In this paper, we consider multi-robot path planning problems for high-level tasks with a finite horizon. In many situations, there is a need tocount how many timesa sub-task is satisfied in order to achieve the overall task. However, existing temporal logic languages, such as linear temporal logic, is not efficient in describing such requirements. To address this issue, we propose a new temporal logic language calledCounting Time Temporal Logic(CTTL) that extends linear temporal logic by explicitly counting the number of times that some tasks are satisfied. To solve the CTTL path planning problem, we propose an efficient integer linear programming-based method to encode task satisfaction. We show that our approach is both sound and complete, while achieving higher efficiency than direct encodings of such requirements. Moreover, we study several variants of the problem. To validate our results, we present several numerical experiments to show the scalability of the proposed approach and a simulation case study of a team of autonomous robots to illustrate the feasibility of the synthesis procedure. Finally, to evaluate the real-world feasibility of our method, we conduct a hardware experiment with two Turtlebot3-Burger mobile robots.

In this paper, we propose a computationally efficient quadratic programming (QP) approach for generating smooth, C1continuous paths for mobile robots using piece-wise quadratic Bezier (PWB) curves. Our method explicitly incorporates safety margins within a structured optimization framework, balancing trajectory smoothness and robustness with manageable numerical complexity suitable for real-time and embedded applications. Comparative simulations demonstrate clear advantages over traditional piece-wise linear (PWL) path planning methods, showing reduced trajectory deviations, enhanced robustness, and improved overall path quality. These benefits are validated through simulations using a Pure-Pursuit controller in representative scenarios, highlighting the practical effectiveness and scalability of our approach for safe navigation.

This paper presents a method for decomposing Linear Temporal Logic (LTL) specifications into independent parts based on structures recognized in their corresponding Büchi automata representations. The goal is to obtain a decomposition that allows the execution of the global mission by identifying and formalizing segments that can be executed concurrently by a team of mobile robots. We introduce formal concurrency characterization for two and three tasks, and provide a structured framework for recognizing these patterns within the automaton. The method algorithmically analyses an accepted run of the trimmed Büchi automaton, partitions it into containers of sequential and concurrent tasks, and incrementally extends this concurrency while reducing the number of synchronization points. Although the current formal framework supports up to three concurrent tasks, it may represent a step towards generalization.

This contribution focuses on the modeling and performance analysis of the manufacturing process for transport platforms at the Alimak Group facility in La Muela, Spain. The objective is to leverage formal tools to gain insights into this complex manufacturing process and explore potential applications such as control and optimization. This work presents a preliminary study, where a Generalized Stochastic Petri net model of the manufacturing process is proposed to be used for simulation, performance analysis, and optimization of the system.

This paper presents a novel approach to analyze and optimize healthcare systems based on clinical pathways, using timed continuous Petri nets (TCPNs) under infinite server semantics. TCPNs allow for an efficient continuous-time analysis of the patient flow and resource utilization dynamics of these types of systems. We demonstrate the feasibility and effectiveness of our method through a case study of a hip fracture pathway at the "Lozano Blesa" University Clinical Hospital, in Zaragoza Spain. Additionally, we propose a method to optimize the behavior of the modeled system by taking a control theory approach, which enables the system to achieve maximum throughput more efficiently. Finally, we provide simulation results to demonstrate the effectiveness of the proposed controller in practical settings.

This paper proposes an extension of an algorithm that decomposes a high-level specification into sub-formulas that are called tasks. The extension consists in enabling repetitive (non-terminating) behaviors expressed in Linear Temporal Logic (LTL), rather than only terminating ones, as the previous version of our method allowed. The LTL specification has the meaning of a global mission that must be accomplished by a team of mobile agents, while the decomposition ensures that the tasks can be executed independently by the robots, thus avoiding communications or synchronizations. An example is illustrating the presented work, while future research will be conducted towards inclusion of negations in formulas.

