arXiv subjects

Calin Belta

Publications and source records attributed to Calin Belta.

At least 19 recordsLinked to original sources

arXiv2026

Does Imitation Learning Preserve Temporal Robustness in Dexterous Manipulation? An Expert-Learner Comparison Across Task Execution Speeds

Dexterous manipulation policies learned by imitation are typically evaluated for robustness to variation in scenes, objects, or instructions, but their performance across task execution speeds is less often examined. This leaves open how much temporal robustness a learner retains relative to the expert it imitates. We compare an expert and learner under the same task conditions, initial-condition draws, and speedup factors. We instantiate the evaluation in ParcelStow, a contact-rich task in which the robot acquires, reorients, and inserts a parcel. The demonstrations span the speedup range for the manipulation phases after parcel acquisition. A scripted expert and an Action Chunking with Transformers (ACT) policy trained from the expert's demonstrations both achieve 100 percent task success at nominal speed. Their success rates diverge within the demonstrated range: at its maximum, expert success is 84 percent and ACT success is 53 percent. Two ACT policies with different parameter initializations show similar degradation, decreasing by 34 and 48 percentage points from nominal speed to the maximum demonstrated speed, compared with 16 points for the expert. Stage-level analysis shows that 35 of ACT's 47 failures at the maximum demonstrated speed are insertion misalignments. Under the relative-motion handoff, every ACT acquisition retains the parcel through reorientation and transfer in free space, but only 64 percent complete the overall task, compared with 95 percent after expert acquisition. Across all evaluated policies and speeds, none of the 414 acquisitions without force closure completes the task. Equal nominal task success therefore does not imply preservation of expert performance across execution speeds. Code, data, and evaluation scripts are available at https://github.com/coenwerem/parcelstow.

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arXiv2026

Exact Signed-Distance Control Barrier Functions via Minkowski Operations for Safe Navigation among Polytopes

Safely navigating polytopic environments while respecting the dynamics, control, and exact geometry of the underlying system is a challenge in robotics. Control barrier functions (CBFs) synthesize safe control policies by rendering the safe set forward invariant, but many existing CBF-based methods approximate polytopes using conservative smooth shapes, such as spheres or ellipsoids, to obtain explicit differentiable distance functions. In this article, we propose an exact Signed Distance Function (SDF) formulation for a {\it polytopic} robot and {\it polytopic} obstacles and integrate it with nonsmooth CBFs. Leveraging Minkowski operations, the proposed method computes the exact SDF via companion convex programs in both the collision-free (positive-sign) and in-collision (negative-sign) cases. Furthermore, by exploiting the convenient geometric properties of 2D Minkowski operations and the optimality conditions of the two companion convex programs, we derive a unified analytical expression for the gradient of the exact SDF via sensitivity analysis. The exact rotational gradient further reveals a previously masked class of local minima induced by the coupling between geometry and nonholonomic kinematics. We demonstrate the effectiveness of the proposed framework through a pure-translation case and three scenarios with unicycle models involving recovery from an unsafe initialization and single- and multiple-obstacle avoidance. Comparisons with baseline methods highlight how the proposed framework enables non-conservative maneuvers and safety recovery.

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arXiv2026

Grasp Execution Without a Planner: Configuration-Space Grasp Distance Fields with Certified Safety & Guaranteed Quality

Mainstream plan-then-track approaches to multifingered grasp execution entail selecting a grasp, planning a collision-free trajectory, and tracking the resulting trajectory via a feedback controller. Pose-estimation error during execution or scene motion can invalidate this open-loop commitment and trigger replanning. We thus present Grasp Distance Fields (GDFs), smooth softmin distances to finite sets of arm-hand grasp configurations. Using their negative gradients as feedback, we jointly select and execute grasps without planning a trajectory. A CBF-CLF quadratic program (QP) enforces self-collision, workspace, object, and obstacle-clearance constraints, while its CLF slack quantifies obstruction of task progress. We bound the softmin approximation error by $\log N/\rho$ and prove forward invariance of the filtered safe set. To handle changes in contact topology, we combine a hysteretic contact-mode transition with a wrench-quality CBF that limits degradation of the realized force-closure margin relative to hold onset. Using our method, a fixed-base manipulator and a Unitree G1 equipped with the same underactuated hand grasp and lift 46 of 50 test objects amid clutter and moving obstacles. The realized grasps also retain a median 94% of their synthesized quality margin, and each QP solve requires 0.09 ms within a 20 ms control interval. Project page: www.clintonenwerem.com/gdf.

