This paper addresses the problem of multi-robot task allocation and trajectory planning in industrial environments. The objective is to optimize the overall cost of robot surveillance patrols in a dynamic high-risk environment. In this context, a hybrid beam search based approach is proposed to plan the patrol trajectories iteratively to accommodate environmental changes under some functional and operational constraints. Moreover, a real-time based system is introduced for remotely monitoring dynamic surveillance missions with automated mobile agents. Finally, a case study is detailed to show the efficiency of our approach in the case of the industrial port area of Fos-sur-Mer city in France.

Abstract Cyber-threats are progressing with unrivaled speed and complexity, and security analysis has become a critical issue for preserving systems reliability. In this paper, the problem of security analysis under cyber threats is studied in a discrete event systems framework, where we attempt to analyse the systems security in a timed and a probabilistic setting. The considered systems are modeled by labeled timed probabilistic automata containing both the normal functioning of the system and the attack scenarios. The main contributions of this paper are ( i ) introducing novel quantitative metrics to evaluate the exposure of the considered systems to the existing cyber threats, ( ii ) the analysis of the effectiveness of attack detection functions, by evaluating their performance in terms of reactivity, correctness, and detection delay. These approaches provide deep and comprehensive insight for analysing, maintaining, and enhancing systems security.

This study presents a comprehensive approach to solving an advanced Multi-Robot Task Allocation (MRTA) problem, in which heterogeneous agents, initially stationed at different depots, are required to perform a set of spatially distributed tasks. A key challenge lies in determining which agent performs each task and defining the order in which each agent executes the assigned tasks, while optimizing travel costs and respecting energy constraints. To address this problem, we propose an approach that combines the Greedy Randomized Adaptive Search Procedure (GRASP) with 2-Opt local search. A comparative analysis was conducted against a Mixed Integer Linear Programming (MILP) solver and standard GRASP variants. The results demonstrate that the GRASP + 2-Opt approach strikes a favorable balance between optimality and execution time. This work provides practical insights for applications such as industrial inspection and environmental monitoring, where autonomous multi-robot coordination and energy constraints are essential for sustained and reliable operation.

This study presents a comprehensive approach to solving an advanced Multi-Robot Task Allocation (MRTA) problem, in which heterogeneous agents, initially stationed at different depots, are required to perform a set of spatially distributed tasks. A key challenge lies in determining which agent performs each task and defining the order in which each agent executes the assigned tasks, while optimizing travel costs and respecting energy constraints. To address this problem, we propose an approach that combines the Greedy Randomized Adaptive Search Procedure (GRASP) with 2-Opt local search. A comparative analysis was conducted against a Mixed Integer Linear Programming (MILP) solver and standard GRASP variants. The results demonstrate that the GRASP + 2-Opt approach strikes a favorable balance between optimality and execution time. This work provides practical insights for applications such as industrial inspection and environmental monitoring, where autonomous multi-robot coordination and energy constraints are essential for sustained and reliable operation.

This paper presents a distributed approach for Multi-Robot Task Allocation (MRTA). We consider assigning sequence of tasks to a group of robots with the aim of maximizing the total received reward while respecting resource constraints. For this, a distributed approach for multi-robot task allocation was developed modeling the problem as a Vehicle Routing Problem (VRP). The approach uses a combination of the Consensus Alternating Direction Method of Multipliers (C-ADMM) with Column Generation (CG) and branch-and-bound to arrive into final assignment through communicating a limited amount of information between the robots. The simulations performed demonstrate the efficiency of the approach by achieving a small relative error with respect to the centralized solution.

In this paper, the problem of cyber-attacks detection in timed probabilistic discrete event systems via artificial neural networks is investigated. We extend the problem of state estimation for timed probabilistic discrete event systems using artificial neural networks, to address attack detection. So that, a detection strategy is implemented to determine whether the system is operating in normal mode or under attack, and to identify the potential type of attack. Two primary cases are examined: (i) attack detection over observations. In this case, the attack detector recognizes whether the system is in a normal mode or an attack mode after each new observation, (ii) attack detection over time. Here, the attack detector evaluates the system’s status at each clock time increment.

