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J.J. van Beers
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5 records found
1
Conference paper
(2025)
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P. Solanki, Nikolaus Vertovec, Yannik Schnitzer, J.J. van Beers, C.C. de Visser, Alessandro Abate
Recent approaches to leveraging deep learning for computing reachable sets of continuous-time dynamical systems have gained popularity over traditional level-set methods, as they overcome the curse of dimensionality. However, as with level-set methods, considerable care needs to be taken in limiting approximation errors, particularly since no guarantees are provided during training on the accuracy of the learned reachable set. To address this limitation, we introduce an ϵ-approximate Hamilton-Jacobi partial differential equation (HJ-PDE), which establishes a relationship between training loss and accuracy of the true reachable set. To formally certify this approximation, we leverage Satisfiability Modulo Theories (SMT) solvers to bound the residual error of the HJ-based loss function across the domain of interest. Leveraging Counter Example Guided Inductive Synthesis (CEGIS), we close the loop around learning and verification, by fine-tuning the neural network on counterexamples found by the SMT solver, thus improving the accuracy of the learned reachable set. To the best of our knowledge, Certified Approximate Reachability (CARe) is the first approach to provide soundness guarantees on learned reachable sets of continuous dynamical systems.
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Recent approaches to leveraging deep learning for computing reachable sets of continuous-time dynamical systems have gained popularity over traditional level-set methods, as they overcome the curse of dimensionality. However, as with level-set methods, considerable care needs to be taken in limiting approximation errors, particularly since no guarantees are provided during training on the accuracy of the learned reachable set. To address this limitation, we introduce an ϵ-approximate Hamilton-Jacobi partial differential equation (HJ-PDE), which establishes a relationship between training loss and accuracy of the true reachable set. To formally certify this approximation, we leverage Satisfiability Modulo Theories (SMT) solvers to bound the residual error of the HJ-based loss function across the domain of interest. Leveraging Counter Example Guided Inductive Synthesis (CEGIS), we close the loop around learning and verification, by fine-tuning the neural network on counterexamples found by the SMT solver, thus improving the accuracy of the learned reachable set. To the best of our knowledge, Certified Approximate Reachability (CARe) is the first approach to provide soundness guarantees on learned reachable sets of continuous dynamical systems.
Unmanned aerial vehicles (UAVs) are becoming an integral part of both industry and society. In particular, the quadrotor is now invaluable across a plethora of fields and recent developments, such as the inclusion of aerial manipulators, only extends their versatility. As UAVs become more widespread, preventing loss-of-control (LOC) is an ever growing concern. Unfortunately, LOC is not clearly defined for quadrotors, or indeed, many other autonomous systems. Moreover, any existing definitions are often incomplete and restrictive. A novel metric, based on actuator capabilities, is introduced to detect LOC in quadrotors. The potential of this metric for LOC detection is demonstrated through both simulated and real quadrotor flight data. It is able to detect LOC induced by actuator faults without explicit knowledge of the occurrence and nature of the failure. The proposed metric is also sensitive enough to detect LOC in more nuanced cases, where the quadrotor remains undamaged but nevertheless losses control through an aggressive yawing manoeuvre. As the metric depends only on system and actuator models, it is sufficiently general to be applied to other systems.
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Unmanned aerial vehicles (UAVs) are becoming an integral part of both industry and society. In particular, the quadrotor is now invaluable across a plethora of fields and recent developments, such as the inclusion of aerial manipulators, only extends their versatility. As UAVs become more widespread, preventing loss-of-control (LOC) is an ever growing concern. Unfortunately, LOC is not clearly defined for quadrotors, or indeed, many other autonomous systems. Moreover, any existing definitions are often incomplete and restrictive. A novel metric, based on actuator capabilities, is introduced to detect LOC in quadrotors. The potential of this metric for LOC detection is demonstrated through both simulated and real quadrotor flight data. It is able to detect LOC induced by actuator faults without explicit knowledge of the occurrence and nature of the failure. The proposed metric is also sensitive enough to detect LOC in more nuanced cases, where the quadrotor remains undamaged but nevertheless losses control through an aggressive yawing manoeuvre. As the metric depends only on system and actuator models, it is sufficiently general to be applied to other systems.
Conference paper
(2024)
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Prashant Solanki, Jasper J. Van Beers, Anahita Jamshidnejad, Coen C. De Visser
Ensuring safety in autonomous systems is essential as they become more integrated with modern society. One way to accomplish this is to identify and maintain a safe operating space. To this end, much effort has been devoted in the field of reachability analysis to obtaining control-invariant sets which ensure that a system inside of these sets can remain in these sets, and are thus essential for guaranteeing a system's safety. However, control invariance does not imply that a system can move from any state in the control-invariant set to any other state in the control-invariant set, within a given time horizon. In this paper, we develop an algorithm to obtain a control-invariant set that allows a given system to move from any state in the set to any other state in the set within a given time horizon without having to leave the set. We call this the 'maneuver set', M. We substantiate the algorithm's efficacy through mathematical proof, affirming that the maneuver set obtained through the algorithm is indeed control-invariant. Furthermore, we prove that the system is indeed able to move from any state within this set to any other state in the set. To illustrate the use of our algorithm, we provide the numerical example of a Dubins car, utilising Hamilton-Jacobi-Bellman reachability analysis along with the proposed algorithm in order to obtain M.
