We present a novel, regulator-driven approach for post hoc safety evaluation of learning-based, black-box autonomous mobile robots, ensuring ongoing compliance with evolving, human-defined safety rules. In our iterative workflow, human safety requirements are translated by regulators into Signal Temporal Logic (STL) specifications. Rollout traces from the black-box model are externally verified for compliance, yielding quantitative safety metrics, Total Robustness Value (TRV) and Largest Robustness Value (LRV), which measure average and worst-case specification adherence. These metrics inform targeted retraining and iterative improvement by model designers. We apply our method across two different applications: a virtual driving scenario and an autonomous mobile robot navigating a complex environment, and observe statistically significant improvements across both scenarios. In the virtual driving scenario, we see a 177% increase in traces adhering to the simulation speed limit, a 1138% increase in traces minimizing off-road driving, and a 16% increase in traces successfully reaching the goal within the time limit. In the autonomous navigation scenario, there is a 300% increase in traces avoiding sharp turns, a 200% increase in traces reaching the goal within the time limit, and a 49% increase in traces minimizing time spent near obstacles. Finally, we validate our approach on a TurtleBot3 robot in the real world, and demonstrate improved obstacle navigation with safety buffers.

Translating natural language instructions into executable motion plans is a fundamental challenge in robotics. Traditional approaches are typically constrained by their reliance on domain-specific expertise to customize planners, and often struggle with spatio-temporal couplings that usually lead to infeasible motions or discrepancies between task planning and motion execution. Despite the proficiency of Large Language Models (LLMs) in high-level semantic reasoning, hallucination could result in infeasible motion plans. In this paper, we introduce the T3 Planner, an LLM-enabled robotic motion planning framework that self-corrects it output with formal methods. The framework decomposes spatio-temporal task constraints via three cascaded modules, each of which stimulates an LLM to generate candidate trajectory sequences and examines their feasibility via a Signal Temporal Logic (STL) verifier until one that satisfies complex spatial, temporal, and logical constraints is found.Experiments across different scenarios show that T3 Planner significantly outperforms the baselines. The required reasoning can be distilled into a lightweight Qwen3-4B model that enables efficient deployment. All supplementary materials are accessible at https://github.com/leeejia/T3_Planner.

In real-time and safety-critical cyber-physical systems (CPSs), control synthesis must guarantee that generated policies meet stringent timing and correctness requirements under uncertain and dynamic conditions. Signal temporal logic (STL) has emerged as a powerful formalism of expressing real-time constraints, with its semantics enabling quantitative assessment of system behavior. Meanwhile, reinforcement learning (RL) has become an important method for solving control synthesis problems in unknown environments. Recent studies incorporate STL-based reward functions into RL to automatically synthesize control policies. However, the automatically inferred rewards obtained by these methods represent the global assessment of a whole or partial path but do not accumulate the rewards of local changes accurately, so the sparse global rewards may lead to non-convergence and unstable training performances. In this paper, we propose an online reward generation method guided by the online causation monitoring of STL. Our approach continuously monitors system behavior against an STL specification at each control step, computing the quantitative distance toward satisfaction or violation and thereby producing rewards that reflect instantaneous state dynamics. Additionally, we provide a smooth approximation of the causation semantics to overcome the discontinuity of the causation semantics and make it differentiable for using deep-RL methods. We have implemented a prototype tool and evaluated it in the Gym environment on a variety of continuously controlled benchmarks. Experimental results show that our proposed STL-guided RL method with online causation semantics outperforms existing relevant STL-guided RL methods, providing a more robust and efficient reward generation framework for deep-RL.

Recent advances in the development of robotic foundation models have led to promising end-to-end and general-purpose capabilities in robotic systems. Trained on vast datasets of simulated and real-world trajectories, these models map multimodal observations directly to action sequences for physical execution. Despite promising real-world capabilities, these models are still data-driven and, therefore, lack explicit notions of behavioral correctness. We address this gap by introducing SafeDec, a constrained decoding framework for autoregressive, robot foundation models that enforces invariant safety specifications on candidate action trajectories. Task-specific safety rules are expressed as Signal Temporal Logic (STL) formulas and are enforced at inference time with minimal overhead. Our method ensures that generated actions provably satisfy STL specifications under assumed dynamics at runtime without retraining , while remaining agnostic of the underlying policy. We evaluate SafeDec on tasks from the CHORES benchmark for state-of-the-art generalist policies (e.g., SPOC, Flare, PoliFormer) across hundreds of procedurally generated environments and show that our decoding-time interventions are useful not only for filtering unsafe actions but also for conditional action generation. Videos are available at constrained-robot-fms.github.io.

