arXiv subjects

Somil Bansal

Publications and source records attributed to Somil Bansal.

At least 19 recordsLinked to original sources

arXiv2026

Unified Overview of Safety Certificate Functions: Techniques from Hamilton--Jacobi Reachability and Control Barrier Functions

Safety is a central concern in modern autonomous systems. Safety certificates---functions whose existence guarantees that a system meets its safety specification---have long been used as a principled tool for rigorously reasoning about safety. Methods for synthesizing such certificates are scattered across research areas, with little guidance on when to use a particular approach. This tutorial provides a holistic treatment of safety certificate synthesis centered on two widely used families: Hamilton--Jacobi (HJ) reachability analysis and control barrier functions (CBFs). For each family of methods, we first introduce its general formulation, along with classical and learning-based tools for certificate synthesis. Next, we introduce two benchmark problems consisting of vehicle systems of differing complexity to assess the certificate quality of different synthesis methods and their effectiveness in safety-critical control. We use these benchmarks to compare various methods and provide practical guidance for selecting an approach.

cs.RO↗

arXiv2026

Gradient-Free Neural Hamilton-Jacobi Reachability for Scalable Safety-Critical Control

Hamilton-Jacobi (HJ) reachability provides a principled framework for synthesizing safety certificates and robust controllers for safety-critical robotic systems. However, applying reachability analysis to high-dimensional nonlinear systems remains challenging: classical grid-based solvers suffer from the curse of dimensionality, continuous-time neural solvers require accurate spatial value gradients, and reinforcement-learning-based approaches often suffer from weak boundary anchoring and non-stationary adversarial policy optimization. We propose a discrete-time neural reachability framework for control-disturbance-affine systems that learns backward reachable tubes (BRTs) and backward reach-avoid tubes (BRATs) through Bellman-Isaacs value propagation. Our key idea is to combine equation-driven self-supervision with structured policy learning: rather than computing explicit PDE-gradients, we exploit the bang-bang structure of optimal safety interventions to construct approximate teacher actions from gradient-free value probes, converting adversarial actor learning into supervised policy learning. To stabilize long-horizon value propagation, we leverage the learned actor to train the value function backward from the terminal boundary using a windowed temporal curriculum, where each window is used as the boundary condition for the next window. Across benchmark problems up to 80 dimensions, our method learns accurate reachability value functions while improving stability over existing learning-based solvers. We further demonstrate observation-space scalability on F1-tenth racing with over 16,000-dimensional egocentric inputs. The learned safety filter generalizes zero-shot to unseen tracks and transfers to a physical RC car, achieving real-time robust collision avoidance.

cs.RO↗

arXiv2026

Where Small Mistakes Matter: Quantifying State Criticality for Imitation Learning

Imitation learning typically treats every demonstration state as equally important, optimizing a behavior-cloning objective uniformly across the dataset. Yet not all states are created equal: in a small number of critical states, even a slight deviation from the expert action can lead to a failure, while in many other states such errors are recoverable and inconsequential. We formalize state criticality in imitation learning as the worst-case degradation in downstream value induced by a bounded perturbation of the expert action at a given state. We then propose SCRIM, a practical State CRIticality Measure that estimates this quantity by training an adversarial disturbance policy and a value critic around a fixed imitation policy. SCRIM assigns each demonstration state a score reflecting how vulnerable the task outcome is to small, policy-relevant action errors. We show that these scores can be used to reweight behavior-cloning losses, improving imitation at consequential states and increasing overall task performance. We further show that SCRIM enables data curation by selecting compact, high-value subsets of demonstrations that preserve performance while substantially reducing the amount of training data. We evaluate SCRIM across various simulated and real-world robotic manipulation tasks, and demonstrate that SCRIM improves policy training, enables efficient data selection, and provides interpretable insights into which moments in a demonstration are most critical for task success. Project website: https://sia-lab-git.github.io/SCRIM/

