A Course in Simulation and Demonstration of Humanoid Robot Motion

IEEE TRANSACTIONS ON EDUCATION, VOL. 54, NO. 2, MAY 2011 255

A Course in Simulation and Demonstrationof Humanoid Robot Motion

Hsin-Yu Liu, Wen-June Wang, Fellow, IEEE, and Rong-Jyue Wang

Abstract—An introductory course for humanoid robot motionrealization for undergraduate and graduate students is presentedin this study. The basic operations of AX-12 motors and the me-chanics combination of a 16 degrees-of-freedom (DOF) humanoidrobot are presented first. The main concepts of multilink systems,zero moment point (ZMP), and feedback control are then intro-duced such that the students can understand the relationship be-tween the ZMP position and the stability of the robot. Finally, thestudents can simulate the desired motion trajectory and realize themotion practically on the real humanoid robot. Taking this course,the students can not only learn robotic theories and control tech-niques for humanoid robot motion, but can also enhance their ex-perience in hands-on experiments in executing the motion of a hu-manoid robot. The proposed educational strategy will enable stu-dents to progress easily to more advanced work on robot designand control in their future study or careers.

Index Terms—Educational strategy, humanoid robot stability,multilink system, zero moment point (ZMP).

I. INTRODUCTION

T HE system of a humanoid robot can be considered asa complex multilink system. [1]–[4] proposed teaching

robotic control methods by using the robot arm as an experi-mental plant. In [5], the educational strategy was proposed ofteaching position control of a dc motor by a proportional-inte-gral-derivative (PID) controller. In [6], a course and experimentwere designed for the control instruction of stepper, medium,low-power dc and brushless motors. [7] and [8] designed someexperimental courses for students to learn the control of mobilerobots by using JavaScript and virtual technique, respectively.

In order to achieve the stable motion of a humanoid robot,zero motion point (ZMP) is considered as a stability index. In[9] and [10], the authors used the ZMP concept to implementthe balance control of a biped robot. [11] and [12] developeda walking pattern generator and gravity compensation functionthat allows the biped robot to walk and carry objects stably.[13] used the fuzzy logic algorithm to reduce trunk motions of abiped robot. [14] established the existence of a periodic orbit in asimple biped robot and analyzed its stability properties. A bipedrobot was designed in [15] to achieve a dynamically stable gait

Manuscript received January 28, 2010; accepted March 24, 2010. Date ofpublication June 10, 2010; date of current version May 04, 2011. This workwas supported by the National Science of Council of Taiwan under grants NSC98-2221-E-008-119-MY3 and NSC 98-2221-E-150-061.

H.-Y. Liu and W.-J. Wang are with the Department of Electrical Engineering,National Central University, Jhongli City 32001, Taiwan (e-mail: [email protected]).

R.-J. Wang is with the Department of Electronic Engineering, National For-mosa University, Huwei Township, Taiwan.

Digital Object Identifier 10.1109/TE.2010.2051157

pattern with high-speed walking. A walking control consistingof a feed-forward dynamic pattern and a feedback sensory reflexwas proposed for the biped robot in [16].

The objective of this paper is to design a course for senior un-dergraduate and graduate students to learn the theory and prac-tice of humanoid robot control and motion design. The exper-imental plant is a humanoid robot that has 16 AX-12 motors.First, the students are introduced to detailed specifications andmethods of operation of the AX-12 motor. Next, the theoriesof ZMP stability index, multilink system, ankle joint adjuster,linear interpolation, and linear regression are taught, accompa-nied with the respective experiments. Finally, this theory andknowledge are applied to achieve the motion control of a hu-manoid robot in a practical experiment. After completing thecourse described in this paper, students will easily be able toprogress to more advanced work on robotic motion design andcontrol in their Master’s degree study or in careers in robotics-based companies.

