Models of computation for reactive control of autonomous mobile robots Gerasimos G. Rigatos Department of Engineering, Harper-Adams University College, TF10 8NB, Shropshire, UK Unit of Industrial Automation, Industrial Systems Institute, 26504, Rion Patras, Greece article info Keywords: Clocked-synchronous model of computation Automata Autonomous mobile robots Reactive control abstract The paper studies computation models for tasks performed by autonomous mobile robots. Such tasks can be accomplished by reactive control algorithms. Reactive control systems can be described using differ- ent models of computation which have as distinguishing feature the abstraction level of time. Thus, three computation models are defined: the untimed model, the synchronous model and the timed model. It is shown that the clocked-synchronous model of computation is more appropriate for describing the con- troller for a parallel parking task. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction The motivation of this paper is to analyze computation models describing reactive control for autonomous mobile robots. Such models can help to analyze the convergence and stability proper- ties of reactive control algorithms (Passino & Burgess, 1998). Reac- tive control has been successfully applied to autonomous mobile robots and has enabled robotic vehicles to perform various tasks, such as parallel parking (Luzeaux & Zavidovique, 1992; Rigatos, Tzafestas, & Evangelidis, 2001) or motion with desirable speed in uncertain environments (Rigatos, 2003). Reactive controllers re- ceive inputs, react to them by computing outputs and wait for the next inputs to arrive. Reactive controllers correspond to finite state machines, which in turn can be represented with the use of automata or Petri nets, as shown in (Jantsch, 2004; Kozen, 1997; Meystel & Albus, 2002; Morderson & Malik, 2002). Reactive control algorithms are also known as processes and can be modeled as finite state machines. First, the untimed model of computation is considered. This adopts the simplest timing ap- proach, in which processes are connected to each others via sig- nals. Signals transport data values which do not carry any time information but preserve their order of emission. Values that are emitted first are assumed to be received first by the receiving pro- cess. Second the synchronous model of computation is considered. This can be based on partition of time either into time slots or into clock cycles. The perfectly synchronous model assumes that the results of a computation on input values are already available in the same cycle. The clocked-synchronous model assumes that every simulation step of a process takes one cycle. Hence the reaction of a process to an input becomes effective in the next cycle. Third, the timed model of computation is examined which assigns a time stamp to each value communicated between processes. This allows to model time-related issues in great detail, but it complicates the model and the task of analysis and simulation. It will be shown that the clocked-synchronous model of computation is appropriate for describing the controller for the parallel parking task. The structure of the paper is as follows: In Section 2 the use of finite state machines and Petri Nets in the modeling of reactive control algorithms (processes) is analyzed. In Section 3 the basic elements of the various models of computation (MoC) for reactive control are presented, and the untimed, synchronous and timed model of computation are explained. In Section 4 the modeling of a parallel parking controller by a finite state machine is analyzed and the associated untimed, synchronous and timed models of computation are studied. In Section 5 simulation tests are given about the efficiency of the proposed reactive control algorithm for the parallel parking task. Finally, in Section 6 concluding re- marks are stated. 2. Modeling approaches for reactive control 2.1. Results on reactive control Reactive controllers are discrete event controllers. They receive events as inputs, process the events against certain logical condi- tions, and generate control outputs. Such controllers have been used in systems that are inherently described by discrete-event models or dynamical systems which after some abstraction of state are also brought to the form of a discrete-event model. In Raisch (1997) it has been shown that by identifying sequences of output symbols with an automaton states, discrete-event descriptions of a continuous-time system can be derived. In Lunze and Nixdorf (2001) nondeterministic and stochastic automata are used as qual- itative models of dynamical systems. Furthermore, in Lunze, Nixdorf, and Schröder (1999) it is investigated under which condi- 0957-4174/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2011.12.024 E-mail address: grigat@ieee.org Expert Systems with Applications 39 (2012) 6767–6773 Contents lists available at SciVerse ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa