arXiv subjects

Sander Tonkens

Publications and source records attributed to Sander Tonkens.

12 recordsLinked to original sources

arXiv2026

Steering with Contingencies: Combinatorial Stabilization and Reach-Avoid Filters

In applications such as autonomous landing and navigation, it is often desirable to steer toward a target while retaining the ability to divert to at least $r$ (out of $p$) alternative sites if conditions change. In this work, we formalize this combinatorial contingency requirement and develop tractable control filters for enforcement. Combinatorial stabilization requires asymptotic stability of a selected equilibrium while ensuring the trajectory remains within the safe region of attraction of at least $r$-out-of-$p$ candidates. To enforce this requirement, we use control Lyapunov functions (CLFs) to construct regions of attraction, which are combined combinatorially within an optimization-based filter. Combinatorial targeting extends this framework to finite-horizon problems using Hamilton-Jacobi backward reach-avoid sets, accommodating shrinking reachable regions due to finite horizons or resource depletion. In both formulations, the resulting combinatorial stability filter and combinatorial reach-avoid filter require only $p+1$ constraints, preventing combinatorial blow-up and enabling safe real-time switching between targets. The framework is demonstrated on two examples where the filters ensure steering with contingency and enable safe diversion.

eess.SY↗

arXiv2026

Refining Almost-Safe Value Functions on the Fly

Control Barrier Functions (CBFs) are a powerful tool for ensuring robotic safety, but designing or learning valid CBFs for complex systems is a significant challenge. While Hamilton-Jacobi Reachability provides a formal method for synthesizing safe value functions, it scales poorly and is typically performed offline, limiting its applicability in dynamic environments. This paper bridges the gap between offline synthesis and online adaptation. We introduce refineCBF for refining an approximate CBF - whether analytically derived, learned, or even unsafe - via warm-started HJ reachability. We then present its computationally efficient successor, HJ-Patch, which accelerates this process through localized updates. Both methods guarantee the recovery of a safe value function and can ensure monotonic safety improvements during adaptation. Our experiments validate our framework's primary contribution: in-the-loop, real-time adaptation, in simulation (with detailed value function analysis) and on physical hardware. Our experiments on ground vehicles and quadcopters show that our framework can successfully adapt to sudden environmental changes, such as new obstacles and unmodeled wind disturbances, providing a practical path toward deploying formally guaranteed safety in real-world settings.

cs.RO↗

arXiv2025

MADR: MPC-guided Adversarial DeepReach

Hamilton-Jacobi (HJ) Reachability offers a framework for generating safe value functions and policies in the face of adversarial disturbance, but is limited by the curse of dimensionality. Physics-informed deep learning is able to overcome this infeasibility, but itself suffers from slow and inaccurate convergence, primarily due to weak PDE gradients and the complexity of self-supervised learning. A few works, recently, have demonstrated that enriching the self-supervision process with regular supervision (based on the nature of the optimal control problem), greatly accelerates convergence and solution quality, however, these have been limited to single player problems and simple games. In this work, we introduce MADR: MPC-guided Adversarial DeepReach, a general framework to robustly approximate the two-player, zero-sum differential game value function. In doing so, MADR yields the corresponding optimal strategies for both players in zero-sum games as well as safe policies for worst-case robustness. We test MADR on a multitude of high-dimensional simulated and real robotic agents with varying dynamics and games, finding that our approach significantly out-performs state-of-the-art baselines in simulation and produces impressive results in hardware.

cs.RO↗

arXiv2025

From Space to Time: Enabling Adaptive Safety with Learned Value Functions via Disturbance Recasting

The widespread deployment of autonomous systems in safety-critical environments such as urban air mobility hinges on ensuring reliable, performant, and safe operation under varying environmental conditions. One such approach, value function-based safety filters, minimally modifies a nominal controller to ensure safety. Recent advances leverage offline learned value functions to scale these safety filters to high-dimensional systems. However, these methods assume detailed priors on all possible sources of model mismatch, in the form of disturbances in the environment -- information that is rarely available in real world settings. Even in well-mapped environments like urban canyons or industrial sites, drones encounter complex, spatially-varying disturbances arising from payload-drone interaction, turbulent airflow, and other environmental factors. We introduce SPACE2TIME, which enables safe and adaptive deployment of offline-learned safety filters under unknown, spatially-varying disturbances. The key idea is to reparameterize spatial variations in disturbance as temporal variations, enabling the use of precomputed value functions during online operation. We validate SPACE2TIME on a quadcopter through extensive simulations and hardware experiments, demonstrating significant improvement over baselines.