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arXiv2026

FIRMGrasp: A Friction-Informed Risk Margin for Robust Grasp Synthesis

Classical grasp quality metrics assume one deterministic friction coefficient and therefore cannot assess whether a grasp maintains force closure across plausible friction values. We present FIRMGrasp, a family of grasp quality metrics that incorporates friction uncertainty through Conditional Value-at-Risk (CVaR). At confidence level $\beta$, we evaluate the force-closure margin at the mean of the adverse friction tail. This evaluation defines the risk-adjusted margin $\varepsilon^{(\beta)}$, the inscribed-ball radius of the corresponding grasp wrench space. We prove that $\varepsilon^{(\beta)}$ varies monotonically with $\beta$, remains differentiable in the grasp parameters, and certifies that any grasp with $\varepsilon^{(\beta)} > 0$ achieves force closure with probability at least $\beta$. Across 1,599 LEAP Hand and Allegro Hand grasps, $\varepsilon^{(\beta)}$ identifies friction-sensitive grasps that receive high nominal Ferrari-Canny scores, and 53% of the nominally force-closed grasps lose closure in the adverse friction tail. The nominal margin ranks a successful grasp above a failed grasp with probabilities of only 0.53 in the shake test and 0.67 in the pick test, whereas $\varepsilon^{(\beta)}$ achieves 0.63 and 0.78. At an adverse friction coefficient of 0.2, 70% of grasps with positive $\varepsilon^{(\beta)}$ withstand a simulated lift and lateral pull, compared with 25% of grasps with positive nominal margin and nonpositive $\varepsilon^{(\beta)}$. We also synthesize grasps with positive $\varepsilon^{(\beta)}$ for the RealHand L6 and LEAP Hand, both of which retain the object during adverse-friction lifts. In MuJoCo trials with the RealHand L6, 95% of grasps that establish contact and have positive $\varepsilon^{(\beta)}$ retain the object at the same adverse friction coefficient.

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arXiv2026

Learning-enabled Parameter Synthesis for Nonlinear Systems from Signal Temporal Logic

Signal Temporal Logic (STL) is increasingly used to describe interpretable objectives and constraints for optimal control and learning methods, especially when no target time series data is available. In this work, we propose to synthesize parameters for nonlinear systems that robustly satisfy continuous-time STL specifications for uncertain initial conditions. To this end, we use gradient-based optimization along with set-based reachability verification to efficiently learn in high-dimensional parameter spaces while providing provable satisfaction guarantees for the optimized parameters. We demonstrate the effectiveness and scalability of our method on three systems with up to 18 parameter dimensions.

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arXiv2026

EquiDexFlow: Contact-Grounded SE(3)-Equivariant Dexterous Grasp Generative Flows

Most learned dexterous grasp generators relegate contact forces to a downstream verification step, so a kinematically-plausible pose can still violate the conditions for a stable physical grasp. We address this with EquiDexFlow, an SE(3)-equivariant flow-matching model that jointly predicts wrist pose, joint angles, fingertip contacts, surface normals, and contact forces from an object point cloud. Our architecture projects contacts onto the object surface and forces into the Coulomb friction cone by construction, so placement and friction compliance hold without loss penalties. We prove end-to-end SE(3) equivariance and verify it empirically over 200 rotations, with wrist residuals below $0.04^\circ$ and exactly zero joint deviation. Trained on 8,100 force-closure grasps across 81 objects for the 16-DoF Allegro Hand, our model achieves zero friction violations, the best composite score, and the lowest wrench residual among all ablation variants. We retarget decoded fingertip contacts to a 16-DoF LEAP Hand via per-finger inverse kinematics, and our hardware-feasible refinement places every joint at least 5% inside its actuator envelope while preserving wrench balance. On the physical robot, retargeted EquiDexFlow-decoded grasps complete open-loop pick-and-hold trials on all six test objects, with every asymmetric object succeeding at both the canonical pose and a $120^\circ$ co-rotation. Videos, code, and checkpoints are available at https://equidexflow.github.io.