In this paper we investigate a supervisory control problem of discrete event systems under attacks. Specially, we consider a type of sensor deception attacks, called replacement attacks, under which the intruder confuses the observation of events by substituting the occurrence of an observation with another. We use labeled Petri nets as the reference formalism to model a discrete event system and represent control specifications in terms of generalized mutual exclusion constraints (GMECs). The concept of a monitor function is proposed to describe the satisfiability of GMECs given an observation by counting the number of occurrences of each label. Due to the existence of attacks, some labels generated by a plant are prone to be altered by an attacker, interfering with a supervisor such that it cannot make correct control decisions. For assisting the monitor function to estimate the number of occurrences of those altered-prone labels, generated by the plant, the notion of label dependency is introduced. Accordingly, a monitor-based supervisor is designed with low online computational effort, avoiding the marking estimation or the reachability analysis of the system. It is verified that the proposed supervisor not only enforces all GMECs no matter whether or not replacement attacks occur, but also keeps the system's behavior as permissive as possible. Note to Practitioners—Cyber physical systems (CPSs) have exhibited multifaceted applications in various fields such as process control systems, smart grids, distributed robotics, autonomous vehicles. Due to the over-reliance on communication networks, CPSs are vulnerable to attacks that can tamper the data collection processes and interfere safety critical decision making processes, resulting in catastrophic damages to the systems. In the frame of discrete event systems, most of existing supervisory control strategies of CPSs under attacks rely on an exhaustive reachability analysis, which is computationally expensive, making such approaches hardly applicable to large systems. In order to address this issue, this work considers a type of sensor deception attacks, called replacement attacks, and proposes a monitor-based supervisor policy, enforcing the control specifications of the systems in the presence of replacement attacks. Without requiring tedious analysis, the designed online supervisor has low computational effort and control decisions only depend on a direct analysis of the observation sequence.

This paper introduces a distributed Multi-Robot Task Allocation (MRTA) approach where each robot can autonomously decide the set of tasks it performs and determine the sequence of sites to visit while optimizing the traveling costs. During the distributed task allocation process, conflicts may arise when multiple robots are able to perform identical tasks. To address this issue, we present a consensus algorithm that combines negotiation and optimization phases. The algorithm allows each robot to decide whether to add or remove conflicting tasks based on information exchanged within the team of robots. Subsequently, we discuss the contribution through a numerical experimentation that compares ascending and descending strategies and compare the performance with a centralized optimization approach.

Attack Graphs are modeling tools to visualize the behaviour of an attacker (intruder) throughout the network. By using attack graphs, the cyber-security agent can evaluate the security of the network as well as know the potential actions of the attacker or even know at what level the system can be compromised. Attack graphs are usually used offline to measure the resilience of a network against cyber-attacks. This paper shows that such models can also be used online to recognize the current actions of an attacker throughout the network, while it is under attack using a conditional state probability. Our setting is that during the attack some events are observed with their time stamps. This information is used to refine the estimation of each mode i.e., attack action, in the graph over time.

This paper deals with the optimisation of a multi-robot inspection mission in an industrial area. We aim to solve a specific combinatorial optimisation problem where a team of sensing mobile robots must gather several measurement tasks distributed over the state space. Based on previous work where a Hybrid Filtered Beam Search (HFBS) approach solves task assignment and planning for this specific problem, we focus on the planning aspect to improve the computed solution. Therefore, this planning problem is modeled as a one-depot multiple Travelling Salesman Problem (mTSP). As the performance of HFBS depends on the challenging selection of its suitable parameters, and considering the coupling between task assignment and task planning problems, we propose a local search algorithm that improves the solution and deals with the optimality issue.

