Temporal Logic Specifications Research Articles

Zonotope-Based Symbolic Controller Synthesis for Linear Temporal Logic Specifications

Zonotope-Based Symbolic Controller Synthesis for Linear Temporal Logic Specifications

Real-time reactive task allocation and planning of large heterogeneous multi-robot systems with temporal logic specifications

Existing methods for the task allocation and planning (TAP) of multi-robot systems with temporal logic specifications mainly rely on optimization-based approaches or graph search techniques applied to the product automaton. However, these methods suffer from high computational cost and scale poorly with the number of robots and the complexity of temporal logic tasks, thus limiting the applicability in real-time implementation, especially for large multi-robot systems. To address these challenges, this work develops a novel TAP framework that can solve reactive temporal logic planning problems for large-scale heterogeneous multi-robot systems (HMRS) in real time. Specifically, we develop a planning decision tree (PDT) to represent the task progression and task allocation specialized for HMRS with temporal logic specifications. Based on the PDT, we develop two key search algorithms—the planning decision tree search (PDTS) and the interactive planning decision tree search (IPDTS)—where PDTS generates an offline plan which will be modified online by PDTS and IPDTS jointly to enable fast reactive planning if environmental changes or temporary tasks occur. Such a design can generate satisfying plan for HMRS with multiple orders of magnitude more robots than those that existing methods can manipulate. Rigorous analysis shows that the PDT-based planning is feasible (i.e., the generated plan is applicable) and complete (i.e., a feasible plan, if exits, is guaranteed to be found). The algorithm complexity further indicates that the solution time is only linearly proportional to the robot numbers and types. Simulation and experiment results demonstrate that reactive plan can be generated for large HMRS in real-time, which outperforms the state-of-the-art methods.

Receding horizon control for persistent monitoring tasks with monitoring count requirements

AbstractThis article presents a reachability‐based receding horizon control (RHC) method for addressing persistent monitoring problems with count requirements. An agent is assigned to monitor multiple targets in a given environment to minimize the average uncertainty metric of all targets, while ensuring the monitoring count requirements of specific targets within predetermined time windows. To account for the spatial and temporal constraints in the monitoring requirements, a persistence predicate within the signal temporal logic (STL) specifications is introduced, which incorporates cumulative target state signals to effectively describe the monitoring count constraints. Considering the complexities arising from global time domain information requirements in STL constraints validation, an STL formula segmentation method based on completion progress is proposed. Subsequently, a reachability‐based controller for the agent is developed by solving a short‐term RHC problem while ensuring the satisfaction of the STL formulae. Simulation results are provided to illustrate the performance of proposed method.

Decomposition-Based Hierarchical Task Allocation and Planning for Multi-Robots Under Hierarchical Temporal Logic Specifications

Decomposition-Based Hierarchical Task Allocation and Planning for Multi-Robots Under Hierarchical Temporal Logic Specifications

Online Modifications for Event-Based Signal Temporal Logic Specifications

Online Modifications for Event-Based Signal Temporal Logic Specifications

Model Predictive Control with Variational Autoencoders for Signal Temporal Logic Specifications.

This paper presents a control strategy synthesis method for dynamical systems with differential constraints, emphasizing the prioritization of specific rules. Special attention is given to scenarios where not all rules can be simultaneously satisfied to complete a given task, necessitating decisions on the extent to which each rule is satisfied, including which rules must be upheld or disregarded. We propose a learning-based Model Predictive Control (MPC) method designed to address these challenges. Our approach integrates a learning method with a traditional control scheme, enabling the controller to emulate human expert behavior. Rules are represented as Signal Temporal Logic (STL) formulas. A robustness margin, quantifying the degree of rule satisfaction, is learned from expert demonstrations using a Conditional Variational Autoencoder (CVAE). This learned margin is then applied in the MPC process to guide the prioritization or exclusion of rules. In a track driving simulation, our method demonstrates the ability to generate behavior resembling that of human experts and effectively manage rule-based dilemmas.

Mining of extended signal temporal logic specifications with ParetoLib 2.0

Cyber-physical systems are complex environments that combine physical devices (i.e., sensors and actuators) with a software controller. The ubiquity of these systems and dangers associated with their failure require the implementation of mechanisms to monitor, verify and guarantee their correct behaviour. This paper presents ParetoLib 2.0, a Python tool for offline monitoring and specification mining of cyber-physical systems. ParetoLib 2.0 uses signal temporal logic (STL) as the formalism for specifying properties on time series. ParetoLib 2.0 builds upon other tools for evaluating and mining STL expressions, and extends them with new functionalities. ParetoLib 2.0 implements a set of new quantitative operators for trace analysis in STL, a novel mining algorithm and an original graphical user interface. Additionally, the performance is optimised with respect to previous releases of the tool via data-type annotations and multi core support. ParetoLib 2.0 allows the offline verification of STL properties as well as the specification mining of parametric STL templates. Thanks to the implementation of the new quantitative operators for STL, the tool outperforms the expressiveness and capabilities of similar runtime monitors.