The Unmanned Aerial Vehicles (UAVs), commonly known as drones, are significant in the agriculture sphere to automate the work such as: data acquisition, crop spraying among others. This paper proposes a path planning solution for a team of UAVs that is required to whiten a greenhouse’s roof, this problem having both social-economic impact, as well as scientific-technical impact. First, the space around the roof is partitioned into cells based on a 3D cell decomposition technique, labeling the cells including the surface of the roof as regions of interest (ROIs). Based on this representation, a Petri net (PN) model captures the motion of drones, while their trajectories are returned by a Mixed Integer Linear Programming (MILP) problem which optimizes the energy consumption. An adaptable strategy is used such that the MILP problem considers only the available UAVs with enough energy to reach the ROIs. The algorithm is implemented in MATLAB and the simulation results are captured in a video link, evaluating the impact of the size of the team and the precision used for mapping the environment over the running time.

We consider the problem of obtaining independent trajectories for robots from a team, such that their movement satisfies a global co-safe Linear Temporal Logic (LTL) mission over some regions of interest from the environment. For this, the environment is abstracted into a discrete event system using an underlying partition and an available method is used for decomposing the LTL formula into more parts that can be independently satisfied by a robot. Then, we translate these parts into a conjunction of Boolean formulas and use another approach for planning a team based on Boolean specifications and Petri net models. The proposed combination among the two methods yields independent robot trajectories that are optimal with respect to the number of traversed cells from the partition. The advantages are also illustrated through simulation examples.

During the last few years, the field of micro aerial vehicles (drones) has encountered a significant focus among the robotics research community. Autonomous maneuvering for indoor environments is highly challenging on one hand due to space topology that can include different storage facilities, and on the other hand due to need for optimal planning that saves drone battery and task accomplishment time. In this paper we study a type of vehicle routing problem applied to an indoor warehouse. In particular, some goods should be transported from storage areas to delivery areas by limited energy drones with finite capacities for transporting goods. The presentation includes a planning solution based on mathematical programming and presents supporting simulations and real-time experiments.

A domain-specific modeling language called Healthcare System Specifications (HSS) was proposed for developing clinical pathways. This high-level language was defined as a Unified Modeling Language (UML) profile. It was also proposed a model to model transformation which obtains from pathways HSS specification, a Stochastic Well-formed Net (SWN). The SWN has the capacity to model the complex healthcare system, however, it is hard to perform qualitative and quantitative analysis in this kind of nets. This paper presents a set of relaxations, abstractions and modifications to be applied in the SWNs in order to obtain subclasses of Petri Nets in which formal analysis can be performed. In particular, we obtain the classes of S4PR and DSSP nets. The first one considers the shared resources of the hospital while the second class allows managing the interchange of information between clinical pathways.

This paper considers the path-planning problem in discretized environments, obtained for example by a cell decomposition approach. The specification for the mobile robot can be the classical navigation problem (reach a given region by avoiding the obstacles) or a high-level specification as a Boolean and/or temporal logic formula. We propose a general methodology to compute piecewise linear trajectories consisting in a sequence of intermediate points (waypoints). The waypoints are computed by solving optimization problems whose solutions permit to optimally select the intermediate points on the common facets of traversed cells from the decomposition. The proposed solution is similar to a Model Predictive Control (MPC) strategy, in each step an optimization problem is solved over a finite horizon, the first action is considered and the problem is iterated. The method developed in this paper has been implemented and integrated in Robot Motion Toolbox allowing a comparison with other methods by simulation.

In this paper, the scheduling problem of elective patients in the Orthopedic Department of the “Lozano Blesa” Hospital in Zaragoza is considered. This problem takes into account two contradictory objectives: obtain a given occupation rate of the Operation Room (OR) and respect as much as possible the preference order of the patients in the waiting list. Three different mathematical models are discussed: 1) Quadratic Assignment Problem (QAP); 2) a Mixed Integer Linear Programing (MILP) model; and 3) Generalized Assignment Problem (GAP). These models solve combinatorial problems with a high computational cost; for this reason, heuristic methods have been used to solve large instances. In particular, 1) a meta-heuristic Genetic Algorithm (GA) for the QAP; 2) a heuristic Steepest Descent Multiplier Adjustment Method (SDMAM) for the GAP; and 3) a heuristic iterative method for MILP. Finally, the models and the heuristics are compared according to the occupation rate and the preference order criteria.

