SLAM Simultaneous Localization & Mapping: Oxford Robotics Demo

Modern autonomous robots use multiple sensor types: (1) 3D LiDAR (Light Detection and Ranging) - uses laser pulses to create point cloud representations of the environment; (2) RGB-D Cameras - provide both color images and depth information (distance to surfaces); (3) IMU (Inertial Measurement Unit) - combines accelerometer (measures acceleration), gyroscope (measures angular velocity), and magnetometer (measures orientation relative to Earth's magnetic field) to track motion and orientation.

Robots use various sensors to perceive their environment: (1) RGB cameras capture images at 30-100 Hz, (2) Stereo 360 cameras provide panoramic views, (3) Depth cameras (RGB-D) measure distance to objects by shooting light rays and measuring return time, (4) Joint encoders measure the angle of robot joints with high precision (down to 6 microns), (5) Wheel encoders count wheel rotations to measure velocity and distance, and (6) Inertial Measurement Units (IMUs) measure acceleration and rotation, similar to the human vestibular system. These sensors work together to give robots a comprehensive understanding of their environment.

Sensors are essential devices that acquire environmental information for robots to make decisions. The more information available, the easier it becomes to make important decisions. There are three main types of distance sensors: Lidar (Light Detection and Ranging), radar, and cameras. Lidar works by emitting light at different angles and measuring distance to objects, providing data in polar coordinates (angle and distance). The polar coordinate system is fundamental for representing sensor data, consisting of angle and distance measurements. The RGB coordinate system (X, Y, Z) is used for 3D visualization. ROS (Robot Operating System) uses a publisher-subscriber architecture for communication between different robot components. Topics are channels for data transmission, each with a specific message type. Point cloud data represents the environment as a collection of 3D points, where each point has X, Y, and Z coordinates. Lidar sensors provide data in polar coordinates, which must be converted to Cartesian coordinates for visualization. Robots use coordinate transformations to convert sensor data between different reference frames: the base frame is fixed relative to the robot, while the world frame is a fixed reference frame in the environment. Sensor data is typically transformed from the sensor frame to the base frame, and then from the base frame to the world frame when needed.

LIDAR (Light Detection and Ranging) is a laser-based ranging device that measures distances using time-of-flight principles. The system sends laser pulses that reflect off objects, and by measuring the return time and knowing the speed of light, distances are calculated. LIDAR systems contain multiple laser emitters (16, 32, or 128 beams) arranged on rotating cylinders that scan environments to generate 3D point clouds with x, y, z coordinates. The technology also measures reflected light intensity, which varies based on surface reflectivity. Inertial Measurement Units (IMUs) measure acceleration and angular rates in three dimensions. Acceleration data can be integrated to obtain velocity and position, while angular rates integrate to give orientation angles. The Kalman filter algorithm combines IMU data with LIDAR measurements to compensate for sensor errors and provide accurate estimates of the robot's position and orientation. LIDAR sensors measure coordinates in their own local coordinate system, which moves with the robot. To build maps in a fixed world frame, sensor measurements must be transformed using the robot's position and orientation. Homogeneous coordinates solve this problem by adding a 1 to coordinate vectors, allowing both translation and rotation to be applied through matrix multiplication. This mathematical framework enables efficient computation of coordinate transformations in robotics.

LIDAR (Light Detection and Ranging) technology uses laser scanning to perform complete 360-degree environmental sweeps, measuring distances through time-of-flight calculations. The RPLIDAR A1 emits laser beams and detects reflections to determine object proximity. Raw data includes distance (millimeters), angle (degrees), quality rating (0-60 indicating reliability), and status bits. Quality ratings below threshold values signal unreliable measurements, while zero readings indicate objects beyond maximum range (~7m) or within minimum range (~130mm). Data processing involves angular segmentation (e.g., 10-degree sectors) and filtering techniques to extract meaningful information from continuous random-angle polling. This foundational understanding enables practical applications in robotics and autonomous systems.

This comprehensive lecture introduces state estimation as the first major topic in probabilistic robotics. The course covers state estimation, control planning, and learning. State estimation involves computing a belief (probability distribution) over the robot's state given measurements and actions. Three core concepts are defined: (1) State is a sufficient statistic for prediction and decision-making, defined per problem (e.g., robot position, joint angles). (2) Measurement (Z_T) is noisy sensor data from LIDAR, cameras, or encoders. (3) Action (U_T) is what the robot executes to change its state. The state estimation problem computes P(X_T | Z_1:T, U_1:T), also called the filtering problem. Probabilistic approaches are necessary because world models are imperfect, sensors are noisy, and unexpected events occur. Dead reckoning (open-loop without feedback) causes drift accumulation over time. The lecture then reviews probability fundamentals: axioms (P(A) ∈ [0,1], P(sample space) = 1, P(∅) = 0, P(A∪B) = P(A) + P(B) - P(A∩B)), discrete vs continuous random variables (PMF sums to 1, PDF integrates to 1), joint and conditional probability (P(X|Y) = P(X,Y)/P(Y)), independence (P(X|Y) = P(X)), marginalization (P(X) = Σ_Y P(X,Y)), and Bayes' Rule (P(X|Y) = P(Y|X)P(X)/P(Y)). These fundamentals are essential for understanding Bayesian filtering.

