arXiv subjects

Jasper van Beers

Publications and source records attributed to Jasper van Beers.

4 recordsLinked to original sources

arXiv2026

Reachability-Preserving Bellman Operator for the Discounted Reach-Cost Value Function: Uniting Hamilton-Jacobi Reachability and Reinforcement Learning

Hamilton-Jacobi (HJ) reachability provides rigorous safety and reachability guarantees for continuous-time dynamical systems, but its numerical solution suffers from the curse of dimensionality. Deep reinforcement learning (DRL), by contrast, offers scalable sample-based methods. However, RL is typically built around additive cumulative rewards; whereas, reachability objectives are inherently non-additive. This mismatch makes a direct bridge between HJ reachability and RL nontrivial. Recent discounted formulations have either introduced contraction by altering the original reachability semantics, or preserved exact semantics on the HJ side without a corresponding Bellman fixed-point characterization. In this paper, we close this gap by building on a semantics-preserving discounted reach-based value function and deriving a non-additive Bellman operator whose unique fixed point exactly matches the value function in the HJ formulation. We prove that discounting makes this operator contractive, yielding existence, uniqueness, and convergence of value iteration. Furthermore, we establish the equivalence between the HJ and Bellman characterizations, and show that RL can be interpreted as a sample-based approximation scheme for the same fixed-point equation. This yields a principled and semantically exact connection between HJ reachability and RL, enabling learning-based methods to approximate reachability value functions while preserving their safety-critical meaning. As a result, the proposed framework opens the door to scalable, data-driven computation of reachable sets and safety certificates in high-dimensional systems. Numerical experiments demonstrate close agreement with HJ solutions, confirm preservation of reachability semantics via alignment of zero level sets, and support the interpretation of reinforcement learning as a sample-based solver of the proposed Bellman operator.

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arXiv2026

Unifying Hamilton-Jacobi Reachability and Reinforcement Learning

We unify Hamilton-Jacobi (HJ) reachability and Reinforcement Learning (RL) through a proposed running cost formulation. We prove that the resultant travel-cost value function is the unique bounded viscosity solution of a time-dependent Hamilton-Jacobi Bellman (HJB) Partial Differential Equation (PDE) with zero terminal data, whose negative sublevel set equals the strict backward-reachable tube. Using a forward reparameterization and a contraction inducing Bellman update, we show that fixed points of small-step RL value iteration converge to the viscosity solution of the forward discounted HJB. Experiments on a classical benchmark validate this connection by demonstrating convergence of learned value functions toward semi-Lagrangian HJB solutions and by quantifying approximation error across the state space. These results empirically support the theoretical analysis, showing that the proposed framework preserves reachability-based safety semantics while remaining compatible with deep RL implementations.

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arXiv2024

A novel metric for detecting quadrotor loss-of-control

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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arXiv2024

Peaking into the Black-box: Prediction Intervals Give Insight into Data-driven Quadrotor Model Reliability

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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