Augmented Neural Lyapunov Control

Machine learning-based methodologies have recently been adapted to solve control problems. The Neural Lyapunov Control (NLC) method is one such example. This approach combines Artificial Neural Networks (ANNs) with Satisfiability Modulo Theories (SMT) solvers to synthesise stabilising control laws and to prove their formal correctness. The ANNs are trained over a dataset of state-space samples to generate candidate control and Lyapunov functions, while the SMT solvers are tasked with certifying the correctness of the Lyapunov function over a continuous domain or by returning a counterexample. Despite the approach’s attractiveness, issues can occur due to subsequent calls of the SMT module at times returning similar counterexamples, which can turn out to be uninformative and may lead to dataset overfitting. Additionally, the control network weights are usually initialised with pre-computed gains from state-feedback controllers, e.g. Linear-Quadratic Regulators. To properly perform the initialisation requires user time and control expertise. In this work, we present an Augmented NLC method that mitigates these drawbacks, removes the need for the control initialisation and further improves counterexample generation. As a result, the proposed method allows the synthesis of nonlinear (as well as linear) control laws with the sole requirement being the knowledge of the system dynamics. The ANLC is tested over challenging benchmarks such as the Lorenz attractor and outperformed existing methods in terms of successful synthesis rate. The developed framework is released open-source at: https://github.com/grande-dev/Augmented-Neural-Lyapunov-Control

Augmented Neural Lyapunov Control

Machine learning-based methodologies have recently been adapted to solve control problems. The Neural Lyapunov Control (NLC) method is one such example. This approach combines Artificial Neural Networks (ANNs) with Satisfiability Modulo Theories (SMT) solvers to synthesise stabilising control laws and to prove their formal correctness. The ANNs are trained over a dataset of state-space samples to generate candidate control and Lyapunov functions, while the SMT solvers are tasked with certifying the correctness of the Lyapunov function over a continuous domain or by returning a counterexample. Despite the approach’s attractiveness, issues can occur due to subsequent calls of the SMT module at times returning similar counterexamples, which can turn out to be uninformative and may lead to dataset overfitting. Additionally, the control network weights are usually initialised with pre-computed gains from state-feedback controllers, e.g. Linear-Quadratic Regulators. To properly perform the initialisation requires user time and control expertise. In this work, we present an Augmented NLC method that mitigates these drawbacks, removes the need for the control initialisation and further improves counterexample generation. As a result, the proposed method allows the synthesis of nonlinear (as well as linear) control laws with the sole requirement being the knowledge of the system dynamics. The ANLC is tested over challenging benchmarks such as the Lorenz attractor and outperformed existing methods in terms of successful synthesis rate. The developed framework is released open-source at: https://github.com/grande-dev/Augmented-Neural-Lyapunov-Control

Autonomous trajectory design system for mapping of unknown sea-floors using a team of AUVs

This research develops a new on-line trajectory planning algorithm for a team of Autonomous Underwater Vehicles (AUVs). The goal of the AUVs is to cooperatively explore and map the ocean seafloor. As the morphology of the seabed is unknown and complex, standard non-convex algorithms perform insufficiently. To tackle this, a new simulationbased approach is proposed and numerically evaluated. This approach adapts the Parametrized Cognitive-based Adaptive Optimization (PCAO) algorithm. The algorithm transforms the exploration problem to a parametrized decision-making mechanism whose real-time implementation is feasible. Upon that transformation, this scheme calculates off-line a set of decision making mechanism’s parameters that approximate the - nonpractically feasible - optimal solution. The advantages of the algorithm are significant computational simplicity, scalability, and the fact that it can straightforwardly embed any type of physical constraints and system limitations. In order to train the PCAO controller, two morphologically different seafloors are used. During this training, the algorithm outperforms an unrealistic optimal-one-step-ahead search algorithm. To demonstrate the universality of the controller, the most effective controller is used to map three new morphologically different seafloors. During the latter mapping experiment, the PCAO algorithm outperforms several gradient-descent-like approaches

Towards Arctic AUV Navigation

The navigational drift for Autonomous Underwater Vehicles (AUVs) operating in open ocean can be bounded by regular surfacing. However, this is not an option when operating under ice. To operate effectively under ice requires an on-board navigation solution that does not rely on external infrastructure. Moreover, some under-ice missions require long-endurance capabilities, extending the operating time of the AUVs from hours to days, or even weeks and months. This paper proposes a particle filter based terrain-aided navigation algorithm specifically designed to be implementable in real-time on the low-powered Autosub Long Range 1500 (ALR1500) vehicle to perform long-range missions, namely crossing the Artic Ocean. The filter performance is analysed using numerical simulations with respect to various key factors, e.g. of the sea-floor morphology, bathymetric update rate, map noise, etc. Despite very noisy on-board measurements, the simulation results demonstrate that the filter is able to keep the estimation error within the mission requirements, whereas estimates using dead-reckoning techniques experience unbounded error growth. We conclude that terrain-aided navigation has the potential to prolong underwater missions to a range of thousands of kilometres, provided the vehicle crosses areas with sufficient terrain variability and the model includes adequate representation of environmental conditions and motion disturbances

