Sofie Haesaert

Shuhao Qi, Qiling Aori, Luyao Zhang et al.

Autonomous driving in interactive traffic scenarios remains challenging because of the mutual influence among vehicles and the inherent uncertainty of surrounding agents. Several model predictive control (MPC) formulations have been proposed to address this challenge, each adopting a different model of inter-agent interaction. While higher-fidelity interaction models enable more intelligent behavior, they incur substantially greater computational cost. Since strong interactions arise only occasionally in real traffic, a practical strategy for balancing performance and computational overhead is to invoke an appropriate controller based on situational demands. To this end, we first conduct a comparative study to assess and hierarchize the interactive capabilities of different MPC formulations. Building on this hierarchy, we then develop a neural network-based classifier for situation-aware switching among these controllers. We demonstrate that, by invoking the most advanced interactive MPC only in rare but critical situations and relying on a basic MPC in the majority of situations, situation-aware switching substantially improves overall performance while significantly reducing computational load.

Ruohan Wang, Zhiyong Sun, Sofie Haesaert

Formal safety guarantees on the synthesis of controllers for stochastic systems can be obtained using correct-by-design approaches. These approaches often use abstractions as finite-state Markov Decision Processes. As the state space of these MDPs grows, the curse of dimensionality makes the computational and memory cost of the probabilistic guarantees, quantified with dynamic programming, scale exponentially. In this work, we leverage decoupled dynamics and unravel, via dynamic programming operations, a tree structure in the Canonical Polyadic Decomposition (CPD) of the value functions. For discrete-time stochastic systems with syntactically co-safe linear temporal logic (scLTL) specifications, we provide provable probabilistic safety guarantees and significantly alleviate the computational burden. We provide an initial validation of the theoretical results on several typical case studies and showcase that the uncovered tree structure enables efficient reductions in the computational burden.

Sofie Haesaert, Sadegh Soudjani, Alessandro Abate

The formal verification and controller synthesis for Markov decision processes that evolve over uncountable state spaces are computationally hard and thus generally rely on the use of approximations. In this work, we consider the correct-by-design control of general Markov decision processes (gMDPs) with respect to temporal logic properties by leveraging approximate probabilistic relations between the original model and its abstraction. We newly work with a robust satisfaction for the construction and verification of control strategies, which allows for both deviations in the outputs of the gMDPs and in the probabilistic transitions. The computation is done over the reduced or abstracted models, such that when a property is robustly satisfied on the abstract model, it is also satisfied on the original model with respect to a refined control strategy.

Lin-Chi Wu, Zengjie Zhang, Sofie Haesaert et al.

Reinforcement learning (RL) is an effective approach to motion planning in autonomous driving, where an optimal driving policy can be automatically learned using the interaction data with the environment. Nevertheless, the reward function for an RL agent, which is significant to its performance, is challenging to be determined. The conventional work mainly focuses on rewarding safe driving states but does not incorporate the awareness of risky driving behaviors of the vehicles. In this paper, we investigate how to use risk-aware reward shaping to leverage the training and test performance of RL agents in autonomous driving. Based on the essential requirements that prescribe the safety specifications for general autonomous driving in practice, we propose additional reshaped reward terms that encourage exploration and penalize risky driving behaviors. A simulation study in OpenAI Gym indicates the advantage of risk-aware reward shaping for various RL agents. Also, we point out that proximal policy optimization (PPO) is likely to be the best RL method that works with risk-aware reward shaping.

Fei Chen, Sofie Haesaert, Alessandro Abate et al.

The analysis of industrial processes, modelled as descriptor systems, is often computationally hard due to the presence of both algebraic couplings and difference equations of high order. In this paper, we introduce a control refinement notion for these descriptor systems that enables analysis and control design over related reduced-order systems. Utilising the behavioural framework, we extend upon the standard hierarchical control refinement for ordinary systems and allow for algebraic couplings inherent to descriptor systems.

Ruohan Wang, Siyuan Liu, Zhiyong Sun et al.

Discrete-time stochastic systems with continuous spaces are hard to verify and control, even with MDP abstractions due to the curse of dimensionality. We propose an abstraction-based framework with robust dynamic programming mappings that deliver control strategies with provable lower bounds on temporal-logic satisfaction, quantified via approximate stochastic simulation relations. Exploiting decoupled dynamics, we reveal a Canonical Polyadic Decomposition tensor structure in value functions that makes dynamic programming scalable. The proposed method provides correct-by-design probabilistic guarantees for temporal logic specifications. We validate our results on continuous-state linear stochastic systems.

Teun van de Laar, Zengjie Zhang, Shuhao Qi et al.