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arXiv2026

On the Stability and Realizability of Recurrent Polynomial Surrogate Ternary Logic Gate Networks

Recurrent Neural Networks (RNNs) can learn to predict Signal Temporal Logic (STL) verdicts online from partial trajectories, but deploying them as runtime monitors in safety-critical systems demands more than predictive accuracy. Standard RNN architectures offer no structural guarantee that outputs degrade gracefully under sensor degradation; a dropped input can silently flip a verdict from safe to unsafe. We introduce the Recurrent Differentiable Ternary Logic Gate Network (R-DTLGN), a recurrent architecture that operates over Kleene's three-valued logic $\{-1, 0, +1\}$, where $0$ explicitly represents unknown. The R-DTLGN trains through continuous polynomial surrogates and hardens to a discrete ternary logic circuit at inference. We analyze the hardened circuit through two gate vocabularies derived from two orderings on the ternary domain: numerically monotone gates ensure stable recurrent dynamics, while information-monotone gates, when present, guarantee principled abstention (unknown inputs never produce wrong outputs) and monotonicity in input certainty (more information can only improve the verdict). We show that the recurrent connections required by bounded STL operators use exclusively AND and OR, which belong to both vocabularies, linking the monitoring task to the architecture's guarantees. A realizability bound derived from the STL formula's temporal operators directly sizes the network's hidden state, replacing hyperparameter search with a formula-driven specification. We evaluate on STL specifications over D4RL PointMaze navigation data, testing prediction accuracy, degradation under predicate dropout, and the accuracy-versus-safety tradeoff between two label construction pipelines. The R-DTLGN is, to our knowledge, the first recurrent architecture that couples learned temporal prediction with formal degradation guarantees rooted in three-valued logic.

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arXiv2026

Variational Neural Belief Parameterizations for Robust Dexterous Grasping under Multimodal Uncertainty

Contact variability, sensing uncertainty, and external disturbances make grasp execution stochastic. Expected-quality objectives ignore tail outcomes and often select grasps that fail under adverse contact realizations. Risk-sensitive POMDPs address this failure mode, but many use particle-filter beliefs that scale poorly, obstruct gradient-based optimization, and estimate Conditional Value-at-Risk (CVaR) with high-variance approximations. We instead formulate grasp acquisition as variational inference over latent contact parameters and object pose, representing the belief with a differentiable Gaussian mixture. We use Gumbel-Softmax component selection and location-scale reparameterization to express samples as smooth functions of the belief parameters, enabling pathwise gradients through a differentiable CVaR surrogate for direct optimization of tail robustness. In simulation, our variational neural belief improves robust grasp success under contact-parameter uncertainty and exogenous force perturbations while reducing planning time by roughly an order of magnitude relative to particle-filter model-predictive control. On a serial-chain robot arm with a multifingered hand, we validate grasp-and-lift success under object-pose uncertainty against a Gaussian baseline. Both methods succeed on the tested perturbations, but our controller terminates in fewer steps and less wall-clock time while achieving a higher tactile grasp-quality proxy. Our learned belief also calibrates risk more accurately, keeping mean absolute calibration error below 0.14 across tested simulation regimes, compared with 0.58 for a Cross-Entropy Method planner. We provide code, simulation assets, and a dataset of 243 force-closed grasps at the following link: www.github.com/coenwerem/vnb-grasp.

