06341112

612 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 18, NO. 2, APRIL 2013

Bioinspired Sinusoidal Finger Joint Synergiesfor a Dexterous Robotic Hand to Screw andUnscrew Objects With Different Diameters

Nareen Karnati, Student Member, IEEE, Benjamin A. Kent, Student Member, IEEE,and Erik D. Engeberg, Member, IEEE

Abstract—This paper addresses the complex task of unscrewingand screwing objects with a dexterous anthropomorphic robotichand in two cases: with the first finger and thumb and also with thelittle finger and thumb. To develop an anthropomorphic solution,human finger synergies from nine test subjects were recorded whileunscrewing and screwing a threaded cap. Human results showedthat the periodic motions exhibited by the finger joints shared acommon frequency for each subject, but differed in amplitude andphase. From the gathered data, a set of sinusoidal trajectories weredeveloped to approximate this motion for application to a robotichand. Because the joint trajectories exhibited the same frequency,a family of sinusoids that share a common time vector can be usedin the path planning of the robotic hand to unscrew and screwobjects. Additionally, the human unscrewing data are highly sim-ilar to the mirror image of the screwing data. This chiastic traitenables screwing to be performed by decreasing the time vector;increasing the time vector produces unscrewing. These factors sig-nificantly reduce the computational cost and complexity of the task.Cartesian and joint space error analyses show that the developedsinusoidal trajectories closely mimic the motion profiles seen in thehuman experiments. Furthermore, this bioinspired sinusoidal so-lution is extended to objects with wide variations in diameters byrelating joint angle offsets of the robotic hand to object diametersize through the forward kinematics equations. The sinusoidal tra-jectories are all implemented within a PID sliding mode controllerfor a dexterous artificial hand to ensure overall system stability. Us-ing the bioinspired sinusoidal joint angle trajectories, the robotichand successfully unscrewed and screwed four different objects inall trials conducted with each object diameter size.

Index Terms—Dexterous hand, distributed parameter systems,grasp synergy, prosthetic hand, sliding mode control.

I. INTRODUCTION

D EXTEROUS robotic hands have become of great interestin the robotics community because of their ability to per-

form complex tasks. Various robotic hands have been developedsuch as the Meta-hand which has been designed with a recon-figurable palm that enables it to take many different poses [1].

Manuscript received November 1, 2011; revised February 15, 2012 andAugust 1, 2012; accepted September 16, 2012. Date of publication October26, 2012; date of current version January 10, 2013. Recommended by GuestEditor K. H. Low. This work was supported in part by The University of AkronFaculty Research Grant 1708.

The authors are with the Department of Mechanical Engineering, The Univer-sity of Akron, Akron, OH 44325-3903 USA (e-mail: [email protected];[email protected]; [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.2012.2222907

The DLR/HIT Hand II [2] and the Gifu Hand [3] are both dex-terous anthropomorphic hands with four fingers and a thumb.The anatomically correct test bed hand mimics the same skeletalstructure and tendon routing as a human hand [4]. The ShadowC6M Motor Hand (Shadow Robot Company, U.K.) is anotherartificial anthropomorphic hand that can closely approximatethe dexterity of a human hand through 18 degrees of freedom(DOFs) in the hand and two DOFs in the wrist [5].

One major problem for dexterous robotic hands is the intelli-gent coordination of all the DOFs to accomplish different goals.Human hand synergies have been investigated as a method to re-duce the complexity of autonomous motion planning for robotichands [6]. This reduces the dimensionality of the motion plan-ning problem by establishing a set of principal directions ofmovement, which are used to recreate hand postures or tasks [7].The study of reach to grasp synergies of humans has also beenunderway for many years [8], [9] to help shape the fingers andthumb in an effective method prior to grasping an arbitrarilyshaped object [10], both for robots and people [11]. Humanhand movement synergies have also been investigated duringforce control [12] while using different tools [13]. Also, peri-odic functions have been used in the past to quantify differentaspects of human handwriting [14]. Human grasp synergieshave been successfully mapped to robotic hands through neuralnetworks [15] and through mechanical design of linkages [16].

