pose = poses_gt[0] # Start at ground truth (can add noise if desired)\n",
    "\n",
    "# Create containers for the first update\n",
    "initial_factors = gtsam.NonlinearFactorGraph()\n",
    "initial_values = gtsam.Values()\n",
    "# The KeyTimestampMap maps variable keys (size_t) to their timestamps (double)\n",
    "initial_timestamps = {}\n",
    "\n",
    "# Add prior factor for the first pose\n",
    "initial_factors.add(gtsam.PriorFactorPose2(initial_pose_key, initial_pose, PRIOR_NOISE))\n",
    "\n",
    "# Add the initial pose estimate to Values\n",
    "initial_values.insert(initial_pose_key, initial_pose)\n",
    "\n",
    "# Add the timestamp for the initial pose\n",
    "initial_timestamps[initial_pose_key] = initial_time\n",
    "\n",
    "# Update the smoother with the initial state\n",
    "print(\"Performing initial smoother update...\")\n",
    "smoother.update(initial_factors, initial_values, initial_timestamps)\n",
    "print(\"Initial update complete.\")\n",
    "\n",
    "# Store initial state for animation\n",
    "current_estimate = smoother.calculateEstimate()\n",
    "current_graph = smoother.getFactors() # Get factors currently managed by smoother\n",
    "# ISAM can serve as marginals object:\n",
    "current_marginals = smoother.getISAM2()\n",
    "\n",
    "history.append(SlamFrameData(0, current_estimate, current_marginals, make_dot(current_graph, current_estimate)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "smoother-loop",
   "metadata": {},
   "source": [
    "### Main Iterative Loop\n",
    "\n",
    "At each step `k`, we process the odometry measurement from `X(k)` to `X(k+1)` and all landmark measurements taken *at* pose `X(k+1)`.\n",
    "\n",
    "1.  **Prepare Data:** Collect new factors (`NonlinearFactorGraph`), initial estimates for *new* variables (`Values`), and timestamps for *new* variables (`KeyTimestampMap`) for the current step.\n",
    "2.  **Predict:** Calculate an initial estimate for the new pose `X(k+1)` based on the previous estimate `X(k)` (retrieved from the smoother) and the odometry measurement.\n",
    "3.  **Initialize Landmarks:** If a landmark is observed for the first time, calculate an initial estimate based on the predicted pose and the measurement, and add it to the `new_values` and `new_timestamps`.\n",
    "4.  **Update Smoother:** Call `smoother.update()` with the collected factors, values, and timestamps. This incorporates the new information, performs optimization (iSAM2), and marginalizes old variables.\n",
    "5.  **Store Results:** Retrieve the current estimate and factor graph from the smoother for visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "smoother-loop-code",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running Incremental Fixed-Lag Smoother SLAM loop (50 steps)...\n"
     ]
    },
    {
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       "  0%|          | 0/50 [00:00<?, ?it/s]"
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     "metadata": {},
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Incremental Fixed-Lag Smoother SLAM finished.\n",
      "Final number of poses in smoother state: 1\n",
      "Final number of landmarks in smoother state: 5\n"
     ]
    }
   ],
   "source": [
    "print(f\"Running Incremental Fixed-Lag Smoother SLAM loop ({NUM_STEPS} steps)...\")\n",
    "\n",
    "for k in tqdm(range(NUM_STEPS)):\n",
    "    # --- Prepare for Update --- \n",
    "    current_time = (k + 1) * DT\n",
    "\n",
    "    # Create containers for the data needed for smoother.update()\n",
    "    new_factors = gtsam.NonlinearFactorGraph()\n",
    "    new_values = gtsam.Values() # Only initial estimates for *new* variables\n",
    "    new_timestamps = {}\n",
    "\n",
    "    # --- Odometry Factor --- \n",
    "    # Add the odometry factor connecting the previous pose to the current one.\n",
    "    odom_k = odometry_measurements[k]\n",
    "    new_factors.add(gtsam.BetweenFactorPose2(X(k), X(k + 1), odom_k, ODOMETRY_NOISE))\n",
    "\n",
    "    # --- Predict Initial Estimate for New Pose --- \n",
    "    # Get the previous pose estimate *from the smoother's current solution*.\n",
    "    prev_pose_estimate = current_estimate.atPose2(X(k))\n",
    "    predicted_pose = prev_pose_estimate.compose(odom_k)\n",
    "    # Add the initial estimate for the new pose X(k+1).\n",
    "    new_values.insert(X(k + 1), predicted_pose)\n",
    "    # Add the timestamp for the new pose.\n",
    "    new_timestamps[X(k + 1)] = current_time\n",
    "\n",
    "    # --- Measurement Factors & New Landmark Initialization --- \n",
    "    measurements_k1 = measurements_sim[k + 1] # Measurements taken AT pose k+1\n",
    "\n",
    "    for lm_key, measured_bearing, measured_range in measurements_k1:\n",
    "        # Add the measurement factor.\n",
    "        new_factors.add(gtsam.BearingRangeFactor2D(X(k + 1), lm_key, \n",
    "                                                     measured_bearing, measured_range,\n",
