an interactive online robotics course - Semantic Scholar

Intelligent Automation and Soft Computing, Vol. 13, No. 1, pp. 105-116, 2007 Copyright © 2007, TSI® Press Printed in the USA. All rights reserved

AN INTERACTIVE ONLINE ROBOTICS COURSE STEPHEN BRUDER Applied Technology Associates (ATA) 1300 Britt St. SE Albuquerque, NM 87123 AND

KEVIN WEDEWARD New Mexico Institute of Mining and Technology Socorro, NM 87801

ABSTRACT—Attempting to convey concepts and ideas in the subject area of robotic manipulators from within the confines of a static two-dimensional printed page can prove quite challenging to even the most gifted of authors. The inherently dynamic and multi-dimensional nature of the subject matter seems better suited to a medium of conveyance wherein a student is allowed to interactively explore topics in this multi-disciplinary field. This article describes the initial development of an online robotics course “textbook” which seeks to leverage recent advances in Web-based technologies to enhance the learning experience in ways not possible with printed materials. The pedagogical approach employed herein is that of multi-modal reinforcement wherein key concepts are first described in words, conveyed visually, and finally reinforced by soliciting student interaction. Key Words: Education, Manipulator kinematics, Robots, Manipulator dynamics, Virtual reality, Symbolic computation, Electronic publishing

1. INTRODUCTION Educators have long since heralded the advent of the Internet-era wherein “online teaching” would become commonplace, however, this vision of the Internet as an educational medium is still in the embryonic stage. Despite this fact, various colloquia [1], conferences [2], symposia [3], and special issues [4] have focused on the topic of robotics education and some authors have addressed online education. Over the past decade, or two, robotics education has bifurcated into the principal sub-categories of mobile robotics and manipulator-based robotics. The accessibility of small inexpensive mobile robots has facilitated the proliferation of these devices in the classroom across a broad spectrum of educational levels [5]. Under the auspices of the KISS Institute for Practical Robotics (KIPR), Stein [6] and her colleagues have ventured to expose even kindergarten students to the benefits of hands-on learning through using primarily LEGO-based robotics. Other authors, such as Wedeward [7], have focused on middle to high school students and have developed complete outreach programs employing mobile robotics as an educational tool to expose the students to concepts in engineering. University level undergraduate [8] and graduate courses [9] remain the most common focus of educators. Many of these, and other similar efforts, have employed the use of the Internet as a medium [9] to widely disseminate robotics related educational material, share ideas with fellow educators, and reach out to distant students. Manipulator-based robotics education has not enjoyed a commensurate growth curve due in part to the startup financial commitment required to secure necessary equipment. By developing Internet-based laboratory environments for teaching, simulating, and studying robotic manipulators, authors such as Candelas [10], Labov [11], McKee [12], and Rohrmeier [13] serve to provide a wider audience with exposure to robots. In a special journal issue on robots in education, Murphy [14] promotes the use of

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robotics to teach artificial intelligence and presents a compelling argument for the inclusion of hands-on learning and robot contests [15]. Sutherland [16] describes a successful approach to exposing undergraduates to robotics relying on a very limited budget while seeking a balance between research and fundamentals. While many authors have used the Internet in their robotics educational efforts some have specifically focused on this medium as a venue and have developed successful visualization tools. The early visualization tools were basic stand-alone software packages [17, 18], which were later followed by sophisticated Internet-based visualization tools such as RobotDraw [19], VRML 2.0 Robot [13, 20], Robolab [21], and RIO [11]. The desirability of employing symbolic manipulation software tools for analyzing robotic manipulators has been widely recognized [22, 23, 24] by numerous authors. However, a means by which this could be readily accomplished over the Internet was not available until quite recently [25]. The motivation for the online robotics course described herein is derived from a conviction that robotics education should be dynamic, interactive, and at least three-dimensional. Concepts in robotic manipulation inherently involve temporal evolution, and as such, in teaching this subject the inclusion of a non-static means of presenting such ideas is desirable. In the opinion of the current authors, by soliciting student interaction in the learning process the educational experience is enhanced, as the student then becomes an active participant rather than a passive observer. As a result of the extensive inclusion of ideas from spatial geometry being embedded in the study of robot manipulators, a medium for illustrating these ideas which is capable of showing more than two-dimensional static projections can enhance the visual representations used to convey concepts. Also, the goal of promoting this subject area to the widest possible audience led to the use of the Internet as a dissemination medium. The work described herein seeks to draw on the lessons learned by earlier efforts and to synergistically combine recently available enabling Internet technologies to enhance the overall learning experience and usability of the material. The organization of the remainder of this paper is next described. Section 2 describes the enabling technologies and gives some examples of their usage. Section 3 provides an outline of the course material and focuses on particular sub-sections to promote the case for online education tools. Section 4 discusses future directions and is followed by the overall conclusion.