cs.RO↗

arXiv2025

Dual-Objective Reinforcement Learning with Novel Hamilton-Jacobi-Bellman Formulations

Hard constraints in reinforcement learning (RL) often degrade policy performance. Lagrangian methods offer a way to blend objectives with constraints, but require intricate reward engineering and parameter tuning. In this work, we extend recent advances that connect Hamilton-Jacobi (HJ) equations with RL to propose two novel value functions for dual-objective satisfaction. Namely, we address: 1) the Reach-Always-Avoid (RAA) problem -- of achieving distinct reward and penalty thresholds -- and 2) the Reach-Reach (RR) problem -- of achieving thresholds of two distinct rewards. In contrast with temporal logic approaches, which typically involve representing an automaton, we derive explicit, tractable Bellman forms in this context via decomposition. Specifically, we prove that the RAA and RR problems may be rewritten as compositions of previously studied HJ-RL problems. We leverage our analysis to propose a variation of Proximal Policy Optimization (DOHJ-PPO), and demonstrate that it produces distinct behaviors from previous approaches, outcompeting a number of baselines in success, safety and speed across a range of tasks for safe-arrival and multi-target achievement.

cs.AI↗

arXiv2025

Reachability Barrier Networks: Learning Hamilton-Jacobi Solutions for Smooth and Flexible Control Barrier Functions

Recent developments in autonomous driving and robotics underscore the necessity of safety-critical controllers. Control barrier functions (CBFs) are a popular method for appending safety guarantees to a general control framework, but they are notoriously difficult to generate beyond low dimensions. Existing methods often yield non-differentiable or inaccurate approximations that lack integrity, and thus fail to ensure safety. In this work, we use physics-informed neural networks (PINNs) to generate smooth approximations of CBFs by computing Hamilton-Jacobi (HJ) optimal control solutions. These reachability barrier networks (RBNs) avoid traditional dimensionality constraints and support the tuning of their conservativeness post-training through a parameterized discount term. To ensure robustness of the discounted solutions, we leverage conformal prediction methods to derive probabilistic safety guarantees for RBNs. We demonstrate that RBNs are highly accurate in low dimensions, and safer than the standard neural CBF approach in high dimensions. Namely, we showcase the RBNs in a 9D multi-vehicle collision avoidance problem where it empirically proves to be 5.5x safer and 1.9x less conservative than the neural CBFs, offering a promising method to synthesize CBFs for general nonlinear autonomous systems.

cs.RO↗

arXiv2025

Back to Base: Towards Hands-Off Learning via Safe Resets with Reach-Avoid Safety Filters

Designing controllers that accomplish tasks while guaranteeing safety constraints remains a significant challenge. We often want an agent to perform well in a nominal task, such as environment exploration, while ensuring it can avoid unsafe states and return to a desired target by a specific time. In particular we are motivated by the setting of safe, efficient, hands-off training for reinforcement learning in the real world. By enabling a robot to safely and autonomously reset to a desired region (e.g., charging stations) without human intervention, we can enhance efficiency and facilitate training. Safety filters, such as those based on control barrier functions, decouple safety from nominal control objectives and rigorously guarantee safety. Despite their success, constructing these functions for general nonlinear systems with control constraints and system uncertainties remains an open problem. This paper introduces a safety filter obtained from the value function associated with the reach-avoid problem. The proposed safety filter minimally modifies the nominal controller while avoiding unsafe regions and guiding the system back to the desired target set. By preserving policy performance while allowing safe resetting, we enable efficient hands-off reinforcement learning and advance the feasibility of safe training for real world robots. We demonstrate our approach using a modified version of soft actor-critic to safely train a swing-up task on a modified cartpole stabilization problem.

eess.SY↗

arXiv2023

Categorical Traffic Transformer: Interpretable and Diverse Behavior Prediction with Tokenized Latent

Adept traffic models are critical to both planning and closed-loop simulation for autonomous vehicles (AV), and key design objectives include accuracy, diverse multimodal behaviors, interpretability, and downstream compatibility. Recently, with the advent of large language models (LLMs), an additional desirable feature for traffic models is LLM compatibility. We present Categorical Traffic Transformer (CTT), a traffic model that outputs both continuous trajectory predictions and tokenized categorical predictions (lane modes, homotopies, etc.). The most outstanding feature of CTT is its fully interpretable latent space, which enables direct supervision of the latent variable from the ground truth during training and avoids mode collapse completely. As a result, CTT can generate diverse behaviors conditioned on different latent modes with semantic meanings while beating SOTA on prediction accuracy. In addition, CTT's ability to input and output tokens enables integration with LLMs for common-sense reasoning and zero-shot generalization.