Safety and risks prevention in numerous industrial domains require a systematic monitoring of areas with high-risk level. The surveillance tasks can be assessed by smart sensor systems. This work is devoted to configure a patrol of mobile robots associated with sets of sensors in order to perform a given sequence of surveillance tasks at minimal cost. The environment to be monitored as the trajectories of the robots are modelled with Petri nets. The objective is reformulated as an initial marking optimization problem in the Petri net framework. A real case is considered with the port area in Le Havre City.

In this paper, the precision evaluation of a class of timed workflow nets (WN) is addressed. A novel method for assessing the precision of a labelled stochastic timed WN (LSWN) with respect to a timed log λtcomposed by traces of dated events is proposed. The evaluation involves the combined use of two separated metrics of precision regarding a) the exceeding language of the untimed WN with respect to the untimed log, and b) the surplus covering of the timed sequences by the stochastic model. The assessment of the temporal precision (b) considers the mean durations extracted from the timed log and frequency of occurrence of the traces in λt.

In this paper we consider timed automata endowed with a single clock that is reset at each event occurrence. A time interval is associated with each transition specifying at which clock values it may occur. We assume that the (logical and timed) structure of a timed automaton is known, and event labels associated with transitions are not observable. The problem addressed in this paper is to estimate and update the set of possible current discrete states as time elapses without any observation being received. By a partitioning of time intervals into regions, we design a λ-observer (λ is the null observed sequence) that, for a given state and a current time value, estimates the set of possible current states and the corresponding regions to which the timer value associated with each possible current state may belong.

This paper is about the design of control sequences for discrete event systems (DESs) modeled with bounded partially controlled timed Petri nets (PC-TPNs) including a set of temporal specifications that correspond to minimal firing durations. Petri nets are well-known mathematical and graphical models that are widely used to describe distributed DESs, including choices, synchronizations, and parallelisms. The domains of application include but are not restricted to manufacturing systems, computer science, and transportation networks. Including the time in the model is important to consider many control problems. This paper is more particularly concerned with control issues in timed context and uncertain environments when unexpected events occur and when control errors disturb the system behavior from the planned policy decided by the controller. To deal with such uncertainties, we propose first to build a timed extended reachability graph (TERG) that includes the time specifications when the PC-TPN behaves with an earliest firing policy. Then, the optimal paths in TERG are found by using an approach based on discrete time Markov decision processes under discounted criterion. Several simulations illustrate the benefit of our method from the computational point of view, in particular for uncertain environments.

This paper concerns the diagnosis of faults for stochastic discrete event systems that behave according to non-Markovian dynamics. k -bounded partially observed Petri nets are used to model the system structure and the sensors. Stochastic processes with probability density functions (pdf) of finite support define the dynamics. Structural and temporal faults are considered. Structural faults correspond to specific sequences of events that should satisfy precedence conditions defined with patterns. Temporal faults are defined with time constraints that must be fulfilled by the firing durations. The probabilities of consistent trajectories are computed with a numerical scheme from the collected timed measurements. The advantage of the proposed scheme is that it can be used for a large variety of pdf that may be defined either with an analytical or a numerical description. It works also for various time semantics. Diagnosis in terms of probability for faulty patterns and temporal constraints is established as a consequence.

The Railway transportation networks can be considered as discrete event systems with time constraints. The time factor is a critical parameter, since it includes dates and schedules to be respected in order to avoid overlaps, delays and collisions between trains. Petri nets have been recognized as powerful modelling and analysis tools for discrete event systems with time constraints. So, they are suitable for railway transportation systems. This article is devoted to the modelling and identification of the Tunisian Railway Network. The proposed approach consists in identifying, from experimental measurements, the dynamical behavior of the system by using interpreted Stochastic P-timed Petri Nets (SP-TPNs). The resulting model is suitable to simulate the traffic and also to evaluate the influence of different types of disturbances on the expected schedule.

Various aspects of security and privacy in many application domains can be assessed based on proper analysis of successive measurements that are collected on a given system. This work is devoted to such issues in the context of timed stochastic Petri net models. We assume that certain events and part of the marking trajectories are observable to adversaries who aim to determine when the system is performing secret operations, such as time intervals during which the system is executing certain critical sequences of events (as captured, for instance, in language-based opacity formulations). The combined use of the k-step trajectory-observer and the Markov model of the stochastic Petri net leads to probabilistic indicators helpful for evaluating language-based opacity of the given system, related timing aspects, and possible strategies to improve them.

