Robot planning based on boolean specifications using petri net models

In this paper, we propose an automated method for planning a team of mobile robots such that a Boolean-based mission is accomplished. The task consists of logical requirements over some regions of interest for the agents'' trajectories and for their final states. In other words, we allow combinatorial specifications defining desired final states whose attainment includes visits to, avoidance of, and ending in certain regions. The path planning approach should select such final states that optimize a certain global cost function. In particular, we consider minimum expected traveling distance of the team and reduce congestions. A Petri net (PN) with outputs models the movement capabilities of the team and the regions of interest. The imposed specification is translated to a set of linear restrictions for some binary variables, the robot movement capabilities are formulated as linear constraints on PN markings, and the evaluations of the binary variables are linked with PN markings via linear inequalities. This allows us to solve an integer linear programming problem whose solution yields robotic trajectories satisfying the task

Toward a decision support system for the clinical pathways assessment

This paper presents a decision support system to be used in hospital management taskswhich is based on the clinical pathways. We propose a very simple graphical modeling lan-guage based on a small number of primitive elements through which the medical doctorscould introduce a clinical pathway for a specific disease. Three essential aspects relatedto a clinical pathway can be specified in this language: (1) patient flow; (2) resource uti-lization; and (3) information interchange. This high-level language is a domain specificmodeling language calledHealthcare System Specification (HSS), and it is defined as anUnified Modeling Language (UML) profile. A model to model transformation is also pro-posed in order to obtain, from the pathways HSS specification, a Stochastic Well-formedNet (SWN) model that enables a formal analysis of the modeled system and, if needed, toapply synthesis methods enforcing specified requirements. The transformation is based onthe application of local rules. The clinical pathway of hip fracture from the “Lozano Blesa”University hospital in Zaragoza is taken as an example

A decision support system for elective surgery scheduling under uncertain durations

The operation room (OR) is one of the most expensive material resources in hospitals. Additionally, the demand for surgical service is increasing due to the aging population, while the number of surgical interventions performed is stagnated because of budget reasons. In this context, the importance of improving the efficiency of the surgical service is accentuated. The main objective of this work is to propose and to evaluate a Decision Support System (DSS) for helping medical staff in the automatic scheduling of elective patients, improving the efficiency of medical teams'' work. First, the scheduling criteria are fixed and then the scheduling problem of elective patients is approached by a mathematical programming model. A heuristic algorithm is proposed and included in the DSS. Moreover, other different features are implemented in a software tool with a friendly user interface, called CIPLAN. Considering realistic data, a simulation comparison of the scheduling obtained using the approach presented in this paper and other similar approaches in the bibliography is shown and analyzed. On the other hand, a case study considering real data provided by the Orthopedic Surgical Department (OSD) of the "Lozano Blesa" hospital in Zaragoza (HCU) is proposed. The simulation results show that the approach presented here obtains similar occupation rates and similar confidence levels of not exceeding the available time than approaches in the bibliography. However, from the point of view of respecting the order of the patients in the waiting list, the approach in this paper obtains scheduling much more ordered. In the case of the Orthopedic Surgical Department of the "Lozano Blesa" hospital in Zaragoza, the occupation rate may be increased by 2.83%, which represents a saving of 110, 000 euros per year. Moreover, medical doctors (who use this tool) consider CIPLAN as an intuitive, rapid and efficient software solution that can make easier the corresponding task

Path planning of multirobot systems using Petri net models. Results and open problems

