Odometry

Odometry provides a relative pose estimate, calculating each new position relative to the previous one, not in a fixed global frame. This is done by integrating small increments of motion (e.g., wheel rotations, visual feature flow).

• Key Implication: The estimate is always relative to the starting point. Without an absolute reference (like GPS or a loop closure), the system has no inherent knowledge of its global location.
• Example: A wheeled robot integrating encoder ticks to calculate distance traveled and a change in heading angle to update its (x, y, θ) pose relative to its startup location.

The most critical limitation of odometry is unbounded error growth or drift. Small errors in each incremental measurement (from wheel slip, sensor noise, or modeling inaccuracies) integrate over time, causing the estimated position to diverge from the true position.

• Error Sources: Systematic errors (e.g., unequal wheel diameters) cause predictable drift, while non-systematic errors (e.g., wheel slip on gravel) cause unpredictable drift.
• Consequence: Pure odometry is unreliable for long-term navigation. It must be periodically corrected by absolute sensing (e.g., GPS, beacons) or loop closure events in SLAM.

Despite long-term drift, odometry typically provides high-frequency, smooth, and accurate pose estimates over short time horizons and distances. This makes it ideal for local control loops and as a high-rate motion prior for other filters.

• Why it's useful: Control algorithms for balance or precise manipulation require millisecond-level updates on body velocity and position change, which odometry from an IMU or encoders can provide.
• Sensor Role: Inertial Measurement Units (IMUs) provide very high-rate angular velocity and linear acceleration data, excellent for short-term propagation between lower-rate camera or LiDAR updates in a fusion pipeline.

Odometry is defined by the primary sensor used for motion estimation, each with unique failure modes and performance characteristics.

• Wheel Odometry: Uses encoders on wheels/tracks. Simple and low-cost but fails with wheel slip or on non-rigid terrain.
• Visual Odometry (VO): Estimates motion by tracking visual features between camera frames. Fails in low-texture environments (blank walls) or under rapid motion causing blur.
• Inertial Odometry: Uses an IMU. Provides motion data during visual/LiDAR outages but suffers from bias drift leading to quadratic error growth in position.
• LiDAR Odometry: Uses scan matching (e.g., ICP) between consecutive 3D point clouds. Robust to lighting changes but can fail in featureless environments (long corridors).

Odometry is rarely used in isolation. It is a fundamental process model or motion prior within larger sensor fusion and state estimation frameworks.

• In Kalman Filters: The odometry prediction step propagates the state estimate forward in time. The process noise covariance is tuned to model the uncertainty of the odometry.
• In Graph-Based SLAM: Odometry measurements create sequential constraints between consecutive robot poses in the factor graph. These constraints are strong but accumulate error, which is later corrected by loop closure constraints.
• In VIO/LIO: Visual or LiDAR odometry provides precise relative pose measurements, which are fused with IMU data in a tightly-coupled filter to estimate pose, velocity, and IMU biases simultaneously.

While often used interchangeably, a technical distinction exists. Dead reckoning traditionally refers to navigation using a known initial fix, then advancing position based on course and speed estimates (e.g., from a compass and log for ships).

• Odometry is a more general term for self-motion tracking using any onboard sensor (encoders, IMU, camera).
• Key Difference: Dead reckoning often implies the use of a heading reference (like a magnetic compass) and speed-over-ground. Odometry, especially visual or inertial, estimates both translation and rotation directly from sensor data without an external heading reference.
• Common Ground: Both are relative, integrative, and drift-prone.

Dead reckoning is the foundational navigation technique of estimating a vehicle's current position by advancing a previously known position based on estimated speed, heading, and elapsed time. It is the principle behind all odometry.

• Inherent Drift: Like odometry, it accumulates error over time due to imperfect measurements of velocity and orientation.
• Historical Use: Predates electronic sensors, used in maritime and aerial navigation with compass and log.
• Modern Implementation: The process model in a Bayesian filter (e.g., using wheel encoder ticks or integrated IMU data) is a formalized dead reckoning step.

Visual-Inertial Odometry (VIO) is a tightly-coupled sensor fusion technique that combines a camera and an Inertial Measurement Unit (IMU) to estimate 3D pose and velocity.

• Complementary Sensors: The camera provides rich, drift-free orientation but fails during fast motion or blur. The IMU provides high-frequency acceleration and angular velocity but drifts quickly.
• Drift Mitigation: The fusion significantly reduces drift compared to pure visual odometry or pure inertial navigation.
• Key Algorithms: Includes MSCKF (Multi-State Constraint Kalman Filter) and optimization-based approaches like VINS-Mono. It is the standard for AR/VR headsets and agile drones.

LiDAR-Inertial Odometry (LIO) is a state estimation method that fuses 3D LiDAR point clouds with IMU data to track ego-motion and build a local map concurrently.

• Precise Geometry: LiDAR provides accurate, direct 3D distance measurements, making it robust to lighting changes where cameras fail.
• Scan Matching: Core to LIO is aligning successive LiDAR scans (e.g., using Iterative Closest Point (ICP) or feature-based matching) to compute motion, aided by the IMU for motion distortion correction and high-frequency prediction.
• Application: Essential for autonomous vehicles and robots operating in GPS-denied, variable-lighting environments like warehouses, mines, and city streets.

The Error State Kalman Filter (ESKF) is a sophisticated implementation of the Kalman filter principle designed for robust attitude and pose estimation, commonly used in inertial and visual-inertial odometry.

• Core Idea: Instead of estimating the full system state (e.g., position, quaternion), it estimates the small error state (the deviation from a nominal state). The nominal state is propagated using the raw IMU data.

• Advantages:

  • Numerical Stability: Keeps the orientation representation (e.g., quaternion) always normalized.
  • Efficiency: The error state is always small and near zero, allowing the use of linearized dynamics in a consistent and accurate way.
  • Standard in Robotics: Foundational to modern IMU processing and VIO pipelines like those in ROS 2.

A factor graph is a bipartite graphical model used to represent and solve large-scale optimization problems in state estimation, such as SLAM and bundle adjustment, which are extensions of odometry.

• Structure: Composed of variable nodes (unknown states like robot poses) and factor nodes (probabilistic constraints between variables from sensors or models).
• Odometry Factors: Sequential odometry measurements create a chain of factors connecting consecutive pose variables.
• Correcting Drift: When a loop closure is detected, it creates a factor between non-sequential poses, allowing a graph optimization to redistribute and correct the accumulated odometric error across the entire trajectory. Frameworks like GTSAM and g2o implement this.

Wheel odometry (or differential drive odometry) is the most common form of odometry for ground robots, estimating pose change by counting wheel rotations.

• Kinematic Model: Uses the robot's kinematic model (e.g., for a differential drive robot: x = (r/2)(φ_left + φ_right)cos(θ)) to integrate encoder ticks into a pose estimate.
• Major Error Sources:
  • Systematic Errors: Unequal wheel diameters, misalignment of wheels, uncertainty in wheelbase measurement.
  • Non-Systematic Errors: Wheel slippage, uneven floors, collisions.
• Calibration: Can be calibrated using the UMBmark method to minimize systematic error. It is typically fused with other sensors (IMU, LiDAR) in a filter for robust operation.