This course can be divided into two parts: the motion trajec-tory functions’ generation and simulation for a humanoid robotand the corresponding robot motion experiments. In the firstpart, students can use computer simulation to design some ofthe motions required from a humanoid robot, such as kicking,bowing, or lifting a hand. These motions, though, may cause therobot to fall down. Therefore, the concept of ZMP is applied asa stability index to guarantee the stability of the motions; ZMPis the point at which contact of the robot with the ground pro-duces no moment. No matter what motion the robot makes, theZMP should be located within the safe region where the robotwill not fall over. In order to keep the ZMP inside the safe re-gion, the ankle joint angle of the support foot (or feet) has tobe adjusted correctly. To find the location of the ZMP, studentsmust first learn the multilink system. Then, the linear interpola-tion method is used to reduce the ZMP errors, and linear regres-sion is applied to approach stable whole motion trajectories. Inthe second part of the course, the students apply the techniqueslearned in the first part to an actual humanoid robot to have itperform any desired motions. Thus, students can learn how tocontrol a real humanoid robot to realize designed motions. Theexperimental experience can enhance the students’ experiencein hands-on experience. Indeed, the student feedback shows thatthis course has improved their robotic knowledge and hands-onexperience. Most of the undergraduate and graduate studentsalso agree that this is a good fundamental robotic course andis useful for undergraduates and Master’s students

II. OVERVIEW OF THE SYSTEM STRUCTURE

The experimental plant of the robotic laboratory course is ahumanoid biped robotic system shown in Fig. 1. It includes a

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256 IEEE TRANSACTIONS ON EDUCATION, VOL. 54, NO. 2, MAY 2011

Fig. 1. System diagram of the humanoid biped robot.

personal computer, the interface (USB2Dynamixel card), andthe humanoid biped robot.

A. Computer System

1) Hardware: A computer is chosen as the control center toachieve the motion execution of a humanoid robot. The CPU ofthe computer is an Intel Core 2 Quad 2.4 GHz with 2 GB RAM.

B. Software

Matlab was chosen to implement the computer simulationsand to verify the stability of the designed motions. Matlab notonly can deal with the complex matrix operation calculation tobuild the multilink system model for the humanoid robot, butalso supports the powerful graphics to display the 3D figuresclearly.

Furthermore, Borland Builder is applied to programthe source codes of all the motions of the humanoid robot, andthe commands are sent to AX-12 motors by using the USB2-Dy-namixel card. Borland Builder provides the convenienceof interface design and high-speed programming process forusers.

C. Interface (USB2-Dynamixel Card)

Serial transmissions are needed between the AX-12 motorsand the computer. The computer not only sends the commandsto all motors but also receives the information from the AX-12motors by using the USB2-Dynamixel card through the USBport of the computer.

D. Humanoid Biped Robot

Fig. 1 shows a photograph of the real humanoid robot, whichconsists of 16 AX-12 motors with some plastic connections. InFig. 2, there are a total of 16 degrees of freedom (DOF) in thehumanoid robot, where 5 DOF are in each leg, and 3 DOF ineach hand. The weight and height of the robot are 1.07 kg and36 cm, respectively. The mechanical structure of the robot isthat of the Bioloid robot kits [17].

E. AX-12 Motors

The AX-12 motor is a small and light actuator, containinga microcontroller. The angular positions of the motor can befed back to the control center (computer) through the micro-controllers and USB2-Dynamixel card. The commands for the

Fig. 2. Multilink structure of a robot.

Fig. 3. Three-link system.

positions, speed, load, and voltage can be sent to the microcon-trollers in the AX-12 motors from a personal computer throughthe USB2-Dynamixel card. All AX-12 motors are connected bya serially connected cable. By serial transmission, the computercan give the commands to all AX-12 motors simultaneously inone instruction packet. Moreover, the maximum torque of theAX-12 motor is 16.5 kg cm, and the speed is about 306 persecond under an operating voltage of 10 V.

III. SOME MAIN CONCEPTS

The structure of a robot can be seen as a mechanical com-bination of multiple links (see Fig. 2). In order to calculate theposition of ZMP, the multilink system concept is used to find themass center of each link. Therefore, the multilink system mustbe introduced here.