In this paper, the human hand grasp synergies while screwingand unscrewing a threaded cap are explored. This necessitatesrolling contact between the fingers and the cap. In general,force control with rolling contact is a difficult nonholonomicproblem [17], [18] which requires numerous robust tactile sen-sors [19]. Unscrewing a jar has been previously explored withthe Shadow Hand [20] and dexterous manipulation planninghas been performed with objects that have surfaces of revolu-tion [21].

Incorporation of tactile feedback into a rolling contact forcecontrol algorithm is computationally expensive and requiresrugged tactile sensors. These are two factors that will limitthe commercial application of the technique into areas suchas prosthetic hands. For these reasons, rolling contact controlalgorithms are being developed that require little to no forcefeedback [22]. The Gifu hand has been used to investigate howwell humans can control motion of the robot without any tac-tile feedback during a sphere swapping task [23]. This kindof ideology would be particularly useful to the field of up-per limb prosthetics where computational power is typically

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KARNATI et al.: BIOINSPIRED SINUSOIDAL FINGER JOINT SYNERGIES FOR A DEXTEROUS ROBOTIC HAND 613

limited as is the availability of tactile force feedback over curvedsurfaces [24]. Outside of research applications, there is usuallyno direct feedback to amputees about the force applied by theprosthesis [25]; this serves to complicate the problem.

To help overcome these problems, an oscillatory temporalcoupling between the finger joints of the human hand that enablerotational motion of a threaded cap is investigated in this paper.Specifically, it is observed that the timing and periodic motionsof the finger joints of nine human test subjects are very similar.A set of sinusoidal trajectories will be developed to approximatewith high accuracy the joint angle data gathered from the testsubjects. This enables a single family of sinusoids to be specifiedfor the joint angles of a robotic hand to create rotational motion atthe fingertips. This technique greatly reduces the computationalcost of motion planning for a dexterous robot [26], [27]. An-other benefit of using sinusoidal trajectories is smooth desiredjoint velocity and acceleration trajectories without the need forhigh-order polynomial equations or parabolic blends. Addition-ally, the speed of the entire synergy comprised of each DOFcan be controlled through a single parameter: the frequency ofthe family of sine waves. Also, the robotic hand can transitionbetween screwing and unscrewing simply by decreasing or in-creasing the time vector within the sine functions. These factorsgreatly simplify this motion planning problem for dexterousrobotic hands.

Another contribution of this paper is the development of ananthropomorphic solution to the rolling contact problem that re-quires no force feedback. This is facilitated by implementing thesinusoidal synergies within a PID sliding mode controller [28]to robustly minimize errors created by the application of unex-pected torques to the joints of the Shadow Hand. Furthermore,the sinusoidal characterization of the synergy enables all theDOFs of the hand to be driven by a single input, the timevector. Because it is difficult to isolate multiple independentcontrol signals from amputees, this anthropomorphic solutionis well suited to the field of upper limb prosthetics, which hashad several recent mechanical advances in five-fingered handsvia the i-Limb [29], the bebionic hand (RSL Steeper), and theMichelangelo hand [30].

Another contribution of this paper is the development ofbioinspired grasp synergies from human test subjects for thelittle finger of a dexterous robotic hand. This is an area that hasnot been deeply explored in the past which acts as an impedi-ment to the future development of dexterous prosthetic hands.After all, if there is no provision to use the full dexterity of eachdigit of the hand, then there is no need for a dexterous design.

Finally, these joint synergies will be tested on objects withdifferent diameters. Joint angle offsets will be determined forthe thumb and fingers as a function of object diameter so thatthe joint synergies can be applied to a wide range of objects.

