Starts with a brief review of the history and the application areas considered in the literature. The author then proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis. In particular, one section is devoted to marked graphs, the concurrent system model most amenable to analysis. Introductory discussions on stochastic nets with their application to performance modeling, and on high-level nets with their application to logic programming, are provided. Also included are recent results on reachability criteria. Suggestions are provided for further reading on many subject areas of Petri nets. >

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Petri nets: Properties, analysis and applications

Survey of robust residual generation and evaluation methods in observer-based fault detection systems

Odometry is the most widely used method for determining the momentary position of a mobile robot. This paper introduces practical methods for measuring and reducing odometry errors that are caused by the two dominant error sources in differential-drive mobile robots: 1) uncertainty about the effective wheelbase; and 2) unequal wheel diameters. These errors stay almost constant over prolonged periods of time. Performing an occasional calibration as proposed here will increase the odometric accuracy of the robot and reduce operation cost because an accurate mobile robot requires fewer absolute positioning updates. Many manufacturers or end-users calibrate their robots, usually in a time-consuming and nonsystematic trial and error approach. By contrast, the method described in this paper is systematic, provides near-optimal results, and it can be performed easily and without complicated equipment. Experimental results are presented that show a consistent improvement of at least one order of magnitude in odometric accuracy (with respect to systematic errors) for a mobile robot calibrated with our method.

https://www.johnloomis.org/ece445/topics/odometry/borenstein/paper58.pdf

Measurement and correction of systematic odometry errors in mobile robots

A variety of important Petri net-based methods to prevent deadlocks arising in flexible manufacturing systems (FMS) are to add some control places and related arcs to strict minimal siphons (SMS) such that no siphon can be emptied. Since the number of minimal siphons grows in general exponentially with respect to a Petri net size, their disadvantages lie in that they often add too many additional places to the net, thereby making the resulting net model much more complex than the original one. This paper explores ways to minimize the new additions of places while achieving the same control purpose. It proposes for the first time the concept of elementary siphons that are a special class of siphons. The set of elementary siphons in a Petri net is generally a proper subset of the set of all SMS. Its smaller cardinality becomes evident in large Petri net models. This paper proves that by adding a control place for each elementary siphon to make sure that it is marked, deadlock can be successfully prevented. Compared with the existing methods, the new method requires a much smaller number of control places and, therefore, is suitable for large-scale Petri nets. An FMS example is used to illustrate the proposed concepts and policy, and show the significant advantage over the previous methods.

Elementary siphons of Petri nets and their application to deadlock prevention in flexible manufacturing systems

Petri nets, as a graphical and mathematical tool, provide a uniform environment for modelling, formal analysis, and design of discrete event systems. The main objective of this paper is to introduce the fundamental concepts of Petri nets to researchers and practitioners, both from academia and industry, who are involved in the work in the areas of modelling and analysis of industrial types of systems, as well as those who may potentially be involved in these areas. The paper begins with an overview of applications of Petri nets, mostly industrial ones. Then, it proceeds with a description of Petri nets, properties, and analysis methods. The discussion of properties is put in the context of industrial applications. The analysis methods are illustrated using an example of a simple robotic assembly system. The performance analysis, using Petri nets, is discussed for deterministic and stochastic Petri nets. The presented techniques are illustrated by examples representing simple production systems. In addition, the paper introduces high-level Petri nets, fuzzy Petri nets, and temporal Petri nets. This is done in the context of application prospects. The paper also briefly discusses some of the reasons restricting the use of Petri nets, mostly, to academic institutions. >

/pdf/petri-nets-and-industrial-applications-a-tutorial-2z7do95d63.pdf

Petri nets and industrial applications: A tutorial

List of Figures List of Tables 1 Introduction 2 Petri Nets and Manufacturing Systems 3 Parallel Mutual Exclusions 4 Sequential Mutual Exclusion 5 Hybrid Synthesis of Petri Nets 6 Illustration of Hybrid Synthesis 7 Discrete Event Control of FMS 8 Augmentation of Petri Nets 9 Petri Nets: Past, Present and Future Appendix A Bibliography Index

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Petri Net Synthesis for Discrete Event Control of Manufacturing Systems

Beginning with a bounded (safe), live, or reversible Petri net as a first-level net model for a system, Petri nets are synthesized by first refining operation places through basic design modules in top-down modular ways, then adding nonshared resource places stepwise, and finally adding shared resource places step by step in a bottom-up manner. Refinement theory is extended to include reversibility of Petri nets. Parallel and sequential mutual exclusions are used to model shared resources. Design of the first-level Petri nets is discussed, and two basic kinds of Petri nets, choice-free and choice-synchronization, are given to cope with different types of manufacturing systems. The major advantages of the method are that the modeling details can be introduced in incremental ways such that complexity can be handled, and the important properties of the resulting Petri net are guaranteed so that costly mathematical analysis for boundedness, liveness, and reversibility can be avoided. A manufacturing system consisting of four machines, one assembly cell, two shared robots, and two buffers is used to illustrate the design methodology. >

A hybrid methodology for synthesis of Petri net models for manufacturing systems

Petri net modeling combined with heuristic search provides a new scheduling method for flexible manufacturing systems. The method formulates a scheduling problem with a Petri net model. Then, it generates and searches a partial reachability graph to find an optimal or near optimal feasible schedule in terms of the firing sequence of the transitions of the Petri net model. The method can handle features such as routing flexibility, shared resources, lot sizes and concurrency. By following the generated schedule, potential deadlocks in the Petri net model and the system can be avoided. Hence the analytical overhead to guarantee the liveness of the model and the system is eliminated. Some heuristic functions for efficient search are explored and the experimental results are presented. >

Scheduling flexible manufacturing systems using Petri nets and heuristic search

The authors study a class of specifications, called generalized mutual exclusion constraints, for discrete event systems modeled using place/transition nets. These specifications may be easily enforced by a set of places called monitors on a net system where all transitions are controllable. However, when some of the transitions of the net are uncontrollable, this technique is not always applicable. For some classes of nets, the authors prove that generalized mutual exclusion constraints may always be enforced by monitors, even in the presence of uncontrollable transitions. >

Generalized mutual exclusion contraints on nets with uncontrollable transitions

A theoretical basis for Petri net synthesis methods is provided that can be used to model systems with shared resources, and to make the resulting nets bounded, live, and reversible. Two resource-sharing concepts, parallel mutual exclusion (PME) and sequential mutual exclusion (SME), are formulated in the context of the Petri net theory. A PME models a resource shared by distinct independent processes, and an SME is a sequential composition of PMEs, modeling a resource shared by sequentially related processes. The conditions under which a net containing such structures remains bounded, live, and reversible are derived. >

Frank DiCesare

Papers

Petri Net Synthesis for Discrete Event Control of Manufacturing Systems

A hybrid methodology for synthesis of Petri net models for manufacturing systems

Scheduling flexible manufacturing systems using Petri nets and heuristic search

Generalized mutual exclusion contraints on nets with uncontrollable transitions

Parallel and sequential mutual exclusions for petri net modeling of manufacturing systems with shared resources