ieee/asme transactions on mechatronics, vol. 20, no. 6,...

IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 20, NO. 6, DECEMBER 2015 2805

Minimizing Energy Consumption of ParallelMechanisms via Redundant Actuation

Giuk Lee, Sumin Park, Donghun Lee, Frank C. Park, Fellow, IEEE, Jay I. Jeong, Member, IEEE, and Jongwon Kim

Abstract—This paper shows that redundant actuation can re-duce the energy consumption of parallel mechanisms, in some casesby a considerable margin. A theoretical analysis for the energy-saving mechanism is elucidated, and an energy consumption modelfor a servo-motor system is proposed. Our hypothesis is experimen-tally verified with a widely used two degree of freedom parallelmechanism design driven by three actuators. Experimental resultsshow that redundant actuation can reduce the electrical energyconsumption of the actuators by up to 45% compared to the cor-responding nonredundantly actuated version of the mechanism.

Index Terms—Energy minimization, parallel mechanism, re-dundant actuation.

I. INTRODUCTION

PARALLEL mechanisms consist of several serial kinematicchains that connect a base to a moving platform [1], [2].

Parallel mechanisms are known to be capable of very fast mo-tion, and of carrying heavier payloads than their serial analogs.These advantages are acquired at the expense of several short-comings: a reduced workspace from singularity configurations,difficulties in the mechanical design procedure, and complexcontrol algorithms. In a singularity configuration, the degrees offreedom (DoF) of a parallel mechanism change instantaneously.The change in DoF can cause the control to fail throughout thesingularity region. Thus, if possible, the singularity configura-tion must be eliminated so as to enlarge the workspace of themechanism and to ensure the stability of the manipulator control[3], [4].

One of the known methods to overcome the singularity con-figuration is to install more actuators than the kinematic DoFof the mechanism. Such mechanisms are called redundantly ac-tuated parallel mechanisms (RAPMs) [5]–[10]. An RAPM candistribute the internal torques in the null space of the torque vec-tor space by using the redundant actuators [5]. This feature can

Manuscript received May 19, 2014; revised November 4, 2014; acceptedJanuary 14, 2015. Date of publication August 21, 2015; date of current versionOctober 21, 2015. Recommended by Technical Editor S. K. Saha. This workwas supported in part by research program of Kookmin University in Korea,the IGPT Project (N0000005) of the Ministry of Knowledge Economy in Koreaand in part by Basic Science Research Program through the National ResearchFoundation of Korea funded by the Ministry of Education (2013055323).

G. Lee, S. Park, F. C. Park, and J. Kim are with the Department of Me-chanical and Aerospace Engineering, Seoul National University, Seoul 151-742, South Korea (e-mail: [email protected]; [email protected];[email protected]; [email protected]).

D. Lee is with the Soongsil University, Seoul 156-743, South Korea (e-mail:[email protected]).

J. I. Jeong is with the Kookmin University, Seoul 136-702, South Korea(e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMECH.2015.2401606

be used in various applications, such as active stiffness enhance-ment, backlash elimination, and motion generation of RAPMs[11]–[14].

In this paper, we investigate the extent to which RAPMs canincrease energy efficiency. Generally, energy loss occurs mainlyin operating the servo-motors and servo-drivers [15]–[17], andthe norm value of the torque vector in the actuating motors isknown to be related to the energy that the mechanism consumes.This is because the torques induced by electric motors have alinear relationship to the current in the electric circuit in themotor [18]. Thus, the squared value of the torque is related tothe squared value of the current, which in turn is linearly relatedto the consumed energy, such as heat loss.

Many studies related to the energy efficiency of typical nonre-dundantly actuated manipulators have been conducted [19]–[23]. Nonredundantly actuated manipulators usually have aunique solution for the actuating torque vector when tracking agiven path, with the solution dependent on the path. Some stud-ies show that minimum-norm torque distribution is one of themost effective ways to determine an energy-efficient path of themanipulator [24], [25]. These studies show that an optimizedpath can be determined by minimizing the norm value of theactuating torques along the path, which can decrease the energyconsumption of the manipulators.