II. DEXTEROUS C6M SHADOW HAND

The Dexterous Shadow Hand is a 24-joint, 20-DOF underac-tuated tendon-driven anthropomorphic manipulator whose kine-matic model can be seen in Fig. 1(a). Hall effect sensors withinthe hand provide joint angle data for all 24 joints of the hand,

Fig. 1. (a) Kinematic model and naming convention of the Shadow Hand.Axes of rotation are visualized as black arrows. Axes of rotation perpendicularto the page are designated by an (X). (b) CyberGlove II and its sensors. (c) Jointand fingertip position nomenclature for the thumb, first finger, and little finger.This convention is used in the calculation of the forward kinematics. Axis y0 isinto the page.

with a resolution <1◦. The first, middle, and ring fingers eachhave four joints and three DOFs. The little finger has an extraDOF in the palm, modeling the carpometacarpal (CMC) joint.The distal interphalangeal (DIP) joints of each finger are kine-matically coupled to the proximal interphalangeal (PIP) joints,both of which are driven by a single motor and single pair oftendons. All 24 joints of the Shadow Hand are driven by 20 mo-tors located below the wrist joints, with a pair of antagonistictendons connecting each motor to the corresponding joint.

A nonlinear model for the Shadow Hand system can be ob-tained through a summation of torques

Jx + Bx + Kx + D = τ . (1)

J ∈ R20×20 is the inertia matrix, B ∈ R20×20 is the dampingmatrix, and K ∈ R20×20 is the stiffness matrix. The 20 elementangular position, velocity, and acceleration vectors are x, x, andx, respectively. The torque applied by the motors is τ∈ R20 .D ∈ R20 is the sum of potentially nonlinear disturbance torquesthat can be applied unexpectedly to any DOF of the hand.

Since the DIP and PIP joints of each finger are coupled, theyare referred to as joint iFJ1a and joint iFJ1b, respectively. Thisjoint relationship applies to all four fingers [where i representsF, M, R, or L from Fig. 1(a)]. A virtual joint iFJ1 is defined asthe sum of joints iFJ1a and iFJ1b, and control of both joints isdefined as a parameter of joint iFJ1. This relationship can also


be described by the following piecewise linear equations:

xi1a=

⎧⎨

⎩

0, 0 < xi1 ≤ π

2(xi1 −

π

2

),

π

2< xi1 ≤ π

(2)

xi1b=

⎧⎨

⎩

xi1 , 0 < xi1 ≤ π

2π

2,

π

2< xi1 ≤ π

(3)

where xi1 is the position of virtual joint iFJ1. xi1a and xi1b

are the angular positions of joints iFJ1a and iFJ1b, respectively[see Fig. 1(a) and (c)]. The position of virtual joint iFJ1 is, thus,xi1 = xi1a + xi1b . This is necessary since the DIP and PIP ofeach of the four fingers are controlled by a single motor. Theextension/flexion of the metacarpophalangeal (MCP) joint iFJ2is xi2 , and abduction/adduction of the MCP joint iFJ3 is xi3[see Fig. 1(c)].

III. CYBERGLOVE II

The hand motion profiles of nine human test subjects wererecorded using the ver. 2.2 22 sensor CyberGlove II (Immer-sion Corporation, San Jose, CA). The glove uses bend-sensingresistive technology to convert hand motions into digital jointangle data, and has been used in previous studies to record mo-tions of the human hand for robotics applications [26], [27].Each of the fingers contains four sensors, two of which recordjoint angle data for the DIP and PIP joints. The remaining twomeasure the extension/flexion and abduction/adduction of theMCP joint. For the purpose of this paper, the extension/flexionand abduction/adduction of the MCP will be referred to as twoseparate joints in order to correlate with the joint conventionestablished for the Shadow Hand [see Fig. 1(a) and (c)].

The thumb of the CyberGlove II contains four sensors. Flex-ion/extension of the DIP and MCP joint are measured by sensorsTJ1 and TJ2 [see Fig. 1(b)]. Abduction/adduction of the thumbMCP joint is not measured by the glove. The CMC joint ismeasured by sensors TJ3 and TJ4. These correspond to the ab-duction and roll, or opposition of the thumb in relation to thepalm.