This paper considers the operation scheduling and planning of elective patients in the Orthopedic Department of the “Lozano Blesa” Hospital in Zaragoza. We assume an ordered list of patients that should be planned for surgery in two available rooms, each room being possible to be used for a specific duration per day. Based on the average durations of surgeries that have been computed by considering historical information, we propose a Mixed Integer Linear Programming (MILP) problem to obtain a specific utilization rate per room. We have developed a Decision Support System (DSS) base on MILP that helps doctors in their daily planning. The results are tested on some real data from the hospital and some simulation results are provided.

This research proposes a centralized method for planning and monitoring the motion of one or a few mobile robots in an environment where regions of interest appear and disappear based on exponential probability density functions. The motion task is given as a linear temporal logic formula over the set of regions of interest. The solution determines robotic trajectories and updates them whenever necessary, such that the task is most likely to be satisfied with respect to probabilistic information on regions. The robots' movement capabilities are abstracted to finite state descriptions, and operations as product automata and graph searches are used in the provided solution. The approach builds up on temporal logic control strategies for static environments by incorporating probabilistic information and by designing an execution monitoring strategy that reacts to actual region observations yielded by robots. Several simulations are included, and a software implementation of the solution is available. The computational complexity of our approach increases exponentially when more robots are considered, and we mention a possible solution to reduce the computational complexity by fusing regions with identical observations.

This paper presents a modeling methodology for clinical guidelines used in hospitals. The clinical guidelines are assumed to be given in a graphical form in a structure obtained by combining few elements. It is shown how the clinical guidelines represented with this syntax can be automatically converted into a mathematical model represented as Petri nets. The main advantage of the new model is the inclusion of resources and patient flow in the same model which makes possible its use in analysis and verification of the guidelines. Moreover, if different clinical guidelines in a hospital or department in a hospital are considered, the models can be used for resource optimization and performance evaluation. The clinical guideline of hip fracture from the ”Lozano Blesa” University hospital in Zaragoza is taken as an example.

This paper proposes a solution for solving a specific problem that requires a team of identical robots to collect in a specific order different types of resources scattered throughout an environment. A Petri net with outputs models the environment, the team possible movements and the regions with resources. An iterative solution plans the team such that each robot collects and assembles resources in the required order. Each iteration step is based on a linear programming problem that is guaranteed to return a feasible firing vector for the Petri net system. A pseudocode description of the procedure is given and a simulation example is included.

This paper approaches the deadlock prevention problem for the well known class of S3PR used in Resource Allocation Systems. The proposed control policy is based on inhibitor arcs and the new Petri net class will be called S3PR2. The liveness characterization of this new class is given. The main application of the approach is to robot motion for a team of robots evolving in a partitioned environment with some limited capacity regions. In a previous work it is shown that the sets of trajectories for robots can be modeled by a particular S3PR and the deadlock-free execution has been solved using a centralized approach. Based on the results in this paper, we show that a decentralized control law for robots can be implemented.

This paper provides a strategy for supervising the motion of some mobile robots that evolve in the same environment. Some regions of the environment are assumed to have a limited capacity in terms of the number of robots that can simultaneously occupy them, and a set of possible trajectories is available for each robot. The solution comprises the construction of a specific Petri net model for the available trajectories, and the use of resource-allocation techniques based on restricted-capacity regions and on deadlock-free execution.

In this paper, we consider the decentralized fault diagnosis problem of discrete event systems modeled by time Petri nets (TPNs). Our approach is based on the fault diagnosis graph which is obtained from the time reachability graph by removing the irrelevant nodes. A coordinator computes the diagnosis states of the global system using information from subsystems. Local systems send small amounts of information to the coordinator for the computation of diagnosis states of the global system.

