Int'l Conf. Frontiers in Education: CS and CE | FECS'15 | 1 SESSION USE OF ROBOTS, GAMIFICATION, AND OTHER TECHNOLOGIES IN EDUCATION Chair(s) TBA 2 Int'l Conf. Frontiers in Education: CS and CE | FECS'15 | Int'l Conf. Frontiers in Education: CS and CE | FECS'15 | 3 Exploring Finite State Automata with Junun Robots: A Case Study in Computability Theory Vladimir Kulyukin Sarat Kiran Andhavarapu Melodi Oliver Christopher Heaps Soren Rasmussen Wesley Rawlins Department of Computer Science Utah State University Logan, UT, USA [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Abstract— A case study in computability theory is presented had they taken a TOC class earlier in their undergraduate on teaching finite state automata with mobile robots. Junun curriculum. Mark III robots were used in several coding assignments on finite The use of robots in undergraduate CS education has state machines and a final coding project in an upper-level gained a significant interest both among researchers and undergraduate course in computability theory. Software and educators [2, 3, 4]. This interest could be attributed to the fact hardware choices are discussed with respect to the robotic platform and the laboratory environment. Several guidelines are that robotics is an inherently multi-disciplinary area bringing presented for integrating robots in theory of computation classes together subjects as diverse as cognitive psychology, electrical to reinforce and enhance students’ understanding of finite state engineering, and computer vision. It has been reported in the machines through practical applications of finite state control literature that the use of robots improves student project mechanisms. engagement [5]. We also believe that the use of robots can improve student Keywords—computability; undergraduate university education; engagement in and appreciation of not only the areas mobile robots; theory of computation; finite state automata traditionally affiliated with robotics (e.g., computer vision and electrical engineering) but also theoretical computer science. I. Introduction Specifically, mobile robots present an effective opportunity to Computability theory, also known as theory of computation motivate topics and concepts seemingly detached from any (TOC), remains one of the most challenging Computer practical applications. Robots can also be used in conjunction Science (CS) courses both for professors and students. with educational software tools such as JFLAP Professors, who teach computability courses, face lack of (www.jflap.org) to illustrate and motivate the practical motivation on the part of the students as well as inadequate significance of theoretical concepts. mathematical maturity and problem solving skills [1]. The effective use of robots in the classroom may require Students, who enroll in TOC courses, especially when such special training and hardware. Some professors who teach courses are required, believe that the covered topics are TOC courses and students who take TOC electives tend to be marginally relevant to having successful IT careers or, even comfortable only with the topics for which pencil and paper when relevant, the topics are not well motivated in the course are the most adequate technology. Some professors and materials. Although many students later realize the students may feel intimidated by the apparent complexity and fundamental and transcendental nature of concepts covered in diversity of robotic platforms. TOC courses, they frequently fail to realize it as they are Fortunately, the advances in commercial robotic platforms actually taking the course due to abundant technical notation, have made the integration of robots into TOC courses much complicated terminology, and the tendency of some professors easier than it used to be a decade ago (e.g., to overformalize intuitively straightforward concepts. www.activrobots.com, www.robotshop.com, www.junun.org). Another problem faced by CS undergraduates is that they There are two key decisions faced by CS professors who want typically take TOC courses in their senior year when they are to use robots in TOC course: the choice of a robotic platform almost finished with the undergraduate curriculum. The first and the choice of topics that the robots will be used to author of this paper has been teaching an undergraduate TOC illustrate, explore, or motivate. While there are many class at Utah State University (USU) for the past seven years outstanding books on computability [6, 7, 8] and various and has heard many CS majors telling him how much easier theoretical aspects of robotics [9, 10], there is a relative the advanced courses on compiler construction, game shortage of practical step-by-step resources that CS instructors development, and programming languages would have been, can use to integrate robots into TOC courses. 