A. Multilink System

In robotic research, the multilink system [18] is usually usedto calculate the end-point position of each link of a robot bythe given corresponding joint angles. Fig. 3 shows a three-linksystem, where are the lengths of three links, link- , where

, 2 and 3, respectively. is the rotated angle of link- in xzplane, is the rotated angle of link- in yz plane. The end-pointpositions can be obtained from the following equations:

(1)

LIU et al.: COURSE IN SIMULATION AND DEMONSTRATION OF HUMANOID ROBOT MOTION 257

Fig. 4. Safe regions of ZMP.

where , , and are the end-point positions of three links,respectively. Furthermore

and . Then, the mass center of each linkcan be calculated by setting the values of in (1). For example,in Fig. 3, if the mass center of link-1 is at the quarter of thelink-1, is changed to such that the masscenter of link–1 can be calculated by (1).

B. Concept of Zero Moment Point

ZMP being the point where contact with the ground producesno moment, it is always used as a stability index for humanoidrobot motions. In Fig. 4, let the gray area be called the “saferegion” for the signal support phase (SSP) (the dark gray area inFig. 4) and the double support phase (DSP) (the light gray areain Fig. 4). The position of ZMP can be calculatedfrom (2) [19].

(2a)

(2b)

where . is the mass of link- , is the grav-itational acceleration, and , , and are the positions ofthe mass center of link- with respect to the – – coordinates.In order to ensure the stability of the humanoid robot under mo-tion, the ZMP must be inside the safe region shown in Fig. 4. Ifthe ZMP is not located in the safe region, a control scheme isused to return the ZMP position to the safe region. Therefore,the ankle joint needs to be adjusted.

C. Scheme of the Ankle Joint Adjuster

Suppose that the robot is standing, and then kicks the left legfrom 0 to 60 . First, several sampled points are adoptedfrom the trajectory from 0 to 60 , and the ZMP position cor-responding to each sampled point should be calculated by (2).Based on the ZMP error feedback, the ankle angle of the rightfoot needs to be adjusted such that the ZMP of every sampledpoint is confirmed as being within the safe region.

Fig. 5. Ankle joint adjuster.

In Fig. 5, (the kicking degree), is the ankle angle ofthe support foot, and is the knee angle of the foot. In order tomaintain the upper body perpendicular to the ground, the kneeangle should be equal to . During the SSP, the ideal ZMPis set as the center of the support foot, as the point inside thedark gray area shown in Fig. 4. During the DSP, the ideal ZMPis set as the center of the region between the two soles, as the

point in the light gray area shown in Fig. 4. Define the ZMPerror as follows:

(3)

where “ ” is the sampled point, , and is theiteration time. Based on the ZMP error feedback (see Fig. 5), theankle angle is adjusted to decrease the ZMP iteratively. Becausethere are two DOF ( - and -directions) in the ankle of the foot,the angle of the ankle joint can be adjusted as

(4)

where and are two small feedback gains that are deter-mined by considering the tradeoff of the convergence speed andovershoot phenomenons from the practical experiment. Further-more, and are the ankle joint angles in the -and -directions at the sampled point and the iteration , re-spectively. The above process [(1)–(4)] runs iteratively, and thenstops until two successive ZMP errors are within betweenand cm (see Fig. 6). Then, the average of the last two

and is taken tobe the final ankle joint angle . In summary, foran assigned motion to the robot, if the above process is doneiteratively for all sampled points, the motion trajectory corre-sponding to the final and the sampled pointwill be obtained; therefore, the robot can follow the trajectoryto carry out the motion and the ZMP is within the safe regionthroughout (see Fig. 7).

IV. MODIFICATION OF THE MOTION TRAJECTORY FUNCTION

A. Linear Interpolation

The final ZMP error found for each sampled point in the lastsection may be smaller than the distance 0.05 cm, but this is stillnot accurate enough. In order to increase the precision of thecalculated ZMP position as much as possible, a linear interpo-lation method (5) is applied to modify the final ankle joint angle

, where the values and are ZMP


Fig. 6. Stop condition of the ankle joint adjuster.

Fig. 7. Motion function of kicking motion.

Fig. 8. Linear interpolation.

errors corresponding to and , respectively.The adjusted final ankle joint angle is obtained from

(5)

which may make the ZMP error much smaller than does theaverage . The formula (5) is suitable in both - or -direc-tions (see Fig. 8).