2. THE ENABLING TECHNOLOGIES The three principal technologies, which facilitated the development of this online book, address the areas of visualization, symbolic manipulation, and mathematical representation of equations on the Web.

2.1 Visualization Currently there exist few candidate technologies which are suitable for modeling and simulation of robotic manipulators on the Web [19]. The Virtual Reality Modeling Language (VRML) [26] was selected for the following reasons: • Requires a comparatively low bandwidth due to small file sizes • Provides a set of basic primitives for simple objects • Inherently supports spatial transformation and animation • Supports client-side hardware accelerated graphical rendering • Accommodates the ability to extend the language by adding nodes and scripts • Provides a future migration path to X3D [27] (an XML-based superset of VRML) • Supports an external authoring interface (EAI) which allows an external Java-based program to control properties of the VRML scene The language allows an intuitively appealing hierarchical approach to modeling robots, which can be performed using a Denavit-Hartenburg (D-H) type transformation node. The robot shown in Figure 1a was created using the VRML code shown in Figure 1b. The “DHRotationalJoint” node was created to extend the VRML language to allow a single line transformation using the four D-H parameters with access to a rotational or translational (DHTranslationalJoint) joint variable. The individual links can be controlled by driving the joint variables

An Interactive Online Robotics Course

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Figure 1a. A VRML model of a simple robot arm. Link0-LynxArm {} CoordFrame {x_label "X0"

y_label "Y0" z_label "Z0"}

DHRotationalJoint { alpha

0.0

children

a

0.0

d

0.0 theta 0.0

[

Link1-LynxArm {} CoordFrame

{x_label "X1"


1.57

y_label "Y1" z_label "Z1"} a 0.0

d

0.0 theta 0.0

children [ Link2-LynxArm {} CoordFrame {x_label "X2"



0.0

a 2.0

d

0.0 theta 0.0




0.0

a 2.0

d

0.0 theta 0.0



………

Figure 1b. VRML code required to produce a robot.

with “joint sliders” or otherwise (animation script or external Java code). The coordinate frames and manipulator links are also user-defined (prototyped) nodes. This environment allows the student to alter his/her viewpoint on the 3-D scene and interact with the image to see how the robot moves as the joints are “driven”. Support for VRML rendering in standard Web-browsers is provided via one of many freely available plug-ins.

2.2 Symbolic Manipulation Analyzing robotic manipulators can involve a significant amount of tedious mathematics. The educational benefits of having a student manually multiply six 4×4 matrices of trigonometric functions once or twice might be argued to have some redeeming value, however, after the tenth time the value of

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such an exercise might become questionable. As an example, consider multiplying the following six matrices wherein, ci = cos(θi (t)) and si = sin(θ i (t )) .

The likelihood of a simple error in manually calculating the result is quite high. Furthermore, as this is typically the first step in developing an analytical model of a robot manipulator, the interdependency of the analysis does not leave much room for error. Currently, there exist many capable computer-based symbolic manipulation packages (e.g. Maple, Mathematica, Derive, MathCad, MATLAB, etc), each having different syntax and requiring a substantial learning curve (cost not withstanding). However, only recently have Web-based symbolic manipulation capabilities become available with applications such as MapleNet [28] and webMathematica [25]. This approach has the following benefits over the non-Web counterparts: • Usage is free to the remote user • No learning curve as the complicated syntax is hidden from the user • Compact task specific code can be written for the problem at hand • Can also be used for more traditional tasks such as numerical calculations, graphing, etc When development of the online material was initiated the only options were webMathematica and an initial release of MapleNet as Mathcad Application Server and MATLAB Web Server did not provide symbolic calculation capabilities. For the work described herein webMathematica was selected, as it seemed to be the most mature and best suited to performing the necessary symbolic calculations and providing simplified results in a compact format. An example of this Web-based symbolic manipulation is shown in Figure 2 wherein a student can use a simple Web-based interface to determine the often-involved calculations necessary to generate a three-dimensional rotational matrix.

Figure 2. An example of web-based symbolic manipulation.

Developing such online symbolic manipulation material in webMathematica is somewhat involved for all but the most seasoned Web-server administrators. Significant knowledge of Web-server technology, including servlet containers, HTML forms, Java programming, and text-editor based coding of Java server pages is unfortunately necessary. The future, however, holds the promise of tools to simplify the authoring process.