It has been an ambition of many to control a robot for a complex task using natural language (NL). The rise of large language models (LLMs) makes it closer to coming true. However, an LLM-powered system still suffers from the ambiguity inherent in an NL and the uncertainty brought up by LLMs. This paper proposes a novel LLM-based robot motion planner, named \textit{VernaCopter}, with signal temporal logic (STL) specifications serving as a bridge between NL commands and specific task objectives. The rigorous and abstract nature of formal specifications allows the planner to generate high-quality and highly consistent paths to guide the motion control of a robot. Compared to a conventional NL-prompting-based planner, the proposed VernaCopter planner is more stable and reliable due to less ambiguous uncertainty. Its efficacy and advantage have been validated by two small but challenging experimental scenarios, implying its potential in designing NL-driven robots.

Xinyuan Qiu, Ruohan Wang, Siyuan Liu et al.

Correct-by-design synthesis provides a principled framework for establishing formal safety guarantees for stochastic multi-agent systems (MAS). However, conventional approaches based on finite abstractions often incur prohibitive computational costs as the number of agents and the complexity of temporal logic specifications increase. In this work, we study homogeneous stochastic MAS under counting linear temporal logic (cLTL) specifications, and show that the corresponding satisfaction probability admits a structured tensor decomposition via leveraging deterministic finite automata (DFA). Building on this structure, we develop a dual-tree-based value iteration framework that reduces redundant computation in the process of dynamic programming. Numerical results demonstrate the proposed approach's effectiveness and scalability for complex specifications and large-scale MAS.

Oliver Schön, Sofie Haesaert, Sadegh Soudjani

The requirement for identifying accurate system representations has not only been a challenge to fulfill, but it has compromised the scalability of formal methods, as the resulting models are often too complex for effective decision making with formal correctness and performance guarantees. Focusing on probabilistic simulation relations and surrogate models of stochastic systems, we propose an approach that significantly enhances the scalability and practical applicability of such simulation relations by eliminating the need to compute error bounds directly. As a result, we provide an abstraction-based technique that scales effectively to higher dimensions while addressing complex nonlinear agent-environment interactions with infinite-horizon temporal logic guarantees amidst uncertainty. Our approach trades scalability for conservatism favorably, as demonstrated on a complex high-dimensional vehicle intersection case study.

Takahiro Sasaki, Kyohei Otsu, Rohan Thakker et al.

In addition to conventional ground rovers, the Mars 2020 mission will send a helicopter to Mars. The copter's high-resolution data helps the rover to identify small hazards such as steps and pointy rocks, as well as providing rich textual information useful to predict perception performance. In this paper, we consider a three-agent system composed of a Mars rover, copter, and orbiter. The objective is to provide good localization to the rover by selecting an optimal path that minimizes the localization uncertainty accumulation during the rover's traverse. To achieve this goal, we quantify the localizability as a goodness measure associated with the map, and conduct a joint-space search over rover's path and copter's perceptual actions given prior information from the orbiter. We jointly address where to map by the copter and where to drive by the rover using the proposed iterative copter-rover path planner. We conducted numerical simulations using the map of Mars 2020 landing site to demonstrate the effectiveness of the proposed planner.

Elizabeth Polgreen, Viraj Wijesuriya, Sofie Haesaert et al.

We present a new method for statistical verification of quantitative properties over a partially unknown system with actions, utilising a parameterised model (in this work, a parametric Markov decision process) and data collected from experiments performed on the underlying system. We obtain the confidence that the underlying system satisfies a given property, and show that the method uses data efficiently and thus is robust to the amount of data available. These characteristics are achieved by firstly exploiting parameter synthesis to establish a feasible set of parameters for which the underlying system will satisfy the property; secondly, by actively synthesising experiments to increase amount of information in the collected data that is relevant to the property; and finally propagating this information over the model parameters, obtaining a confidence that reflects our belief whether or not the system parameters lie in the feasible set, thereby solving the verification problem.

Sofie Haesaert, Robert Babuska, Alessandro Abate

This article deals with stochastic processes endowed with the Markov (memoryless) property and evolving over general (uncountable) state spaces. The models further depend on a non-deterministic quantity in the form of a control input, which can be selected to affect the probabilistic dynamics. We address the computation of maximal reach-avoid specifications, together with the synthesis of the corresponding optimal controllers. The reach-avoid specification deals with assessing the likelihood that any finite-horizon trajectory of the model enters a given goal set, while avoiding a given set of undesired states. This article newly provides an approximate computational scheme for the reach-avoid specification based on the Fitted Value Iteration algorithm, which hinges on random sample extractions, and gives a-priori computable formal probabilistic bounds on the error made by the approximation algorithm: as such, the output of the numerical scheme is quantitatively assessed and thus meaningful for safety-critical applications. Furthermore, we provide tighter probabilistic error bounds that are sample-based. The overall computational scheme is put in relationship with alternative approximation algorithms in the literature, and finally its performance is practically assessed over a benchmark case study.