IV. EXPERIMENTAL METHODS: HUMAN TEST SUBJECTS

A. Finger Joint Angle Data Acquisition

Nine human test subjects gave informed consent prior to ex-periments in accordance with IRB protocol. After signing theconsent forms, the test subjects donned a wrist brace to preventwrist motions from affecting the motions of the fingers and toproduce more consistent results. They then underwent a briefCyberGlove calibration procedure. Each test subject next placedhis or her right hand flat on the table to create a steady-state base-line of comparison among test subjects. After two seconds, theparticipant was asked to unscrew and screw a 30-mm diameterbottle cap initially using only the thumb and first finger and thenusing only the thumb and little finger [see Fig. 2(a) and (d)]. Forconsistency, the bottle was mounted to the table with a clampduring all the experiments. This procedure was repeated threetimes for each test subject.

Fig. 2. (a) CyberGlove with the bottle. (b) Virtual Simulink model of theShadow Hand with the bottle. (c) Virtual Simulink model of the skeletal structureof the human hand with the bottle. (d) CyberGlove with the bottle. (e) VirtualSimulink model of the Shadow Hand with the bottle. (f) Virtual Simulink modelof a skeletal structure of the human hand with the bottle.

Fig. 3. There was a similar nearly constant frequency oscillatory trend amongall nine test subjects for each thumb and finger joint of the hand. (a) Thumbjoint TJ1 when unscrewing the bottle cap. The dotted line (xD 1 ) is the sinu-soidal approximation of the TJ1 CyberGlove data. (b) LJ2 when screwing thebottle cap. The dotted line (xD L 2 ) is the sinusoidal approximation of the LJ2CyberGlove data.

B. Principal Components Analysis (PCA)

After data collection, the hand motion profiles of the individ-ual trials were analyzed. A PCA was performed on the data todetermine the impact of each joint during the screwing and un-screwing tasks with the princomp function in MATLAB. PCAis commonly used as a data reduction method to eliminate re-dundant variables in high-dimensional problems [13], [16].

V. HUMAN FINGER JOINT SYNERGY RESULTS

The acquired human finger joint angle data were first filteredand normalized with respect to time. Observation of the datarevealed two tendencies: first, the individual finger joints exhib-ited a periodic motion. Second, the frequency of this periodicmotion remained relatively constant for all joints throughout theduration of each trial. Due to the periodic and wavelike nature ofthe motion, the data could be approximated well by sine waves(see Fig. 3).


Fig. 4. These plots show how the angles change for each joint while screwingthe bottle cap during [(a) and (b)] first finger and thumb experiments and whileunscrewing with [(c) and (d)] little finger and thumb.

Contour plots from a single trial for each subject were con-structed for each joint (see Fig. 4). These plots show all fingerand thumb joint angles for each test subject with respect to nor-malized time. Data are presented for the screwing motion of thethumb and first finger and also for the unscrewing motion whileusing the thumb and little finger. These illustrate the similari-

ties in joint trajectories between all test subjects. As observedfor each trial, the frequency and amplitude of each joint remainrelatively constant (see Fig. 4). There exists, however, phaseoffsets between the respective joints.

Results from the PCA analysis of the joint angles show thatthe first principal component (PC) for each test subject accountsfor 83% of the variance, on average. The scalar coefficients ofthe first PC for each test subject were converted to percentagesto determine the contribution of each joint variable to that PC.The PCA shows very similar trends among all nine test subjectsrelated to which finger joints had the most impact in the screwingand unscrewing tasks [see Fig. 5(a) and (b)].

Averaged results show that joint FJ1b has the largest effect onthe synergy while using the thumb and first finger [see Fig. 5(c)]while joint LJ1b has the largest effect on the motion when usingthe thumb and little finger [see Fig. 5(d)]. The average percentcontribution of each joint across all subjects was also calculatedfor both unscrewing and screwing data. Because these are aver-aged values across all nine test subjects, they do not necessarilysum to 100%. The average difference between unscrewing andscrewing PCA data is 3.5%. This indicates that the approachtaken by the test subjects to unscrew the bottle cap was verysimilar to their motions required to screw the cap back on.

