arXiv subjects

Cristian-Ioan Vasile

Publications and source records attributed to Cristian-Ioan Vasile.

At least 19 recordsLinked to original sources

arXiv2026

Expressive Power of WSTL Formulas for Learning to Rank

Weighted Signal Temporal Logic (WSTL) is increasingly used as a scoring function in learning-to-rank problems of trajectories with safety guarantees, where its weighted quantitative semantics serve as a parametrized utility function. Despite the growing interest, prior work only assumes the expressiveness of WSTL formulas and empirically demonstrates its utility in capturing diverse preferences. This work focuses on the correctness of this assumption and asks whether using WSTL formulas as scoring functions is theoretically justified. We formalize two concepts: first, rank-realizability, which asks whether all rankings of a given signal set are achievable by varying weights, and, second, rank-capacity, the maximum signal set size for which the formula is rank-realizable. We propose a Mixed-Integer Linear Program to decide rank-realizability, and derive constructive lower bounds for rank-capacity. Experiments on a robotic navigation task show that while a practical WSTL specification may fail to be rank-realizable on a set with similar trajectories, its rank-capacity exceeds the size of the trajectory set. Analysis of Boolean-equivalent formulas reveals that formula structure affects expressivity and that rank-capacity can be increased without altering qualitative semantics.

eess.SY↗

arXiv2026

ViTL: Temporal Logic-Guided Zero-Shot Natural Language Navigation via Vision-Language Models

Enabling robots to follow natural language commands to complete zero-shot long-horizon tasks remains challenging. It requires extracting implicit temporal and logical constraints from natural language commands and executing multiple sub-tasks accordingly. Recent zero-shot object navigation methods use vision-language models (VLMs) to guide frontier-based exploration in unknown environments, but they are limited to single-target tasks. Real-world commands such as "Clean either the chair or the couch, then turn on the tv." require navigating to multiple targets in a temporally constrained order, which no existing zero-shot system can handle. We present ViTL, a framework that addresses this gap at two levels. At the task level, we use a large language model (LLM) to compile natural language commands into Linear Temporal Logic (LTL) formulas, which are then converted into Deterministic Finite Automata~(DFA) that coordinate multi-channel value maps and trigger dynamic replanning when new objects are detected. At the navigation level, we introduce directional score: rather than producing a direction-agnostic value across the entire field of view, we label frontier directions on the observation image and extract per-direction scores from the VLM. Experiments on Habitat-Matterport 3D (HM3D) show that the full framework enables zero-shot long-horizon completion of natural language navigation tasks with temporal constraints, and that directional score improves single-target navigation accuracy and efficiency over the baseline.

cs.RO↗

arXiv2026

Differentiable SpaTiaL: Symbolic Learning and Reasoning with Geometric Temporal Logic for Manipulation Tasks

Executing complex manipulation in cluttered environments requires satisfying coupled geometric and temporal constraints. Although Spatio-Temporal Logic (SpaTiaL) offers a principled specification framework, its use in gradient-based optimization is limited by non-differentiable geometric operations. Existing differentiable temporal logics focus on the robot's internal state and neglect interactive object-environment relations, while spatial logic approaches that capture such interactions rely on discrete geometry engines that break the computational graph and preclude exact gradient propagation. To overcome this limitation, we propose Differentiable SpaTiaL, a fully tensorized toolbox that constructs smooth, autograd-compatible geometric primitives directly over polygonal sets. To the best of our knowledge, this is the first end-to-end differentiable symbolic spatio-temporal logic toolbox. By analytically deriving differentiable relaxations of key spatial predicates--including signed distance, intersection, containment, and directional relations--we enable an end-to-end differentiable mapping from high-level semantic specifications to low-level geometric configurations, without invoking external discrete solvers. This fully differentiable formulation unlocks two core capabilities: (i) massively parallel trajectory optimization under rigorous spatio-temporal constraints, and (ii) direct learning of spatial logic parameters from demonstrations via backpropagation. Experimental results validate the effectiveness and scalability of the proposed framework.

cs.RO↗

arXiv2026

Safe and Optimal Learning from Preferences via Weighted Temporal Logic with Applications in Robotics and Formula 1

Autonomous systems increasingly rely on human feedback to align their behavior, expressed as pairwise comparisons, rankings, or demonstrations. While existing methods can adapt behaviors, they often fail to guarantee safety in safety-critical domains. We propose a safety-guaranteed, optimal, and efficient approach for solving the learning problem from preferences, rankings, or demonstrations using Weighted Signal Temporal Logic (WSTL). WSTL learning problems, when implemented naively, lead to multi-linear constraints in the weights to be learned. By introducing structural pruning and log-transform procedures, we reduce the problem size and recast it as a Mixed-Integer Linear Program while preserving safety guarantees. Experiments on robotic navigation and real-world Formula 1 data demonstrate that the method captures nuanced preferences and models complex task objectives.