We investigate the task and motion planning problem for Signal Temporal Logic (STL) specifications in robotics. Existing STL methods rely on pre-defined maps or mobility representations, which are ineffective in unstructured real-world environments. We propose the \emph{Structured-MoE STL Planner} (\textbf{S-MSP}), a differentiable framework that maps synchronized multi-view camera observations and an STL specification directly to a feasible trajectory. S-MSP integrates STL constraints within a unified pipeline, trained with a composite loss that combines trajectory reconstruction and STL robustness. A \emph{structure-aware} Mixture-of-Experts (MoE) model enables horizon-aware specialization by projecting sub-tasks into temporally anchored embeddings. We evaluate S-MSP using a high-fidelity simulation of factory-logistics scenarios with temporally constrained tasks. Experiments show that S-MSP outperforms single-expert baselines in STL satisfaction and trajectory feasibility. A rule-based \emph{safety filter} at inference improves physical executability without compromising logical correctness, showcasing the practicality of the approach.

This paper presents a novel approach to motion planning and risk analysis for enhancing human-robot collaboration using a Multi-Rotor Aerial Vehicle (MRAV). The proposed method uses Signal Temporal Logic (STL) to encode key mission objectives, such as safety, timing, and human preferences, with a strong focus on ergonomics and comfort. An optimization framework generates dynamically feasible trajectories while considering the MRAV's physical constraints. Given the nonlinear and non-convex nature of the problem, smooth approximations and gradient-based techniques assist in handling the problem's computational complexity. Additionally, an uncertainty-aware risk analysis is incorporated to assess potential deviations from the mission specifications, providing insights into the likelihood of mission success under uncertain conditions. Further, an event-triggered replanning strategy is implemented to respond to unforeseen events and external disturbances. The approach is validated through MATLAB and Gazebo simulations, using an object handover task in a mock-up environment inspired by power line maintenance scenarios. The results highlight the method's effectiveness in achieving safe, efficient, and resilient human-robot collaboration.

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.

This work presents a novel co-design strategy that integrates trajectory planning and control to handle STL-based tasks in autonomous robots. The method consists of two phases: $(i)$ learning spatio-temporal motion primitives to encapsulate the inherent robot-specific constraints and $(ii)$ constructing an STL-compliant motion plan from these primitives. Initially, we employ reinforcement learning to construct a library of control policies that perform trajectories described by the motion primitives. Then, we map motion primitives to spatio-temporal characteristics. Subsequently, we present a sampling-based STL-compliant motion planning strategy tailored to meet the STL specification. The proposed model-free approach, which generates feasible STL-compliant motion plans across various environments, is validated on differential-drive and quadruped robots across various STL specifications. Demonstration videos are available at https://tinyurl.com/m6zp7rsm.

Learning to solve complex tasks with signal temporal logic (STL) specifications is crucial to many real-world applications. However, most previous works only consider fixed or parametrized STL specifications due to the lack of a diverse STL dataset and encoders to effectively extract temporal logic information for downstream tasks. In this paper, we propose TeLoGraF, Temporal Logic Graph-encoded Flow, which utilizes Graph Neural Networks (GNN) encoder and flow-matching to learn solutions for general STL specifications. We identify four commonly used STL templates and collect a total of 200K specifications with paired demonstrations. We conduct extensive experiments in five simulation environments ranging from simple dynamical models in the 2D space to high-dimensional 7DoF Franka Panda robot arm and Ant quadruped navigation. Results show that our method outperforms other baselines in the STL satisfaction rate. Compared to classical STL planning algorithms, our approach is 10-100X faster in inference and can work on any system dynamics. Besides, we show our graph-encoding method's capability to solve complex STLs and robustness to out-distribution STL specifications. Code is available at https://github.com/mengyuest/TeLoGraF

We propose a novel, multi-layered planning approach for computing paths that satisfy both kinodynamic and spatiotemporal constraints. Our three-part framework first establishes potential sequences to meet spatial constraints, using them to calculate a geometric lead path. This path then guides an asymptotically optimal sampling-based kinodynamic planner, which minimizes an STL-robustness cost to jointly satisfy spatiotemporal and kinodynamic constraints. In our experiments, we test our method with a velocity-controlled Ackerman-car model and demonstrate significant efficiency gains compared to prior art. Additionally, our method is able to generate complex path maneuvers, such as crossovers, something that previous methods had not demonstrated.