cs.LG↗

arXiv2026

Active Reachability Learning for Humanoid Recoverability Monitoring

Deploying humanoid task policies requires reliable runtime monitors that anticipate unrecoverable falls in time to trigger a fallback. We formulate this task as learning the stochastic, finite-horizon recoverability envelope of a given fallback policy. Synthesizing this monitor is challenging: existing methods assume training data naturally covers the recoverability envelope, yet acquiring such data remains a major bottleneck for contact-rich systems. Consequently, they recover only a fraction of the true envelope, leaving them prone to optimistic hallucinations for out-of-distribution (OOD) inputs. We resolve this via a unified framework that iterates between value learning and active exploration. Data exploration is reframed as a reach-avoid problem, where an uncertainty-guided explorer systematically uncovers unseen states while avoiding confidently unrecoverable regions. This loop is further supported by a combined Temporal Difference and Monte Carlo objective for accurate in-distribution value prediction and reliable uncertainty estimation. By explicitly treating the remaining high-uncertainty regions as unrecoverable, the monitor mitigates optimistic OOD hallucinations. Evaluated on stochastic benchmarks and a 29-DoF Unitree G1 humanoid, our approach drastically improves monitor coverage and accuracy and successfully transfers zero-shot to real-world hardware.

cs.RO↗

arXiv2026

Back on Track: Deployment-time Policy Improvement via World Model Planning

State-of-the-art visuomotor policies are increasingly capable of executing complex tasks, yet can fail during deployment in ways they cannot predict or recover from on their own. Improving their performance and robustness typically requires collecting more data, retraining, or modifying the policy architecture, all of which are time- and resource-intensive in practice. We instead propose an offline-trained monitoring-and-intervention framework that improves a policy during deployment using only black-box query access. From a limited set of labeled on-policy rollouts, we learn a policy-conditioned liveness value that measures the nominal policy's progress toward task completion; we additionally train a compact latent world model using these rollouts together with play data. At deployment, the liveness value continuously monitors execution. When it detects a loss of progress, a short-horizon planner searches the world model for corrective actions using the same value as its planning objective, after which control returns to the nominal policy. We evaluate our method on the LIBERO-Goal task suite and on a Franka Panda manipulator, using the vision-language-action model $π_{0.5}$ and a diffusion policy as nominal policies, and demonstrate significant improvements in task success rates, while supporting real-time control. Additional results and videos are available on the project website (https://policy-improvement-wm.pages.dev/).

cs.RO↗

arXiv2026

Context-Conditioned Hamilton-Jacobi Reachability for Adaptive Safety Filtering

Hamilton-Jacobi reachability constructs safety certificates for specified dynamics and safety constraints, tying each certificate to the deployment context for which it is synthesized. We ask whether a single certificate can instead represent a family of context-dependent safety problems and be queried across deployment conditions without re-synthesis. We learn a backward reachable tube for an eight-state vehicle model conditioned on local boundary geometry, friction coefficient, and adversarial disturbance scale. Geometry enters through an ego-frame boundary observation that defines the local containment constraint, while friction and disturbance scale enter as explicit operating-condition variables. This allows the same value function to be queried across friction coefficients from 0.4 to 2.0 and on geometries absent from synthesis. On 11 held-out evaluation geometries, the certificate maintains containment across the full tested friction range, including simultaneous geometry and grip shifts, while remaining within 1.2 percentage points in intervention rate and 0.09 m/s in speed of certificates re-synthesized with knowledge of the test geometry. We then deploy the certificate as a sampled discrete-time control barrier function filter on a full-scale vehicle near the handling limit. Lateral containment holds in every hardware session under both adversarial driving and autonomous racing, with 99th-percentile acceleration magnitude reaching 0.99 g. Across three certificates evaluated under a fixed autonomous racing controller, lap time varies by only 3.1%, demonstrating that a context-conditioned reachability certificate can transfer to deployment geometries absent from synthesis with modest performance cost.

eess.SY↗

arXiv2026

When Reasoning Helps Action: Monitoring and Steering Chain-of-Thought in Vision-Language-Action Policies