VI. BIOINSPIRED CONTROL ALGORITHM DEVELOPMENT

A. Simulations of the Human Hand and Shadow Hand

Solid model CAD drawings of the skeletal structure of thehuman hand, Shadow Hand, and bottle were exported in .vrmlfile format and imported into Simulink via the 3-D animationtoolbox [see Fig. 2(b), (c), (e), and (f)]. This was done to visu-alize the motions of the human test subjects from the recordedjoint angle data and to simulate the Shadow Hand. The kine-matic model of the skeletal structure of the human hand wasmodeled the same as that of the Shadow Hand [see Fig. 1(a) and(c)].

B. Mapping Joint Angle Data From the CyberGlove to theSkeletal Structure of the Human Hand

Sensors TJ1, TJ2, TJ3 and TJ4 of the CyberGlove [seeFig. 1(b)] are, respectively, mapped to joints THJ1, THJ2, THJ4,and THJ5 of the thumb of the human skeletal structure [seeFig. 1(a)]. The CyberGlove finger sensors iJ1a, iJ1b, iJ2, andiJ3 are, respectively, mapped to joints iFJ1a, iFJ1b, iFJ2, andiFJ3 of the fingers of the skeletal structure.

THJ3 (x3) of the skeletal structure was held at a constant 0rad which produced a four-DOF kinematic model of the thumbbecause this joint variable cannot be measured by the Cyber-Glove. Since the range of abduction motion of the MCP joint ofthe human thumbs is quite small [31], the overall impact of thisis minimal. Furthermore, the appropriate kinematic model to beused for the human thumb is still under debate [32]. However,it has been postulated that the anatomical variability betweenhuman test subjects can be captured with a limited numberof kinematic models [33]. Due to the constrained nature ofthe screwing and unscrewing tasks in this paper, the functional


Fig. 5. (a) Results of the PCA for each test subject when unscrewing thebottle cap by using the thumb and first finger and (b) by using the thumb andlittle finger. (c) Average PCA results of the nine test subjects when unscrewing,screwing, and the difference between the two, with thumb and first finger and(d) with the thumb and little finger. Percentage contribution is obtained fromthe coefficients of the first PC for each subject.

TABLE ISINE WAVE SCALING PARAMETERS FOR THE SHADOW HAND DURING THE

THUMB AND FIRST FINGER EXPERIMENTS

TABLE IISINE WAVE SCALING PARAMETERS FOR THE SHADOW HAND DURING THE

THUMB AND LITTLE FINGER EXPERIMENTS

variability among test subjects is minimal and a single modelapproximates well the kinematic motions of the test subjects.This statement is substantiated by the PCA of the raw Cyber-Glove joint angle data which illustrates a very consistent trendamong the nine test subjects [see Fig. 5(a) and (b)].

C. Joint Space Error Analysis

Based on the contour plots (see Fig. 4) and the average PCAdata (see Fig. 5), a sinusoid was created to approximate thehuman data for each joint of the thumb, little, and first fingers.Tables I and II define the gains and phase shifts of the sine waveapproximations used for any joint, k, during the thumb–firstfinger and thumb–little finger experiments, respectively.

The absolute average error was calculated between the datafrom the nine test subjects and the generated sinusoids for eachjoint during the thumb–first finger and thumb–little finger ex-periments. The mean error is less than 0.07 rad in all cases (seeFigs. 6 and 7).

D. Cartesian Space Error Analysis

Next, a Cartesian space error analysis was performed. Thefingertip and thumb tip positions [see Fig. 1(c)] of the humantest subjects were calculated in Cartesian space with the for-ward kinematics equations [Appendix I, (12)–(20)] with thehuman hand skeletal structure using the measured human jointangle data and also using the generated sinusoidal joint angle


Fig. 6. Mean and standard deviation of absolute difference between Cyber-Glove data and average sinusoidal approximation in joint space when using thethumb and first finger to screw and unscrew.

Fig. 7. Mean and standard deviation of absolute difference between Cyber-Glove data and average sinusoidal approximation in joint space when using thethumb and little finger to screw and unscrew.

