Receding Horizon Control for Signal Temporal Logic Using Robustness-Conserving Partial Formula Evaluation

We present a general framework for risk semantics on Signal Temporal Logic (STL) specifications for stochastic dynamical systems using axiomatic risk theory. We show that under our recursive risk semantics, risk constraints on STL formulas can be expressed in terms of risk constraints on atomic predicates. We then show how this allows a (stochastic) STL risk constraint to be transformed into a risk-tightened deterministic STL constraint on a related deterministic nominal system, enabling the application of existing STL methods. For affine predicate functions and a (coherent) Distributionally Robust Value at Risk measure, we show how risk constraints on atomic predicates can be reformulated as tightened deterministic affine constraints. We demonstrate the framework using a Model Predictive Control (MPC) design with an STL risk constraint.

We consider the problem of controlling a system with unknown, stochastic dynamics to achieve a complex, time-sensitive task. An example of this problem is controlling a noisy aerial vehicle with partially known dynamics to visit a pre-specified set of regions in any order while avoiding hazardous areas. In particular, we are interested in tasks which can be described by signal temporal logic (STL) specifications. STL is a rich logic that can be used to describe tasks involving bounds on physical parameters, continuous time bounds, and logical relationships over time and states. STL is equipped with a continuous measure called the robustness degree that measures how strongly a given sample path exhibits an STL property [4, 3]. This measure enables the use of continuous optimization problems to solve learning [7, 6] or formal synthesis problems [9] involving STL.

We study control synthesis under Signal Temporal Logic (STL) specifications for driving scenarios where strict rule satisfaction is not always feasible and human experts exhibit context-dependent flexibility. We represent such behavior using robustness slackness—learned rule-wise lower bounds on STL robustness—and introduce sub-goals that encode intermediate intent in the state/output space (e.g., lane-level waypoints). Prior learning-based MPC–STL methods typically infer slackness with VAE priors and plug it into MPC, but these priors can underrepresent multimodal and rare yet valid expert behaviors and do not explicitly model intermediate intent. We propose a diffusion-guided MPC–STL framework that jointly learns slackness and sub-goals from demonstrations and integrates both into STL-constrained MPC. A conditional diffusion model generates pairs of (rule-wise slackness, sub-goal) conditioned on features from the ego vehicle, surrounding traffic, and road context. At run time, a few denoising steps produce samples for the current situation; slackness values define soft STL margins, while sub-goals shape the MPC objective via a terminal (optionally stage) cost, enabling context-dependent trade-offs between rule relaxation and task completion. In closed-loop simulations on held-out highD track-driving scenarios, our method improves task success and yields more realistic lane-changing behavior compared to imitation-learning baselines and MPC–STL variants using CVAE slackness or strict rule enforcement, while remaining computationally tractable for receding-horizon MPC in our experimental setting.

Cyber-physical system applications such as autonomous vehicles, wearable devices, and avionic systems generate a large volume of time-series data. Designers often look for tools to help classify and categorize the data. Traditional machine learning techniques for time-series data offer several solutions to solve these problems; however, the artifacts trained by these algorithms often lack interpretability. On the other hand, temporal logics, such as Signal Temporal Logic (STL) have been successfully used in the formal methods community as specifications of time-series behaviors. In this work, we propose a new technique to automatically learn temporal logic formulae that are able to cluster and classify real-valued time-series data. Previous work on learning STL formulas from data either assumes a formula-template to be given by the user, or assumes some special fragment of STL that enables exploring the formula structure in a systematic fashion. In our technique, we relax these assumptions, and provide a way to systematically explore the space of all STL formulas. As the space of all STL formulas is very large, and contains many semantically equivalent formulas, we suggest a technique to heuristically prune the space of formulas considered. Finally, we illustrate our technique on various case studies from the automotive, transportation and healthcare domain.