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2.3 Mathematical Expressions on the Web When publishing scientific material on the Internet one must face the challenge of how best to represent mathematical equations. The Hyper Text Markup Language (HTML) provides very limited capabilities (subscripts and superscripts) in this regard and many authors resort to converting equations to images. The Portable Document Format (pdf files) allows for fairly acceptable formatting of equations, however, this approach requires a proprietary viewer and does not integrate well with other Web-based technology. In 1999 the Math for HTML effort of the W3C organization began to develop MathML [29] and the current version (2.0) has received native support in browsers such as Netscape 7.0, Amaya, Mozilla, and others. Internet Explorer 6.0, however, has not yet embraced this standard and requires the use of a free plug-in. MathML encodes both structure and presentation of mathematical expressions for the Web and allows equations to be cut-and-pasted from a Web document into other applications while preserving their mathematical meaning. By so doing one can take MathML equations from a Web document into Mathematica (say) and use them for symbolic calculations. This approach allows smaller file sizes and improved rendering, both visual and printed, while allowing tight format control. One might say that MathML is an XML version of TeX for the Internet. Unfortunately, this technology is sufficiently new that authoring tools are few and far between. Finally, the “R” matrix generated, as shown in Figure 2, is MathML code and hence the output generated by the Web-based symbolic manipulation tool can be used as a beginning for further analysis or documentation.

3. THE ONLINE TEXTBOOK The current version of the online material can be found at http://isrg.nmt.edu/robotics_class/new/ and runs on the Apache Tomcat servlet container with webMathematica 2.0. The source code consists of XML files containing MathML 2.0 coded equations and the illustrations use VRML 2.0 with Javascript (for internal NODES) and the EAI 2.0 with Java for externally controlled simulations. Users can view the material using: • Netscape 7 + a VRML plugin, or • IE 6 + a VRML plugin + MathML plugin The outline of the material is as follows: Chap. 1 Introduction Chap. 2 3D Transformations - 3D Positional Relationships - 3D Orientational Relationships - Minimal Descriptions of Orientation - Position and Orientation Transformations Chap. 3 Robot Kinematics - Forward Kinematics - Inverse Kinematics Chap. 4 Motion Kinematics - Angular Velocity Kinematics - Translational Velocity Kinematics - Summarizing the Approaches for Constructing the Manipulator Jacobian - Singularities of the Manipulator Jacobian Chap. 5 Robot Dynamics - Static Forces and Moments - Lagrangian Dynamics Appendices The following sub-sections provide representative highlights from various chapters in the online textbook.

3.1 Topics in 3-D Orientation In this section, students are introduced to the topic of three-dimensional orientation, rotation matrices, and various types of three-parameter descriptions of orientation. The distinction between fixed-axis (roll, pitch, and yaw) and relative-axis (Euler angles) rotations is often a point of confusion for students.

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Based on the experiences of the current authors, presenting a three-step sequence of rotations (Figure 3) interspersed with static images leading to an analytical result allows most students to grasp the fundamental concepts.

Figure 3. A static image depicting rotations.

However, by supplementing this static presentation with an opportunity for a student to interactively select the sequence of rotations (Figure 4) while visually receiving dynamic stimulus on their actions, the underlying ideas can be reinforced. Proceeding one step further, the student is allowed to explore the analytical result derived by performing various types of rotations (e.g. fixed, relative, or angle-axis) using either/both numeric or/and symbolic angles. This is done using the “Orientation Explorer” shown in Figure 2. As the final result is dynamically generated as a MathML equation it can be cut and pasted into local software for documentation or further manipulation.

3.2 Topics in Robot Kinematics The topic of robot kinematics typically begins with a procedure for assigning coordinate frames to robot links. The most prevalent approach, commonly referred to as the D-H method, utilizes four parameters ( α i −1 , ai −1 , d i ,θ i ) to define a six dimensional spatial relationship between two adjacent coordinate frames by imposing two constraints. The ensuing textual description followed by an illustration, such as shown in Figure 5, can prove challenging to grasp. By providing an animation of the sequential motion resulting from the transformation induced by the four D-H parameters, their definitions and usage are substantially clarified. The online animation shows the motion of a coordinate frame on an image similar to that of Figure 5 (see online course Section 3.1). These ideas are then used to assign coordinate frames to example robot designs, such as the very low-cost commercially available arm illustrated in Figure 1. The analysis then proceeds to calculate the homogeneous 4×4 transformation matrix, which relates the position and orientation of the base frame to the “tool” frame. Unfortunately, this calculation typically involves the multiplication of six 4×4 matrices of trigonometric functions. The likelihood of an error when employing manual derivation of such results is quite high and due to the interdependency of later calculations tolerance of such errors is very low. To assist in overcoming this obstacle a “Manipulator Kinematic Explorer” has been developed using webMathematica [25] wherein the student can enter the D-H table characterizing the robot of interest without having to learn the syntax of the symbolic mathematics program. An example session is shown below in Figure 6 for the case of a commercial robot arm used on a mobile manipulator. The section, which follows in the online textbook, employs similar tools to address the topic of inverse manipulator kinematics.


