Optimal robotic cell scheduling with controllers using mathematically based timed Petri nets

Abstract

This paper presents an optimal solution to the robotic cell scheduling problem for robot movement controllers using timed Petri nets (TPNs). The suggested TPN approach is used to generate a mathematical transition model, based on a From/To transition matrix and the properties of the TPN, that considers all possible movements of robots between cell stations. The mathematical model thus obtained is solved to identify the optimal firing sequence of TPN transitions for the considered robotic cell problem to minimize the time elapsed before the firing of the last transition (the cycle time). Finally, the optimal sequence of transitions is used to generate robotic cell controllers and construct the final TPN model. A numerical example is used to demonstrate the proposed approach.

Introduction

Modern manufacturing systems, such as robotic cells, incorporate automation and repetitive processing to speed up production and meet the strict requirements specified by customers. System performance is an important factor that must be considered in the design and operation of manufacturing cells to ensure that they are commercially competitive. Many industries use automated handling systems, such as industrial robots, to convey raw materials through multiple production stages. To obtain the maximum return on investment using such systems, efficient action sequences and parts schedules must be determined [1]. Many methods of scheduling have been applied to obtain the maximum output from these automated systems. However, scheduling is a very difficult task in real-life manufacturing systems because of complex part routings, the necessity for man-machine interactions, and variations in the manufactured products, among other concerns. A major challenge encountered in applying scheduling algorithms to real systems is that most algorithms follow a specific framework, i.e., that of a job shop or a flow shop, and these frameworks rarely perfectly correspond to real systems [2]. Thus, flow shop scheduling is an attractive research area for both researchers and practitioners [3].

Many modern manufacturing systems use robot-served manufacturing cells, or robotic cells, which comprise particular types of computer-controlled manufacturing systems. A robotic cell is a complex system consisting of an input device; a series of processing stages, each of which performs a different operation (on each part in a particular sequence); an output device; and one or more robots that transport parts within the cell. A major application of robots in manufacturing involves the loading and unloading of production machines in manufacturing cells. A robot in such a cell performs repeated sequences of pick-up, movement, loading, unloading and dropping operations, and thus, the performance of the cell strongly depends on the sequence of robotic activities and on the sequence of the different parts produced in the cell [4], [5], [6], [7], [8].

In robotic cell scheduling, the most important task is to determine the sequence of robot movements and optimize the cycle time. This problem is related to how the robotic cell is controlled, although other problems, such as deadlocks and machine blocking, must also be considered. Most cell controllers that have been proposed to date are based on Petri net (PN) approaches [34], [41], [44], [47], [48], [49], [50]. Deadlocks are an important control issue in robotic cells because their occurrence always blocks the operation of the affected cells, which may be catastrophic in highly automated systems [9], [10], [11], [12], [13]. Petri nets are widely used to solve deadlock problems in automated systems, such as robotic cells, and in deadlock control [9], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24]. Additionally, Petri nets can be used for deadlock prevention by designating a supervisor to administer a system following certain control specifications. A supervisor consists of a set of control places and the arcs connecting them to transitions that belong to the system. The main goal of deadlock prevention based on either structural analysis techniques [23], [31], [32], [33], [35], [36], [37], [38], [46] or reachability graph analysis [39], [40], [42], [43], [45] is to impose constraints on a system to prevent it from reaching deadlock states.

Unfortunately, most of the existing deadlock-control approaches for automated production systems have been suggested based on static and untimed system behavior and have been considered in isolation from other fundamental operational issues, such as planning and scheduling. As a result, these proposed control systems are inapplicable to robotic cells because such systems are dynamic in nature and depend on time-related factors (such as processing times and handling times between system stations) that must be considered during the design and operation of such systems. In addition to deadlock prevention, it is also necessary to allow for sequences of operations with shared resources and robot movements when designing optimal supervisors for real-life robotic cell management. However, most existing scheduling solutions for robotic cells can lead to deadlocks because of a lack of cell controller integration.

This paper presents a novel mathematical transition model based on timed Petri nets (TPNs) to solve the robotic cell scheduling problem by taking advantage of the properties of TPNs. The proposed model determines an optimal firing sequence for the transitions in the TPN model, and the control robot moves between the cell stations of the robotic cell of interest to minimize the firing times. The remainder of the paper is organized as follows. Section 2 reviews the literature related to addressing scheduling problems in robotic cells using PN approaches. Section 3 presents the proposed approach. Section 4 provides an illustrative example to demonstrate the proposed method. Finally, Section 5 concludes the paper and offers recommendations for future research.