In the case of RAPMs, on the other hand, various combina-tions of actuation torques are possible, even though the manip-ulator moves on a predetermined pathway [9]. Because of thisfeature, the RAPM could distribute the actuating torques opti-mally, to minimize the required values of the actuating torques.Thus, the energy to operate the manipulator would be saved inthe same path.

As an example, the nonredundantly actuated manipulator andthe RAPM are shown with the same kinematic positions inFig. 1. In the case of the non-RAPM manipulator, as shownin Fig. 1(a), the actuation torques of each motor are uniquelydetermined as 200 and 70 N·m, respectively. According to thesetorques, the norm value of the torque vector is 212 N·m. How-ever, the RAPM can optimally distribute the actuator torques.To minimize the norm value of the torque vector, the actuationtorques of each motor can be set as 101.2, 1.4, and 100.5 N·m,such as in Fig. 1(b). The norm torque can be reduced to143 N·m.

In this way, we could decrease the norm torque by 33% com-pared to the non-RAPM for the same operation. Even thoughthe reduced torques are related to the total energy saved, thedetailed relationship between the torque and the energy has notbeen discussed in previous work, and need to be analyzed thor-oughly. There have been some studies about the torque control

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2806 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 20, NO. 6, DECEMBER 2015

Fig. 1. Example of torque distribution, and norm value of the torques. (a)Nonredundant parallel manipulator. (b) Redundant parallel manipulator.

of RAPMs, but to our knowledge, there is no previous work thatfocuses on saving energy by using a RAPM.

Here, we prove that a RAPM can consume less energy than atypical nonredundantly actuated mechanism with a proper dis-tribution of actuating torques. A 2-DoF mechanism that is gen-erally used for welding applications of industrial manipulatorsis used for the verification of the suggested methods. The orig-inal 2-DoF mechanism is modified by installing an additionalactuator, and the total operating energies of the two mechanismsare compared for the same pathway. A simulated comparisonof the energy consumption of the two mechanisms is presented.Moreover, an experimental verification is also conducted usingthe test mechanisms.

This paper is organized as follows. A kinematic and energymodel analysis for a 2-DoF RAPM and a non-RAPM are pre-sented in Section II. Two types of torque distribution algorithmsfor saving energy with a 2-DoF RAPM are also presented inthis section. In Section III, the simulation and experimentalresults for saving energy by using redundant actuation are pre-sented. Finally, some concluding remarks follow in Section IV.

II. THEORY AND METHODOLOGY

A. Test Mechanism and Kinematic Analysis

A parallel mechanism with 2-DOF is used to verify the en-ergy saving feature of the redundant actuation. Fig. 2 shows thetest parallel mechanism and its original commercial manipula-tor. The test manipulator is based on the main link mechanismof a commercial manipulator (ABB IRB1410). The schematicdiagram of the test mechanism is shown in Fig. 3(a). The mainlink, l4 , is connected to two chains, (l1 , l2) and (l3), on whichtwo actuators, B1 and B2 , are installed.

Fig. 2. IRB1410 and the test mechanism.

Fig. 3. Test mechanism and modified mechanism with redundant actuation.(a) Nonredundant actuation. (b) Redundant actuation.

TABLE ISPECIFICATIONS OF THE 2-DOF TEST MECHANISM

Part Material Length (mm) Weight (kg) Moment of inertia (kg·m2)

l1 C45 230 3.7 0.07l2 AlMg1SiCu 960 3.7 1.21l3 C45 800 16 2.61l4 C45 1310 21 6.99l5 C45 230 3.7 0.07l6 AlMg1SiCu 710 2.8 0.50

As shown in Fig. 3(b), the test mechanism is modified toestablish a redundant mechanism with two additional linkages,l5 and l6 , and an additional actuator, B3 . As a result, the modifiedmechanism consists of a main link, l4 , and three connectingchains: (l1 , l2), (l3), and (l5 , l6).

This mechanism still has 2-DOF but is operated by threeactuators. Table I presents the specifications of the linkages of

LEE et al.: MINIMIZING ENERGY CONSUMPTION OF PARALLEL MECHANISMS VIA REDUNDANT ACTUATION 2807

the test RAPM. In the case of the original mechanism, twoactive actuators at B1 and B2 are sufficient to realize the 2-DoFmotion.