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Figure 4. The outcome of an interactive session.

Figure 5. An illustration of the four D-H parameters.

3.3 Topics in Robot Dynamics The final chapter in the online textbook presents an approach for developing a closed form model of the non-linear differential equations describing the dynamics of a robotic manipulator, assuming rigid links and joints. This topic draws upon most of the main ideas previously developed in the material and is often not addressed in a first undergraduate course primarily due to the time consuming nature of the calculations involved therein. By presenting a systematic step-by-step approach, based on the Euler-Lagrange equations applied to the energy of the robot, a straightforward methodology for obtaining the dynamic equations is introduced. The six step procedure can be summarized as follows (please consult online course material for a detailed explanation):

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Figure 6. The Manipulator Kinematic Explorer.

Step 1: Compute the inertia matrix for each link ( I i ), in a coordinate system located at the link's center of mass (frame { ci }, i = 1,...,n). Step 2: Construct the D-H table, and thus the forward kinematic relationships 01T , 02T ,..., 0n T . Transform these matrices to link center of mass coordinates:

T ( q1 , q2 ,..., qi ) = 0iT ( q1 , q2 ,..., qi ) ciiT

0 ci

r

i = 0,.., n

r

From these we can get 0d c ,0 zˆi , and c 0 R . i i r r r Step 3: Construct 0 vc which can be obtained by differentiating 0d c , and then transform 0ω i into frame i i r r { ci }, i.e. ω c = c 0R T 0ω i . i

i

n

Step 4: Develop expressions for the kinetic energy K = ∑ K i , where K i = n

r

r

i =1

(

)

r T r 1 r Tr mi vci vci + ω ci I iω ci and 2

potential energy V = ∑Vi , where Vi = g T 0d c mi . i i =1

Step 5: Apply the scalar Euler-Lagrange equations to the Lagrangian L=K-V, i = 1,...,n to develop:

∂L (⋅) d ⎛ ∂L (⋅) ⎞ − ⎜ ⎟ = −τ k ; k = 1,.., n dt ⎝ ∂q& k ⎠ ∂q k Step 6: Collect the terms and rewrite the expressions generated from Step 5 in the matrix form:

r r r r r r r r D ( q ) q&& + C ( q , q& ) q& + G ( q ) = τ

To allow students to check the final result obtained and to encourage exploration, an online “Manipulator Dynamics Explorer” was developed. To demonstrate the use of the “Manipulator Dynamics Explorer” consider the following example involving a simple two-link rotary/prismatic (RP) robotic manipulator shown in Figure 7. The D-H table for the robot is given by:


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The D-H frames are labeled with numeric subscripts and the center of mass coordinate frames are denoted by the subscripts ci .

Figure 7. A simple two-link robot.

The following information must be entered into the “Manipulator Dynamics Explorer” as shown in Figure 8:

Figure 8. Manipulator Dynamics Explorer.

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• • • • •

The D-H parameters, the link masses, the gravity vector, the Inertia matrices (in center of mass coordinates), and the transformation matrices from D-H frames to center of mass coordinates.

This simple example demonstrates the desirability of employing symbolic manipulation software.

4. FUTURE DIRECTIONS To accommodate a larger concurrent audience than is currently possible this online book will be hosted on dedicated servers at Sandia National Labs and New Mexico Tech. The development of an online robot builder which would allow a student to design, analyze, and visualize robots is currently underway, however, such an effort requires a higher level of sophistication. It is the intention of the current authors that this work serve as a starting point for more advanced topics in robotics and as such will undergo continual improvements. This paper is a first discussion of the online book and precedes its formal dissemination in the classroom. It is the intent of the authors to utilize the online book in the near future and encourage others to adopt it as well. Recognizing the value in assessing the book’s effectiveness, feedback from these implementations will be collected, reported, and used to improve the online material.