Anomaly detection and fault diagnostics for underwater gliders using deep learning

Underwater Gliders (UGs) (Fig. 1) are a type of Autonomous Underwater Vehicle (AUV) that are being used extensively for long-term observation of key physical oceanographic parameters [1]. They operate remotely at a low surge speed of approximately 0.3ms−1, with deployments of several months [2]. However, developing Near Real-Time (NRT) anomaly detection and fault diagnostics systems for such vehicles remains challenging as decimated sensor data can only be transmitted off-board periodically during operations when the UG is on the surface. As part of an ongoing collaboration, the authors have previously developed anomaly detection systems for UGs via different approaches. In [3], a simple but effective system was developed to detect the wing loss using the roll angle. In [4], system identification techniques were employed to detect changes in model parameters which further successfully deduced simulated and natural marine growth. Anderlini, et al. [5] further conducted a field test to validate a marine growth detection system for UGs using ensembles of regression trees. In [6], the use of a range of deep learning techniques was investigated to achieve over-the-horizon anomaly detection for UGs. In [7], an anomaly detection system based on an improved Bi-directional Generative Adversarial Network (BiGAN) was prototyped to enable generic anomaly detection for different types of anomalies. For UGs operated over the horizon, some faults can only be revealed when the faulty UGs are recovered. Also, it is not clear when the faults developed. Some undetected faults can lead to critical failures and the loss of vehicle and/or data cargo. Therefore, it is essential to understand the actual causes of high anomaly scores during remote monitoring to allow operators to take appropriate mitigations to minimise subsequent risks and maximise the successful delivery of the remainder of the deployment. This paper further compares the results acquired in [7] with other baseline approaches. In addition, a new supervised fault diagnostics method for UGs is proposed. The BiGAN-based anomaly detection system is applied to estimate when the faults are developed, such that the training dataset for the supervised fault diagnostics model can be accurately annotated. The results suggest that the BiGAN-based anomaly detection system has successfully detected different types of anomalies, in good agreement with model-based and rule-based approaches. The supervised fault diagnostics system has achieved high fault diagnostics accuracy on the available test dataset

Terrain-aided navigation for long-range AUVs in dynamic under-mapped environments

Deploying long‐range autonomous underwater vehicles (AUVs) mid‐water column in the deep ocean is one of the most challenging applications for these submersibles. Without external support and speed over the ground measurements, dead‐reckoning (DR) navigation inevitably experiences an error proportional to the mission range and the speed of the water currents. In response to this problem, a computationally feasible and low‐power terrain‐aided navigation (TAN) system is developed. A Rao‐Blackwellized Particle Filter robust to estimation divergence is designed to estimate the vehicle's position and the speed of water currents. To evaluate performance, field data from multiday AUV deployments in the Southern Ocean are used. These form a unique test case for assessing the TAN performance under extremely challenging conditions. Despite the use of a small number of low‐power sensors and a Doppler velocity log to enable TAN, the algorithm limits the localisation error to within a few hundreds of metres, as opposed to a DR error of 40 km, given a 50 m resolution bathymetric map. To evaluate further the effectiveness of the system under a varying map quality, grids of 100, 200, and 400 m resolution are generated by subsampling the original 50 m resolution map. Despite the high complexity of the navigation problem, the filter exhibits robust and relatively accurate behaviour. Given the current aim of the oceanographic community to develop maps of similar resolution, the results of this study suggest that TAN can enable AUV operations of the order of months using global bathymetric models

Terrain‐aided navigation for long‐endurance and deep‐rated autonomous underwater vehicles

Terrain‐aided navigation (TAN) is a localisation method which uses bathymetric measurements for bounding the growth in inertial navigation error. The minimisation of navigation errors is of particular importance for long‐endurance autonomous underwater vehicles (AUVs). This type of AUV requires simple and effective on‐board navigation solutions to undertake long‐range missions, operating for months rather than hours or days, without reliance on external support systems. Consequently, a suitable navigation solution has to fulfil two main requirements: (a) bounding the navigation error, and (b) conforming to energy constraints and conserving on‐board power. This study proposes a low‐complexity particle filter‐based TAN algorithm for Autosub Long Range, a long‐endurance deep‐rated AUV. This is a light and tractable filter that can be implemented on‐board in real time. The potential of the algorithm is investigated by evaluating its performance using field data from three deep (up to 3,700 m) and long‐range (up to 195 km in 77 hr) missions performed in the Southern Ocean during April 2017. The results obtained using TAN are compared to on‐board estimates, computed via dead reckoning, and ultrashort baseline (USBL) measurements, treated as baseline locations, sporadically recorded by a support ship. Results obtained through postprocessing demonstrate that TAN has the potential to prolong underwater missions to a range of hundreds of kilometres without the need for intermittent surfacing to obtain global positioning system fixes. During each of the missions, the system performed 20 Monte Carlo runs. Throughout each run, the algorithm maintained convergence and bounded error, with high estimation repeatability achieved between all runs, despite the limited suite of localisation sensors