Fig. 8. Tip of the thumb and little finger in Cartesian space using CyberGlovedata and sinusoidal input trajectories. From the kinematic diagram given inFig. 1(c), the Cartesian coordinate locations of the thumb tip and little fingertipare (xT , yT , zT ) and (xL , yL , zL ), respectively.

trajectories. Sample fingertip data are presented from one testsubject and compared to the fingertip trajectories of the skeletalstructure simulation using the idealized sinusoidal joint angletrajectories (see Fig. 8). The resulting fingertip profiles showrepetitious crescent patterns, further illustrating the periodic na-ture of the synergy.

Next, an error was calculated to indicate how well the si-nusoids approximate the observed human joint angle data inCartesian space at the fingertips. The error was calculated be-tween the developed crescent-shaped fingertip and thumb tip

TABLE IIIAVERAGE CARTESIAN SPACE ERROR AND STANDARD DEVIATION BETWEEN

HUMAN CYBERGLOVE DATA AND SINUSOIDAL TRAJECTORIES WITH THE

SKELETAL STRUCTURE FOR A 30-mm BOTTLE CAP

Fig. 9. (a) Unscrewing and (b) screwing sinusoidal trajectory plots for thethumb joints of the Shadow Hand. (c) Unscrewing and (d) screwing sinusoidaltrajectory plots for the little finger joints of the Shadow Hand. Note the mirrorsymmetry of screwing compared to unscrewing.

trajectories created from the sinusoidal approximations and theexperimental human fingertip data in each Cartesian direction.Results of this error analysis show that the created sine trajec-tories for the skeletal structure closely approximate the humandata recorded with the CyberGlove (see Table III). The magni-tude of the average relative difference is less than 2.7 and 6.2 mmfor the little finger and thumb experiment in all XYZ directions.Similarly, the average magnitude of the error is less than 3.3and 5.3 mm for the first finger and thumb, respectively. Thisindicates that the sinusoidal approximation of the human fingerjoint data replicates with high accuracy the Cartesian positionof the fingertips for the Shadow Hand.

E. Shadow Hand Finger and Thumb Joint Synergies

The sinusoidal thumb joint angles for the Shadow Hand [seeFig. 9(a) and (b)] can be directly determined from the humantest subject data (see Figs. 3, 4, and 5) because they do nothave any underactuated joint coupling like the fingers. Thus,the amplitudes of sine waves are the same for the simulation ofthe Shadow Hand thumb and the human hand skeletal thumbmodel.


However, because of the piecewise linear coupling of theDIP and PIP of the four fingers of the Shadow Hand describedby (2) and (3), the simulated finger joint sinusoids cannot bedirectly applied to the physical system. Now, results from thePCA analysis (see Fig. 5) show that the abduction joints FJ3 andLJ3 play a negligible role in the overall motion of human synergyresults. Given this, the little and first fingers of the Shadow Handcan be modeled as two link planar manipulators with jointsiFJ1b and iFJ2. Next, the simulated fingertip trajectories (seeFig. 8) based on the idealized sinusoidal joint angle trajectorieswere used as a desired path for the two link planar fingersof the physical Shadow Hand. From this desired path, inversekinematics equations [Appendix II, (21)–(23)] were used tosolve for the joint angles of the fingers of the Shadow Hand.The resulting sinusoidal joint angle amplitudes for the first andlittle fingers are shown in Tables I and II, respectively.

The little finger joint trajectories calculated using the inversekinematics are shown in Fig. 9(c) and (d). These trajectoriesof the Shadow Hand fingers may differ slightly from the hu-man fingers in the joint space because of the piecewise linearcoupling of the DIP and PIP described by (2) and (3). This isbecause both the DIP and PIP joints of human fingers typically(but not always) bend simultaneously. However, the impact ofthis in Cartesian space is quite small because the distal pha-langes (LJ1a and FJ1a) contribute much less to the synergiesin comparison to LJ1b and FJ1b, respectively (see Fig. 5). Thisstatement is further substantiated by a Cartesian space erroranalysis between the physical Shadow Hand and the measuredhuman data that will be subsequently presented. The solution ofthe inverse kinematics problem does not need to be performedin real time while operating the Shadow Hand.