4 Int'l Conf. Frontiers in Education: CS and CE | FECS'15 | In this paper, we contribute to overcoming this shortage of Figure 1 and reach the state of the world in Q2 by executing .ሻܣ ǡܤǡ ܶሻ and ܲݑݐ݋݊ሺܣstep-by-step materials by sharing some of our experiences of ܲݑݐ݋݊ሺ using Junun robots to motivate, illustrate, and explore the topic of finite state automata (FSA). These experiences are primarily based on the TOC course taught by the first author in the fall 2014 semester. The second author was the teaching assistant for this course. The other four authors are USU CS undergraduate students who were enrolled in the course. The remainder of our paper is organized as follows. In Section II, we present the basic theoretical concepts for which we used mobile robots. These concepts were covered in the fall 2014 TOC course (CS 5000) taught by the first author at USU. CS 5000 used to be a required course with an average student enrollment of approximately forty students per semester until 2008. The course has been an elective since 2008 with the student enrollment ranging from five to fifteen students. In Section III, we describe the Junun Mark III platform, its modules, and assembly requirements. The three Figure 1. A robotic camera-arm unit text books were used for the course: the book by Davis et al. [6] was used for computability; Brooks Webber’s text [7] and the book by Hopcroft and Ullman [8] were used for finite state machines. In Section IV, we present several coding assignments given to the students and the final project of the course. Section V summarizes our experiences, analyzes our successes and failures, and presents recommendations that interested CS instructors or students may want to consider if they want to integrate mobile robots into their coursework. II. Basic Concepts In this section, we present several formal concepts enhanced and illustrated with mobile robots in our computability course. These concepts are related to the basic notion of the finite state Figure 2. Finite state control for two-block domain automaton (FSA). We chose the FSA, because there is a natural fit between robotic control and finite state machines that has been successfully and repeatedly illustrated in many research projects on mobile robots [9, 10]. A. Finite State Automata as Directred Graphs In an introductory lecture, a finite state automaton (FSA) was informally described as a directed graph whose nodes are states and whose edges are transitions on specific symbols. We pointed out to the students that input symbols processed by the FSA can be as simple as 0 and 1 or as complex as robot action sequences. For example, suppose we want to design a control system for a robotic camera and arm unit for building two-block towers from blocks A and B, as shown in Figure 1. We can arbitrarily assume that the sensor-motor system of Figure 3. A Mealy Machine the unit can execute one action, ܲݑݐ݋݊ሺܺǡ ܻሻ, and two predicates: ܥ݈݁ܽݎሺܺǡ ܻሻ and ܱ݊ሺܺǡ ܻሻ. The action A well-known limitation of the FSA is that the output is ݑݐ݋݊ሺܺǡ ܻሻ places block X on block Y or on table T, limited to the binary decision of acceptance or rejection. Theܲ ܥ݈݁ܽݎሺܺǡ ܻሻ verifies that the top of block X is clear, and FSA can be modified by choosing the output from an alphabet ܱ݊ሺܺǡ ܻሻ verifies that block X is either on top of another block other than the input, which brings us to the concepts of the or on top of the table T. Mealy and Moore machines [8]. The Moore machine Figure 2 shows a finite control for the two-block domain. associates outputs with states whereas the Mealy machine The control consists of three states Q0, Q1, and Q2. Each state associates outputs with transitions. In both types of automata, is a set of predicates that describe a state of the world. In state the outputs can be interpreted as commands to robot hardware. Q0, both blocks are on the table. In state Q1, A is on B. In Figure 3 gives an example of how a finite state machine state Q2, B is on A. The camera-arm unit can start in any of shown in Figure 2 can be transformed into a Mealy machine. the three states. For example, the unit can start in Q1 shown in Int'l Conf. Frontiers in Education: CS and CE | FECS'15 | 5 In Figure 3, The X/Y notation means that when the machine theorem about the equivalence of DFA and NFA by using the sees X in the input, it outputs Y and transitions to a new state. subset construction [7]. In Figure 3, we have defined the following complex symbols: We concluded the formalization of the finite state S0 = {On(A,T), On(B,T), Clear(A), Clear(B)}, S1 = {On(A,B), automata with a lecture on the Mealy and Moore machines. A On(B,T), Clear(A)}, S2 = {On(B,A), On(A,T), Clear(B)}, A0 = Moore machine M is a six-tuple ሺܳǡ ߑǡ߂ǡ ߜǡ ߣǡ ݍ଴ሻ, where Puton(A,B), A1=Puton(A,T), A2=Puton(B,A), A3=Puton(B,T).