The equations of motion for the proposed RAPM can bederived from the constraint equation of the parallel mechanism,which represents the geometrical constraint of the mechanismduring its operation. The constraint equation can be written asfollows:

⎡⎢⎣

g1

g2

g3

⎤⎥⎦ =

⎡⎢⎢⎣

∥∥PB1 (qr1) − PB

2 (qr2)∥∥ − J1J2∥∥PB

2 (qr2) − PB3 (qr3)

∥∥ − J2J3∥∥PB3 (qr3) − PB

1 (qr1)∥∥ − J3J1

⎤⎥⎥⎦ =

⎡⎢⎣

0

0

0

⎤⎥⎦ (1)

where PBi (qi) denotes a position vector of joint Ji with respect

to the base coordinate {B}. The position PBi depends on the

angular value qi of joint Ji . The value of qri is the angle com-mand value of actuator Bi . JjJk represents the length betweenjoint Jj and joint Jk . The velocity relationship between jointangles can be elucidated using the constraint Jacobian relation-ship [4]–[12]. This relationship can be obtained by taking thetime derivative of the geometric constraint equation. The rela-tionship between the velocities of the independent joint vectorqu and the actuating joint vector qr can be acquired by selectingthe actuating joints from the independent joints qu and from thedependent joints vector with actuators qv , and the relationshipcan be written as follows:

q̇r =

[q̇u

q̇v

]= V U

[I2×2

Φ

]q̇u = Γq̇u (2)

where U is a transfer matrix from a joint vector with the inde-pendent and dependent joints order to a full joint vector withascending order. V is the selection matrix to pick up the actuat-ing joints. Φ is a Jacobian mapping matrix from the independentjoint vector to the actuating dependent joint vector. Γ is a Jaco-bian mapping matrix from the independent joints to all of theactuating joints.

The number of active joints is larger than the number of inde-pendent joints in the case of the RAPM. Thus, it is important todetermine the best way to distribute the torques of the actuatorsinstalled on the redundant mechanisms using the null space ofthe torque vector. From the result of (2), the relationship betweenthe actuating torques for redundant actuation and the torques fornonredundant actuation can be expressed as (3). Here, the trans-pose of the Jacobian Γ is used, which maps the velocities of theindependent joints to the velocities of the redundantly actuatedjoints

τu = ΓT τr (3)

where τu is a torque vector of the actuators in nonredundantactuation and τr is a torque vector of the actuators in redun-dant actuation. The torques of redundant actuation can alsobe expressed as (4) with minimum-norm torque distributionschematics:

τr = Γ(ΓT Γ)−1τu . (4)

The dynamic equation of the redundantly actuated parallelmanipulator can finally be established as follows:

Mq̈u + Cq̇u + N = ΓT τr . (5)

B. Power Consumption Model

Energy consumption modeling for the actuators is required tosimulate the amount of energy consumed by the test manipulator.The power consumption model is known to consist of an outputpower consumption Poutput and the subsidiary electrical lossPloss , such as in [22]–[27]:

Ptotal = Poutput + Ploss (6)

where the output power consumption refers to the actual me-chanical power. The output power can be calculated by multi-plying the torques and angular velocities of the actuating joints,such as in

Poutput =n∑

i=1

[τi q̇i ]+ (7)

where τi and q̇i are the torque and the angular velocity, respec-tively, of the ith actuating joint Bi . The [a]+ means that if theargument a is greater than zero, the value of [a]+ is a. If theargument is less than zero, the output value of the function iszero. That is, negative output power cannot be regenerated andis dissipated as heat.

The electrical power loss can be categorized into four kindsof losses of the servo-motors and servo-drives: coil loss, coreloss, conduction loss, and switching loss. The coil loss is heatlost when the current flows through the resistances of a circuit.The relationship can be expressed as follows:

Pcoil =n∑

i=1

RiI2i (8)

where R is the resistance of the coil. Ii is the current the of ithactuator in joint Bi .