This paper is about the incremental computation of control sequences for complex discrete event systems (DES) in uncertain environments. Transition-timed Petri nets (T-TPN) that behave under earliest firing policy are used to model a class of flexible manufacturing systems (FMS) where operations are proceeded with partial routing flexibility (namely hybrid FMS). Uncertainties are assumed to occur due to interruption of operations or unreliable resources. The objective is to find a control sequence from an initial state to a reference one with a trade-off between performance and robustness. For that, a systematic T-TPN-based multi-level formalism is used for the modelling. Then a new cost function is introduced to estimate the time and risk to reach the reference. A modified beam search algorithm is also proposed to selectively explore the PN state space and search for the best control sequence.

The reliance of many emerging applications on shared cyber-infrastructures has prompted the study of various notions for security and privacy, including notions for deterministic, non-deterministic, and probabilistic systems. The main contribution of this work is to extend these ideas to timed stochastic systems, by introducing and analyzing timing aspects of initial-state opacity, as measures of vulnerability to security violations. More specifically, we consider partially observed stochastic Petri net (POSPN) models that behave according to Markovian dynamics. We assume that certain events are observable to an outside observer (intruder) and we are interested in initial-state opacity, i.e., determining whether an intruder can infer that the initial marking of the system necessarily lies within a given secret set of initial states. In case initial-state opacity is violated for some behavior in the system, we are also interested in knowing how much time the system remains safe before this violation occurs.

The paper focuses on robust scheduling for flexible manufacturing systems (FMSs) with unreliable resources modelled by timed Petri nets (TPNs). For this purpose, the paper shows that schedulers based on beam search method can be combined with liveness-enforcing supervisors in a straightforward way. This combination is motivated by some properties in the set of reachable markings of a TPN. The use of the liveness-enforcing supervisor improves the robustness of the scheduling without degrading the performance for a particular class of job-shop systems. An example is given to illustrate the proposed strategy.

The regular increase in the number of passengers makes the management of transportation systems more and more complex. Railway transport requires specific needs. Indeed, many decision and optimization problems occur from the planning phase to the implementation phase. Railway transport networks can be considered as discrete event systems with time constraints. The time factor is a critical parameter, since it includes dates and schedules to be respected in order to avoid overlaps, delays and collisions between trains. The uncertainties affect the service and the availability of transportation resources and, consequently, the planned transport schedule. Petri nets have been recognized as powerful modelling and analysis tools for discrete event systems with time constraints. Consequently, they are suitable for railway transport systems. This article is devoted to the modelling, analysis and performance evaluation of the railway transport network system of the Sahel Tunisia in order to help operators to design efficient and robust schedules.

This paper concerns the diagnosis of temporal faults for stochastic discrete event systems that behave according to non-Markovian dynamics. K-bounded partially observed Petri nets are used to model the system structure and the sensors. Stochastic processes with probability density functions of finite support model the dynamics. Temporal faults are defined according to time constraints that must be fulfilled by the firing durations. From the proposed modelling and the collected timed measurements, the probabilities of consistent trajectories are computed with a numerical scheme. The advantage of the proposed scheme is that it can be used for a large variety of probability density functions. It works also for various time semantics. Diagnosis in terms of probability is established as a consequence.

In this paper a systematic method is proposed for the modeling of hybrid flexible manufacturing systems (FMS) with timed Petri nets including buffer places. Hybrid FMS are workshops consisting of a combination of operations, some in job shop and others in open shop. Three basic functions are proposed to iteratively construct the complete model. The method automatically builds the incidence matrices, the initial marking vector and the temporal parameter vector from a synthetic description of the workshop.