Bayesian filtering provides the theoretical foundation for state estimation by combining prior beliefs, likelihood functions, and observations to compute posterior distributions. The Markov property simplifies computation by assuming the next state depends only on the current state, eliminating the need to track entire history. The Kalman filter emerges by making four critical assumptions: Gaussian priors, linear process models with additive Gaussian noise, linear measurement models with additive Gaussian noise, and uncorrelated noise with initial state. These assumptions ensure the posterior remains Gaussian, enabling efficient computation through matrix operations.

The Kalman Filter is a special case of Bayesian Filtering that performs state estimation by recursively predicting and updating beliefs about hidden states using noisy measurements; it achieves computational tractability by assuming linear relationships between states and measurements, and that both follow Gaussian distributions, allowing analytical solutions to the otherwise intractable integrals in Bayesian filtering equations.

The Kalman filter is a recursive Bayesian filter requiring Gaussian probability distributions and linear models. It performs prediction (applying controls to predict state) and correction (incorporating observations to refine estimates). Under Gaussian-linear assumptions, it becomes statistically optimal, producing identical results to least squares. The framework maintains Gaussian beliefs through marginalization, conditioning, and convolution operations, enabling recursive state estimation without batch processing.

The state estimation problem involves computing P(X_T | U_1:T, Z_1:T), the probability distribution of the current state given past actions and measurements. Key probability rules include: probabilities sum to 1, joint probability of independent events equals product of individual probabilities, and Bayes' Rule P(X|Y) = P(Y|X)P(X)/P(Y). The fundamental challenge is that we never directly observe the true state—we only receive noisy measurements and must infer the state from these observations.

Localization requires a map as input to determine the robot's position, while mapping requires position as input to build the map. This circular dependency prevents solving either problem independently. SLAM (Simultaneous Localization and Mapping) solves this by simultaneously solving both problems. The robot always starts from a known position (the charger) at time zero with identity transformation. By observing landmarks and knowing their positions relative to itself, the robot can establish the initial map and its position. This initialization provides the reference frame needed to break the circular dependency.

Simultaneous Localization and Mapping (SLAM) is a computational problem that enables devices to simultaneously build a map of an unknown environment and track their own position within it, using sensor data from cameras, lidar, radar, or other sensors to extract features, match them across frames, estimate pose changes, and refine the map through loop closure and bundle adjustment; this technology powers applications ranging from mobile phones and augmented reality to autonomous vehicles and drones.

SLAM (Simultaneous Localization and Mapping) is the problem of simultaneously estimating the robot's trajectory (where it has been at different points in time) and building a map of the environment. Unlike simple mapping where the robot's position is known, SLAM addresses the chicken-and-egg problem where neither the map nor the robot's location is known initially. These two problems are interdependent—knowing the environment helps localize the robot, and knowing the robot's position helps build a better map.

SLAM (Simultaneous Localization and Mapping) is a fundamental robotics process enabling robots to simultaneously determine their position while building a map of an unknown environment. The core challenge is the circular dependency between knowing position and building a map. Robot position is represented using coordinate systems with X and Y axes and orientation (heading). Particle filters represent possible robot positions as weighted particles, where computational efficiency depends on balancing particle count against accuracy. SLAM integrates sensor data from odometry (wheel encoders) and external observations (cameras, LiDAR) to achieve accurate localization and mapping. The system works in a continuous loop where the robot uses its current position estimate to interpret sensor observations while simultaneously updating its map. This integration allows autonomous navigation in unknown environments.

SLAM (Simultaneous Localization and Mapping) is a fundamental problem in robotics where a robot estimates its own position and orientation (pose) while simultaneously building a map of an unknown environment. The key insight is that localization and mapping are synergistic: a more accurate map enables more precise localization, and more accurate localization enables more precise map building. The solution involves augmenting the robot's state space to include both the robot's pose (x, y, θ) and environmental feature parameters (such as wall locations), then applying Kalman filter variants (Extended Kalman Filter, Unscented Kalman Filter, or Particle Filter) to jointly estimate and update these parameters as the robot explores its environment.