We appreciate the valuable comments from the reviewers. We will answer reviewers' questions from three aspects, i.e., In respond to Reviewer 5, this paper's major novelty is developing a new STL-based learning framework to Our method creates a practical way to ensure the logic rules' satisfaction in an end-to-end manner. Our approach achieves promising results on real city datasets, i.e., significantly We have carefully compared our work with all the related papers pointed out by the reviewers. Therefore, we also choose STL to express the model properties. Using STL to specify CPS properties is not our novelty.

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.

This paper addresses a motion planning problem to achieve spatio-temporal-logical tasks, expressed by syntactically co-safe linear temporal logic specifications (scLTL\next), in uncertain environments. Here, the uncertainty is modeled as some probabilistic knowledge on the semantic labels of the environment. For example, the task is "first go to region 1, then go to region 2"; however, the exact locations of regions 1 and 2 are not known a priori, instead a probabilistic belief is available. We propose a novel automata-theoretic approach, where a special product automaton is constructed to capture the uncertainty related to semantic labels, and a reward function is designed for each edge of this product automaton. The proposed algorithm utilizes value iteration for online replanning. We show some theoretical results and present some simulations/experiments to demonstrate the efficacy of the proposed approach.

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.

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.

-- Ensuring continuous-time control of multiple quadrotors in constrained environments under signal temporal logic (STL) specifications is challenging due to nonlinear dynamics, safety constraints, and disturbances. This letter proposes a two-stage framework to address this challenge. First, exponentially decaying tracking error bounds are derived with multidimensional geometric control gains obtained via differential evolution. These bounds are less conservative, while the resulting tracking errors exhibit smaller oscillations and improved transient performance. Second, leveraging the time-varying bounds, a mixed-integer convex programming (MICP) formulation generates piecewise Bézier reference trajectories that satisfy STL and velocity limits, while ensuring inter-agent safety through convex-hull properties. Simulation results demonstrate that the proposed approach enables formally verifiable multi-agent coordination in constrained environments, with provable tracking guarantees under bounded disturbances. I. INTRODUCTION As drone technology progresses, quadrotors are increasingly required to execute complex tasks in confined environments--particularly narrow passages and strict terminal zones [1]. In this context, signal temporal logic (STL) offers a formal language to define tasks over continuous signals with explicit time semantics.

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

Task and motion planning (TAMP) for multi-robot systems, which integrates discrete task planning with continuous motion planning, remains a challenging problem in robotics. Existing TAMP approaches often struggle to scale effectively for multi-robot systems with complex specifications, leading to infeasible solutions and prolonged computation times. This work addresses the TAMP problem in multi-robot settings where tasks are specified using expressive hierarchical temporal logic and task assignments are not pre-determined. Our approach leverages the efficiency of hierarchical temporal logic specifications for task-level planning and the optimization-based graph of convex sets method for motion-level planning, integrating them within a product graph framework. At the task level, we convert hierarchical temporal logic specifications into a single graph, embedding task allocation within its edges. At the motion level, we represent the feasible motions of multiple robots through convex sets in the configuration space, guided by a sampling-based motion planner. This formulation allows us to define the TAMP problem as a shortest path search within the product graph, where efficient convex optimization techniques can be applied. We prove that our approach is both sound and complete under mild assumptions. Additionally, we extend our framework to cooperative pick-and-place tasks involving object handovers between robots. We evaluate our method across various high-dimensional multi-robot scenarios, including simulated and real-world environments with quadrupeds, robotic arms, and automated conveyor systems. Our results show that our approach outperforms existing methods in execution time and solution optimality while effectively scaling with task complexity.

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.