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arXiv2026

Ternary Logic Encodings of Temporal Behavior Trees with Application to Control Synthesis

Behavior Trees (BTs) provide designers an intuitive graphical interface to construct long-horizon plans for autonomous systems. To ensure their correctness and safety, rigorous formal models and verification techniques are essential. Temporal BTs (TBTs) offer a promising approach by leveraging existing temporal logic formalisms to specify and verify the executions of BTs. However, this analysis is currently limited to offline post hoc analysis and trace repair. In this paper, we reformulate TBTs using a ternary-valued Signal Temporal Logic (STL) amenable for control synthesis. Ternary logic introduces a third truth value \textit{Unknown}, formally capturing cases where a trajectory has neither fully satisfied or dissatisfied a specification. We propose mixed-integer linear encodings for partial trajectory STL and TBTs over ternary logic allowing for correct-by-construction control strategies for linear dynamical systems via mixed-integer optimization. We demonstrate the utility of our framework by solving optimal control problems.

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arXiv2026

Learning from Imperfect Demonstrations via Temporal Behavior Tree-Guided Trajectory Repair

Learning robot control policies from demonstrations is a powerful paradigm, yet real-world data is often suboptimal, noisy, or otherwise imperfect, posing significant challenges for imitation and reinforcement learning. In this work, we present a formal framework that leverages Temporal Behavior Trees (TBT), an extension of Signal Temporal Logic (STL) with Behavior Tree semantics, to repair suboptimal trajectories prior to their use in downstream policy learning. Given demonstrations that violate a TBT specification, a model-based repair algorithm corrects trajectory segments to satisfy the formal constraints, yielding a dataset that is both logically consistent and interpretable. The repaired trajectories are then used to extract potential functions that shape the reward signal for reinforcement learning, guiding the agent toward task-consistent regions of the state space without requiring knowledge of the agent's kinematic model. We demonstrate the effectiveness of this framework on discrete grid-world navigation and continuous single and multi-agent reach-avoid tasks, highlighting its potential for data-efficient robot learning in settings where high-quality demonstrations cannot be assumed.

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arXiv2026

Risk-Constrained Belief-Space Optimization for Safe Control under Latent Uncertainty

Many safety-critical control systems operate under latent uncertainty that sensors cannot resolve at decision time. Such uncertainty, arising from unknown physical properties, disturbances, or unobserved geometry, affects dynamics, task feasibility, and safety margins. Standard methods optimize expected performance and offer limited protection against rare but severe outcomes, while robust formulations treat uncertainty conservatively without exploiting its probabilistic structure. We consider systems with measured state and an unknown, time-invariant parameter represented by a belief distribution. We propose a risk-sensitive belief-space Model Predictive Path Integral (MPPI) controller that plans under this belief, regularizes performance using Conditional Value-at-Risk (CVaR), and imposes a CVaR constraint on a trajectory safety margin over the horizon. For the exact risk-constrained formulation underlying this controller, we establish three properties: (1) the CVaR constraint implies a probabilistic safety guarantee, (2) the controller recovers the risk-neutral optimum as the objective risk weight tends to zero, and (3) a union-bound argument extends the per-horizon guarantee to cumulative safety over repeated solves. In contact-rich MuJoCo simulations of vision-guided dexterous stowing, where a manipulator inserts a grasped object into an occupied slot with pose uncertainty exceeding prescribed lateral clearance requirements, our method achieves 82% success with zero contact violations at high risk aversion, compared with 55% and 50% for a risk-neutral configuration and a chance-constrained baseline, both of which incur nonzero exterior contact forces. Project page: https://clintonenwerem.com/belief-cvar-mppi/.