This paper concerns the design of optimal control sequences for timed Petri nets under earliest firing policy. Optimality is defined with respect to the sequences duration. The proposed method computes the control firing sequence and its duration by solving integer linear problems constrained by a set of matrix inequalities that must be fulfilled by a sequence of elementary firing count vectors. To reduce the error that may affect the estimation of the sequence duration, an expansion of the net structure is proposed with respect to the time parameters. The estimation error is proved to be bounded depending on a granularity parameter used for expansion.

This paper deals with problems of detection and isolation of temporal faults in timed stochastic discrete event systems. Partially labeled timed Petri nets are used to model the considered systems. Temporal faults corresponding to significant variations of the support of the probability density function (pdf) are considered. A pdf represents the firing duration of each transition. A Moving Average control chart (also known as a Moving Mean chart) is applied in order to detect the variation of mean duration. The advantages of the proposed analysis are to detect variations in time series when parameters vary slowly and to isolate the faults thanks to the signature table.

This paper proposes algorithms to design control sequences for untimed Petri nets. The aim of the controller is to incrementally compute sequences of transition firings with minimal or near-minimal size from an initial marking to a reference one, avoiding forbidden markings and non-promising branches. The approach combines a partial exploration of the reachability graph with a model predictive control strategy. The main contribution is to explore only a small area of the reachability graph according to a double limitation in breadth and in depth in order to provide solution with a low computational effort. Thanks to its reduced computational effort and to the good performance of model predictive control in uncertain and perturbed environments, the method is suitable for proactive deadlock-free scheduling problems. It is applicable to a large class of discrete event systems in particular in the domain of flexible manufacturing, communication and computer science or transportation and traffic.

This paper concerns the fault diagnosis of stochastic discrete event systems that behave with non-Markovian dynamics. Partially observed Petri nets are used to model the system structure and the sensors. Stochastic processes with arbitrary probability density functions and various time semantics are used to model the dynamics including the failure processes. From the proposed modelling and the collected timed measurements, the probabilities of consistent trajectories are computed with a numerical scheme. The advantage of the proposed scheme is that it can be used for arbitrary probability density functions of the firing durations. It works for race or preselection choice policies. Diagnosis in terms of faults probability is established as a consequence. An example is presented to illustrate the method.

This paper is about the detection of tire defects in multi-textural radiographic images. We consider the tire defects characterization problem in ways of local regularity analysis and scale characteristic. Optimal scale and threshold parameters are selected using a defect edge measurement model to frame defect edge detection. This framework distinguishes the defects from the background textures. Finally, a novel method for detection of tire defects is proposed based on wavelet multiscale analysis. We provide examples with a consistent dataset of 400 images selected over 3700 industrial images in order to illustrate and validate the obtained results which demonstrate substantial improvement over the state of the art.

The main contribution of this note is to propose algorithms that incrementally compute control sequences that drive the marking of timed Petri nets from an initial value to a reference one with a duration that approaches the minimal duration. These algorithms are based on a partial exploration of the reachability graph that is inspired from model predictive control. They include perturbation rejection and forbidden marking avoidance and are suitable to track trajectories when the initial and reference markings are far from each other. Application cases illustrate the efficiency of the method.

This paper presents a XY-Theta micrometric platform, which is extremely compact and offers a wide 300 × 300 mm workspace. This platform is held by a serial kinematic chain of four revolute joints, constituting a redundant robot. Each point of the horizontal platform can be positioned under a vertical axis in a two-step approach: in a coarse positioning mode, the four axes are controlled to position and orientate the object with a position error less than 7 µm; in a fine mode, two axes are mechanically blocked while two others are controlled to reduce the final position error below 2 µm. The choice of the blocked and moving axes depends on the lever arm length and the mechanism is designed to optimize the link lengths to reduce the final position error. The aim of the paper is to characterize the platform repeatability performances. An estimation of the repeatability is performed with a camera. These results are then compared to previous results based on the stationary cube method. The two measurements methods lead to similar results with a repeatability close to 2 µm showing a significant improvement of the performances.