B. Linear Regression

If a motion trajectory has been sampled in points, thereare just points , , to be found. If thenumber of sampled points is very large, calculating the com-plete motion trajectory needs a lot of time. Therefore, to save

Fig. 9. Approximated motion trajectory of the bowing and the kicking side-ways motion.

computation time, the linear regression method (6) can be usedto approximate the complete motion trajectory.

(6)

By using (6), the approximated trajectory function of motionssuch as bowing and kicking sideways are shown in (7) and (8),respectively.

(7)

(8)

where is the ankle joint angle for the bowing motion in the-direction and is the bowing degree; is the ankle joint

angle of kicking sideways motion in the -direction and isthe kicking sideways degree; and are all between 0 and90 (see Fig. 9).

All of the above-mentioned motions are simple ones, forwhich it is easy to find the approximated motion trajectory inone direction. If a complex motion contains two directions,two motion trajectories corresponding to the two directions,respectively, can be generated.

V. SIMULATION AND EXPERIMENTAL RESULTS

Two motions (bowing and kicking sideways) of a humanoidrobot are simulated and realized experimentally to verify theeffectiveness of the proposed methods.

A. Part A: Simulation of the Humanoid Robot

By using (7) and (8), two motions of bowing and kickingsideways for a humanoid robot are simulated by a computer.Fig. 10(a) and (b) show the stick frameworks of the two mo-tions from 0 to 90 , respectively, where the motion is exe-cuted from the initial status (light gray sticks) to the dark graysticks gradually. Fig. 11 shows the ZMP errors of the two mo-tions from 0 to 90 , respectively. The safe region of ZMP is

cm cm and cm cm .

B. Part B: Experiment on a Real Humanoid Robot

In order to verify the effectiveness of the proposed methods,two motions (bowing and kicking sideways) are performed on


Fig. 10. (a) Stick framework of the bowing motion. (b) Stick framework of thekicking sideways motion.

Fig. 11. Simulated ZMP error in bowing and kicking sideways motion.

Fig. 12. (a) Real experiment for the bowing motion. (b) Real experiment forthe kicking sideways motion.

the real humanoid robot. Fig. 12(a) and (b) show a series of pic-tures of bowing motion and kicking sideways motion, respec-tively. It is seen that the ZMP errors are always inside the saferegion, as shown in Fig. 13. The experimental results show thatthe humanoid robot can achieve the two motions smoothly andstably.

VI. PEDAGOGICAL METHOD OF THE COURSE

“Special Project on Controls—Simulation and Demonstra-tion for Humanoid Robot Motions” is a one-semester (54 h)course at National Central University, Taiwan. It is designed forsenior undergraduate and graduate students who have taken theprerequisite courses “Automatic Control Engineering” and “Ad-vanced Engineering Mathematics.” The students are required toattend a 1-h lecture on theory and a 2-h lab session for simu-lation and experiments each week. The teachers of the courseinclude one professor and two teaching assistants. The students

Fig. 13. Experimental ZMP error of the bowing and kicking sideways motion.

should be divided into several groups, and each group has abouttwo or three students. The syllabi of the course are as follows.

The first 15 h cover the following material: 1) the specifica-tions and basic operations of the AX-12 motors; 2) the assemblyof the humanoid robot using AX-12 motors; 3) the connectionbetween the AX-12 motors and the computer; 4) the basic op-erations of AX-12 motors using Borland Builder; and5) practice in the operation of AX-12 motors and the basic mo-tions of the humanoid robot.

In the next 15 h, the main concepts and theories of the courseare taught, which include: 1) ZMP stability; 2) the multilinksystem; 3) feedback concept for the ankle joint adjuster; and4) the methods of linear interpolation and linear regression. Inthis section of the course, the teachers teach the formulas forthe multilink system (1) and the ZMP position (2). The studentslearn to use Matlab software in the lab for the simulation toadjust the ankle joint angle, such that the ZMP falls in the saferegion. Next, the students need to apply the linear interpolationmethod to modify the ankle joint angles. Finally, the desiredmotion functions such as (7) and (8) can be obtained by usinglinear regression and Matlab software.

In the third set of 15 course hours, students are largely basedin the lab doing the experiments to achieve robot motion byusing Borland builder. The suggested motions to realizeare bowing, one leg kicking sideways, kicking forward, squat-ting, and so on.