Reasoning-enabled VLA policies expose chain-of-thought (CoT) traces that appear to explain and guide their actions, creating a potential interface for runtime safety through reasoning monitoring and correction. In this work, we define and operationalize two evaluation axes for assessing when this interface can improve embodied behavior: correctability, which measures whether unreliable reasoning can be detected and improved during generation, and actionability, which measures whether reasoning corrections produce behaviorally meaningful changes in the intended direction. To enable correctability, we introduce Token-level Reward for Utility-Steered Chain-of-Thought (TRUST), an offline-trained value model that predicts eventual reasoning correctness from partial prefixes and uses these estimates to monitor and selectively steer reasoning generation in frozen VLA policies. On the Alpamayo 1.5 driving VLA, TRUST monitors correctness with 88.9% accuracy and improves reasoning correctness from 75.9% to 90.0%. On a baseline-defined challenging subset in AlpaSim, TRUST reduces collision rate by 30.4% and maximum trajectory error by 11.5% relative to the unsteered policy, outperforming a compute-matched Best-of-4 baseline. On the DeepThinkVLA manipulation VLA, TRUST improves the correctness of grasp-state claims from 69.3% to 90.2% and action-choice claims from 68.8% to 85.9%, yet closed-loop task performance on LIBERO-Plus remains largely unchanged. Empirical analysis reveals intent-consistent behavioral effects in Alpamayo 1.5 but limited effects in DeepThinkVLA, helping interpret these different task-level outcomes. Together, our results show that gains in reasoning correctness do not automatically imply gains in embodied performance, motivating evaluation of correctability and actionability when using CoT as a runtime safety interface.

cs.RO↗

arXiv2026

When World Models Lie: Adaptive Safety Analysis Under Wrong Imaginations

World models offer a powerful substrate for safety reasoning in high-dimensional robotic systems, but they are also fallible: their predictions can be biased, miscalibrated, or confidently wrong. This creates a central challenge for latent-space safety filters, which often learn Hamilton-Jacobi safety value functions on the dynamics of a world model. If the world model is incorrect, the resulting value function can inherit its errors and produce overconfident safety estimates. Existing latent safety filters often rely on auxiliary signals such as ensemble disagreement or value-target consistency residuals for adaptation, but these signals can remain small even when the world model's predictions deviate from observations. We propose an adaptive latent safety filter that calibrates safety reasoning using directly observed world-model error. Our method uses Adaptive Conformal Inference to construct online uncertainty sets from discrepancies between predicted and observation-inferred latent states, then evaluates safety pessimistically by minimizing the learned value function over these sets. This allows the filter to remain minimally conservative when the world model is accurate, while becoming more cautious when observations reveal model mismatch. We provide a finite-time coverage guarantee for the adaptive uncertainty radius. Through simulation and hardware experiments, we show that our method significantly reduces failures relative to state-of-the-art latent safety filters while preserving task completion.

cs.RO↗

arXiv2026

Hamilton-Jacobi Reachability for Hybrid Systems: Unified Goal-Driven Control with Safety Guarantees

Hybrid dynamical systems provide a powerful modeling framework for robotic systems, particularly in contact-rich environments. However, ensuring safety and performance in such systems remains challenging due to the intricate coupling between continuous dynamics and discrete mode transitions. In this work, we extend classical Hamilton-Jacobi (HJ) reachability analysis, a formal verification method for continuous-time nonlinear systems, to hybrid dynamical systems. Our framework characterizes safe sets for hybrid systems through a generalized value function defined over both discrete and continuous states while accounting for control constraints and model uncertainty. We additionally provide a numerical algorithm to compute this value function. Building on these safe sets, we propose two different mechanisms to integrate performance objectives. First, we introduce a hybrid least-restrictive safety filter that intervenes on both the discrete and continuous components of a nominal controller only when necessary to avoid unsafe states, thereby preserving nominal behavior whenever possible. Second, we formulate and compute hybrid backward reach-avoid tubes, enabling the simultaneous enforcement of safety and goal-reaching behavior, an extension not previously addressed within hybrid HJ reachability. This enables the synthesis of continuous and discrete control policies that guarantee both safety and task completion. We validate our framework through simulation studies and real-world experiments on a quadrupedal robot, demonstrating its effectiveness in hybrid mode planning and safety-critical applications.

cs.RO↗

arXiv2026

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↗

arXiv2026

Unsupervised Discovery of Failure Taxonomies from Deployment Logs

As robotic systems become increasingly integrated into real-world environments, ranging from autonomous vehicles to household assistants, they inevitably encounter diverse and unstructured scenarios that lead to failures. While such failures pose safety and reliability challenges, they also provide rich perceptual data for improving system robustness. However, manually analyzing large-scale failure datasets is impractical and does not scale. In this work, we introduce the problem of unsupervised discovery of failure taxonomies from large volumes of raw failure logs, aiming to obtain semantically coherent and actionable failure modes directly from perceptual trajectories. Our approach first infers structured failure explanations from multimodal inputs using vision language reasoning, then clusters them in the resulting semantic reasoning space, discovering recurring failure modes rather than isolated episode-level descriptions. We evaluate our method across robotic manipulation, indoor navigation, and autonomous driving domains, demonstrating that the discovered taxonomies are consistent, interpretable, and useful in practice. In particular, we show that structured failure taxonomies guide targeted data collection for offline policy refinement and enhance runtime failure monitoring systems. Website: https://mllm-failure-clustering.github.io/