5. CONCLUSION This article describes the development of an online introductory robotic manipulator book, which leverages recent advances in Web-based technologies to enhance the learning experience. The three underlying enabling technologies were described and examples of their usage were given. A flavor of the approaches employed in this “book” was presented and justification for the pedagogical methodology provided. Further improvements in these initial efforts will rely on the feedback received from users of this online book.

ACKNOWLEDGMENT The authors wish to recognize the support of the Intelligent Systems and Robotics Center at Sandia National Labs for facilitating the start of this effort, Jacqueline Lacoursiere as the main Web-content developer, and two NMT graduate students Steven Wasson and Scott Dearie for assistance with the online Java and webMathematica examples.

REFERENCES 1. 2. 3. 4. 5. 6. 7.

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8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

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N. M. F. Ferreira and J. A. T. Machado, “RobLib: an educational program for robotics,” Symposium on Robot Control (SYROCO 2000), Vienna, Austria, Volume: 2, pp. 563-568, 2000. IEEE Robotics and Automation Magazine: Special Issue on robots on the Web, Volume: 7, 2000. F. A. Candelas, S. T. Puente, F. Torres, G. Ortiz, P. Gil, and J. Pomares, “A virtual laboratory for teaching robotics,” International Journal of Engineering Education, Volume: 19, Issue: 3, pp. 363370, 2003. A. Lobov, J. L. M. Lastra, and R. Tuokko, “A collaborative framework for learning robot mechanics: RIO-robotics illustrative software,” 33rd Annual Frontiers in Education, Boulder, CO, USA, 2003. G. T. McKee, “The development of Internet-based laboratory environments for teaching robotics and artificial intelligence,” 2002 IEEE International Conference on Robotics and Automation, Washington, DC, USA, Volume: 3, pp. 2695-700, 2002. M. Rohrmeier, “Web based robot simulation using VRML,” Proceedings of the 2000 Winter Simulation Conference, Orlando, FL, USA, 2000. R. R. Murphy, “Robots and education,” IEEE Intelligent Systems, Volume: 16, Issue: 6, pp. 14-15, 2000. R. R. Murphy, “Competing for a robotics education,” IEEE Robotics & Automation Magazine, Volume: 8, Issue: 2, pp. 44-55, 2001. K. T. Sutherland, “Undergraduate robotics on a shoestring,” IEEE Intelligent Systems, Volume: 15, Issue: 6, pp. 28-31, 2000. R. B. White, R. K. Read, M. W. Koch, and R. J. Schilling, “A graphics simulator for a robotic arm,” IEEE Transactions on Education, Volume: 32, Issue: 4, pp. 417-429, 1989. T. Raz, “Graphics robot simulator for teaching introductory robotics,” IEEE Transactions on Education, Volume: 32, Issue: 2, pp. 153-159, 1989. M. F. Robinette and R. Manseur, “Robot-Draw, an Internet-based visualization tool for robotics education,” IEEE Transactions on Education, Volume: 44, Issue: 1, pp. 29-34, 2001. VRML 2.0 Robot, Available: http://martin.rohrmeier.tripod.com/robot/. ROBOLAB, Available: http://disclab.ua.es/robolab/. J. F. Nethery and M. W. Spong, “Robotica: a Mathematica package for robot analysis,” IEEE Robotics & Automation Magazine, Volume: 1, Issue: 1, pp. 13-20, 1994. K. Sridharan, “Teaching computer graphics and robotics using symbolic computation software,” Computer Applications in Engineering Education, Volume: 8, Issue: 1, pp. 18–30, 2000. N. Vira and E. Tunstel, “Use of symbolic computation in robotics education,” IEEE Transactions on Education, Volume: 35, Issue: 1, pp. 18–30, 1992. webMathematica, Available: www.wolfram.com/products/webmathematica. Virtual Reality Modeling Language (VRML), Available: www.web3d.org/vrml/vrml.htm. X3D, Available: www.web3d.org. MapleNet, Available: http://www.maplesoft.com/products/maplenet/. MathML, Available: www.w3.org/Math/.

ABOUT THE AUTHORS

S. Bruder is a senior control engineer with Applied Technology Associates in Albuquerque NM, prior to which, he was an Associate Professor of Electrical Engineering specializing in Robotics and Control. He received a Ph.D. in Electrical Engineering from Queens University, Kingston, Ontario, Canada in 1994 in multi-sensor robotics.

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K. Wedeward received the Ph.D. degree in Mechanical Engineering from New Mexico State University, Las Cruces, NM, in 1995. He is currently an Associate Professor of Electrical Engineering at the New Mexico Institute of Mining and Technology, Socorro, NM. His interests are in engineering education, robotics and complex networks.