The second is a core loss. The core loss occurs by means of aneddy current phenomenon and hysteresis in servo-motors. Gen-erally, it can be neglected in the case of manipulator operation[15].

The other two types of power loss occur in servo-amplifiersor servo-drives, and include conduction loss and switching loss.Each loss occurs when current flows in an insulated-gate bipolartransistor of the servo-amplifier. The conduction loss and theswitch loss can be described by [16]:

Pconduction =n∑

i=1

μai Ii + μb

i I2i (9)

Pswitching =n∑

i=1

ηiIi (10)

where μai and μb

i are coefficients for the conduction loss. Thecurrent has a quadratic relationship to the conduction loss. ηi isa coefficient between the current and the switching loss.

As a result, the power loss Ploss can be obtained from thesum of the following terms: coil power loss, conduction loss,


Fig. 4. Experimental results for power loss model.

and switching loss, as in

Ploss = Pcoil + Pconduction + Pswitching =n∑

i=1

(λai Ii + λb

i I2i )

(11)where λa

i and λbi are coefficients for the current and power loss of

the ith actuator. In the case of typical servo-motors, the actuatingtorque is linearly proportional to the current in the circuit. Thus,(11) can be expressed as follows:

Ploss =n∑

i=1

(κai |τi | + κb

i τ2i ) (12)

where κai and κb

i are coefficients for the power loss of the ith ac-tuator. Ii is substituted to |τi | because the current is proportionalto the absolute value of the torque.

The coefficients in (12) were obtained by measuring powerconsumption while several static loads were induced on eachactuator. The torque of each actuator was measured by a straingauge, and the power loss of the actuators was measured witha power meter that was installed on the power source of theservo-drivers.

The experiment was executed during stop position control ofthe servo-motor, and the mechanical output power was zero.Fig. 4 shows the experimental results of the power consumptionof the servo-motors and servo-drivers with respect to the load.The experiments were conducted for each set of servo-motorsand servo-drivers, which included two sets in the 4.4 kW·h classand one set in the 3.0 kW·h class. The red solid line and bluedotted lines, marked with circles and crosses, respectively, arethe estimated power loss models for the two sets in the 4.4 kW·hclass. The green dashed line marked with rectangles is the esti-mated power loss model for the 3.0 kW·h class. The markers aremeasurement points of the experiment. The coefficients of thepower consumption models are obtained through mathematicalcurve fitting by MATLAB by (12). The results are shown inTable II.

Consequently, the power consumption model of the test ma-nipulator can be derived as follows:

Ptotal =n∑

i=1

([τi q̇i ]+ + κa

i |τi | + κbi τ

2i

). (13)

TABLE IIPOWER LOSS MODEL FOR ACTUATION PARTS

i Class of power κai κb

i

1 4.4 kW·h 5.302 ×10−1 4.896 ×10−4

2 4.4 kW·h 4.335 ×10−1 5.197 ×10−4

3 3.0 kW·h 3.633 ×10−1 5.654 ×10−4

C. Cost Functions for Torque Distribution

The nonredundant mechanism usually has a unique solutionfor the actuation torques during motion. However, a redundantmanipulator can have various sets of actuation torques. Amongthe set of torque combinations, a unique actuation torque set canminimize the electrical power consumption. Thus, the torquedistribution strategy or algorithm for a given motion should beassigned and studied. First, a conventional torque distribution al-gorithm is adopted and tested to verify the energy saving featureof RAPMs. The minimum-norm torque distribution algorithmis selected. The redundant torques of the minimum-norm torquedistribution condition are derived by minimizing the sum ofsquares of each redundant torque so as to reduce the total elec-trical power. The minimizing process is executed for the overalloperation time. The performance index for the minimizing pro-cess is as follows [23]:

Ψ1(τ) =∫ tf

ti

n∑i=1

τ 2i dt. (14)

By minimizing (14), the actuating torques can be obtained.For the RAPMs, it is reported that independent PID control foreach actuator with respect to the inverse kinematic solution canrealize the minimum norm distribution [26]. This distribution al-gorithm is not purposed to minimize the energy consumption ofrobotic system. It shows the energy-saving feature of redundantactuation can be realized by the simple control algorithm.