This paper concerns the prevention of faults in discrete event systems modeled with partially observed Petri nets (POPNs) that include the definition of sensors used to measure the events and markings. Observation sequences result from this modeling, and the firing sequences and initial marking consistent with a given observation sequence are systematically obtained. The degree of confidence of past and future states and events are computed: state estimation fault diagnosis and fault prediction result from this computation. Finally, diagnosability, detectability, and predictability are defined for observation sequences and POPNs and are discussed with respect to the sensor configuration.

This article concerns the prevention of fault in discrete event systems (DES). For this purpose, DES are modeled with partially observed Petri nets (POPNs) that include the definition of sensors used to measure the events and markings. Observation sequences result from this modeling. The firing sequences and initial markings consistent with a given observation sequence are systematically obtained. Future states and events are predicted and degrees of confidence are computed for these predictions. State estimation and fault prediction result from this computation. Finally detectability and predictability are defined for POPNs and discussed with respect to the sensor configuration in order to quantify the quality of estimation and prediction.

This paper addresses the problems of fault detection and diagnosis for dynamic discrete event systems modeled with Petri nets. The proposed method provides diagnosis decisions via the analysis of observation sequences that include some observable events and the partial measurement of the successive states visited by the system. The method is applied on a production and distribution system.

In this paper, we consider the identification problem of stochastic and deterministic stochastic Petri nets (PNs). The approach herein proposed consists of inferring a PN structure and identifying its parameters. Hence, the first step leads to the synthesis of a PN structure with the measurable sequence of events and states. This approach determines the measurable part and estimates the nonmeasurable part of the PN to be established. Once both parts are obtained, the PN structure and the initial marking of the nonmeasurable places are obtained thanks to the integer linear programming technique. In the second step of this approach, the parameters of the obtained model are estimated. Stochastic and deterministic stochastic PNs with deterministic and exponentially distributed transition durations are considered. A systematic identification method is proposed based on event sequences that are recorded by supervision systems. This method is based on a Markov model whose state space is isomorphic to the reachability graph of the untimed PN model.

This paper is devoted to multisource renewable energy systems. A modeling approach is proposed that brings a detailed understanding of the coupling and uncoupling of DC/DC power converters on a DC bus including the regulation of the DC bus voltage and the driving of current provided by each converter to the load. This approach is systematic and the resulting average state-space model depends only on the number and characteristics of the converters. The model has a generic expression the parameters of which switch according to the converters coupling and uncoupling on the DC bus. The model has been identified and validated with an experimental device developed by GREAH Research Group for the optimization of energies transfers for multisource renewable energy systems. Our approach can be used in the context of power management as support for performance evaluation (converter design, supervisory control design, and so on).

This paper is about fault detection and identification of discrete event systems. The proposed approach is based on Petri nets (PNs) that are used to design reference and faulty models. The main contribution concerns the design and identification of these models according to the statistical analysis of the alarm sequences that are collected on the considered system. The model structure is described as a state graph, and the parameters of the probability density functions (pdfs) for transition firing periods are estimated. Normal and exponential pdfs are considered, and estimation is detailed in case of concurring behaviors. The reference models, described as timed PNs, are then used for fault detection and isolation issues. Finally, stochastic PNs with normal and exponential pdfs are considered to include a representation of the faulty behaviors.

In this paper, a new method for the estimation of orientation repeatability index is proposed for industrial manipulator robots. First, we compute orientation repeatability in different locations of the workspace using the experimental covariance matrix and the stochastic ellipsoid modeling. Then we display experimental results about the direct measurement of orientation repeatability for an industrial Samsung robot in different workspace locations and with different loads. The two proposed procedures are compared. We analyze the incidence of workspace location on orientation repeatability and bring additional results to the existing literature.

