7.2 Inertial navigation and dead reckoning
7 min read•july 30, 2024
Underwater robots rely on inertial navigation and dead reckoning to navigate without . These techniques use motion and rotation sensors to estimate position and orientation. However, they're prone to over time, requiring clever solutions to maintain accuracy.
To combat drift, underwater robots use , combining data from multiple sources. This might include pressure sensors for depth, Doppler velocity logs for speed, and for feature tracking. These methods help robots stay on course in challenging underwater environments.
Inertial Navigation for Underwater Robots
Principles and Components
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- Inertial navigation is a self-contained navigation technique that uses motion sensors (accelerometers) and rotation sensors (gyroscopes) to continuously calculate the position, orientation, and velocity of a moving object without the need for external references
- Underwater robots use inertial navigation and dead reckoning to estimate their position and orientation in the absence of GPS signals or other external references
- Accelerometers measure linear acceleration, while gyroscopes measure angular velocity
- These measurements are integrated over time to estimate the robot's position, velocity, and orientation
- Magnetometers can provide heading information by measuring the Earth's magnetic field, aiding in the determination of the robot's orientation (compass)
Dead Reckoning
- Dead reckoning is the process of estimating the current position of a vehicle by using a previously determined position and advancing that position based on known or estimated speeds over elapsed time and course
- Dead reckoning relies on estimating the direction and distance traveled rather than using landmarks, astronomical observations, or radio navigation methods
- Example: A robot starts at a known position (0, 0) and travels forward at a speed of 1 m/s for 10 seconds, then turns 90 degrees to the right and travels for another 5 seconds. Using dead reckoning, the robot's estimated position would be (10, 5) relative to the starting point
- Inertial navigation systems (INS) are subject to drift over time due to the accumulation of small errors in the sensor measurements, leading to increasing uncertainty in the estimated position and orientation
- Example: If the has a small error of 0.01 m/s², after 1 hour of operation, the position error due to this bias alone would be around 65 meters
Sensor Fusion for Underwater Navigation
Principles and Algorithms
- Sensor fusion is the process of combining data from multiple sensors to improve the accuracy and reliability of the navigation solution
- Sensor fusion algorithms, such as Kalman filters or particle filters, can be used to estimate the robot's state (position, velocity, and orientation) by combining measurements from different sensors
- Example: A Kalman filter can be used to estimate the robot's position by combining measurements from an accelerometer, a , and a pressure sensor, taking into account the uncertainties associated with each sensor
- Sensor fusion techniques must account for the different characteristics and uncertainties of each sensor, such as sampling rates, noise levels, and measurement biases
- The choice of sensor fusion algorithm depends on factors such as the available computational resources, the required accuracy, and the specific characteristics of the sensors being used
Fusion with Other Navigation Sensors
- Inertial navigation data can be fused with measurements from other sensors, such as pressure sensors (depth), Doppler velocity logs (DVL), sonar, or visual odometry, to improve the overall navigation accuracy
- Pressure sensors provide depth information, which can be used to constrain the vertical position estimate
- DVLs measure the robot's velocity relative to the seabed, providing more accurate velocity estimates than those derived from accelerometer measurements alone
- Sonar or visual odometry can provide position updates by detecting and tracking features in the environment, helping to correct drift in the inertial navigation solution
- Example: An underwater robot equipped with an INS, a pressure sensor, and a DVL can use sensor fusion to estimate its 3D position and orientation by combining the depth information from the pressure sensor, the velocity measurements from the DVL, and the acceleration and angular velocity measurements from the INS
Inertial Navigation Performance in Underwater Environments
Factors Affecting Performance
- The performance of inertial navigation systems in underwater environments is affected by various factors, including sensor quality, calibration, and environmental conditions
- High-quality sensors with low noise, high sensitivity, and good temperature stability are essential for accurate inertial navigation
- Proper calibration of the sensors is crucial to minimize biases and scale factor errors, which can lead to significant drift in the navigation solution over time
- Example: A high-end with fiber-optic gyroscopes and low-noise accelerometers can provide more accurate navigation than a low-cost MEMS IMU
Challenges in Underwater Environments
- The accuracy of inertial navigation systems degrades over time due to the accumulation of errors from sensor drift, noise, and biases
- The rate of drift depends on the quality of the sensors and the effectiveness of the sensor fusion algorithms used to estimate the robot's state
- Underwater environments pose specific challenges for inertial navigation, such as the absence of GPS signals, the presence of currents, and the potential for magnetic disturbances
- Currents can cause the robot to drift off course, introducing errors in the dead reckoning estimate
- Magnetic disturbances, such as those caused by the robot's own electrical systems or nearby ferromagnetic objects, can affect the accuracy of magnetometer readings used for heading determination