Finite-step approximately bi-similar symbolic model for switched systems

Obtaining an approximately bi-similar symbolic model for a continuous-state system is a crucial step in symbolic control. Symbolic control aims to design switching logic to achieve temporal logic specifications. Most existing approaches to approximate bi-simulation are developed over infinite time horizons. However, many control tasks are set within finite periods in practical scenarios. Hence, it makes sense to consider the behavior of trajectories within finite-time horizons. Therefore, this paper introduces two new notions: finite-time uniform incremental stability (FUI-stability) and finite-step approximate bi-simulation. Furthermore, a FUI-stability condition for switched system is derived using the multiple incremental Lyapunov-like functions technique. A symbolic model is constructed for switched system by the state space grid technique. Subsequently, a sufficient condition for finite-step approximate bi-simulation between the finite-time uniformly incrementally stable (FUI-stable) switched system and the constructed symbolic model is derived. Finally, the obtained results are illustrated by two numerical examples.

Statistical Verification using Surrogate Models and Conformal Inference and a Comparison with Risk-Aware Verification

Uncertainty in safety-critical cyber-physical systems can be modeled using a finite number of parameters or parameterized input signals. Given a system specification in Signal Temporal Logic (STL), we would like to verify that for all (infinite) values of the model parameters/input signals, the system satisfies its specification. Unfortunately, this problem is undecidable in general. Statistical model checking (SMC) offers a solution by providing guarantees on the correctness of CPS models by statistically reasoning on model simulations. We propose a new approach for statistical verification of CPS models for user-provided distribution on the model parameters. Our technique uses model simulations to learn surrogate models , and uses conformal inference to provide probabilistic guarantees on the satisfaction of a given STL property. Additionally, we can provide prediction intervals containing the quantitative satisfaction values of the given STL property for any user-specified confidence level. We compare this prediction interval with the interval we get using risk estimation procedures. We also propose a refinement procedure based on Gaussian Process (GP)-based surrogate models for obtaining fine-grained probabilistic guarantees over sub-regions in the parameter space. This in turn enables the CPS designer to choose assured validity domains in the parameter space for safety-critical applications. Finally, we demonstrate the efficacy of our technique on several CPS models.

Adaptive Reactive Synthesis for LTL and LTLf Modulo Theories

Reactive synthesis is the process of generate correct con- trollers from temporal logic specifications. Typically, synthesis is restricted to Boolean specifications in LTL. Recently, a Boolean abstraction technique allows to translate LTLT specifications that contain literals in theories into equi-realizable LTL specifications, but no full synthesis procedure exists yet. In synthesis modulo theories, the system receives valuations of environment variables (from a first-order theory T ) and outputs valuations of system variables from T . In this paper, we address how to syntheize a full controller using a combination of the static Boolean controller obtained from the Booleanized LTL specification together with on-the-fly queries to a solver that produces models of satisfiable existential T formulae. This is the first synthesis method for LTL modulo theories. Additionally, our method can produce adaptive responses which increases explainability and can improve runtime properties like performance. Our approach is applicable to both LTL modulo theories and LTLf modulo theories.

Sequential control barrier functions for mobile robots with dynamic temporal logic specifications

We address a motion planning and control problem for mobile robots to satisfy rich, time-varying tasks expressed as Signal Temporal Logic (STL) specifications. The specifications may include tasks with nested temporal operators or time-conflicting requirements (e.g., achieving periodic tasks or tasks defined within the same time interval). Moreover, the tasks can be defined in locations changing with time (i.e., dynamic targets), and their future motions are not known a priori. This unpredictability requires an online control approach which motivates us to investigate the use of control barrier functions (CBFs). The proposed CBFs take into account the actuation limits of the robots and a feasible sequence of STL tasks. They define time-varying feasible sets of states the system must always stay inside. We show the feasible sequence generation process that even includes the decomposition of periodic tasks and alternative scenarios due to disjunction operators. The sequence is used to define CBFs, ensuring STL satisfaction. We also show some theoretical results on the correctness of the proposed method. We illustrate the benefits of the proposed method and analyze its performance via simulations and experiments with aerial robots.

On reward distribution in reinforcement learning of multi-agent surveillance systems with temporal logic specifications

In multi-agent systems, it is important to design a reward based on the contribution of each agent for efficient learning. In this paper, we propose a reward distribution method for a surveillance system based on our previously proposed multi-agent reinforcement learning method with an aggregator, in which a control specification is described by a linear temporal logic formula. In this method, the aggregator computes and distributes rewards according to the actions that agents take on the surveillance system. Finally, the effectiveness of the proposed method is presented through a numerical simulation of a surveillance problem addressing a specific type of linear temporal logic specification.