F. Shadow Hand Bioinspired Sinusoidal Synergy Controller

From the joint angle data obtained from the human trials, sinewave approximations of each joint position were developed.Because the human finger joint trajectories are periodic andshare the same frequency (ω), a single family of sinusoidalinputs can be used in the path planning of the robot to performthis task with high accuracy. The desired joint angles (xD ∈ Rn )within the synergies that involve n joints for the Shadow Handusing the thumb and first or little finger to screw or unscrewobjects can thus be written as

xD = Aσ + b (4)

where A ∈ Rn×n is a constant diagonal square matrix

A =

⎡

⎣

A1 · · · 0...

. . ....

0 · · · An

⎤

⎦ . (5)

σ ∈ Rn is a vector of sinusoids

σ = [sin (ωt + ϕ1) · · · sin(ωt + ϕn )]T . (6)

b ∈ Rn is a vector of joint angle offsets

b = [b1 · · · bn ]T . (7)

Ak is the amplitude, ϕk is the phase shift, and bk is the jointangle offset for any joint k. These terms define the families ofsinusoids that best approximated the human finger and thumbjoint angle motions (see Tables I and II).

This sinusoidal synergy technique significantly reduces thecomputational expense and complexity of the task because theentire synergy can be driven by a single family of sinusoids (seeFig. 10). Also, the integral and derivative of xD will be smoothwhich facilitates PID sliding mode control. Additionally, thespeed of rotational motion of the object at the fingertips can becontrolled by a single value, ω. Finally, these chiastic trajectoriescan be used to screw or unscrew different objects by simplyincreasing or decreasing the time vector within the family ofsinusoids.

In other words, increasing the time vector creates an unscrew-ing motion at the fingertips while decreasing the time vector im-plements the screwing synergy. This mirror-symmetric conceptenables the same set of sinusoidal trajectories to be used forscrewing and unscrewing which greatly reduces the computa-tional expense of the problem. This concept is illustrated graph-ically in Fig. 9 which shows the desired joint angle inputs forboth unscrewing and screwing trajectories to be implementedfor the thumb and little finger. In this case, the time starts atzero and ends at 14 s, which produces an unscrewing motionat the fingertips. Then, the time vector decreases from 14 s andends at zero which leads to screwing. This mirror-symmetricattribute was observed in the human data as well; the differencein PCA data between screwing and unscrewing was minimal(see Fig. 5). The sinusoidal inputs xD cannot be simply invertedto transition from screwing to unscrewing because that wouldproduce the same synergy with a π radian phase shift.

VII. PID SLIDING MODE JOINT ANGLE CONTROLLER

Sliding mode control is a nonlinear technique that is oftenused to robustly control nonlinear systems like the ShadowHand [28], [34]. The benefit is that excellent error minimiza-tion attributes are guaranteed within certain bounds even thoughnonlinear disturbances are applied. This is a particularly usefultrait for this application to track the desired sinusoidal posi-tion trajectories as the intermittent contact with the object to bescrewed or unscrewed will apply torques to the motors involvedin the synergy. To facilitate sliding mode control of the ShadowHand (see Fig. 10), an error state vector is defined as

e = xD − x. (8)

The sliding manifold for the system is written as

ξ = KI

∫

edt + KP e + KDe. (9)

KI ∈ Rn×n , KP ∈ Rn×n , and KD ∈ Rn×n are the diago-nal integral, proportional, and derivative gain matrices, respec-tively. In this particular case, the KI , KP , and KD gain ma-trices are chosen so that the characteristic polynomials of thesystem are Hurwitz.