This paper presents a modular Petri net approach for modeling a health system. In particular, the Spanish national health system is considered as case study. After a global description of the health system structure, it is shown that it can be composed by different modules with inputs and outputs. Each module can be modeled separately and the procedure consists in two steps: (1) model the medical protocols as state-machine Petri nets and (2) add the (shared) medical resources. The global model is obtained by composing these modules by fusing the input and output places and adding information on the population. It is proved that by following these procedure, the obtained Petri net system is a S4PR. Finally, it is shown how the model can be exploited in order to check different properties of the system.

The paper presents a procedure for planning and controlling a team of identical mobile robots such that a set of target regions are reached. We consider a partitioned environment cluttered with a set of obstacles that randomly change their positions. Our approach abstracts both the control capabilities of robots and the information on obstacle locations into probabilistic discrete Petri net models, and it uses an online algorithm for planning and adjusting the sequences of regions the robots should traverse. At each iteration of the online algorithm we solve a linear programming problem that optimizes the robot paths by weighting the probabilities of following a sequence of partition regions and the steady-state probabilities of encountering obstacles along the resulted sequences. The approach is implemented as a fully automated Matlab package.

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, namelyN,U, andF, 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 complexity.

The paper presents a procedure for creating a probabilistic finite-state model for a mobile robot and for finding a sequence of controllers ensuring the highest probability for reaching a desired region. The approach starts by using results for controlling affine systems in simpliceal partitions, and then it creates a finite representation with history-based probabilities on transition. This representation is embedded into a Petri Net model with probabilistic costs on transitions, and a highest probability path to reach a target region is found. This probabilistic framework is suitable for controlling mobile robots based on more complex specifications.

This paper deals with fault detection of manufacturing systems modeled by Petri nets. We show that the theoretical results obtained for continuous Petri nets allow us to treat with systems that are intractable using the theory developed for discrete Petri nets. In particular systems in which the unobservable part contains cycles can be studied. On the other hand, only three diagnosis states can be defined making impossible the splitting of the uncertain state into two different states, to obtain different degrees alarm for the uncertainty.

In this paper, we develop an automated framework for formal verification of timed continuous Petri nets (ContPNs). Specifically, we consider two problems: (1) given an initial set of markings, construct a set of unreachable markings and (2) given a Linear Temporal Logic (LTL) formula over a set of linear predicates in the marking space, construct a set of initial states such that all trajectories originating there satisfy the LTL specification. The starting point for our approach is the observation that a ContPN system can be expressed as a Piecewise Affine (PWA) system with a polyhedral partition. We propose an iterative method for analysis of PWA systems from specifications given as LTL formulas over linear predicates. The computation mainly consists of polyhedral operations and searches on graphs, and the developed framework was implemented as a freely downloadable software tool. We present several illustrative numerical examples.

This paper addresses several questions related to the control of timed continuous Petri nets under infinite server semantics. First, some results regarding equilibrium states and control actions are given. In particular, it is shown that the considered systems are piecewise linear, and for every linear subsystem the possible steady states are characterized. Second, optimal steady-state control is studied, a problem that surprisingly can be computed in polynomial time, when all transitions are controllable and the objective function is linear. Third, an interpretation of some controllability aspects in the framework of linear dynamic systems is presented. An interesting finding is that noncontrollable poles are zero valued. Note to Practitioners-Petri nets are a well-known formalism for the analysis and design of discrete event systems. Due to the state- explosion problem some kind of relaxation is frequently used. In particular, fluidification is a classical approximation technique that it is usually employed in the analysis of manufacturing or logistic systems, specially when heavily loaded. This work focuses on timed continuous Petri nets which are a fluidified version of discrete Petri nets with timing associated to transitions (representing stations with servers that perform activities). Furthermore, transitions have associated control actions which can slow down the corresponding activities from an initial maximum speed, that depends on the marking, and possibly halt them completely. The steady-state control problem of this kind of system and some invariant-dynamical properties are addressed.