In the last 9 h, each group of students should present theirachievement report and perform their robot motion show. Thestudents are also requested to complete the student perceptionsurvey, answer three open-ended questions, and give an in-depthinterview to assess the learning effectiveness of this course.

The estimated cost per workstation for a group of two or threestudents is not expensive, being about US $1100 for a robot and$1000 for a PC. Based on the educational strategy of this paper,the students should at least have learned the following skills:1) basic operations of AX-12 motors by using BorlandBuilder; 2) motion simulation by Matlab software; 3) feedbackand ZMP concept for the motion control of the humanoid robot.Furthermore, the practical experiment can increase students’hands-on experience and enhance their interest in the roboticresearch and development.


VII. REACTION FROM STUDENTS

A survey was designed, which contains 14 questions andthree open-ended questions, to evaluate the perceptions oftwo kinds of students (undergraduate and graduate) on theimportance and necessity of this course.

A. Quantitative Analysis

The quantitative samples consisted of 25 undergraduates (22surveys were deemed complete and usable) and 15 graduates(all were complete and usable) in the Department of ElectricalEngineering at National Central University. All the studentshad taken the one-semester course “Automatic Control Engi-neering” and the two-semester course “Advanced EngineeringMathematics.” The survey is divided into five major sectionswith a total number of 14 survey items, shown in Table I, on thehardware of the humanoid robot (Q1 and Q2), the operation andcommunication of AX-12 motors (Q3 and Q4), the approachesand theories of the stable motion generation (Q5–Q8), the sim-ulation and practical experiment (Q9–Q12), and the perceptionsof students (Q13 and Q14). The five-point Likert scale, rangingfrom “1” indicating not at all to “5” indicating very strongly,was used to measure their agreement. The quantitative analysesof this survey are shown as follows.

a. To assess the internal consistency of the survey, Cron-bach’s Alpha value [20] is computed. A Cronbach’sAlpha value larger than 0.70 is considered as the evi-dence of reliability. In this survey, , which isconsidered to be high and indicates the good reliabilityof the survey.

b. For the answers to Q1 and Q2, the perceptions of all stu-dents are quite positive, and the mean scores are all higherthan 4.

c. From the score of Q3, the agreement of graduatesis much stronger than that of

undergraduates because the un-dergraduates are less experienced in the operations ofAX-12 motors and in communication between a PC andthe motors. Therefore, this course must have a detailedlecture on the AX-12 motors and approaches to theiroperation such that the students can easily operate them.

d. The mean scores of are lower than the otherquestions, and the mean scores (about 3.57) of Q6 andQ7 are the lowest. This means the approaches to and the-ories of stable motion generation are difficult for the stu-dents, especially for undergraduates. It is also seen that theagreement to Q6 and Q7 for undergraduates is obviouslymuch lower than that of graduates. Therefore, this courseneeds much more time (21 h) spent on the theorems andin illustrating simple examples that explain them.

e. According to the mean scores (about 4.06) of ,most of the students are interested in the humanoid robotand its laboratory course. In particular, the mean score

of Q11 is the highest in the table, which showsthat this course can enhance students’ control knowledgeand their hands-on experience with the humanoid robot.

f. The mean score of Q13 indicates that most ofthe students agree that the hands-on experience and thecontrol theories learned in this course can apply to other

TABLE IFREQUENCIES AND MEANS FOR “STUDENT’S OPINIONS” OF THIS COURSE

courses or future study. The score of Q14 shows that 50%of the undergraduates choose the score 3 because theyhave not yet decided their future research topics. On the


other hand, the graduate students strongly agree with Q14because they have had the practical experience in researchin the areas of robotics and control theory.

g. From the last row in Table I, the sum of the averagepercentage of scores 5 and 4 is larger than that of theother three scores, which means that most of the stu-dents strongly agree with the educational strategy of thiscourse. However, there are some different opinions be-tween undergraduate and graduate students. Because thetheorems of controller design and robotics are difficultfor undergraduate students, their responses to all ques-tions are lower than that of graduate students. However,the mean score of undergraduate students still is 3.75, in-dicating that most of the students think that this coursehas improved their robotic knowledge and hands-on ex-perience. Most of the undergraduate and graduate stu-dents also agree that it is a good fundamental roboticscourse and is useful for undergraduates intending to dotheir Master’s research.

