Signal Temporal Logic Research Articles

Diverse Controllable Diffusion Policy With Signal Temporal Logic

Diverse Controllable Diffusion Policy With Signal Temporal Logic

Hand It to Me Formally! Data-Driven Control for Human-Robot Handovers With Signal Temporal Logic

Hand It to Me Formally! Data-Driven Control for Human-Robot Handovers With Signal Temporal Logic

Scaling Learning based Policy Optimization for Temporal Logic Tasks by Controller Network Dropout

This paper introduces a model-based approach for training feedback controllers for an autonomous agent operating in a highly nonlinear (albeit deterministic) environment. We desire the trained policy to ensure that the agent satisfies specific task objectives and safety constraints, both expressed in Discrete-Time Signal Temporal Logic (DT-STL). One advantage for reformulation of a task via formal frameworks, like DT-STL, is that it permits quantitative satisfaction semantics. In other words, given a trajectory and a DT-STL formula, we can compute the robustness , which can be interpreted as an approximate signed distance between the trajectory and the set of trajectories satisfying the formula. We utilize feedback control, and we assume a feed forward neural network for learning the feedback controller. We show how this learning problem is similar to training recurrent neural networks (RNNs), where the number of recurrent units is proportional to the temporal horizon of the agent's task objectives. This poses a challenge: RNNs are susceptible to vanishing and exploding gradients, and naïve gradient descent-based strategies to solve long-horizon task objectives thus suffer from the same problems. To tackle this challenge, we introduce a novel gradient approximation algorithm based on the idea of dropout or gradient sampling. One of the main contributions is the notion of controller network dropout , where we approximate the NN controller in several time-steps in the task horizon by the control input obtained using the controller in a previous training step. We show that our control synthesis methodology, can be quite helpful for stochastic gradient descent to converge with less numerical issues, enabling scalable backpropagation over long time horizons and trajectories over high dimensional state spaces. We demonstrate the efficacy of our approach on various motion planning applications requiring complex spatio-temporal and sequential tasks ranging over thousands of time-steps.

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.

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.

Multiple tasks control of nonlinear systems under signal temporal logic and its application to mobile robots

AbstractThis paper addresses the control problem of complex temporal logic tasks for nonlinear systems. A new control barrier function (CBF) called time‐varying extent‐compatible control barrier function (TV‐ECCBF) is proposed, which extends the traditional CBF by considering time‐varying extent or volumes. The main aim of TV‐ECCBF is to tackle the issue of avoiding obstacles in real‐world situations that have irregular or dynamically changing shapes, which cannot be efficiently resolved through traditional CBF methods. To encode complex task specifications, a control framework is presented based on signal temporal logic (STL). Additionally, we introduce robust semantics to discuss the satisfaction of target formulas. Moreover, the control framework generates controllers automatically based on different types of tasks, exhibiting global performance in achieving complex tasks. Finally, two examples of mobile robot systems are presented to demonstrate the effectiveness of the TV‐ECCBF and the proposed design framework.

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.

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.

Planning for heterogeneous teams of robots with temporal logic, capability, and resource constraints

This paper presents a comprehensive approach for planning for teams of heterogeneous robots with different capabilities and the transportation of resources. We use Capability Temporal Logic (CaTL), a formal language that helps express tasks involving robots with multiple capabilities with spatial, temporal, and logical constraints. We extend CaTL to also capture resource constraints, where resources can be divisible and indivisible, for instance, sand and bricks, respectively. Robots transport resources using various storage types, such as uniform (shared storage among resources) and compartmental (individual storage per resource). Robots’ resource transportation capacity is defined based on resource type and robot class. Robot and resource dynamics and the CaTL mission are jointly encoded in a Mixed Integer Linear Programming (MILP), which maximizes disjoint robot and resource robustness while minimizing spurious movement of both. We propose a multi-robustness approach for Multi-Class Signal Temporal Logic (mcSTL), allowing for generalized quantitative semantics across multiple predicate classes. Thus, we compute availability robustness scores for robots and resources separately. Finally, we conduct multiple experiments demonstrating functionality and time performance by varying resources and storage types.

Estimating event probabilities via signal temporal logic and first occurrence distributions

Abstract Estimating the probability of events is a significant challenge in many fields, often requiring a probabilistic model or additional labels and tasks for accurate prediction. However, those methods have limited scalability or unnecessary computational resource consumption due to predicting unrelated values. To address these issues, we propose a novel approach that estimates event probabilities based on the distributions of their first occurrence in the time domain. By using Signal Temporal Logic formulas to describe events and applying an algorithm that estimates complex events’ probabilities through simple event occurrence distributions, this study presents an efficient approach that does not depend on high-precision prediction. We evaluate the performance of our method on simulated scenarios of unmanned aerial vehicle motion and autonomous driving.

Temporal Logic Explanations for Dynamic Decision Systems Using Anchors and Monte Carlo Tree Search (Abstract Reprint)

For many automated perception and decision tasks, state-of-the-art performance may be obtained by algorithms that are too complex for their behavior to be completely understandable or predictable by human users, e.g., because they employ large machine learning models. To integrate these algorithms into safety-critical decision and control systems, it is particularly important to develop methods that can promote trust into their decisions and help explore their failure modes. In this article, we combine the anchors methodology with Monte Carlo Tree Search to provide local model-agnostic explanations for the behaviors of a given black-box model making decisions by processing time-varying input signals. Our approach searches for descriptive explanations for these decisions in the form of properties of the input signals, expressed in Signal Temporal Logic, which are highly likely to reproduce the observed behavior. To illustrate the methodology, we apply it in simulations to the analysis of a hybrid (continuous-discrete) control system and a collision avoidance system for unmanned aircraft (ACAS Xu) implemented by a neural network.