[EN] This paper presents a trajectory planning approach in multirobot systems based on Petri net models. This type of models is very useful for high-level specifications since, in this case, the classical planning methods (potential functions, RRT algorithms, RRT*) cannot be used being dicult to determine a priori the sequence of configurations for each robot. This work presents the formal definition of the Robot Motion Petri net t hat i s obtained from a partition of the environment in cells. Using the s tructure of the Petri net, in case of specifications defined as Boolean or Linear Temporal Logic (LTL) formulas, dierent optimization problems are presented that can be used to obtain trajectories for robots. The main advantage of models based on Petri nets is their scalability with respect to the number of robots. This makes it possible to reciently solve planning problems with a large number of robots. In the second part of the paper, some extensions and new results for distributed planning in unknown environments and with partial communications between robots are presented.[ES] Este trabajo presenta una estrategia de planificacón de trayectorias en equipos de robots moviles basada en el uso de modelos definidos con redes de Petri. Estos tipos de modelos son muy útiles para especificaciones de alto nivel ya que, en este caso, los métodos clásicos de planificación (funciones potenciales, algoritmos RRT, RRT*) no se pueden utilizar, siendo difícil determinar a priori la secuencia de configuraciones para cada robot. Este trabajo presenta la definición formal de la Red de Petri de Movimiento de Robots que se obtiene a partir de una partición del entorno en celdas. Utilizando la estructura de la red de Petri, en caso de especificaciones definidas como fórmulas Booleanas o fórmulas en lógica temporal lineal (LTL), se presentan diferentes problemas de optimización que se pueden utilizar para obtener trayectorias para los robots. La principal ventaja de los modelos basados en redes de Petri es su escalabilidad con respecto al número de robots. Ello permite resolver con eficiencia problemas de planificación de equipos con un número grande de robots. En la segunda parte del trabajo, se presentan algunas extensiones y resultados nuevos para la planificación distribuida en entornos desconocidos y con comunicaciones parciales entre los robots.Los resultados de esta línea de investigación son fruto de la participación de varios compañeros, investigadores de la Universidad de Zaragoza y de otras Universidades extranjeras. Queremos agradecer la participación de todos ellos, mencionando muy especialmente a Marius Kloetzer (profesor de la Universidad Técnica de Iasi, Rumanía). Este trabajo ha sido financiado parcialmente por los proyectos PGC2018-098719-B-I00 and PGC2018-098817-A-I00 (MCIU/AEI/FEDER, UE) y la ONR Global NICOP grant N62909-19-1-2027.Mahulea, C.; González, R.; Montijano, E.; Silva, M. (2020). Planificación de trayectorias en sistemas multirobot utilizando redes de Petri. Resultados y problemas abiertos. Revista Iberoamericana de Automática e Informática industrial. 18(1):19-31. https://doi.org/10.4995/riai.2020.13785OJS1931181Baier, C., Katoen, J.P., 2008. Principles of model checking. MIT Press.Belta, C., Bicchi, A., Egerstedt, M., Frazzoli, E., Klavins, E., Pappas, G.-J., 2007. Symbolic planning and control of robot motion. IEEE Robotics and Automation Magazine 14 (1), 61-71. https://doi.org/10.1109/MRA.2007.339624Belta, C., Habets, L., 2006. Controlling a class of nonlinear systems on rectangles. IEEE Transactions on Automatic Control 51 (11), 1749-1759. https://doi.org/10.1109/TAC.2006.884957Brown, F., 2012. Boolean Reasoning: The Logic of Boolean Equations, 2nd Edition. Dover Publications.Castellanos, J. G., Cervantes, M. V., Santana, J. S., Martínez, S. R., 2014. Seguimiento de trayectorias de un robot movil (3,0) mediante control acotado. Rev. Iberoamericana de Automatica e Informática industrial 11 (4), 426-434. https://doi.org/10.1016/j.riai.2014.09.005Choset, H., Lynch, K. M., Hutchinson, S., Kantor, G., Burgard, W., Kavraki, L. E., Thrun, S., 2005. Principles of Robot Motion: Theory, Algorithms, and Implementations. MIT Press, Boston.Clarke, E.-M.-M., Peled, D., Grumberg, O., 1999. Model checking. MIT Press.DeCastro, J., Ehlers, R., Runggers, M., Balkan, A., Kress-Gazit, H., 2016. Automated generation of dynamics-based runtime certificates for high-level control. Discrete Event Dynamic Systems 27 (2), 371-405. https://doi.org/10.1007/s10626-016-0232-7Ding, X., Smith, S.-L., Belta, C., Rus, D., 2014. Optimal control of Markov decision processes with linear temporal logic constraints. IEEE Transactions on Automatic Control 59 (5), 1244-1257. https://doi.org/10.1109/TAC.2014.2298143Duret-Lutz, A., Lewkowicz, A., Fauchille, A., Michaud, T., Renault, E., Xu, L., 2016. Spot 2.0 - a framework for ltl and ω-automata manipulation. In: Proc. of ATVA'16. pp. 122-129. https://doi.org/10.1007/978-3-319-46520-3_8Fainekos, G. E., Girard, A., Kress-Gazit, H., Pappas, G. J., 2009. Temporal logic motion planning for dynamic robots. Automatica 45 (2), 343-352. https://doi.org/10.1016/j.automatica.2008.08.008Garrido, S., Moreno, L., Gomez, J.-V., Lima, P.