cs.RO↗

arXiv2026

MAD-PINN: A Decentralized Physics-Informed Machine Learning Framework for Safe and Optimal Multi-Agent Control

Co-optimizing safety and performance in large-scale multi-agent systems remains a fundamental challenge. Existing approaches based on multi-agent reinforcement learning (MARL), safety filtering, or Model Predictive Control (MPC) either lack strict safety guarantees, suffer from conservatism, or fail to scale effectively. We propose MAD-PINN, a decentralized physics-informed machine learning framework for solving the multi-agent state-constrained optimal control problem (MASC-OCP). Our method leverages an epigraph-based reformulation of SC-OCP to simultaneously capture performance and safety, and approximates its solution via a physics-informed neural network. Scalability is achieved by training the SC-OCP value function on reduced-agent systems and deploying them in a decentralized fashion, where each agent relies only on local observations of its neighbours for decision-making. To further enhance safety and efficiency, we introduce an Hamilton-Jacobi (HJ) reachability-based neighbour selection strategy to prioritize safety-critical interactions, and a receding-horizon policy execution scheme that adapts to dynamic interactions while reducing computational burden. Experiments on multi-agent navigation tasks demonstrate that MAD-PINN achieves superior safety-performance trade-offs, maintains scalability as the number of agents grows, and consistently outperforms state-of-the-art baselines.

cs.RO↗

arXiv2026

Offline Policy Evaluation for Manipulation Policies via Discounted Liveness Formulation

Policy evaluation is a fundamental component of the development and deployment pipeline for robotic policies. In modern manipulation systems, this problem is particularly challenging: rewards are often sparse, task progression of evaluation rollouts are often non-monotonic as the policies exhibit recovery behaviors, and evaluation rollouts are necessarily of finite length. This finite length introduces truncation bias, breaking the infinite-horizon assumptions underlying standard methods relying on Bellman equations/principle of optimality. In this work, we propose a framework for offline policy evaluation from sparse rewards based on a liveness-based Bellman operator. Our formulation interprets policy evaluation as a task-completion problem and yields a conservative fixed-point value function that is robust to finite-horizon truncation. We analyze the theoretical properties of the proposed operator, including contraction guarantees, and show how it encodes task progression while mitigating truncation bias. We evaluate our method on two simulated manipulation tasks using both a Vision-Language-Action model and a diffusion policy, and a cloth folding task using human demonstrations. Empirical results demonstrate that our approach more accurately reflects task progress and substantially reduces truncation bias, outperforming classical baselines such as TD(0) and Monte Carlo policy evaluation.

cs.RO↗

arXiv2026

Neural Backward Reach-Avoid Tubes with MPC Supervision for High-Dimensional Systems: An Application to Safe Spacecraft Docking

Autonomous spacecraft docking requires control policies that simultaneously ensure collision avoidance and target reachability under coupled, high-dimensional translational-rotational dynamics. Hamilton-Jacobi (HJ) reachability provides formal reach-avoid guarantees, but classical solvers are limited to low-dimensional systems. Learning-based approaches have begun to scale HJ analysis, yet they struggle in reach-avoid settings, especially where goal and failure sets are tightly coupled, as in docking. We propose a learning-based Backward Reach-Avoid Tube (BRAT) framework that addresses this challenge by tightly integrating HJ structure with MPC-based supervision. In the offline phase, we train a neural approximation of the HJ value function using PDE-based losses augmented with curriculum-driven MPC supervision, which provides informative value targets and stabilizes training in regions where purely PDE-based methods fail. In the online phase, the learned value function is deployed through two real-time controllers: (i) a value gradient-driven controller, and (ii) a value-function-augmented terminal MPC that explicitly enforces reachability at the horizon. We evaluate the proposed method on a 6D planar docking problem against grid-based ground truth and then scale to the full 13D system. Across both settings, our approach outperforms existing methods in success rate and computational efficiency.