The paper proposes a new procedure to compare the repeatability of serial and parallel robots based on the stochastic ellipsoid theory. The ISO9283 position repeatability index is estimated but also other performance criteria built upon the stochastic ellipsoid geometrical characteristics. The choice of the best comparison criterion is investigated and different solutions are proposed, associated with the task specificity. For each criterion, maps are built to determine the set of workspace points where the serial robot is better than the parallel robot. The ratio of the workspace surface where one robot is better than the other is computed and the results are analysed. Contrary to the common opinion that parallel robots are more accurate than serial robots, we prove here that the repeatability performance depends mainly on the chosen performance criterion. Another result found is that the considered R̲RRRR̲ parallel robot keeps the same repeatability in all its workspace.

Early detection and isolation of faults can help avoid major system breakdowns. This paper presents a non parametric fault diagnosis method to detect and isolate faults in industrial environment. The proposed Input Output Classification Mapping (IOCM) algorithm is based on mapping the input parameters from Gaussian hidden layer functions of an RBF neural network to an output layer. In result the input data of each situation is clustered in a specific surface so every machine state, whether it is normal or faulty it will be represented with its own output layer. Parameters are extracted from input signals or input sub-signals after applying wavelet decomposition and then classified using IOCM. The two techniques before and after decomposition are applied on mechanical system and Tennessee Eastman Challenge Process (TECP) chemical reactor to detect and identify the faults.

Event sequences estimation is an important issue for fault diagnosis of Discrete event systems, so far as fault events cannot directly be measured. This paper is about event sequences estimation with Petri net models. Events are assumed to be represented with transitions, and firing sequences are estimated from measurements of the marking variation. Estimation with and without measurement errors are discussed inn-dimensional vector space over alphabetZ3= {-1, 0, 1}. Sufficient conditions and estimation algorithms are provided. Performance is evaluated, and the efficiency of the approach is illustrated on two examples from manufacturing engineering.

We study the statistical relationship between angular position and target for industrial robots on a micrometric scale and this leads us to understand the angular position stochastic structure. The concept of granular angular space is introduced and transposed in the Cartesian space. Modeling is based on experimental work performed for a Kuka and a Samsung robot. The influence of workspace location, posture and angular granularity ratio on the Cartesian granular space are then analysed.

The diagnosis of discrete event systems is strongly related to events estimation. This paper focuses on faulty behaviors modeled with ordinary Petri nets with some "fault" transitions. Partial but unbiased measurement of the places marking variation is used in order to estimate the firing sequences. The main contribution is to decide which sets of places must be observed for the exact estimation of some given firing sequences. Minimal diagnosers are defined that detect and isolate the firing of fault transitions immediately. Causality relationships and directed paths are also investigated to characterize the influence and dependence areas of the fault transitions. Delayed diagnosers are obtained as a consequence. Note to Practitioners-Structural tools are provided for the analysis of models used in the context of fault detection and isolation for discrete event systems. The systems that are concerned are either manufacturing processes, batch processes, digital devices, or communication protocols with single or multiple failures. Methods are proposed to decide, in a systematic way, if the considered failures can be detected and isolated according to the existing sensors. The obtained results can also be used by designers for sensor selection

In this paper, we display experimental results about the measurement of repeatability of an industrial Kuka robot. We first study the distributions of the angular positions and show that these distributions can be considered as Gaussian. We compute repeatability in different locations of the workspace using the experimental angular covariance matrix and the stochastic ellipsoid modeling. We measure repeatability and observe a high variability. We explain the phenomenon by drawing the distribution of the 30 sample repeatability index. We then compare the computed andmeasured repeatability and conclude that our modeling gives good results. We analyse the incidence of weight and workspace location on repeatability and bring additional results to the existing literature.

Petri net (PN) models are useful tools for the modeling of discrete event systems and hybrid systems. This paper is about the parameters estimation for two classes of timed PNs: T-timed PNs and continuous PNs with variable speeds. The parameters to be estimated are either incidence or temporal parameters. Data- and model-based methods are proposed. In each case, on-line and off-line implementations are detailed. As a consequence, identification and monitoring applications for hybrid systems are described.