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arXiv2026

Long-Horizon Geometry-Aware Navigation among Polytopes via MILP-MPC and Minkowski-Based CBFs

Autonomous navigation in complex, non-convex environments remains challenging when robot dynamics, control limits, and exact robot geometry must all be taken into account. In this paper, we propose a hierarchical planning and control framework that bridges long-horizon guidance and geometry-aware safety guarantees for a polytopic robot navigating among polytopic obstacles. At the high level, Mixed-Integer Linear Programming (MILP) is embedded within a Model Predictive Control (MPC) framework to generate a nominal trajectory around polytopic obstacles while modeling the robot as a point mass for computational tractability. At the low level, we employ a control barrier function (CBF) based on the exact signed distance in the Minkowski-difference space as a safety filter to explicitly enforce the geometric constraints of the robot shape, and further extend its formulation to a high-order CBF (HOCBF). We demonstrate the proposed framework in U-shaped and maze-like environments under single- and double-integrator dynamics. The results show that the proposed architecture mitigates the topology-induced local-minimum behavior of purely reactive CBF-based navigation while enabling safe, real-time, geometry-aware navigation.

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arXiv2026

RRT$^\eta$: Sampling-based Motion Planning and Control from STL Specifications using Arithmetic-Geometric Mean Robustness

Sampling-based motion planning has emerged as a powerful approach for robotics, enabling exploration of complex, high-dimensional configuration spaces. When combined with Signal Temporal Logic (STL), a temporal logic widely used for formalizing interpretable robotic tasks, these methods can address complex spatiotemporal constraints. However, traditional approaches rely on min-max robustness measures that focus only on critical time points and subformulae, creating non-smooth optimization landscapes with sharp decision boundaries that hinder efficient tree exploration. We propose RRT$^\eta$, a sampling-based planning framework that integrates the Arithmetic-Geometric Mean (AGM) robustness measure to evaluate satisfaction across all time points and subformulae. Our key contributions include: (1) AGM robustness interval semantics for reasoning about partial trajectories during tree construction, (2) an efficient incremental monitoring algorithm computing these intervals, and (3) enhanced Direction of Increasing Satisfaction vectors leveraging Fulfillment Priority Logic (FPL) for principled objective composition. Our framework synthesizes dynamically feasible control sequences satisfying STL specifications with high robustness while maintaining the probabilistic completeness and asymptotic optimality of RRT$^\ast$. We validate our approach on three robotic systems. A double integrator point robot, a unicycle mobile robot, and a 7-DOF robot arm, demonstrating superior performance over traditional STL robustness-based planners in multi-constraint scenarios with limited guidance signals.

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arXiv2025

STL-based Optimization of Biomolecular Neural Networks for Regression and Control

Biomolecular Neural Networks (BNNs), artificial neural networks with biologically synthesizable architectures, achieve universal function approximation capabilities beyond simple biological circuits. However, training BNNs remains challenging due to the lack of target data. To address this, we propose leveraging Signal Temporal Logic (STL) specifications to define training objectives for BNNs. We build on the quantitative semantics of STL, enabling gradient-based optimization of the BNN weights, and introduce a learning algorithm that enables BNNs to perform regression and control tasks in biological systems. Specifically, we investigate two regression problems in which we train BNNs to act as reporters of dysregulated states, and a feedback control problem in which we train the BNN in closed-loop with a chronic disease model, learning to reduce inflammation while avoiding adverse responses to external infections. Our numerical experiments demonstrate that STL-based learning can solve the investigated regression and control tasks efficiently.

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arXiv2025

SPLASH! Sample-efficient Preference-based inverse reinforcement learning for Long-horizon Adversarial tasks from Suboptimal Hierarchical demonstrations

Inverse Reinforcement Learning (IRL) presents a powerful paradigm for learning complex robotic tasks from human demonstrations. However, most approaches make the assumption that expert demonstrations are available, which is often not the case. Those that allow for suboptimality in the demonstrations are not designed for long-horizon goals or adversarial tasks. Many desirable robot capabilities fall into one or both of these categories, thus highlighting a critical shortcoming in the ability of IRL to produce field-ready robotic agents. We introduce Sample-efficient Preference-based inverse reinforcement learning for Long-horizon Adversarial tasks from Suboptimal Hierarchical demonstrations (SPLASH), which advances the state-of-the-art in learning from suboptimal demonstrations to long-horizon and adversarial settings. We empirically validate SPLASH on a maritime capture-the-flag task in simulation, and demonstrate real-world applicability with sim-to-real translation experiments on autonomous unmanned surface vehicles. We show that our proposed methods allow SPLASH to significantly outperform the state-of-the-art in reward learning from suboptimal demonstrations.