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Ensuring safety in autonomous systems is essential as they become more integrated with modern society. One way to accomplish this is to identify and maintain a safe operating space. To this end, much effort has been devoted in the field of reachability analysis to obtaining control-invariant sets which ensure that a system inside of these sets can remain in these sets, and are thus essential for guaranteeing a system's safety. However, control invariance does not imply that a system can move from any state in the control-invariant set to any other state in the control-invariant set, within a given time horizon. In this paper, we develop an algorithm to obtain a control-invariant set that allows a given system to move from any state in the set to any other state in the set within a given time horizon without having to leave the set. We call this the 'maneuver set', M. We substantiate the algorithm's efficacy through mathematical proof, affirming that the maneuver set obtained through the algorithm is indeed control-invariant. Furthermore, we prove that the system is indeed able to move from any state within this set to any other state in the set. To illustrate the use of our algorithm, we provide the numerical example of a Dubins car, utilising Hamilton-Jacobi-Bellman reachability analysis along with the proposed algorithm in order to obtain M.
Ensuring the reliability and validity of data-driven quadrotor model predictions is essential for their accepted and practical use. This is especially true for grey- and black-box models wherein the mapping of inputs to predictions is not transparent and subsequent reliability notoriously difficult to ascertain. Nonetheless, such techniques are frequently and successfully used to identify quadrotor models. Prediction intervals (PIs) may be employed to provide insight into the consistency and accuracy of model predictions. This paper estimates such PIs for polynomial and Artificial Neural Network (ANN) quadrotor aerodynamic models. Two existing ANN PI estimation techniques - the bootstrap method and the quality driven method – are validated numerically for quadrotor aerodynamic models using an existing high-fidelity quadrotor simulation. Quadrotor aerodynamic models are then identified on real quadrotor flight data to demonstrate their utility and explore their sensitivity to model interpolation and extrapolation. It is found that the ANN-based PIs widen considerably when extrapolating and remain constant, or shrink, when interpolating. While this behaviour also occurs for the polynomial PIs, it is of lower magnitude. The estimated PIs establish probabilistic bounds within which the quadrotor model outputs will likely lie, subject to modelling and measurement uncertainties that are reflected through the PI widths.
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Ensuring the reliability and validity of data-driven quadrotor model predictions is essential for their accepted and practical use. This is especially true for grey- and black-box models wherein the mapping of inputs to predictions is not transparent and subsequent reliability notoriously difficult to ascertain. Nonetheless, such techniques are frequently and successfully used to identify quadrotor models. Prediction intervals (PIs) may be employed to provide insight into the consistency and accuracy of model predictions. This paper estimates such PIs for polynomial and Artificial Neural Network (ANN) quadrotor aerodynamic models. Two existing ANN PI estimation techniques - the bootstrap method and the quality driven method – are validated numerically for quadrotor aerodynamic models using an existing high-fidelity quadrotor simulation. Quadrotor aerodynamic models are then identified on real quadrotor flight data to demonstrate their utility and explore their sensitivity to model interpolation and extrapolation. It is found that the ANN-based PIs widen considerably when extrapolating and remain constant, or shrink, when interpolating. While this behaviour also occurs for the polynomial PIs, it is of lower magnitude. The estimated PIs establish probabilistic bounds within which the quadrotor model outputs will likely lie, subject to modelling and measurement uncertainties that are reflected through the PI widths.
Loss of control (LOC) is a prevalent cause of drone crashes. Onboard prevention systems should be designed requiring low computing power, for which data-driven techniques provide a promising solution. This study proposes the use of recurrent neural networks (RNNs) for LOC prediction. Four architectures were trained in order to identify which RNN configuration is most suitable and if this model can predict LOC for changing aerodynamic characteristics, wind conditions, quadcopter types, and LOC events. One-hundred and seventy-two real-world LOC events were conducted using a 53 g Tiny Whoop, a 73 g URUAV UZ85, and a 265 g GEPRC CineGO quadcopter. For these flights, LOC was initiated by demanding an excessive yaw rate (2000 deg/s), which provokes an unrecoverable upset and subsequent crash. All RNNs were trained using only onboard sensor measurements. It was found that the commanded rotor values provided the clearest early warning signals for LOC because these values showed saturation before LOC. Moreover, all four architectures could correctly and reliably predict the impending LOC event 2 s before it actually occurred. Furthermore, to investigate generality of the methodology, the predictors were successfully applied to flight data in which the quadcopter mass, blade diameter, and blade count were varied.
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Loss of control (LOC) is a prevalent cause of drone crashes. Onboard prevention systems should be designed requiring low computing power, for which data-driven techniques provide a promising solution. This study proposes the use of recurrent neural networks (RNNs) for LOC prediction. Four architectures were trained in order to identify which RNN configuration is most suitable and if this model can predict LOC for changing aerodynamic characteristics, wind conditions, quadcopter types, and LOC events. One-hundred and seventy-two real-world LOC events were conducted using a 53 g Tiny Whoop, a 73 g URUAV UZ85, and a 265 g GEPRC CineGO quadcopter. For these flights, LOC was initiated by demanding an excessive yaw rate (2000 deg/s), which provokes an unrecoverable upset and subsequent crash. All RNNs were trained using only onboard sensor measurements. It was found that the commanded rotor values provided the clearest early warning signals for LOC because these values showed saturation before LOC. Moreover, all four architectures could correctly and reliably predict the impending LOC event 2 s before it actually occurred. Furthermore, to investigate generality of the methodology, the predictors were successfully applied to flight data in which the quadcopter mass, blade diameter, and blade count were varied.