Minimizing the queue length and vehicle delay time at crossroads is a major problem in the regulation of the traffic urban networks. This paper deals with two formal approaches based on Petri nets for a single crossroad. On one hand, these approaches make it possible to study the traffic behavior at crossroad in a microscopic point of view and in a macroscopic one. On other hand, the developed models provide a tool for the performance analysis of the different traffic signal's control. For this purpose, we show the performance indices of the vehicle interval control, which are obtained from simulation examples.

Petri nets are a suitable tool for the modeling, analysis, and control design of hybrid systems because they offer the opportunity to combine discrete dynamics with continuous ones in a comprehensive way. This paper is about the structural sensitivity of the nodes (places or transitions) with respect to the firing and staying conditions attached to the Petri nets. The sensitivity of subnets is also concerned. The proposed results are interesting to decide if the marking of a given place or the firing sequence of a given transition depends or not on the value of a given parameter that is attached to a particular node or subnet. Conflicts are considered as a particular class of subnets. As a consequence, the structural sensitivity provides some information about the influence and dependence areas of conflicts.

This article is about the design and simulation of hybrid dynamic systems modelled by Petri nets without conflict. For this purpose, a fuzzy multi-model is developed that combines a discrete event description and a continuous approximation of the transitions firing. The transitions are characterised by local clocks, firing rates, and starting orders that are described as fuzzy variables. The definition of the fuzzy sets is related to balance parameters that are suitable to represent the discrete and continuous parts of the hybrid Petri nets. In fact, the fuzzy multi-model has two limit behaviours that correspond to T-timed Petri nets and continuous Petri nets with variable speeds when the balance parameters tend either to zero or to infinity. Thus, the spatial distribution of the balance parameters is useful to design and simulate hybrid systems with a unique model.

Proposes a fuzzy multimodel to describe the behavior of vehicles at a road crossing in order to improve the analysis and performance evaluation of traffic systems. This new model inspired by stochastic Petri nets consists of linear local models based on a Takagi-Sugeno model and may be used for other stochastic systems. The approach is illustrated by a simple road crossing.

This article deals with the modeling of traffic networks by means of fuzzy granular systems. Such systems are useful to combine discrete event descriptions and continuous approximations of the occurrence of events. For this reason, fuzzy granular systems are interesting in the context of traffic modeling because the traffic is alternatively described with macroscopic continuous models and microscopic discrete event ones. In that context, fuzzy granular systems offer an unique opportunity to associate both categories of models and to pass progressively from a continuous approach to a discrete event one and vice-versa.

The traffic flow theory is concerned with finding a relation among the variables of traffic flow. We propose a new approach which consists of representing these variables by those of continuous Petri nets with variable speed (VCPN). A model of VCPN is suggested for the analysis and control design in urban and interurban networks. The proposed model provides representation for both motorway corridors and complex road junctions.

This paper deals with discrete event systems (DES) modeled either by discrete timed Petri nets without conflict or by continuous Petri nets. A fuzzy rule-based multimodel is developed for this kind of system. The behavior of each Petri net transition is described by the combination of two linear local fuzzy models. Using the Takagi-Sugemo model in a systematic way, we define the exact modeling for both classes of timed Petri nets. As a result, we notice that classical sets result in the exact description of discrete timed Petri nets. On the contrary, only fuzzy sets are suitable to describe continuous Petri nets exactly. The proposed fuzzy multimodels are very interesting from a control point of view. In that sense, general results such as convergence for timed Petri nets are given.

Petri nets (PNs) are useful tools for the modeling and analysis of discrete event systems. This work deals with the estimation of firing and enabling sequences for timed transition PNs with unknown time delays. The marking and reserved marking of the places are measured online. The estimation problem has exact and approximated solutions that are described. Sufficient conditions are given on the measurement accuracy of the marking and reserved marking vectors, so that the estimation of firing and enabling sequences is an exact one. If the estimation provides several solutions, the PN is extended in order to give a unique solution. Numerical aspects of the estimation are also investigated. As a consequence of this, the proposed method provides interesting tools for the modeling, performance analysis, and above all the monitoring of manufacturing systems and road traffic networks.