cs.RO↗

arXiv2025

A*-based Temporal Logic Path Planning with User Preferences on Relaxed Task Satisfaction

In this work, we consider the problem of planning for temporal logic tasks in large robot environments. When full task compliance is unattainable, we aim to achieve the best possible task satisfaction by integrating user preferences for relaxation into the planning process. Utilizing the automata-based representations for temporal logic goals and user preferences, we propose an A*-based planning framework. This approach effectively tackles large-scale problems while generating near-optimal high-level trajectories. To facilitate this, we propose a simple, efficient heuristic that allows for planning over large robot environments in a fraction of time and search memory as compared to uninformed search algorithms. We present extensive case studies to demonstrate the scalability, runtime analysis as well as empirical bounds on the suboptimality of the proposed heuristic.

cs.RO↗

arXiv2025

An Iterative Approach for Heterogeneous Multi-Agent Route Planning with Resource Transportation Uncertainty and Temporal Logic Goals

This paper presents an iterative approach for heterogeneous multi-agent route planning in environments with unknown resource distributions. We focus on a team of robots with diverse capabilities tasked with executing missions specified using Capability Temporal Logic (CaTL), a formal framework built on Signal Temporal Logic to handle spatial, temporal, capability, and resource constraints. The key challenge arises from the uncertainty in the initial distribution and quantity of resources in the environment. To address this, we introduce an iterative algorithm that dynamically balances exploration and task fulfillment. Robots are guided to explore the environment, identifying resource locations and quantities while progressively refining their understanding of the resource landscape. At the same time, they aim to maximally satisfy the mission objectives based on the current information, adapting their strategies as new data is uncovered. This approach provides a robust solution for planning in dynamic, resource-constrained environments, enabling efficient coordination of heterogeneous teams even under conditions of uncertainty. Our method's effectiveness and performance are demonstrated through simulated case studies.

cs.RO↗

arXiv2025

Safe Navigation in Dynamic Environments Using Data-Driven Koopman Operators and Conformal Prediction

We propose a novel framework for safe navigation in dynamic environments by integrating Koopman operator theory with conformal prediction. Our approach leverages data-driven Koopman approximation to learn nonlinear dynamics and employs conformal prediction to quantify uncertainty, providing statistical guarantees on approximation errors. This uncertainty is effectively incorporated into a Model Predictive Controller (MPC) formulation through constraint tightening, ensuring robust safety guarantees. We implement a layered control architecture with a reference generator providing waypoints for safe navigation. The effectiveness of our methods is validated in simulation.

cs.RO↗

arXiv2024

Accelerating Proximal Policy Optimization Learning Using Task Prediction for Solving Environments with Delayed Rewards

In this paper, we tackle the challenging problem of delayed rewards in reinforcement learning (RL). While Proximal Policy Optimization (PPO) has emerged as a leading Policy Gradient method, its performance can degrade under delayed rewards. We introduce two key enhancements to PPO: a hybrid policy architecture that combines an offline policy (trained on expert demonstrations) with an online PPO policy, and a reward shaping mechanism using Time Window Temporal Logic (TWTL). The hybrid architecture leverages offline data throughout training while maintaining PPO's theoretical guarantees. Building on the monotonic improvement framework of Trust Region Policy Optimization (TRPO), we prove that our approach ensures improvement over both the offline policy and previous iterations, with a bounded performance gap of $(2ςγα^2)/(1-γ)^2$, where $α$ is the mixing parameter, $γ$ is the discount factor, and $ς$ bounds the expected advantage. Additionally, we prove that our TWTL-based reward shaping preserves the optimal policy of the original problem. TWTL enables formal translation of temporal objectives into immediate feedback signals that guide learning. We demonstrate the effectiveness of our approach through extensive experiments on an inverted pendulum and a lunar lander environments, showing improvements in both learning speed and final performance compared to standard PPO and offline-only approaches.