This paper reports on a new approach to Signal Temporal Logic (STL) control synthesis, that 1) utilizes a navigation function as the basis to construct a Control Barrier Function (CBF), and 2) composes navigation function-based barrier functions using nonsmooth mappings to encode Boolean operations between the predicates that those barrier functions encode. Because of these two key features, the reported approach 1) covers a larger fragment of STL compared to existing approaches, 2) alleviates the computational cost associated with evaluation of the control law for the system in existing STL control barrier function methodologies, and 3) simultaneously relaxes some of the conservativeness of smooth combinations of barrier functions as a means of implementing Boolean operators. The paper demonstrates the efficacy of this new approach with three simulation case studies, one aiming at illustrating how complex STL motion planning specification can be realized, the second highlights the less-conservativeness of the approach in comparison to the existing methods, and another that shows how this technology can be brought to bear to push the envelope in the context of human-robot social interaction.

Motion planning classically concerns the problem of accomplishing a goal configuration while avoiding obstacles. However, the need for more sophisticated motion planning methodologies, taking temporal aspects into account, has emerged. To address this issue, temporal logics have recently been used to formulate such advanced specifications. This paper will consider Signal Temporal Logic in combination with Model Predictive Control. A robustness metric, called Discrete Average Space Robustness, is introduced and used to maximize the satisfaction of specifications which results in a natural robustness against noise. The comprised optimization problem is convex and formulated as a Linear Program.

We develop a distributed motion planner for multi-robot systems with Signal Temporal Logic (STL) objectives. Existing approaches to STL-based motion planning are limited to fragments of STL that might not capture all desired behaviors or safety requirements. Focusing on the case of a fleet of multi-rotor Unmanned Aerial Vehicles (UAVs) jointly tasked with satisfying a given STL mission, we develop a distributed method, Fly-by-Distributed-Logic (FBDL), for trajectory planning. The proposed method generates trajectories that maximize the smooth robustness of STL specifications, where the associated optimization is solved in a distributed manner. This, to the best of our knowledge, is the first distributed method that can handle the full grammar of STL (bounded time). Simulation studies show the applicability of our approach to a variety of STL missions, including those with nested STL operators and the Until operator. We also compare its performance to a centralized approach and show that our method is computationally faster, but generally computes trajectories with lower robustness.

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.

Deep Reinforcement Learning (DRL) has the potential to be used for synthesizing feedback controllers (agents) for various complex systems with unknown dynamics. These systems are expected to satisfy diverse safety and liveness properties best captured using temporal logic. In RL, the reward function plays a crucial role in specifying the desired behaviour of these agents. However, the problem of designing the reward function for an RL agent to satisfy complex temporal logic specifications has received limited attention in the literature. To address this, we provide a systematic way of generating rewards in real-time by using the quantitative semantics of Signal Temporal Logic (STL), a widely used temporal logic to specify the behaviour of cyber-physical systems. We propose a new quantitative semantics for STL having several desirable properties, making it suitable for reward generation. We evaluate our STL-based reinforcement learning mechanism on several complex continuous control benchmarks and compare our STL semantics with those available in the literature in terms of their efficacy in synthesizing the controller agent. Experimental results establish our new semantics to be the most suitable for synthesizing feedback controllers for complex continuous dynamical systems through reinforcement learning.

Timed reach-avoid specifications, a subset of Signal Temporal Logic (STL), provide an expressive framework for specifying complex tasks in dynamic systems. This letter introduces a novel framework that encodes these specifications into a quadratic programming (QP) controller using backup control barrier functions (backup CBFs). Unlike existing approaches that rely on predefined safe sets, we utilize a backup control strategy within a prediction horizon to construct time-varying implicit sets online. Specifically, we address the limitation of standard backup CBFs regarding finite-time convergence by introducing contractive implicit sets. Rigorous analysis of the time-varying properties confirms that backup CBFs enforce system forward invariance within these contractive sets, driving real-time trajectories to satisfy given specifications. Our method unifies high-level planning with continuous control, while does not require explicit safe set computation for Eventually formulas or predefined performance functions. Numerical simulations validate the performance of our approach in safe planning and control of mobile robots.