- Example: In an environment with strong currents (1 m/s), an underwater robot relying solely on dead reckoning could drift by 3.6 km after just one hour of operation
Performance Evaluation
- The performance of inertial navigation systems can be evaluated through simulations, controlled experiments, and field trials in representative underwater environments
- Metrics such as position error, orientation error, and drift rate can be used to quantify the system's performance
- Comparison with ground truth data, such as GPS measurements obtained at the surface or acoustic positioning systems, can help assess the accuracy of the inertial navigation solution
- Example: A field trial comparing the inertial navigation solution with GPS measurements obtained at the surface can reveal the accumulated position error over time and help identify the main sources of drift (e.g., sensor biases, currents, or magnetic disturbances)
Error Correction for Inertial Navigation Systems
Sensor Calibration Techniques
- Sensor calibration techniques can be used to estimate and compensate for sensor biases, scale factor errors, and misalignment
- Static calibration involves measuring the sensor outputs in known orientations and comparing them with reference values to determine the calibration parameters
- Dynamic calibration methods, such as the six-position test or the angular rate test, can be used to estimate sensor biases and scale factors during motion
- Example: A six-position test involves placing the IMU in six different orientations (upright, inverted, and four 90-degree rotations) and measuring the sensor outputs in each orientation to estimate the biases and scale factors
Aiding with External References
- Sensor fusion with external aiding sources, such as GPS, acoustic positioning systems, or visual landmarks, can provide periodic position and orientation updates to correct drift in the inertial navigation solution
- When the robot surfaces, GPS measurements can be used to reset the position estimate and correct accumulated errors
- Acoustic positioning systems, such as long baseline (LBL) or ultra-short baseline (USBL) systems, can provide position updates underwater by measuring the robot's range and bearing relative to acoustic beacons
- Visual landmarks, such as known features on the seabed or artificial markers, can be used to provide position updates through visual odometry or simultaneous localization and mapping (SLAM) techniques
- Example: An underwater robot equipped with an INS and a USBL system can use the USBL measurements to periodically correct its position estimate and reduce the accumulated drift
Model-Based Approaches
- Model-based approaches can be used to predict and compensate for the expected drift in the inertial navigation solution based on models of the sensor errors and the robot's dynamics
- Gravity models can be used to estimate and remove the effect of gravity on the accelerometer measurements, improving the accuracy of the velocity and position estimates
- Magnetic field models can be used to predict and compensate for the expected variations in the Earth's magnetic field, improving the accuracy of the heading estimate from magnetometer measurements
- Example: By using a high-resolution gravity model, such as the Earth Gravitational Model (EGM2008), the effect of gravity on the accelerometer measurements can be estimated and removed, reducing the drift in the velocity and position estimates
Advanced Sensor Fusion Techniques
- Advanced sensor fusion techniques, such as adaptive Kalman filtering or particle filtering with map-based aiding, can be used to estimate and compensate for time-varying sensor errors and improve the robustness of the navigation solution in the presence of environmental disturbances
- Adaptive Kalman filters can automatically adjust the filter parameters based on the estimated sensor errors and the observed navigation performance
- Particle filters can handle non-linear and non-Gaussian error models and incorporate map-based aiding, such as terrain matching or feature-based localization
- Example: A particle filter with a digital terrain map can be used to estimate the robot's position by comparing the measured depth and altitude with the expected values from the map, reducing the drift in the inertial navigation solution
Key Terms to Review (18)
Accelerometer: An accelerometer is a device that measures acceleration forces acting on it, allowing it to determine changes in velocity and orientation. These measurements are crucial for understanding motion and position, which are vital for navigation systems and robotics, especially in applications like inertial navigation and dead reckoning.
Autonomous Underwater Vehicle (AUV): An Autonomous Underwater Vehicle (AUV) is a type of underwater robot designed to operate without human intervention, capable of navigating, collecting data, and performing tasks in underwater environments. These vehicles are engineered for efficiency, enabling them to perform various missions such as mapping, exploration, and monitoring while maintaining stability and maneuverability underwater.
Bias: Bias refers to a systematic error or deviation in measurements or observations that leads to inaccurate results. In the context of inertial navigation and dead reckoning, bias can significantly impact the accuracy of navigation systems, as it can skew position and orientation calculations over time, leading to errors in determining an underwater vehicle's location.
Course correction: Course correction refers to the adjustments made to a vehicle's trajectory to ensure it stays on its intended path. In underwater robotics, this involves recalibrating navigation systems and compensating for any deviations caused by environmental factors or errors in the initial navigation calculations.