cs.LG↗

arXiv2024

STLGame: Signal Temporal Logic Games in Adversarial Multi-Agent Systems

We study how to synthesize a robust and safe policy for autonomous systems under signal temporal logic (STL) tasks in adversarial settings against unknown dynamic agents. To ensure the worst-case STL satisfaction, we propose STLGame, a framework that models the multi-agent system as a two-player zero-sum game, where the ego agents try to maximize the STL satisfaction and other agents minimize it. STLGame aims to find a Nash equilibrium policy profile, which is the best case in terms of robustness against unseen opponent policies, by using the fictitious self-play (FSP) framework. FSP iteratively converges to a Nash profile, even in games set in continuous state-action spaces. We propose a gradient-based method with differentiable STL formulas, which is crucial in continuous settings to approximate the best responses at each iteration of FSP. We show this key aspect experimentally by comparing with reinforcement learning-based methods to find the best response. Experiments on two standard dynamical system benchmarks, Ackermann steering vehicles and autonomous drones, demonstrate that our converged policy is almost unexploitable and robust to various unseen opponents' policies. All code and additional experimental results can be found on our project website: https://sites.google.com/view/stlgame

cs.RO↗

arXiv2024

Learning Optimal Signal Temporal Logic Decision Trees for Classification: A Max-Flow MILP Formulation

This paper presents a novel framework for inferring timed temporal logic properties from data. The dataset comprises pairs of finite-time system traces and corresponding labels, denoting whether the traces demonstrate specific desired behaviors, e.g. whether the ship follows a safe route or not. Our proposed approach leverages decision-tree-based methods to infer Signal Temporal Logic classifiers using primitive formulae. We formulate the inference process as a mixed integer linear programming optimization problem, recursively generating constraints to determine both data classification and tree structure. Applying a max-flow algorithm on the resultant tree transforms the problem into a global optimization challenge, leading to improved classification rates compared to prior methodologies. Moreover, we introduce a technique to reduce the number of constraints by exploiting the symmetry inherent in STL primitives, which enhances the algorithm's time performance and interpretability. To assess our algorithm's effectiveness and classification performance, we conduct three case studies involving two-class, multi-class, and complex formula classification scenarios.

cs.LG↗

arXiv2024

Control Barrier Function for Linearizable Systems with High Relative Degrees from Signal Temporal Logics: A Reference Governor Approach

This paper considers the safety-critical navigation problem with Signal Temporal Logic (STL) tasks. We developed an explicit reference governor-guided control barrier function (ERG-guided CBF) method that enables the application of first-order CBFs to high-order linearizable systems. This method significantly reduces the conservativeness of the existing CBF approaches for high-order systems. Furthermore, our framework provides safety-critical guarantees in the sense of obstacle avoidance by constructing the margin of safety and updating direction of safe evolution in the agent's state space. To improve control performance and enhance STL satisfaction, we employ efficient gradient-based methods for iteratively learning optimal parameters of ERG-guided CBF. We validate the algorithm through both high-order linear and nonlinear systems. A video demonstration can be found on: \url{https://youtu.be/ZRmsA2FeFR4}

eess.SY↗

arXiv2024

Optimal Control Synthesis with Relaxed Global Temporal Logic Specifications for Homogeneous Multi-robot Teams

In this work, we address the problem of control synthesis for a homogeneous team of robots given a global temporal logic specification and formal user preferences for relaxation in case of infeasibility. The relaxation preferences are represented as a Weighted Finite-state Edit System and are used to compute a relaxed specification automaton that captures all allowable relaxations of the mission specification and their costs. For synthesis, we introduce a Mixed Integer Linear Programming (MILP) formulation that combines the motion of the team of robots with the relaxed specification automaton. Our approach combines automata-based and MILP-based methods and leverages the strengths of both approaches while avoiding their shortcomings. Specifically, the relaxed specification automaton explicitly accounts for the progress towards satisfaction, and the MILP-based optimization approach avoids the state-space explosion associated with explicit product-automata construction, thereby efficiently solving the problem. The case studies highlight the efficiency of the proposed approach.

cs.RO↗

arXiv2024

TLINet: Differentiable Neural Network Temporal Logic Inference

There has been a growing interest in extracting formal descriptions of the system behaviors from data. Signal Temporal Logic (STL) is an expressive formal language used to describe spatial-temporal properties with interpretability. This paper introduces TLINet, a neural-symbolic framework for learning STL formulas. The computation in TLINet is differentiable, enabling the usage of off-the-shelf gradient-based tools during the learning process. In contrast to existing approaches, we introduce approximation methods for max operator designed specifically for temporal logic-based gradient techniques, ensuring the correctness of STL satisfaction evaluation. Our framework not only learns the structure but also the parameters of STL formulas, allowing flexible combinations of operators and various logical structures. We validate TLINet against state-of-the-art baselines, demonstrating that our approach outperforms these baselines in terms of interpretability, compactness, rich expressibility, and computational efficiency.