We present a controller for human-robot handovers that is automatically synthesized from high-level specifications in Signal Temporal Logic (STL). In contrast to existing controllers, this approach can provide formal guarantees on the timing of each of the handover phases. Using synthesis also allows end-users to specify and dynamically change the robot's behaviors using high-level requirements of goals and constraints rather than by tuning low-level controller parameters. We illustrate the proposed approach by replicating the behavior of existing handover strategies from the literature. We also identify specification parameters that are likely to lead to successful handovers using a public database of human-human handovers.

A major goal of air traffic management is to strategically control the flow of traffic so that the demand at an airport meets but does not exceed the operational capacity in a dynamic environment. This paper uses the concept of receding horizon control (RHC) to conduct real-time planning for airport capacity management (ACM). It is shown that RHC provides a generic and flexible framework for developing real-time allocation algorithms for airport capacity in a dynamic and uncertain environment, and existing approaches such as the one step ahead adjustment can be considered as special cases of this approach. Robustness against the change of the environment and demands and computational efficiency are two advantages when applying RHC to the ACM problem, which are illustrated by a case study.

Vehicle trajectory prediction is essential to autonomous driving tasks. Accurate trajectory prediction of other traffic agents can significantly improve the ability of scene understanding and eventually improve the driving safety level of autonomous vehicles. Popular trajectory prediction methods leverage traffic rules by considering maps or lane graphs as a part of the input. However, this implicit representation is insufficient and can not guarantee an accurate understanding of traffic rules through the model. In this paper, we introduce a novel framework called forecasting using continuous unlikelihood and signal temporal logic (FCUS), which incorporates traffic rules in vehicle motion forecasting by explicitly modeling them as continuous signal temporal logic (STL) features into a GAN-style neural network. By doing so, a strong rule prior can be introduced. Meanwhile, an auxiliary unlikelihood loss is adopted to make the model more rule-aware. Extensive experiments evaluated on the real-world driving dataset show that our framework enables state-of-the-art prediction models to improve 8.92% performance on MinADE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</inf> and 19.73% on avoiding rule violation. Demo videos and code are available at https://chantsss.github.io/FCUS/.

The need for cost-effective fuel economy improvements has driven the introduction of automatic transmissions with an increasing number of gear ratios. Incorporation of interlocking dog clutches in these transmissions decreases package space and increases efficiency, as compared to conventional dry or wet clutches. Unlike friction based clutches, interlocking dog clutches require very precise rotational speed matching prior to engagement. Precise engine speed control is therefore critical to maintaining high shift quality. This research focuses on controlling the engine speed during a gearshift period by manipulating throttle position and combustion phasing. Model predictive control (MPC) is advantageous in this application since the speed profile of a future prediction horizon is known with relatively high confidence. The MPC can find the optimal control actions to achieve the designated speed target without invoking unnecessary actuator manipulation and violating hardware and combustion constraints. This research utilizes linear parameter varying (LPV) MPC to control the engine speed during the gearshift period. Combustion stability constraints are considered with a control oriented covariance of indicated mean effective pressure model (COV of IMEP). The proposed MPC engine speed controller is validated with a high-fidelity 0-dimensional engine model with crank angle resolution. Four case studies, based on simulation, investigate the impact of different MPC design parameters. They also demonstrate that the proposed MPC engine controller successfully achieves the speed reference tracking objective while considering combustion variation constraints.

There is a growing trend toward AI systems interacting with humans to revolutionize a range of application domains such as healthcare and transportation. However, unsafe human-machine interaction can lead to catastrophic failures. We propose a novel approach that predicts future states by accounting for the uncertainty of human interaction, monitors whether predictions satisfy or violate safety requirements, and adapts control actions based on the predictive monitoring results. Specifically, we develop a new quantitative predictive monitor based on Signal Temporal Logic with Uncertainty (STL-U) to compute a robustness degree interval, which indicates the extent to which a sequence of uncertain predictions satisfies or violates an STL-U requirement. We also develop a new loss function to guide the uncertainty calibration of Bayesian deep learning and a new adaptive control method, both of which leverage STL-U quantitative predictive monitoring results. We apply the proposed approach to two case studies: Type 1 Diabetes management and semi-autonomous driving. Experiments show that the proposed approach improves safety and effectiveness in both case studies.