Maneuvering control simulation of underwater vehicle based on combined discrete-event and discrete-time modeling

Abstract

When designing or acquiring underwater vehicles such as submarines and torpedoes, it is necessary to predict their performance precisely and perform tests repeatedly using modeling and simulation at both the engineering level and the tactical engagement level. For simulation performed for analysis purposes at the engineering level, which requires a considerable amount of computation power, a discrete-time system simulation that computes significant values at every single unit time using the established mathematical model or engineering model is mainly employed. To simulate a complex or complicated task such as a traffic analysis or tactical measure of effectiveness (MOE) analysis at the engagement level, it is appropriate to use a discrete-event system simulation that causes transition between model states through the triggering of events on the basis of the passing of messages between simplified mathematical models coupled in various ways. In this paper, we studied a maneuvering control of underwater vehicle from the perspective of a combined discrete-event and discrete-time system simulation; the simulation model is established on the basis of discrete-event system specification (DEVS) formalism, which is a representative modeling formalism of a discrete-event system simulation. In detail, the simulation includes DEVS modeling implementations of simulation execution time control and discrete-time step size control in real time at the time of performing a discrete-time system simulation for the purpose of three-dimensional visualization or carrying out a performance analysis using the DEVS model. This hybrid approach makes possible to build a simulation-based expert system which supports the decision making for the acquisition of an underwater vehicle.

Introduction

The development and construction of a submarine requires a large budget and a long period of time. Accurately predicting the performance of a submarine before its construction reduces both the cost and the time required and enhances productivity. Modeling and simulation is a way to minimize the development risk caused by errors in the design and construction processes, and it can also be used to optimize the design. Various types of simulation are required for underwater vehicles such as submarines or torpedoes; these include engineering-level simulations for predicting performance and engagement-level simulations for examining the effectiveness of certain tactics.

An engineering-level simulation is a continuous-time simulation that determines solutions of the ordinary differential equation (ODE) or the partial differential equation (PDE). Computer-aided engineering (CAE) is a representative example of such a simulation. Several researches have been conducted on the engineering-level simulation of underwater vehicles. For example, for performance analysis, Bettle et al. performed the unsteady analysis of the six-degree-of-freedom (DOF) motion of a buoyantly rising submarine using computational fluid dynamics (CFD) (Bettle, Gerber, & Watt, 2009) for the case of a discrete-time system simulation, Bozorg et al. researched the specific responses obtained in different ocean environments and at different operation speeds using the numerical analysis method (Bozorg, Jalili, & Eftekhari, 2007). But, depending on the purpose of the analysis, the engineering-level simulation can be implemented using a discrete-event simulation. For example, Qu and Meng proposed a simulation model for ship movements in the narrow and busy shipping channel using discrete-event simulation (Qu & Meng, 2012).

An engagement-level simulation is a discrete-event simulation that presents the engagements between various platforms according to series of significant events. Other related studies include a target motion analysis (TMA) simulation of a submarine in engagement against surface vessels (Bakos, 1995, Coll, 1994, Son et al., 2010), the torpedo evasion simulation of a submarine for developing evasion tactics (Armo, 2000), and a research that established this scenario using the discrete-event system specification (DEVS) formalism (Cho et al., 2007) and using the fuzzy logic-based decision making method (Son & Kim, 2012).

In all the aforementioned related studies, the simulation object is assumed to be either a discrete-event system or a discrete-time system, in order to accomplish a certain simulation goal. A discrete-event system simulation is suitable for a speedy analysis, because of its fast execution speed. However, it is necessary to define all events previously that would be occurred in the system or to establish the event generator using the distribution that is most similar to simulated system. In addition, the discrete-event system simulation is not appropriate for the analysis of continuous state variation with time.

A discrete-time system simulation is appropriate for visualization in three dimensions and the analysis of the simulation through plotting of results. However, it requires a relatively longer execution time and the variation of the target system’s state with time has to be given in the form of a function.

Thus, with the aim of overcoming these disadvantages and benefiting from the merits of each simulation, numerous researches have been conducted, in which attempts have been made to combine these two simulations. Conceptually, Cellier introduced applications that require a combined continuous/discrete modeling methodology together with techniques (concepts) that characterize this type of simulation approach (Cellier, 1986). Franck suggested a formalism to establish a computation model that combines continuous-time and discrete-event elements (Franck & Zerbe, 2003). Dammasch suggested a different approach to hybrid simulation on the basis of colored stochastic Petri nets (Dammasch & Horton, 2008). Fishwick researched an animation technique in computer graphics using combined discrete-event and continuous-time system simulation (Fishwick & Porr, 1993). Some researches have proposed extended DEVS to cover a continuous system (Cellier and Kofman, 2006, Giambiasi and Carmona, 2006, Kofman, 2003), and further others have proposed a new formalism to model such a combined system (Choi et al., 2006, Fishwick and Zeigler, 1992).