cs.LO↗

arXiv2024

Distributed Fair Assignment and Rebalancing for Mobility-on-Demand Systems via an Auction-based Method

In this paper, we consider fair assignment of complex requests for Mobility-On-Demand systems. We model the transportation requests as temporal logic formulas that must be satisfied by a fleet of vehicles. We require that the assignment of requests to vehicles is performed in a distributed manner based only on communication between vehicles while ensuring fair allocation. Our approach to the vehicle-request assignment problem is based on a distributed auction scheme with no centralized bidding that leverages utility history correction of bids to improve fairness. Complementarily, we propose a rebalancing scheme that employs rerouting vehicles to more rewarding areas to increase the potential future utility and ensure a fairer utility distribution. We adopt the max-min and deviation of utility as the two criteria for fairness. We demonstrate the methods in the mid-Manhattan map with a large number of requests generated in different probability settings. We show that we increase the fairness between vehicles based on the fairness criteria without degenerating the servicing quality.

cs.FL↗

arXiv2023

A Flexible and Efficient Temporal Logic Tool for Python: PyTeLo

Temporal logic is an important tool for specifying complex behaviors of systems. It can be used to define properties for verification and monitoring, as well as goals for synthesis tools, allowing users to specify rich missions and tasks. Some of the most popular temporal logics include Metric Temporal Logic (MTL), Signal Temporal Logic (STL), and weighted STL (wSTL), which also allow the definition of timing constraints. In this work, we introduce PyTeLo, a modular and versatile Python-based software that facilitates working with temporal logic languages, specifically MTL, STL, and wSTL. Applying PyTeLo requires only a string representation of the temporal logic specification and, optionally, the dynamics of the system of interest. Next, PyTeLo reads the specification using an ANTLR-generated parser and generates an Abstract Syntax Tree (AST) that captures the structure of the formula. For synthesis, the AST serves to recursively encode the specification into a Mixed Integer Linear Program (MILP) that is solved using a commercial solver such as Gurobi. We describe the architecture and capabilities of PyTeLo and provide example applications highlighting its adaptability and extensibility for various research problems.

cs.LO↗

arXiv2023

Energy-Constrained Active Exploration Under Incremental-Resolution Symbolic Perception

In this work, we consider the problem of autonomous exploration in search of targets while respecting a fixed energy budget. The robot is equipped with an incremental-resolution symbolic perception module wherein the perception of targets in the environment improves as the robot's distance from targets decreases. We assume no prior information about the total number of targets, their locations as well as their possible distribution within the environment. This work proposes a novel decision-making framework for the resulting constrained sequential decision-making problem by first converting it into a reward maximization problem on a product graph computed offline. It is then solved online as a Mixed-Integer Linear Program (MILP) where the knowledge about the environment is updated at each step, combining automata-based and MILP-based techniques. We demonstrate the efficacy of our approach with the help of a case study and present empirical evaluation in terms of expected regret. Furthermore, the runtime performance shows that online planning can be efficiently performed for moderately-sized grid environments.

cs.RO↗

arXiv2023

Learning Signal Temporal Logic through Neural Network for Interpretable Classification

Machine learning techniques using neural networks have achieved promising success for time-series data classification. However, the models that they produce are challenging to verify and interpret. In this paper, we propose an explainable neural-symbolic framework for the classification of time-series behaviors. In particular, we use an expressive formal language, namely Signal Temporal Logic (STL), to constrain the search of the computation graph for a neural network. We design a novel time function and sparse softmax function to improve the soundness and precision of the neural-STL framework. As a result, we can efficiently learn a compact STL formula for the classification of time-series data through off-the-shelf gradient-based tools. We demonstrate the computational efficiency, compactness, and interpretability of the proposed method through driving scenarios and naval surveillance case studies, compared with state-of-the-art baselines.

cs.FL↗

arXiv2023

Robustness Measures and Monitors for Time Window Temporal Logic

Temporal logics (TLs) have been widely used to formalize interpretable tasks for cyber-physical systems. Time Window Temporal Logic (TWTL) has been recently proposed as a specification language for dynamical systems. In particular, it can easily express robotic tasks, and it allows for efficient, automata-based verification and synthesis of control policies for such systems. In this paper, we define two quantitative semantics for this logic, and two corresponding monitoring algorithms, which allow for real-time quantification of satisfaction of formulas by trajectories of discrete-time systems. We demonstrate the new semantics and their runtime monitors on numerical examples.

cs.FL↗