B. Three Open-Ended Questions and In-Depth Interview

Three open-ended questions and an in-depth interview (qual-itative analysis) were use to enhance the results of quantitativeanalysis.

a. What did you learn by taking this course?This is the same as the analysis results of survey

; the students express the view that this course canprovide them with robotic knowledge, the control conceptof the robots, and simulation and experiment skills. Theyalso think that this course is indeed a good fundamentalcourse for robotics research.

b. What should be improved for this course?The undergraduate students indicate that the multilinksystem and feedback control theories are a bit esotericfor them (refer to the Quantitative analysis “d”). In orderto overcome this problem, this course should take moretime for lecturing on this topic and use easier examplesfor undergraduate students.

c. What could you apply the knowledge of this course to?The quantitative and qualitative analysis all show that themethods and knowledge of this course could be applied totheir future studies and careers in the automatic control orrobotics fields.

VIII. CONCLUSION

This course is an introductory course for humanoid robotmotionrealizationforundergraduateandgraduatestudents.Theyshould have taken courses in automatic control engineering andadvanced engineering mathematics before they take this course.Based on the educational strategy taken, after completing thiscourse, students will have learned, at a minimum, the followingskills: 1) basic operations of AX-12 motors by using Borland

Builder; 2) motion simulation by Matlab software;3) feedback and the ZMP concept for the motion controlof a humanoid robot. Furthermore, the practical experiments

can increase students’ hands-on experience and enhance theirinterest in robotic research and development.

According to the qualitative analysis of the survey for thecourse, it is possible that two different programs can be de-signed for graduate and undergraduate students, respectively,in the future because of their different requirements and studyexperience.

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Hsin-Yu Liu was born in I-Lan, Taiwan, in 1983. He received the B.S. degreefrom the Department of Electrical Engineering, Tamkang University, Tamsui,Taiwan, in 2001, and the M.S. degree from the Department of Electrical Engi-neering, National Taiwan Ocean University, Keelung, Taiwan, in 2005. He hasbeen pursuing the Ph.D. degree with the Department of Electrical Engineering,National Central University, Chung-Li, Taiwan, since 2007. His current researchinterests include fuzzy control, image processing, and intelligent robots.

Wen-June Wang (F’08) was born in Hsinchu, Taiwan, in 1957. He received theB.S. degree in control engineering from National Chiao-Tung University, Hsin-Chu, Taiwan, in 1980; the M.S. degree in electrical engineering from TatungUniversity, Taipei, Taiwan, in 1984; and the Ph.D. degree from the Institute ofElectronics, National Chiao-Tung University, Hsinchu, Taiwan, in 1987.

He is presently a Chair Professor with the Department of Electrical Engi-neering, National Central University, Chung-Li, Taiwan. He has published morethan 120 journal papers and 120 conference papers. His research interests in-clude the areas of fuzzy theory and systems, robust control, neural networks,and pattern recognition.

Dr. Wang received the Distinguished Research Award from the National Sci-ence Council of Taiwan in 1999, 2001, and 2003. He serves as a member ofthe Editorial Board of numerous journals, including the Asian Journal of Con-trol, the International Journal of Electrical Engineers, the IEEE TRANSACTIONS

ON FUZZY SYSTEMS, and the IEEE TRANSACTIONS ON SYSTEMS, MAN, AND

CYBERNETICS—PART B: CYBERNETICS. He is also the Editor in Chief of the In-ternational Journal of Fuzzy Systems.

Rong-Jyue Wang was born in Tai-Chung, Taiwan, in 1967. He received theB.S. and Ph.D. degrees from the Department of Electrical Engineering, NationalCentral University, Chung-Li, Taiwan, in 1990 and 1995, respectively.

He has been an Associate Professor with the Department of ElectronicEngineering, National Formosa University, Huwei, Taiwan, since 2007. Hispresent research interests include robust control, intelligence control, fuzzycontrol, image recognition, and intelligent robots.

A Course in Simulation and Demonstration of Humanoid Robot Motion

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