    "                                                     MEASUREMENT_NOISE))\n",
    "        \n",
    "        # --- Initialize New Landmark Estimates --- \n",
    "        if not current_estimate.exists(lm_key):\n",
    "            # Calculate initial guess based on the *predicted* current pose and the measurement.\n",
    "            delta_x = measured_range * math.cos(measured_bearing.theta())\n",
    "            delta_y = measured_range * math.sin(measured_bearing.theta())\n",
    "            lm_initial_guess = predicted_pose.transformFrom(gtsam.Point2(delta_x, delta_y))\n",
    "            \n",
    "            # Add the initial estimate for the new landmark.\n",
    "            new_values.insert(lm_key, lm_initial_guess)\n",
    "             \n",
    "            # Add the timestamp for the new landmark (first time seen).\n",
    "            # Important: Timestamps must be provided for all keys in `new_values`.\n",
    "            new_timestamps[lm_key] = current_time\n",
    "                        \n",
    "    # --- Update Smoother --- \n",
    "    # Pass the new factors, initial estimates for new variables, and their timestamps.\n",
    "    # The smoother internally manages adding these to the ISAM2 backend, optimizing,\n",
    "    # and removing marginalized variables/factors.\n",
    "    smoother_result = smoother.update(new_factors, new_values, new_timestamps)\n",
    "    # Optionally, inspect smoother_result for info like iterations, error, etc.\n",
    "    # print(f\"Step {k+1}: Iterations={smoother_result.getIterations()}, Error={smoother_result.getError():.4f}\")\n",
    "\n",
    "    # --- Get Results for Visualization --- \n",
    "    current_estimate = smoother.calculateEstimate() # Get estimates for variables within the lag\n",
    "    current_graph = smoother.getFactors() # Get factors currently managed by smoother\n",
    "    # ISAM can serve as marginals object:\n",
    "    current_marginals = smoother.getISAM2()\n",
    "\n",
    "    # Store the current state for visualization\n",
    "    history.append(SlamFrameData(k+1, current_estimate, current_marginals, make_dot(current_graph, current_estimate)))\n",
    "\n",
    "\n",
    "print(\"\\nIncremental Fixed-Lag Smoother SLAM finished.\")\n",
    "final_estimate = smoother.calculateEstimate()\n",
    "print(f\"Final number of poses in smoother state: {len([key for key in final_estimate.keys() if gtsam.Symbol(key).chr() == ord('x')])}\")\n",
    "print(f\"Final number of landmarks in smoother state: {len([key for key in final_estimate.keys() if gtsam.Symbol(key).chr() == ord('l')])}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "plotly-animation-fls",
   "metadata": {},
   "source": [
    "## 5. Create Plotly Animation\n",
    "\n",
    "Visualize the results using the `gtsam_plotly` module. The animation shows the evolution of the robot's path estimate and mapped landmarks *within the smoother's active window*. The full ground truth path is shown for reference. If `plot_full_estimated_trajectory=True`, the entire estimated trajectory (including marginalized poses) is shown faintly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "plotly-animation-call-code-fls",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generating Plotly animation...\n"
     ]
    },
    {
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      "text/plain": [
       "Creating Frames:   0%|          | 0/51 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotly animation generated.\n",
      "Displaying animation...\n"
     ]
    },
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
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    "fig = create_slam_animation(\n",
    "    history,\n",
    "    X=X,  # Pass symbol functions\n",
    "    L=L,\n",
    "    max_landmark_index=NUM_LANDMARKS,\n",
    "    landmarks_gt_array=landmarks_gt_array,\n",
    "    poses_gt=poses_gt, # Plot full ground truth for reference\n",
    "    world_size=WORLD_SIZE,\n",
    ")\n",
    "\n",
    "print(\"Displaying animation...\")\n",
    "fig.show()"
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    "## 6. Discussion\n",
    "\n",
    "*   **Fixed-Lag Smoothing:** The `IncrementalFixedLagSmoother` successfully performed online SLAM, maintaining a bounded computational load by marginalizing variables older than the specified `SMOOTHER_LAG`.\n",
    "*   **`smoother.update()`:** This core method efficiently integrated new measurements and optimized the active variable window using iSAM2.\n",
    "*   **Lag Parameter (`SMOOTHER_LAG`):** This parameter controls the trade-off between computational cost and accuracy. A smaller lag (e.g., `1.0 * DT`) acts like a filter, while a larger lag allows for more smoothing over recent history.\n",
    "*   **Visualization:** The animation displays the estimates for variables currently *within* the smoother's lag. The faint grey line (if enabled) shows the complete history of estimated poses, including those that have been marginalized out."
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