On the other hand, the cost function that minimizes the powerconsumption mentioned earlier is also tested. The performanceindex for minimum-energy torque distribution can be written asfollows:

Ψ2(τ) =∫ tf

ti

Ptotaldt

=∫ tf

ti

n∑i=1

([τi q̇i ]+ + κa

i |τi | + κbi τ

2i

)dt. (15)

By minimizing (15), the actuating torque vector can be ob-tained. The total electric power consumed by the test robot isdependent not only on the square of the torque, but also on theabsolute value of the torque and the mechanical output. In otherwords, the consumed power consists of the sum of the outputpower and the electric loss power, and can be minimized byfollowing this minimum-energy torque distribution. These twocost functions are used to obtain the torque distribution of theactuators with respect to the given pathway.


Fig. 5. Test pathway for energy consumption.

III. SIMULATION AND EXPERIMENTAL RESULTS

The simulation has been conducted for three cases of torquedistribution algorithms for the same pathway. The simulationsare carried out to compare energy consumption between conven-tional mechanisms with nonredundant torque distribution, theRAPM with the minimum-norm torque distribution algorithm,and the RAPM with the minimum-energy torque distributionalgorithm.

A 2-DoF RAPM is selected and modified to verify the en-ergy saving feature of the RAPM with two redundant torquedistribution algorithms and nonredundant actuation. The testmechanism is based on typical welding manipulators. A 10 kgpayload is assumed to be mounted at the end-effector of themain link, l4 , of the manipulator.

The test pathway is depicted in Fig. 5. The test pathway startsat position 1 and ends at position 7. This pathway is used ina spot welding process in the automotive industry. The overallrun-time is 78 s, and the maximum velocity of the end-effectoris set to 290 mm/s. In the simulations, the test manipulatorswith and without redundant actuation are operated in the samepathway with the same velocity.

Fig. 6 shows the simulation results of actuation torques ofnonredundant and redundant actuation. Fig. 6(a) shows the ac-tuation torques for nonredundant actuation. Fig. 6(b) shows theactuation torques of redundant actuation with the minimum-norm torque distribution algorithm. Fig. 6(c) shows the actua-tion torques of redundant actuation with the minimum-energytorque distribution algorithm. The red solid lines, blue dashedlines, and green dotted lines represent the actuation torquesat joints B1 , B2 , and B3 , respectively. The actuating torques ofnonredundant actuation are reduced in both cases; the minimum-norm and minimum-energy torque distribution actuation. Theminimum-energy torque distribution actuation has unusual ar-eas using only two actuating torques (0–47 s, 49–73 s). It isbecause that the energy consumption model of the robotic sys-tem, which is the cost function for optimization, is not only afunction of the square torques but also a function of the absolutevalue of torques.

Fig. 7 depicts the simulation results of the consumed powerfor the three actuation cases. The red solid line represents the

Fig. 6. Simulation results of actuating torques for nonredundantly actu-ated mechanism, and for redundantly actuated mechanism with minimum-norm torque distribution and minimum-energy torque distribution actuation.(a) Nonredundant actuation. (b) Minimum-norm torque distribution actuation.(c) Minimum-energy torque distribution actuation.

Fig. 7. Simulation results of energy consumption for nonredundantly actu-ated mechanism, and for redundantly actuated mechanism with minimum-normtorque distribution and minimum-energy torque distribution actuation.


Fig. 8. Experimental results of actuating torques for nonredundantly actu-ated mechanism, and for redundantly actuated mechanism with minimum-normtorque distribution and minimum-energy torque distribution actuation. The solidand dashed lines represent the experimental and simulation results, respectively.(a) Nonredundant actuation. (b) Minimum-norm torque distribution actuation.(c) Minimum-energy torque distribution actuation.

consumed power of the nonredundantly actuated parallel ma-nipulator for the test pathway, where only the two actuators atB1 and B2 are assumed to be operated. The blue dashed line rep-resents the consumed power of the RAPM with the minimum-norm distribution algorithm. The green dotted line representsthe consumed power of the RAPM with the minimum-energytorque distribution algorithm. The RAPM uses an additionallinkage set and three actuators at B1 , B2 , and B3 . The energyconsumption of the minimum-energy torque distribution actu-ation is slightly lesser than that of the minimum-norm torquedistribution actuation.

