Elzbieta Roszkowska

Conflict Resolution in Free-Ranging Multivehicle Systems: A Resource Allocation Paradigm

We propose a novel paradigm for conflict resolution in multivehicle traffic systems, where a number of mobile agents move freely in a finite area, with each agent following a prespecified-motion profile. The key idea behind the proposed method is the tessellation of the underlying motion area in a number of cells and the treatment of these cells as resources that must be acquired by the mobile agents for the execution of their motion profiles, according to an appropriate resource allocation protocol. We capitalize upon the existing literature on the real-time management of sequential resource allocation systems (RASs) and develop such protocols that can formally guarantee the safe and live operation of the underlying traffic system, while they remain scalable with respect to the number of the moving agents. Collective past experience with the considered policies indicates that they also provide a pretty large coverage of the RAS behavioral space that characterizes its safe and live operation. Finally, we also establish that the aforementioned approach is applicable even in traffic systems where all vehicles must be in perpetual motion until their retirement.

Supervisory control for deadlock avoidance in compound processes

Most of the research devoted to the supervisory control for deadlock avoidance in automated manufacturing systems has employed various models that represent concurrent sequential processes. In this paper, we address this problem for compound processes, that is, sequences of operations related in the fork/join manner and interacting as consumers/producers. The abstraction is used to model the flow of materials where independently processed components can be joined together and undergo further processing as a whole (e.g., to make an assembly or for a common transport), or material units can be split up so that their components will follow separate routes (e.g., at disassembly or separate processing of parts delivered in magazines), as well as to model the flow of objects that require a temporary meeting (e.g., independently routed pallets with the base components and pallets with parts to be mounted onto the base). Each process is represented with a marked graph, and the dynamics of the system are restricted with a feasibility function ensuring the feasible access to the shared resources. Unlike in sequential processes, in the class considered here, not all processes are realizable, i.e., possess a deadlock-free execution sequence. We prove that the problem of the distinction between realizable and unrealizable systems is NP-complete (thus intractable in practice) and propose a constraint that in a sufficient way allows us to distinguish a subclass of realizable compound processes. It is shown that the optimal, i.e., the minimally restrictive, supervisory control for this subclass of processes also poses an NP-hard problem. Therefore, we propose a compromise solution: a more restrictive, yet computationally acceptable admissibility function for guarding the event occurrence. The correctness of the control is proved formally by demonstrating the liveness and reversibility of the resulting model.

On the Complexity of Maximally Permissive Deadlock Avoidance in Multi-Vehicle Traffic Systems

The establishment of collision-free and live vehicle motion is a prominent problem for many traffic systems. Past work studying this problem in the context of guidepath-based and free-range vehicular systems has implicitly assumed that its resolution through maximally permissive supervision is NP-hard, and therefore, it has typically pursued suboptimal (i.e., more restrictive) solutions. The work presented in this technical note offers formal proof to this implicit assumption, closing the apparent gap in the existing literature. In the process, it also derives an alternative proof for the NP-hardness of maximally permissive liveness-enforcing supervision in Linear, Single-Unit Resource Allocation Systems, that is more concise and more lucid than the currently existing proof.

On the Liveness of Guidepath-Based, Zone-Controlled Dynamically Routed, Closed Traffic Systems

Zone-controlled, guidepath-based, dynamically routed, closed traffic systems constitute the modelling abstraction for a large set of industrial and public transport systems. An important requirement for the traffic flow of these systems is that the vehicles maintain their ability to access every location in the underlying guidepath-network, throughout the entire, presumably infinite, length of the system operation. States in which the system preserves the aforementioned property are said to be live. This work provides a structural characterization of state liveness that: (i) enables the identification of live states while foregoing an extensive enumeration of the underlying behavioral space and (ii) facilitates the design of computationally efficient liveness-enforcing supervisors.

