Deadlock-free Supervisor Design for Robotic Manufacturing Cells With Uncontrollable and Unobservable Events Bo Huang, Senior Member, IEEE, MengChu Zhou, Fellow, IEEE, Cong Wang, Member, IEEE, Abdullah Abusorrah, Senior Member, IEEE, and Yusuf Al-Turki, Senior Member, IEEE Abstract—In this paper, a deadlock prevention policy for robotic manufacturing cells with uncontrollable and unobservable events is proposed based on a Petri net formalism. First, a Petri net for the deadlock control of such systems is defined. Its admissible markings and first-met inadmissible markings (FIMs) are introduced. Next, place invariants are designed via an integer linear program (ILP) to survive all admissible markings and prohibit all FIMs, keeping the underlying system from reaching deadlocks, livelocks, bad markings, and the markings that may evolve into them by firing uncontrollable transitions. ILP also ensures that the obtained deadlock-free supervisor does not observe any unobservable transition. In addition, the supervisor is guaranteed to be admissible and structurally minimal in terms of both control places and added arcs. The condition under which the supervisor is maximally permissive in behavior is given. Finally, experimental results with the proposed method and existing ones are given to show its effectiveness. Index Terms—Deadlock prevention, Petri nets, robotic manufacturing cells, structure-minimized supervisor, supervisory control, uncontrollability, unobservability.   I. Introduction R OBOTIC manufacturing cells play an important role in the manufacturing industry, including automobiles, semiconductors, etc. For instance, cluster tools and track systems are typical robotic manufacturing cells that perform core processes in semiconductor fabrication [1]. In such systems, available resources (such as machines and robots) are shared among concurrently running processes (such as vehicles and parts). The competition for the limited resources by different processes may lead to deadlocks where two or more processes are each indefinitely waiting for the other to release their acquired resources. Deadlocks can lead to unnecessary economic costs and sometimes catastrophic results. To handle deadlocks in these systems, Petri nets (PNs) are widely used since they are suitable to graphically describe concurrency, conflict, and synchronization as well as conveniently detect behavioral properties of such systems [2]–[7]. Based on PNs, the theory of regions [8] is adopted in [9] to derive optimal (maximally permissive) and deadlock- free supervisors for plant nets where such supervisors exist. Some improvements are made in [10]–[12] to design optimal and structurally simple supervisors. Many studies in the literature assume that all events in the systems are controllable and observable. However, controllability and observability are two properties that should never be taken for granted in practice since machine and sensor downtime is inevitable. To prevent deadlocks in the plant nets with uncontrollable transitions, an optimal (maximally permissive in behavior) supervisor synthesis method based on event separation instances is proposed in [13]. For a kind of ordinary nets with uncontrollable transitions, a bottom-up optimal supervisor synthesis approach is presented in [14] and a linear constraint transformation approach is given in [15]. For the nets with both uncontrollable and unobservable transitions, an approach that transforms a given generalized mutual exclusion constraint into an admissible one is proposed in [16]. Based on it, an efficient method about the equivalent transformation of a class of constraints is given in [17]. Focusing on LS 3 PR, which is a kind of ordinary PN, Qin et al. [18] develop a method to design supervisors by enforcing constraints on minimal siphons of the net model. In [19], an optimal supervisory control policy with polynomial complexity is proposed to handle a particular class of ordinary PNs with uncontrollable and unobservable transitions. Besides behavioral permissiveness, structural complexity is also an important criterion that should be considered in the deadlock-free supervisor synthesis. Usually, a structurally minimal supervisor has the lowest implementation cost in the Manuscript received February 26, 2020; revised April 5, 2020; accepted April 17, 2020. This work was in part supported by the National Natural Science Foundation of China (61773206), the Natural Science Foundation of Jiangsu Province of China (BK20170131), Jiangsu Overseas Visiting Scholar Program for University Prominent Young & Middle-aged Teachers and Presidents (2019-19), and the Deanship of Scientific Research (DSR) at King Abdulaziz University (RG-20-135-38). Recommended by Associate Editor Shouguang Wang. (Corresponding author: MengChu Zhou.) Citation: B. Huang, M. C. Zhou, C. Wang, A. Abusorrah, and Y. Al-Turki, “Deadlock-free supervisor design for robotic manufacturing cells with uncontrollable and unobservable events,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 3, pp. 597–605, Mar. 2021. B. Huang is with the School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China (e- mail: huangbo@njust.edu.cn). M. C. Zhou and C. Wang are with the Department of Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, NJ 07102 USA (e-mail: zhou@njit.edu; cong.wang@njit.edu). A. Abusorrah and Y. Al-Turki are with the Center of Research Excellence in Renewable Energy and Power Systems and the Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia (e-mail: aabusorrah@hotmail.com; yaturki@yahoo.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JAS.2020.1003207 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 3, MARCH 2021 597