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.

BUSTLE: a Versatile Tool for the Evolutionary Learning of STL Specifications from Data.

Describing the properties of complex systems that evolve over time is a crucial requirement for monitoring and understanding them. Signal Temporal Logic (STL) is a framework that proved to be effective for this aim because it is expressive and allows state properties as human-readable formulae. Crafting STL formulae that fit a particular system is, however, a difficult task. For this reason, a few approaches have been proposed recently for the automatic learning of STL formulae starting from observations of the system. In this paper, we propose BUSTLE (Bi-level Universal STL Evolver), an approach based on evolutionary computation for learning STL formulae from data. BUSTLE advances the state-of-the-art because it (i) applies to a broader class of problems, in terms of what is known about the state of the system during its observation, and (ii) generates both the structure and the values of the parameters of the formulae employing a bi-level search mechanism (global for the structure, local for the parameters). We consider two cases where (a) observations of the system in both anomalous and regular state are available, or (b) only observations of regular state are available. We experimentally evaluate BUSTLE on problem instances corresponding to the two cases and compare it against previous approaches. We show that the evolved STL formulae are effective and human-readable: the versatility of BUSTLE does not come at the cost of lower effectiveness.

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.

Hybrid Knowledge and Data Driven Synthesis of Runtime Monitors for Cyber-Physical Systems

Recent advances in sensing and computing technology have led to the proliferation of Cyber-Physical Systems (CPS) in safety-critical domains. However, the increasing device complexity, shrinking technology sizes, and shorter time to market have resulted in significant challenges in ensuring the reliability, safety, and security of CPS. This paper presents a hybrid knowledge and data-driven approach for designing run-time context-aware safety monitors that can detect early signs of hazards and mitigate them in CPS. We propose a framework for formal specification of unsafe system context using Signal Temporal Logic (STL) combined with two optimization approaches for scenario-specific refinement and integration of STL specifications using data collected from closed-loop CPS simulations. We demonstrate the effectiveness of our approach in simulation using an autonomous driving system (ADS) and two closed-loop artificial pancreas systems (APS) as well as a publicly-available clinical trial dataset. The results show that a safety monitor developed with the proposed approaches demonstrates up to 4.7 times increase in average prediction accuracy (F1 score) over several well-designed baseline monitors while reducing both false-positive and false-negative rates in most scenarios.

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.

Power management via STL specifications of a DC microgrid integrating renewables and storage devices: a smart railway station case study

This paper presents a method for defining and managing complex power management behaviors in microgrids that incorporate renewable energy sources, storage devices with different characteristics, and a connection to the main grid. In particular, we focus on a smart railway station that integrates regenerative braking energy from trains. The challenge lies in coordinating diverse microgrid components while adhering to constraints across multiple control levels. We use signal temporal logic (STL) to precisely define these complex objectives and integrate them into a model predictive control (MPC) framework. We present numerical simulations using a mixed-integer strategy to demonstrate the approach’s effectiveness.

Cooperative control of heterogeneous multi-agent systems under spatiotemporal constraints

A current trend in research on multi-agent control systems is to consider high-level task specifications that go beyond traditional control objectives and take into account the heterogeneity of each agent in the system, i.e., the different capabilities of the agents in terms of actuation, sensing, communication and computation. This article provides an overview of our work on the problem of control of heterogeneous multi-agent systems under both spatial and temporal constraints as well as our perspective on the challenges and open problems associated with the consideration of such spatiotemporal constraints. Initially, we review a set of control strategies introduced by the authors addressing the satisfaction of cooperative tasks such as formation control as well as individual objectives such as reference tracking. The satisfaction of those objectives is ensured using prescribed performance control. Building upon these approaches we then review recent results on control under high-level spatiotemporal objectives expressed in Signal Temporal Logic, a formal language that allows to express complex spatial tasks that must be satisfied within pre-defined deadlines. Theoretical results considering multi-agent systems with various capabilities under spatiotemporal constraints are presented.

LB4TL: A Smooth Semantics for Temporal Logic to Train Neural Feedback Controllers

This paper presents a framework for training neural network (NN)-based feedback controllers for autonomous agents with deterministic nonlinear dynamics to satisfy task objectives and safety constraints expressed in discrete-time Signal Temporal Logic (DT-STL). Control synthesis that uses the robustness semantics of DT-STL poses challenges due to its non-convexity, non-differentiability, and recursive definition, in particular when it is used to train NN-based controllers. We introduce a smooth neuro-symbolic computation graph to encode DT-STL robustness to represent a smooth approximation of the robustness, enabling the use of powerful stochastic gradient descent and backpropagation-based optimization for training. Our approximation guarantees that it lower bounds the robustness value of a given DT-STL formula, and shows orders of magnitude improvement over existing smooth approximations when applied to control synthesis. We demonstrate our approach on planning to satisfy complex spatio-temporal and sequential tasks, and show scalability with formula complexity.

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.