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arXiv2025

Safety-Aware Reinforcement Learning for Control via Risk-Sensitive Action-Value Iteration and Quantile Regression

Mainstream approximate action-value iteration reinforcement learning (RL) algorithms suffer from overestimation bias, leading to suboptimal policies in high-variance stochastic environments. Quantile-based action-value iteration methods reduce this bias by learning a distribution of the expected cost-to-go using quantile regression. However, ensuring that the learned policy satisfies safety constraints remains a challenge when these constraints are not explicitly integrated into the RL framework. Existing methods often require complex neural architectures or manual tradeoffs due to combined cost functions. To address this, we propose a risk-regularized quantile-based algorithm integrating Conditional Value-at-Risk (CVaR) to enforce safety without complex architectures. We also provide theoretical guarantees on the contraction properties of the risk-sensitive distributional Bellman operator in Wasserstein space, ensuring convergence to a unique cost distribution. Simulations of a mobile robot in a dynamic reach-avoid task show that our approach leads to more goal successes, fewer collisions, and better safety-performance trade-offs than risk-neutral methods.

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arXiv2025

Accelerated Learning with Linear Temporal Logic using Differentiable Simulation

Ensuring that reinforcement learning (RL) controllers satisfy safety and reliability constraints in real-world settings remains challenging: state-avoidance and constrained Markov decision processes often fail to capture trajectory-level requirements or induce overly conservative behavior. Formal specification languages such as linear temporal logic (LTL) offer correct-by-construction objectives, yet their rewards are typically sparse, and heuristic shaping can undermine correctness. We introduce, to our knowledge, the first end-to-end framework that integrates LTL with differentiable simulators, enabling efficient gradient-based learning directly from formal specifications. Our method relaxes discrete automaton transitions via soft labeling of states, yielding differentiable rewards and state representations that mitigate the sparsity issue intrinsic to LTL while preserving objective soundness. We provide theoretical guarantees connecting B\"uchi acceptance to both discrete and differentiable LTL returns and derive a tunable bound on their discrepancy in deterministic and stochastic settings. Empirically, across complex, nonlinear, contact-rich continuous-control tasks, our approach substantially accelerates training and achieves up to twice the returns of discrete baselines. We further demonstrate compatibility with reward machines, thereby covering co-safe LTL and LTL$_\text{f}$ without modification. By rendering automaton-based rewards differentiable, our work bridges formal methods and deep RL, enabling safe, specification-driven learning in continuous domains.

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arXiv2025

Control Barrier Functions via Minkowski Operations for Safe Navigation among Polytopic Sets

Safely navigating around obstacles while respecting the dynamics, control, and geometry of the underlying system is a key challenge in robotics. Control Barrier Functions (CBFs) generate safe control policies by considering system dynamics and geometry when calculating safe forward-invariant sets. Existing CBF-based methods often rely on conservative shape approximations, like spheres or ellipsoids, which have explicit and differentiable distance functions. In this paper, we propose an optimization-defined CBF that directly considers the exact Signed Distance Function (SDF) between a polytopic robot and polytopic obstacles. Inspired by the Gilbert-Johnson-Keerthi (GJK) algorithm, we formulate both (i) minimum distance and (ii) penetration depth between polytopic sets as convex optimization problems in the space of Minkowski difference operations (the MD-space). Convenient geometric properties of the MD-space enable the derivatives of implicit SDF between two polytopes to be computed via differentiable optimization. We demonstrate the proposed framework in three scenarios including pure translation, initialization inside an unsafe set, and multi-obstacle avoidance. These three scenarios highlight the generation of a non-conservative maneuver, a recovery after starting in collision, and the consideration of multiple obstacles via pairwise CBF constraint, respectively.

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