cs.RO↗

arXiv2026

Using Language Models as Closed-Loop High-Level Planners for Robotics Applications: A Brief Overview and Benchmarks

Large Language Models (LLMs) and Vision Language Models (VLMs) have become popular tools for embodied high-level planning. However, their deployment in black-box settings often leads to unpredictable or costly errors. To harness their capabilities more reliably in robotic systems, we empirically investigate practical strategies for integrating language models as closed-loop planners. Concretely, we study how the control horizon and warm-starting impact the performance of language model-based planners. We design and conduct controlled experiments to extract actionable insights, providing recommendations that can help improve the performance and robustness of language model-based embodied planning. The full implementation and experiments are available on the project website

cs.RO↗

arXiv2026

Cooptimizing Safety and Performance Using Safety Value-Constrained Model Predictive Control

Autonomous systems are increasingly deployed in real-world environments, where they must achieve high performance while maintaining safety under state and input constraints. Although Model Predictive Control (MPC) provides a principled framework for constrained optimal control, guaranteeing safety beyond its finite planning horizon remains a fundamental challenge. In this work, we augment MPC with a safety value function-based terminal constraint that enforces membership in a control-invariant safe set at the end of each planning horizon. This formulation enables real-time synthesis of trajectories that are both high-performing and provably safe. We show that, under an exact safety value function and a feasible initialization, the proposed MPC scheme is recursively feasible, thereby ensuring persistent safety. In contrast to traditional terminal set constructions that rely on local linearizations or conservative approximations, our approach incorporates a reachability-based safety value function for terminal constraints, yielding less conservative and more expressive safety guarantees. We validate the proposed framework through simulation and hardware experiments on a Flexiv Rizon 10s manipulator. Results demonstrate improved constraint satisfaction and robustness compared to standard state-constrained MPC and reactive safety filtering, while maintaining competitive task performance. The full implementation and experiments are available on the project website.

cs.RO↗

arXiv2026

Robust Verification of Controllers under State Uncertainty via Hamilton-Jacobi Reachability Analysis

As perception-based controllers for autonomous systems become increasingly popular in the real world, it is important that we can formally verify their safety and performance despite perceptual uncertainty. Unfortunately, the verification of such systems remains challenging, largely due to the complexity of the controllers, which are often nonlinear, nonconvex, learning-based, and/or black-box. Prior works propose verification algorithms that are based on approximate reachability methods, but they often restrict the class of controllers and systems that can be handled or result in overly conservative analyses. Hamilton-Jacobi (HJ) reachability analysis is a popular formal verification tool for general nonlinear systems that can compute optimal reachable sets under worst-case system uncertainties; however, its application to perception-based systems is currently underexplored. In this work, we propose RoVer-CoRe, a framework for the Robust Verification of Controllers via HJ Reachability. To the best of our knowledge, RoVer-CoRe is the first HJ reachability-based framework for the verification of perception-based systems under perceptual uncertainty. Our key insight is to concatenate the system controller, observation function, and the state estimation modules to obtain an equivalent closed-loop system that is readily compatible with existing reachability frameworks. Within RoVer-CoRe, we propose novel methods for formal safety verification and robust controller design. We demonstrate the efficacy of the framework in case studies involving aircraft taxiing and NN-based rover navigation. Code is available at the link in the footnote.

cs.RO↗

arXiv2026

Boundary Sampling to Learn Predictive Safety Filters via Pontryagin's Maximum Principle

Safety filters provide a practical approach for enforcing safety constraints in autonomous systems. While learning-based tools scale to high-dimensional systems, their performance depends on informative data that includes states likely to lead to constraint violation, which can be difficult to efficiently sample in complex, high-dimensional systems. In this work, we characterize trajectories that barely avoid safety violations using the Pontryagin Maximum Principle. These boundary trajectories are used to guide data collection for learned Hamilton-Jacobi Reachability, concentrating learning efforts near safety-critical states to improve efficiency. The learned Control Barrier Value Function is then used directly for safety filtering. Simulations and experimental validation on a shared-control automotive racing application demonstrate PMP sampling improves learning efficiency, yielding faster convergence, reduced failure rates, and improved safe set reconstruction, with wall times around 3ms.

cs.RO↗