With the aim of applying the combined discrete-event and time system simulation method practically, the method was adopted in designing a smart automated highway system (AHS) (Antoniotti et al., 1997, Kourjanski et al., 1997), screening for diabetic retinopathy in a healthcare (Brailsford, Gutjahr, Rauner, & Zeppelzauer, 2007), a supply-chain (Godding et al., 2007, Lee et al., 2002), micro-air vehicles (MAVs) (Xia & Lin, 2003), and autonomous underwater vehicles (AUVs) (Xiang, Xu, Zhang, Xiao, & Huang, 2007).

Lättilä et al. mentioned that by using hybrid simulation models it is possible to create more accurate and reliable expert systems (Lttil, Hilletofth, & Lin, 2010). In this context, the combined discrete-event and time system simulation, in order words, a hybrid simulation makes possible to build a simulation-based expert system (Fassi et al., 2012, Yoo et al., 2010) which supports the decision making for the acquisition of an underwater vehicle.

There are various ways in which a simulation can be classified: according to the purpose, time increment, execution speed, and environment (Lee, 2006). Since we focus mainly on a standard simulation model architecture that is closely related to the time increment, we use this time increment to classify our simulations. We consider three different types of simulations. The first is a discrete-event simulation that is driven by individual events, the second is a discrete-time simulation that is processed in distinct time steps, and the third is a hybrid simulation, which is a combination of the first two types.

A discrete-event simulation is one that progresses each time an event occurs. In this type of simulation, each event has a triggering point. This implies that the events are organized chronologically and then triggered in sequence. Generally, when an event occurs, the state of the system changes and the simulation time advances. Because this simulation is controlled by the occurrence of events, it is also referred to as an event-driven simulation.

A discrete-time simulation is one that checks and computes the system states in uniform time increments, the length of which is fixed at the start of the simulation. In a discrete-time simulation of a moving object with a 1 s time step, for example, the position of the object is computed every second. In other words, the system state variables are computed and updated at regular time intervals. The discrete-time simulation may also be referred to as a time-stepped simulation.

A combined discrete-event/discrete-time simulation is one that uses both discrete events and discrete times when determining the time increment. In most cases, the simulation progresses at high speed because of discrete events. However, for specific user-defined events, the time increment changes to that of the discrete-time method, at which point the analysis of certain performance parameters or CAE and dynamic simulation are possible. During the discrete-time simulation phase, the time increment can be changed back to that of the discrete-event method for specific events. This is referred to as a hybrid simulation.

In the example of air-conditioner control shown in Fig. 1, when the ambient temperature is less than the user setting of temperature (30 °C), the state of the air conditioner is IDLE. When the temperature reaches the preset temperature, a Job Start event is generated. Simultaneously, the state of the air conditioner changes to WORKING and the time increment method changes to a discrete-time simulation, which repeatedly calculates the change in temperature due to the action of the air conditioner at specified time steps. When the temperature drops below the preset temperature again, a Job Done event is generated, the state of the air conditioner returns to IDLE, and the simulation returns to a discrete-event simulation.

In this paper, we have studied a motion model of the underwater vehicle to implement the maneuvering control simulation from the perspective of a combined discrete-event and discrete-time system simulation using classical DEVS formalism (Zeigler, 1990, Zeigler et al., 2000). To this end, we implemented the following models on the basis of the DEVS formalism: command and control (C2) coupled model that consists of two different atomic models, one that receives the maneuvering control command and the simulation control command from the user, and the other that processes data; a motion atomic model that calculates the posture and position of the underwater vehicle according to linearized six-DOF equations; and a visualization atomic model that carries out three-dimensional (3D) real-time visualization. All these models were incorporated into a single coupled model and the simulation was performed using this model. In addition, for the real-time visualization of the simulation, we implemented a 3D visualization program that is specific to underwater vehicle visualization, using the open scene graph (OSG), which is an OpenGL-based open source visualization library. The position and posture of the underwater vehicle were transferred to this visualization program from the models by real-time user datagram protocol (UDP) communication.

The rest of this paper is organized as follows. Section 2 presents the underwater vehicle motion model for maneuvering control using simple mathematics and dynamics. Section 3 describes implemented DEVS-based models and the interaction between them. In addition, the description of the overall simulation process is presented. Section 4 presents the DEVS-formalism-based implementation methodology for a combined discrete-event and discrete-time system simulation. Section 5 presents an analysis of the simulation results and a discussion of their application. Finally, Section 6 presents our conclusions and future work.