-U., 2013. International Journal ' of Advanced Robotic Systems 10 (1), 64. https://doi.org/10.5772/53999Gastin, P., Oddoux, D., 2001. Fast ltl to buchi automata translation. In: Proc. of the 13th Conference on Computer Aided Verification (CAV). pp. 53-65. https://doi.org/10.1007/3-540-44585-4_6Gonzalez, R., Mahulea, C., Kloetzer, M., 2015. A Matlab-Based Interactive Simulator for Mobile Robotics. In: IEEE CASE'2015: Int. Conf. on Autom. Science and Engineering. Gothenburg, Sweden, pp. 310-315. https://doi.org/10.1109/CoASE.2015.7294097Gonzalez, R., Rodriguez, F., Guzman, J. L., 2014. Autonomous Tracked Robots in Planar Off-Road Conditions. Modelling, Localization and Motion Control. Series: Studies in Systems, Decision and Control. Springer. https://doi.org/10.1007/978-3-319-06038-5Guo, M., Dimarogonas, D.-V., 2015. Multi-agent plan reconfiguration under local LTL specifications. Int. Journal of Robotics Research 34 (2), 218-235. https://doi.org/10.1177/0278364914546174Habets, L. C. G. J. M., Collins, P. J., van Schuppen, J. H., 2006. Reachability and control synthesis for piecewise-affine hybrid systems on simplices. IEEE Transactions on Automatic Control 51, 938-948. https://doi.org/10.1109/TAC.2006.876952Julian, B.-J., Angermann, M., Schwager, M., Rus, D., 2012. Distributed robotic sensor networks: An information-theoretic approach. The International Journal of Robotics Research 31 (10), 1134-1154. https://doi.org/10.1177/0278364912452675Kloetzer, M., Mahulea, C., 2014. A Petri net based approach for multi-robot path planning. Discrete Event Dynamic Systems: Theory and Applications 24 (4), 417-445. https://doi.org/10.1007/s10626-013-0162-6Kloetzer, M., Mahulea, C., 2014. An assembly problem with mobile robots. In: ETFA'2014: IEEE Emerging Technology and Factory Automation. pp. 1-7. https://doi.org/10.1109/ETFA.2014.7005116Kloetzer, M., Mahulea, C., 2015. LTL-based planning in environments with probabilistic observations. IEEE Transactions on Automation Science and Engineering 12 (4), 1407-1420. https://doi.org/10.1109/TASE.2015.2454299Kloetzer, M., Mahulea, C., 2020. Path planning for robotic teams based on LTL specifications and Petri net models. Discrete Event Dynamic Systems: Theory and Applications 30 (1), 55-79. https://doi.org/10.1007/s10626-019-00300-1Lacerda, B., Lima, P. U., 2019. Petri net based multi-robot task coordination from temporal logic specifications. Robotics and Autonomous Systems 122, 343-352. https://doi.org/10.1016/j.robot.2019.103289LaValle, S. M., 2006. Planning Algorithms. Cambridge, available at http://planning.cs.uiuc.edu. https://doi.org/10.1017/CBO9780511546877Leahy, K., Cristofalo, E., Vasile, C.-I., Jones, A., Montijano, E., Schwager, M., Belta, C., 2019. Control in belief space with temporal logic specifications using vision-based localization. The International Journal of Robotics Research 38 (6), 702-722. https://doi.org/10.1177/0278364919846340Mahulea, C., Kloetzer, M., 2018. Robot Planning based on Boolean Specifications using Petri Net Models. IEEE Trans. on Automatic Control 63 (7), 2218-2225. https://doi.org/10.1109/TAC.2017.2760249Mahulea, C., Kloetzer, M., Gonzalez, R., 2020a. Path Planning of Cooperative ' Mobile Robots Using Discrete Event Models. IEEE Wiley. https://doi.org/10.1002/9781119486305Mahulea, C., Kloetzer, M., Lesage, J.-J., 2020b. Multi-robot path planning with boolean specifications and collision avoidance. In: WODES'2020: 15th Workshop on Discrete Event Systems.Mahulea, C., Montijano, E., Kloetzer, M., 2020c. Distributed Multirobot Path Planning in Unknown Maps Using Petri Net Models. IFACPapersOnLine21th IFAC World Congress.Mesbahi, M., Egerstedt, M., 2010. Graph theoretic methods in multiagent networks. Princeton University Press. https://doi.org/10.1515/9781400835355Montijano, E., Montijano, J.-I., Sagues, C., Feb 2013. Chebyshev polynomials in distributed consensus applications. IEEE Transactions on Signal Processing 61 (3), 693-706. https://doi.org/10.1109/TSP.2012.2226173Montijano, E., Sagües, C., 2015. Distributed consensus with visual perception ' in multi-robot systems. Springer. https://doi.org/10.1007/978-3-319-15699-6Parrilla, L., Mahulea, C., Kloetzer, M., 2017. RMTool: Recent Enhancements. IFAC-PapersOnLine 50 (1), 5824 - 5830, 20th IFAC World Congress. https://doi.org/10.1016/j.ifacol.2017.08.539Schillinger, P., Burger, M., Dimarogonas, D., 2018. Simultaneous task allocation and planning for temporal logic goals in heterogeneous multi-robot systems. The International Journal of Robotics Research 37 (7), 818-838. https://doi.org/10.1177/0278364918774135Siegwart, R., Nourbakhsh, I., 2004. Introduction to Autonomous Mobile Robots, First Edition. A Bradford book. The MIT Press, USA. Silva, M., 1985. Las Redes de Petri : en la Automatica y la Informática; 1a ed. Editorial AC Madrid.Silva, M., Colom, J.-M., 1988. On the Computation of Structural Synchronic Invariants in P/T Nets. Advances in Petri Nets'87 340, 386-417. https://doi.org/10.1007/3-540-50580-6_39Silva, M., Teruel, E., Colom, J.-M., 1998. Linear Algebraic and Linear Programming Techniques for the Analysis of P/T Net Systems. Lecture on Petri Nets I: Basic Models 1491, 309-373. https://doi.org/10.1007/3-540-65306-6_19Tumova, J., Dimarogonas, D., 2016. Multi-agent planning under local LTL specifications and event-based synchronization. Automatica 70, 239-248. https://doi.org/10.1016/j.automatica.2016.04.006Ulusoy, A., Smith, S., Ding, X., Belta, C., 2012. Robust multi-robot optimal path planning with temporal logic constraints. In: ICRA 2012: IEEE Conference on Robotics and Automation. pp. 4693-4698. https://doi.org/10.1109/ICRA.2012.6224792Wolper, P., Vardi, M., Sistla, A., 1983. Reasoning about infinite computation paths. In: Proc. of the 24th IEEE Symposium on Foundations of Computer Science. pp. 185-194. https://doi.org/10.1109/SFCS.1983.51Yen, J.-Y., 1971. Finding the k shortest loopless paths in a network. Management Science 17 (11), 712-716. https://doi.org/10.1287/mnsc.17.11.71