To verify the simulation results, experiments are carried outwith the 2-DoF RAPM depicted in Fig. 3(b). The test manip-ulators are controlled by a Turbo-UMAC controller from theDeltaTau Company. Fig. 8 shows the comparison between thesimulation and experimental results of the actuation torques.The torques of the actuators were measured from the con-troller. The solid and dashed lines represent the experimentaland simulated results, respectively. The red, blue, and greenlines represent the torque of B1 , B2 , and B3 , respectively. The

Fig. 9. Experimental results of energy consumption for nonredundantly actu-ated mechanism, and for redundantly actuated mechanism with minimum-normtorque distribution and minimum-energy torque distribution actuation.

total consumed energy is measured by a power meter (CW121,YOGAKAWA) at the power source of all actuation parts. Theconsumed energy includes the total energy of the servo-motorsand servo-drivers.

The experiments were carried out for the general manipulatorand the RAPM. The RAPM was operated with two types of con-trol: minimum-norm torque distribution and minimum-energytorque distribution. Each experiment was performed for a testpathway with a 10 kg payload, where the maximum velocity ofthe end-effector is set to 290 mm/s. Fig. 9 shows the experimen-tal results for the consumed energy for three cases of actuation.In the figure, the red solid line, the blue dashed line, and thegreen dotted line represent the consumed energy of the generalmanipulator, the RAPM with the minimum-norm torque dis-tribution algorithm, and the RAPM with the minimum-energytorque distribution algorithm, respectively. The differences be-tween the experimental and simulation data of Figs. 8 and 9 aredue to the friction force on the actuating joints, especially in thegearhead.

Fig. 10 shows the energy saved by the RAPM with theminimum-norm torque distribution algorithm control and theminimum-energy torque distribution algorithm control. Thesolid and dashed lines represent the experimental and simu-lated results, respectively. The energy-saving effect is appeareddifferently in the test pathway according to the position of end-effector. It is shown largely in 8–24 and 44–47 s.

The experimental results were similar to the results of the sim-ulation. They show that the energy consumed by the RAPM withthe minimum-norm torque distribution and the minimum-energytorque distribution are 41.4% and 45.0% lower, respectively,than that of the general mechanism. The amounts of energysaved were 8703 and 9466 J, respectively. Table III comparesthe experimental and simulated results for the energy consumedin the three cases.

Consequently, the energy consumed by the RAPM can bemore effectively reduced by minimum-energy torque distribu-tion control, which minimizes the sum of the output power of


Fig. 10. Energy saved by redundantly actuated mechanism with minimum-norm torque distribution and minimum-energy torque distribution actuation.(a) Minimum-norm torque distribution actuation. (b) Minimum-energy torquedistribution actuation.

TABLE IIISIMULATION AND EXPERIMENTAL RESULTS OF ENERGY CONSUMPTION

Energy(Joule)

Nonredundantcase

Minimum-normtorque distribution

Minimum-energytorque distribution

Simulation 20 270 J 11 751 J 11 038 JPercentsaved

N/A 42.0% 45.6%

Experiment 21 022 J 12 319 J 11 556 JPercentsaved

N/A 41.4% 45.0%

the servo-motors and the electric power loss of the servo-motorsand servo-drivers.

IV. CONCLUSION

This paper presents an energy saving feature by using aRAPM. A 2-DoF manipulator was operated by minimum-norm torque distribution control. A detailed energy consumptionmodel was suggested, and verified experimentally. Both the sim-ulated and the experimental results showed that the RAPM hadthe advantage of reducing the consumed energy compared toa nonredundant parallel manipulator. The energy consumptionwas reduced because the torque distribution with the additionalactuators of the RAPM could reduce the norm torque of the ma-nipulator by minimum-norm torque distribution control. Theseresults showed a novel advantage of RAPMs from an energyperspective.

