Mission Accomplished: An Introduction to Formal Methods in Mobile Robot Motion Planning and Control

Lin, Hai

doi:10.1142/s2301385014300029

Cited by 38 publications

(7 citation statements)

References 73 publications

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“…Recent years have seen an increasing interest in applying formal methods in robotic motion planning for a systematic, provably correct and top-down design framework [1], [2]. In practice considering the environment uncertainties, sensor noise and actuator imperfection, such control problems have been extended to probabilistic systems such as Markov Chain (MC) or Markov Decision Process (MDP) recently [3].…”

Section: Introductionmentioning

confidence: 99%

Counterexample-guided permissive supervisor synthesis for probabilistic systems through learning

Lin

2015

2015 American Control Conference (ACC)

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Formal methods in robotic motion planning have emerged as a hot research topic recently due to its correctby-design nature, and most results haven been based on nonprobabilistic discrete models. To better handle the environment uncertainties, sensor noise and actuator imperfection, control problems in probabilistic systems like Markov Chain (MC) and Markov Decision Process (MDP) have also been studied. Most existing methods are either based on probabilistic model checking or through reinforcement learning oriented optimization. On the other hand, in the literature of supervisory control of discrete event systems, people usually design supervisors with maximum permissive nature. In other words, a collection of schedulers, instead of a single one scheduler, that satisfy the given specification is designed at the same time. We are therefore motivated to propose a novel learning based automated supervisor synthesis framework to automatically generate permissive supervisor so that the supervised system satisfies the given specification. Our approach is based on a modified L* learning algorithm and runs iteratively. It is guaranteed to be correct and terminate in finite steps.

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Section: Introductionmentioning

confidence: 99%

Counterexample-guided permissive supervisor synthesis for probabilistic systems through learning

Lin

2015

2015 American Control Conference (ACC)

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“…The notion of refinement has been extended to continuous behaviors. Simulation relations and temporal logics over reals have been defined in [23]- [25]. However, compared to discrete models, few modeling frameworks allow to reason on the refinement of continuous behaviors.…”

Section: Motivationmentioning

confidence: 99%

“…c) Event refinement: The refinement of continuous events is close to the one of discrete events. It is based on a simulation relationship defined on states continuously observed (continuous simulation as defined in [23]- [25]). One may consider that an abstract plant is refined by several plants (e.g.…”

Section: Refining Continuous Systemsmentioning

confidence: 99%

Handling Refinement of Continuous Behaviors: A Proof Based Approach with Event-B

Dupont

Aït‐Ameur

Pantel

et al. 2019

2019 International Symposium on Theoretical Aspects of Software Engineering (TASE)

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Cyber-physical systems (CPS) are taking a crucial role in various areas of our society and industry. Yet, because of their hybrid nature (i.e. the integration of both continuous and discrete features), their design and verification are not easy to handle, in particular when they are part of a critical system. Their certification requires to exhibit a formal argumentation that formal methods should be able to provide.This paper addresses the formal development of CPS using correct-by-construction refinement and proof based approaches. It relies on the Event-B formal method. In addition to modeling both the discrete and continuous parts of a CPS, this paper presents a novel approach in two steps.First it shows that the generic formal model we have defined, integrating both discrete and continuous behaviors, can be instantiated by various kinds of CPS. Fundamentally, continuous behaviors modeled by differential equations mingle with discrete transition systems (mode automaton), which model discrete behaviors. Here, refinement is used as a decomposition mechanism.Second, it expands the refinement operation, well mastered in the discrete world, to cover continuous behaviors. We show that different levels of abstraction of continuous aspects can be glued in a refinement chain. The proposed approach has been completely formalized using Event-B on the Rodin platform and a case study based on water tanks is used to illustrate it.

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“…Much recent progress towards the goal of effective CPS control has been made through the use of temporal logic [1]. Temporal logics like Linear Temporal Logic (LTL), Computation Tree Logic (CTL), and Signal Temporal Logic (STL), encode complex system behaviors as logical formulas.…”

Section: Introduction and Related Workmentioning

confidence: 99%

Trajectory Optimization for High-Dimensional Nonlinear Systems Under STL Specifications

Kurtz

Lin

2021

IEEE Control Syst. Lett.

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Signal Temporal Logic (STL) has gained popularity in recent years as a specification language for cyber-physical systems, especially in robotics. Beyond being expressive and easy to understand, STL is appealing because the synthesis problemgenerating a trajectory that satisfies a given specification-can be formulated as a trajectory optimization problem. Unfortunately, the associated cost function is nonsmooth and non-convex. As a result, existing synthesis methods scale poorly to high-dimensional nonlinear systems. In this letter, we present a new trajectory optimization approach for STL synthesis based on Differential Dynamic Programming (DDP). It is well known that DDP scales well to extremely high-dimensional nonlinear systems like robotic quadrupeds and humanoids: we show that these advantages can be harnessed for STL synthesis. We prove the soundness of our proposed approach, demonstrate order-of-magnitude speed improvements over the state-of-the-art on several benchmark problems, and demonstrate the scalability of our approach to the full nonlinear dynamics of a 7 degree-of-freedom robot arm.

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Mission Accomplished: An Introduction to Formal Methods in Mobile Robot Motion Planning and Control

Cited by 38 publications

References 73 publications

Counterexample-guided permissive supervisor synthesis for probabilistic systems through learning

Counterexample-guided permissive supervisor synthesis for probabilistic systems through learning

Handling Refinement of Continuous Behaviors: A Proof Based Approach with Event-B

Trajectory Optimization for High-Dimensional Nonlinear Systems Under STL Specifications

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