cs.LG↗

arXiv2023

Patching Approximately Safe Value Functions Leveraging Local Hamilton-Jacobi Reachability Analysis

Safe value functions, such as control barrier functions, characterize a safe set and synthesize a safety filter, overriding unsafe actions, for a dynamic system. While function approximators like neural networks can synthesize approximately safe value functions, they typically lack formal guarantees. In this paper, we propose a local dynamic programming-based approach to "patch" approximately safe value functions to obtain a safe value function. This algorithm, HJ-Patch, produces a novel value function that provides formal safety guarantees, yet retains the global structure of the initial value function. HJ-Patch modifies an approximately safe value function at states that are both (i) near the safety boundary and (ii) may violate safety. We iteratively update both this set of "active" states and the value function until convergence. This approach bridges the gap between value function approximation methods and formal safety through Hamilton-Jacobi (HJ) reachability, offering a framework for integrating various safety methods. We provide simulation results on analytic and learned examples, demonstrating HJ-Patch reduces the computational complexity by 2 orders of magnitude with respect to standard HJ reachability. Additionally, we demonstrate the perils of using approximately safe value functions directly and showcase improved safety using HJ-Patch.

cs.RO↗

arXiv2022

Refining Control Barrier Functions through Hamilton-Jacobi Reachability

Safety filters based on Control Barrier Functions (CBFs) have emerged as a practical tool for the safety-critical control of autonomous systems. These approaches encode safety through a value function and enforce safety by imposing a constraint on the time derivative of this value function. However, synthesizing a valid CBF that is not overly conservative in the presence of input constraints is a notorious challenge. In this work, we propose refining a candidate CBF using formal verification methods to obtain a valid CBF. In particular, we update an expert-synthesized or backup CBF using dynamic programming (DP) based reachability analysis. Our framework, refineCBF, guarantees that with every DP iteration the obtained CBF is provably at least as safe as the prior iteration and converges to a valid CBF. Therefore, refineCBF can be used in-the-loop for robotic systems. We demonstrate the practicality of our method to enhance safety and/or reduce conservativeness on a range of nonlinear control-affine systems using various CBF synthesis techniques in simulation.

cs.RO↗

arXiv2021

Optimizing Vaccine Allocation Strategies in Pandemic Outbreaks: An Optimal Control Approach

Since early 2020, the world has been dealing with a raging pandemic outbreak: COVID-19. A year later, vaccines have become accessible, but in limited quantities, so that governments needed to devise a strategy to decide which part of the population to prioritize when assigning the available doses, and how to manage the interval between doses for multi-dose vaccines. In this paper, we present an optimization framework to address the dynamic double-dose vaccine allocation problem whereby the available vaccine doses must be administered to different age-groups to minimize specific societal objectives. In particular, we first identify an age-dependent Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model including an extension capturing partially and fully vaccinated people, whereby we account for age-dependent immunity and infectiousness levels together with disease severity. Second, we leverage our model to frame the dynamic age-dependent vaccine allocation problem for different societal objectives, such as the minimization of infections or fatalities, and solve it with nonlinear programming techniques. Finally, we carry out a numerical case study with real-world data from The Netherlands. Our results show how different societal objectives can significantly alter the optimal vaccine allocation strategy. For instance, we find that minimizing the overall number of infections results in delaying second doses, whilst to minimize fatalities it is important to fully vaccinate the elderly first.

q-bio.PE↗

arXiv2021

Soft Robot Optimal Control Via Reduced Order Finite Element Models

Finite element methods have been successfully used to develop physics-based models of soft robots that capture the nonlinear dynamic behavior induced by continuous deformation. These high-fidelity models are therefore ideal for designing controllers for complex dynamic tasks such as trajectory optimization and trajectory tracking. However, finite element models are also typically very high-dimensional, which makes real-time control challenging. In this work we propose an approach for finite element model-based control of soft robots that leverages model order reduction techniques to significantly increase computational efficiency. In particular, a constrained optimal control problem is formulated based on a nonlinear reduced order finite element model and is solved via sequential convex programming. This approach is demonstrated through simulation of a cable-driven soft robot for a constrained trajectory tracking task, where a 9768-dimensional finite element model is used for controller design.

cs.RO↗