Problems of Process Flow Feasibility in FAS

Abstract A general model of concurrent, asynchronous process flow in flexible assembly systems (FASs) is considered. It allows all feasible (with respect to the physical constraints of the system operation) process realizations, hence also the realizations leading to a deadlock. The main investigations are focused on the problems of process realizability, i.e. existence of a deadlock-free process realization, and (for cases where such realizations exist) of the least-restrictive deadlock avoidance policy. The problems addressed at process realizability testing and deadlock avoidance policy are proved to be NP-hard, hence practically intractable. Thus, a pragmatic, more restrictive but practically applicable, solution for handling the deadlock problems in FAS is also discussed.

Generalized Algebraic Deadlock Avoidance Policies for Sequential Resource Allocation Systems

Currently, one of the most actively researched approaches regarding the design of deadlock avoidance policies for sequential resource allocation systems is based on concepts and techniques provided by the, so called, theory of regions, that addresses the broader problem of synthesizing PN models with prespecified behaviors. However, one limitation of the theory of regions and its aforementioned derivatives is that they cannot be applied when the target behavior has a nonconvex representation in the underlying state space. In this note, we show how this problem can be circumvented by appropriately generalizing the employed class of the candidate policies.

A distributed protocol for motion coordination in free-range vehicular systems

This work extends our research on motion coordination of free-range vehicular systems based on concepts and results borrowed from resource allocation systems (RAS) theory, to vehicular systems with limited communication range among the vehicles. Similar to the earlier work, the employed model assumes the tessellation of the motion plane into cells, which are allocated to the traveling vehicles in a controlled manner that ensures collision-free and live motion. On the other hand, the limited communication range of the vehicles implies that full synchronization of their access to the considered cells is not possible any more, and yields new challenges for the deployed supervisory control policies. To enable the development of supervisory policies capable of providing the necessary partial synchronization of the cell allocation, we modify the structure of the adopted tessellation by allowing the concurrent occupation of a cell by up to two vehicles at a time, instead of only one, that was assumed earlier. This modification renders polynomially computable the relevant maximally permissive cell allocation policy, and it enables the implementation of this policy in the form of a distributed protocol that is feasible in the context of the communication constraints that are considered in this work.

Provably Correct Closed-Loop Control for Multiple Mobile Robot Systems

This paper introduces and advocates a new approach to the coordination of the motion of multiple mobile robots. In contrast to the current literature solutions, based on the execution of off-line generated plans, this work develops a state-based, closed-loop control mechanism ensuring in a provable manner the correct concurrent robot movement. The concept consists of partitioning the robots’ paths into sectors and allowing each robot to move freely within a sector, whereas sector crossing is guarded with a real-time policy that guarantees collision and deadlock avoidance.

Conflict resolution in multi-vehicle systems: A resource allocation paradigm

This paper proposes a novel paradigm for conflict resolution in multi-vehicle traffic systems where a number of mobile agents move freely in a finite area, each agent following a motion profile designated to it. The key idea underlying the proposed method is the tesselation of the underlying motion area in a number of cells of a certain shape and size, and the treatment of these cells as resources that must be acquired by the mobile agents for the execution of the corresponding segments of their motion profiles, through an appropriate resource allocation protocol. In this way, it is possible to capitalize upon the existing literature on the real-time management of sequential resource allocation systems, and develop supervisory control policies that can formally guarantee the safe and live operation of the underlying traffic system, while they remain scalable with respect to the number of the moving agents.

Undirected colored Petri net for modelling and supervisory control of AGV systems

This paper presents closed AGV systems with bidirectional guide path networks, zone control for avoiding collisions, and dynamic route planning. An AGV system is represented as a colored Petri net with undirected arcs and directed tokens, which substantially reduces the number of net components and simplifies the insight into the model. We study the problem of marking liveness and associate this property with the permanent ability of the vehicles to attain any edge in the network. The requirement is a weak form of marking liveness, as it does not require that each transition be live with respect to each of its colors. For the analysis of the net dynamics, we introduce the notion of a partially directed graph, that is, a graph which can have both directed and undirected edges. The results allow us to determine uniquely the character (live or not-live) of states in the system, which can thus be applied in the design of the supervisory control for AGV systems.