Predictive Control of Timed Hybrid Petri Nets

Abstract Hybrid Petri nets represent a powerful modeling formalism that offers the possibility of integrating in a natural way continuous and discrete dynamics in a single net model. Usual control approaches for hybrid nets can be divided into discrete-time and continuous-time approaches. Continuous-time approaches are usually more precise but can be computationally prohibitive. Discrete-time approaches are less complex but can entail mode-mismatch errors due to fixed time discretization. This work proposes an optimization-based event-driven control approach that applies on continuous time models and where the control actions change when discrete events occur. Such an approach is computationally feasible for systems of interest in practice and avoids mode-mismatch errors. In order to handle modelling errors and exogenous disturbances, the proposed approach is implemented in a closed-loop strategy based on event-driven model predictive control

Fault Diagnosis of Discrete-Event Systems using Continuous Petri Nets

When discrete-event systems are used to model systems with a large number of possible (reachable) states, many problems such as simulation, optimization, and control, may become computationally prohibitive because they require some enumeration of such states. A common way to effectively address this issue is fluidization. The goal of this paper is that of studying the effect of fluidization on fault diagnosis. In particular, we focus on the purely logic Petri net (PN) model that results in the untimed continuous PN model after fluidization. In accordance to most of the literature on discrete-event systems, we define three diagnosis states, namely N, U, and F , corresponding respectively to no fault, uncertain, and fault state. We prove that, given an observation, the resulting diagnosis state can be computed solving linear programming problems rather than integer programming problems as in the discrete case. The main advantage of fluidization is that it enables to deal with much more general PN structures. In particular, the unobservable subnet needs not be acyclic as in the discrete case. Moreover, the compact representation of the set of consistent markings using convex polytopes can be seen in some cases as an improvement in terms of computational complexit

Proceedings of the 8th International Workshop on Discrete Event Systems

On performance monotonicity and basic servers semantics o

On decentralized observability of discrete event systems

In this paper we deal with the problem of decentralized observability of discrete event systems. We consider a set of sites that observe a subset of events. Each site transmits its own observation to a coordinator that decides if the word observed belongs to a legal behavior or not. We study two different properties: uniform q-observability and q-diagnosability. Then, we prove that both properties are decidable for regular languages. Finally, we give an algorithm to compute starting from a given initial state, the time instants at which the synchronization has to be done so as to guarantee that if an illegal word has occurred it is immediately detected