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Giuk Lee received the B.S. and Ph.D. degrees fromthe School of Mechanical and Aerospace Engineer-ing, Seoul National University, Seoul, South Korea,in 2010 and 2014, respectively.

He is currently a Postdoctoral Researcher in theInstitute of Advanced Machinery and Design, SeoulNational University. His research interests includeenergy-efficient control of redundantly actuated par-allel mechanisms and design of climbing robots.

Sumin Park received the B.S. degree from the KoreaAdvanced Institute of Science and Technology, Dae-jeon, South Korea, in 2013, and is currently workingtoward the Ph.D. degree in the School of Mechanicaland Aerospace Engineering, Seoul National Univer-sity, Seoul, South Korea.

His research interests include design of redun-dantly actuated parallel mechanisms.

Donghun Lee received the B.S. degree in mechanicalengineering from Soongsil University, Seoul, SouthKorea, in 2004, and the M.S. and Ph.D. degrees fromthe School of Mechanical and Aerospace Engineer-ing, Seoul National University, Seoul, in 2009.

He was a Postdoctoral Researcher in the Schoolof Mechanical and Aerospace Engineering, Seoul Na-tional University, from 2009 to 2010. He was a SeniorResearcher of the Mechatronics Center at SamsungHeavy Industry, Daejeon, Korea, from 2010 to 2012.He is currently an Assistant Professor in the School

of Mechanical Engineering, Soongsil University. His current research interestsinclude mechanism design for redundantly actuated parallel mechanisms, anddevelopment of wearable robot especially about the human–robot interactions.

Frank C. Park (F’13) received the B.S. degree inelectrical engineering from MIT, Cambridge, MA,USA, in 1985, and the Ph.D. degree in applied mathe-matics from Harvard University, Cambridge, in 1991.

From 1991 to 1995, he was an Assistant Profes-sor of mechanical and aerospace engineering at theUniversity of California, Irvine. Since 1995, he hasbeen a Professor of mechanical and aerospace engi-neering at Seoul National University, Seoul, SouthKorea. His research interests are in robot mechanics,planning and control, visual tracking, and related ar-

eas of applied mathematics.Dr. Park is an Editor-in-Chief of the IEEE TRANSACTIONS ON ROBOTICS.

In 2007–2008, he was an IEEE Robotics and Automation Society (RAS) Dis-tinguished Lecturer, and has served as Secretary of RAS from 2009 to 2010and 2012 to 2013. He has served, an Area Editor of the Springer Handbook ofRobotics and Advanced Tracts in Robotics (STAR), and as an Associate Editorof the ASME Journal of Mechanisms and Robotics.

Jay I. Jeong (M’14) received the B.S., M.S., andPh.D. degrees from the School of Mechanical andAerospace Engineering, Seoul National University,Seoul, South Korea, in 1995, 1997, and 2002, respec-tively.

He was a Postdoctoral Researcher in the Depart-ment of Mechanical Engineering, The Johns HopkinsUniversity, Baltimore, MD, USA, from 2003 to 2006.Since 2006, he has been an Associate Professor in theSchool of Mechanical Engineering, Kookmin Uni-versity, Seoul. His current research interests include

mechanism design for redundantly actuated manipulator robots especially aboutenergy saving feature, and mobile robot design for advanced driving automotivesafety systems.

Jongwon Kim received the B.S. degree from theSchool of Mechanical Engineering, Seoul NationalUniversity, Seoul, South Korea, in 1978, the M.S. de-gree in mechanical and aerospace engineering fromthe Korea Advanced Institute of Science and Technol-ogy, Daejeon, Korea, in 1980, and the Ph.D. degree inmechanical engineering from the University of Wis-consin, Madison, WI, USA, in 1987.

He was with Daewoo Heavy Industry and Machin-ery, Korea, from 1980 to 1984. From 1987 to 1989,he was the Director of the Central Research and De-

velopment Division at Daewoo Heavy Industry and Machinery. From 1989 to1993, he was a Researcher at the Automation and Systems Research Institute,Seoul National University. He is currently a Professor in the School of Mechani-cal and Aerospace Engineering, Seoul National University. His current researchinterests include parallel mechanisms, Taguchi methodology, and field robots.

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