Autosub Long Range 1500: A continuous 2000 km field trial

Long Range Autonomous Underwater Vehicles (LRAUVs) offer the potential to monitor the ocean at higher spatial and temporal resolutions compared to conventional ship-based techniques. The multi-week to multi-month endurance of LRAUVs enables them to operate independently of a support vessel, creating novel opportunities for ocean observation. The National Oceanography Centre’s Autosub Long Range is one of a small number of vehicles designed for a multi-month endurance. The latest iteration, Autosub Long Range 1500 (ALR1500), is a 1500 m depth-rated LRAUV developed for ocean science in coastal and shelf seas or in the epipelagic and meteorologic regions of the ocean. This paper presents the design of the ALR1500 and results from a five week continuous deployment from Plymouth, UK, to the continental shelf break and back again, a distance of approximately 2000km which consumed half of the installed energy. The LRAUV was unaccompanied throughout the mission and operated continuously beyond visual line of sight

Terrain-Aided Navigation for Long-Range AUVs Operating in Uncertain Environments

The ever-increasing demand from scientific and oceanographic communities for conducting research activities in remote deep oceans has led to the development of long-range Autonomous Underwater Vehicles (AUVs). These platforms open up a world of new AUV applications, including persistent monitoring and data-collection in some of the most inaccessible areas on Earth. The extreme range of these vehicles could facilitate the completion of currently impossible tasks. However, deploying AUVs for long periods of time comes with its own challenges. Even though considerable effort has been directed towards developing navigation techniques for AUVs, a self-contained low-power solution yet remains a challenge for missions of the order of months, rather than days or hours. In answer to the presently limited navigation capability, this work develops a TerrainAided Navigation (TAN) technique which, relying on a small number of low-power sensors, is able to prolong underwater missions without the need for external support or regular surfacing. Bathymetric observations are collected using low-informative sonars. State estimation is performed by utilising the Rao-Blackwellized Particle Filter (RBPF). To make the navigation algorithm computationally feasible for low-power processing boards with limited computational resources, the filter estimates the 2-D position of the vehicle and the 2-D speed of the water-currents near the vehicle. The performance of the proposed navigation solution is evaluated using unique field data that was collected during three multi-day AUV deployments of up to approximately 200 km range and depths greater than 3000 m in the Southern Ocean. To assess whether TAN can cope with coarse bathymetric maps typically available for remote deep oceans, the original ship-constructed 50 m resolution map is degraded through a sub-sampling process and three additional maps of 100 m, 200 m and 400 m resolution are generated. Provided techniques to escape from local minima, the algorithm demonstrates sufficient robustness to face challenging conditions, such as strong water currents, motion along a low-informative terrain, or even the absence of bathymetric information for prolonged time periods. The use of Dead-Reckoning (DR) navigation resulted in an error of over 40 km after only a three-day long mission, whereas TAN appears to be able to place a bound on the localisation error growth. Depending on the resolution of the employed map, TAN accuracy varies from a few meters to 1.5 kilometres on average. To extend further the navigation challenge, the TAN algorithm is evaluated during an aspirational example of a science-driven mission for continuous mid-water column survey from Svalbard (Norway) to Barrow (Alaska) under the Arctic sea-ice, a range in excess of 3200 km. The inability to surface in conjunction with the degraded performance of heading sensors and the drift caused by water-currents make the overall navigation problem extremely challenging. A simulated environment is developed incorporating heading error models, both for a magnetic compass or a gyrocompass, and water-currents derived from models of the water circulation in the Arctic Ocean. The performance of the TAN algorithm is examined with respect to the employed heading sensor and a range of vertical distortions applied to the Arctic terrain map. In this case, DR navigation inevitably drifts from hundreds to thousands of kilometres, whereas the simulation results show that TAN can provide acceptable localisation accuracy given a moderate distortion applied to the terrain model. By degrading further the terrain model, simulations show that TAN can fail when the vehicle crosses large areas of the map subject to interpolations. To reduce the risk associated with the filter divergence, it is demonstrated that the TAN performance can massively be improved by using a Rapidly-exploring Random Tree Star (RRT∗) algorithm to optimise a priori the path of the vehicle such that the AUV avoids crossing highly uncertain regions of the Arctic terrain map. Simulation results show no filter divergence when utilising the optimised path, despite the use of a heavily distorted bathymetric map and an echo-sounder with a pinging period of 60 seconds