A leader‐follower communication protocol for motion planning in partially known environments under temporal logic specifications

AbstractThis paper considers the problem of communication protocols between leaders and its followers for motion planning in an initially partially known environment. In this setting, the leader observes the environment information to satisfy its own local objective and and the follower completes its own local objective by estimating the states of the leader and communicating with the leader to update its knowledge about the environment when it is necessary, where the local objectives can be expressed in temporal logic. A verifier construction is built first to contain all possible communication protocols between the leaders and the followers. Then, a two‐step synthesis procedure is proposed to capture all feasible communication protocol that satisfy the local objectives for the leader and follower, respectively. In the first step, a sub‐verifier is synthesized to satisfy the objective of the follower. In the second step, based on the obtained sub‐verifier, an iterative algorithm is proposed to extract communication protocols such that the objectives of the leader and follower are satisfied, respectively. A running example is provided to illustrate the proposed procedures.

Dynamic event‐triggered prescribed performance control for nonlinear systems with signal temporal logic

AbstractThis article is concerned with the problem of dynamic event‐triggered prescribed performance control for nonlinear systems under signal temporal logic tasks. By utilizing the method of prescribed performance control, the constrained plant can be transformed into an unconstrained one, and a dynamic event‐triggered feedback control law is generated for the transformed system to ensure that the signal temporal logic specification is satisfied. A dynamic event‐triggered mechanism is designed to guarantee the event‐triggered stability, safety and complex specification. Besides, Zeno phenomenon is definitely avoided. Compared with the continuous‐time feedback controller, the event‐triggered controller has proven to be effective in reducing sensing, communication and computation costs. Finally, two simulations are given to illustrate the effectiveness of theoretical results.

Control/physical systems co-design with spectral temporal logic specifications and its applications to MEMS

‘Co-design’ problems try to simultaneously design the physical and control components to improve the overall system performance. However, existing co-design paradigms cannot deal with complex frequency temporal domain specifications. In this paper, we investigate the co-design problem for a class of linear parameter-varying (LPV) systems with frequency temporal domain specifications. Firstly, the frequency temporal domain specifications are written in a formal language called spectral temporal logic (STL). Secondly, the satisfaction conditions of the spectral temporal logic specifications have been transformed into non-linear matrices inequality forms with necessary and sufficient conditions. Thirdly, the co-design problem is transformed into a non-convex optimisation problem with mixed-integer linear matrix inequalities (MILMIs) constraints, and then an iterative algorithm is proposed to solve the co-design problem with semidefinite programming (SDP). Finally, the performance of the algorithm and the expressiveness of spectral temporal logic are illustrated with the applications to micro-electromechanical systems (MEMS).

Direct data-driven control with signal temporal logic specifications

Most control synthesis methods under temporal logic properties require a model of the system, however, identifying such a model can be a challenging task. In this work, we develop a direct data-driven control synthesis method for temporal logic specifications, which does not require this explicit modeling step, capable of providing certificates for the general class of linear systems. After collecting a single sequence of input-output data from the system, we synthesize a controller, such that the controlled system satisfies a (possibly unbounded) temporal logic specification. The underlying optimization problem is solved by mixed-integer linear programming. We demonstrate the applicability of the results through simulation examples.

Risk-Aware MPC for Stochastic Systems with Runtime Temporal Logics

This paper concerns the risk-aware control of stochastic systems with temporal logic specifications dynamically assigned during runtime. Conventional risk-aware control typically assumes that all specifications are predefined and remain unchanged during runtime. In this paper, we propose a novel, provably correct model predictive control scheme for linear systems with additive unbounded stochastic disturbances that dynamically evaluates the feasibility of runtime signal temporal logic specifications and automatically reschedules the control inputs accordingly. The control method guarantees the probabilistic satisfaction of newly accepted specifications without sacrificing the satisfaction of the previously accepted ones. The proposed control method is validated by a robotic motion planning case study.

Reinforcement Learning for Multi-Agent Systems with Temporal Logic Specifications

Reinforcement Learning for Multi-Agent Systems with Temporal Logic Specifications

Reactive Planner Synthesis Under Temporal Logic Specifications

Reactive Planner Synthesis Under Temporal Logic Specifications

Iterative Optimization-based Control of a Class of Mixed Logical Dynamical Systems with STL Specifications: A Case Study on Microgrids

Motivated by the interest in modeling real-world systems as mixed logical dynamical (MLD) systems with signal temporal logic (STL) specifications, this paper introduces an efficient iterative optimization scheme for this class of systems. We focus on a microgrid system with energy losses, providing two formulations: a mixed-integer-based model and a model tailored to the proposed technique. A numerical case study using model predictive control (MPC) demonstrates that the proposed method significantly improves computation time compared to the classical mixed-integer linear programming (MILP) approach for longer time horizons, while also addressing discontinuity and volatility issues sometimes observed in the MILP approach.