Dr. John L. McCarthy: Dr. John L. McCarthy is a notable figure in the field of robotics and automation, particularly recognized for his contributions to the development of inertial navigation systems and algorithms for dead reckoning. His work has had a significant impact on how autonomous underwater vehicles (AUVs) and remotely operated vehicles (ROVs) determine their position and orientation in real-time, improving their accuracy and reliability in navigation tasks.
Drift: Drift refers to the gradual deviation of a measurement or position from its true value over time, often caused by errors in sensors or external factors. In underwater robotics, understanding drift is crucial for accurately interpreting data from inertial measurement units and pressure sensors, as well as ensuring reliable navigation using inertial navigation and dead reckoning methods.
GPS: GPS, or Global Positioning System, is a satellite-based navigation system that allows users to determine their precise location (latitude, longitude, and altitude) anywhere on Earth. It is crucial for modern navigation, providing real-time data that supports various applications including positioning, mapping, and timing. Its integration with other systems enhances accuracy and reliability in determining movement and location.
Gyroscope: A gyroscope is a device that uses the principles of angular momentum to maintain orientation and stability in navigation systems. It helps measure and maintain the direction of an object, which is crucial for accurate positioning and movement control, especially in vehicles like underwater robots where GPS signals may be unreliable.
Inertial Measurement Unit (IMU): An Inertial Measurement Unit (IMU) is a device that measures and reports a body's specific force, angular velocity, and sometimes magnetic field surrounding the body, using a combination of accelerometers, gyroscopes, and sometimes magnetometers. It plays a critical role in robotics and navigation systems by providing essential data that allows for precise motion tracking and orientation estimation, making it vital in sensor fusion and navigation techniques.
Initial position: Initial position refers to the starting location or coordinates of an object before any movement occurs. In navigation systems, especially those relying on inertial navigation and dead reckoning, this position serves as the reference point from which all subsequent movements are calculated, making it crucial for tracking an object's path and ensuring accuracy in navigation.
Integrated navigation system: An integrated navigation system is a technology that combines various navigation methods and sensors to provide accurate positioning and guidance for vehicles, including underwater robots. This system typically integrates data from inertial navigation, global positioning systems (GPS), and other sensor inputs to enhance reliability and precision in determining a vehicle's location and trajectory.
Kinematic Equations: Kinematic equations are mathematical formulas that describe the motion of objects in terms of their velocity, acceleration, displacement, and time. These equations allow for the prediction of an object's future position and speed based on its initial conditions, which is essential in analyzing motion in underwater robotics. Understanding these equations is crucial for effective navigation and control, enabling vehicles to make accurate adjustments during operation.
Prof. John B. Muir: Prof. John B. Muir is a notable figure in the field of robotics, particularly known for his contributions to the development and understanding of inertial navigation systems and dead reckoning techniques. His work emphasizes the importance of accurate navigation methods in underwater robotics, helping to enhance the performance and reliability of autonomous underwater vehicles (AUVs). This has paved the way for advancements in marine exploration and research.
Remotely operated vehicle (ROV): A remotely operated vehicle (ROV) is an uncrewed, underwater robot controlled from the surface, primarily used for exploration, research, and inspection of underwater environments. These vehicles are equipped with cameras, sensors, and manipulative tools, allowing them to perform tasks in areas that are difficult or dangerous for human divers. ROVs play a critical role in various applications such as surveying marine environments and assisting in underwater operations.
Sensor fusion: Sensor fusion is the process of integrating data from multiple sensors to produce more accurate, reliable, and comprehensive information than what could be achieved with individual sensors. This technique is crucial in robotics and automation, as it enhances navigation, localization, and overall system performance by leveraging the strengths of different types of sensors.
Sonar: Sonar, which stands for Sound Navigation and Ranging, is a technique that uses sound propagation to navigate, communicate, or detect objects underwater. It plays a crucial role in underwater sensing technologies, helping to identify and map the marine environment, locate objects like shipwrecks, and aid in navigation and communication through acoustic signals.
Temperature gradients: Temperature gradients refer to the rate of change of temperature in a particular direction within a medium. In underwater environments, these gradients can significantly affect the behavior of water masses, influencing buoyancy, currents, and the distribution of marine life. Understanding temperature gradients is essential for navigation and exploration, as they can impact sensor readings and the performance of underwater vehicles.
Water currents: Water currents are the continuous, directed movement of water in oceans, rivers, and lakes, influenced by factors such as wind, temperature, salinity, and the Earth's rotation. They play a vital role in the dynamics of aquatic environments, affecting everything from marine navigation to the behavior of underwater robotics. Understanding water currents is crucial for accurately determining position and navigation when operating underwater vehicles, especially when using techniques like inertial navigation and dead reckoning.