The PID sliding mode control law is then written as

E = −Csat(ξ) (10)


Fig. 10. PID sliding mode synergy controller to unscrew or screw objects of different diameters using sinusoidal trajectories. Angles xL 3 , xL 4 , x4 , and x5 areoffset based upon the diameter of the object to be screwed or unscrewed, which is calculated in diameter planning (see Fig. 11). ω is the same for all joints and canbe varied to control the speed of the synergy. ε is used to change the slope of the sliding manifold.

where E ∈ Rn is the voltage input vector to the motors. C ∈Rn×n is a diagonal matrix that is chosen as an upper boundestimate on the motor voltages required to overcome the torquesapplied to the joints of the Shadow Hand that are involved in thesynergies. The sat term is the vector saturation function suchthat

sat (ξ) = [sat(ξ1) · · · sat(ξn )]T . (11)

The sat function is used instead of the signum function be-cause it is piecewise continuous. The sat function partially lin-earizes the control law to alleviate the chattering phenomenonthat is common with mechanical systems that use a fully non-linear control law associated with the signum function. Incorpo-ration of the integral error state ensures zero steady-state error.See [28] for a stability analysis of sliding mode control for abroad class of systems.

VIII. PLANNING FOR DIFFERENT OBJECT DIAMETER SIZES

To enable a more versatile solution for the sinusoidal synergyapproach to screw and unscrew, joint angle offsets are deter-mined via the forward kinematics to accommodate objects withdifferent diameters. While screwing and unscrewing with thethumb and little finger, it is convenient to alter xL3 and xL4 tovary the distance between the thumb and the first finger becausethose joints are not actively used in the sinusoidal synergy. Useof the forward kinematics (see Appendix I) shows the possiblejoint angle combinations of xL3 and xL4 as a function of capdiameter [see Fig. 11(a)].

While unscrewing and screwing with the thumb and firstfinger of the Shadow Hand, it is convenient to offset the x4and x5 angles of the thumb to accommodate different sizes ofobjects to screw and unscrew. This is different from the strategyfor the little finger because there is no actuated CMC joint forany of the Shadow Hand fingers except the little finger. Also,any significant abduction values of the MCP joint of the first,middle, or ring fingers would be likely to cause interferenceamong the digits. Thus, the x4 and x5 thumb joints are varied toaccommodate objects of different diameter to be screwed andunscrewed when using the first finger [see Fig. 11(b)].

The control action taken depending upon the object diameteraffects the joint angle offsets (see Fig. 10). In the case that thethumb and first finger are used, data from Fig. 11(b) are used tobias the offsets of x4 and x5 depending upon the diameter of theobject. However, if the thumb and little finger are used, then thethumb joints are controlled as previously described and xL3 andxL4 are given angle offsets as shown in Fig. 11(a). Also shown

Fig. 11. (a) Relationship between xL 3 , xL 4 and the diameter of the object tobe unscrewed/screwed while using the thumb and little finger. Specific joint an-gles used for 30 mm (∗) and 72 mm (+) diameter bottle cap are shown. (b) Rela-tionship between x4 , x5 and the diameter of the object to be screwed/unscrewedwhile using the thumb and first finger. Also shown are the specific thumb offsetangles while using the thumb and first finger for the 30-mm (�) and 40-mm (�)bottle caps.

in Fig. 11 are the specific values for x4 , x5 , xL3 , and xL4 usedin the experiments that are to be subsequently presented whichinvolve different object diameter sizes.

IX. EXPERIMENTAL METHODS: SHADOW HAND SYNERGIES

The Shadow Hand and bottle were securely mounted to a tablesuch that the orientation of the bottle relative to the Shadow Handclosely replicated human trials. With the 30-mm diameter bottlecap screwed down and in position, the joints of the Shadow


Fig. 12. Thumb tip and little fingertip comparison in Cartesian space be-tween human data and the Shadow Hand. From the kinematic diagram given inFig. 1(c), the Cartesian coordinate locations of the thumb tip and little fingertipare (xT , yT , zT ) and (xL , yL , zL ), respectively.

TABLE IVAVERAGE TRAJECTORY ERROR AND STANDARD DEVIATION IN CARTESIAN

SPACE BETWEEN SHADOW HAND AND HUMAN CYBERGLOVE DATA FOR A

30-mm BOTTLE CAP DIAMETER

Hand were driven sinusoidally by xD (4) to unscrew the bottlecap by starting the time vector at zero and incrementing to apredetermined stop time. The time vector was then reversed anddecremented from the stop time back to zero to screw the bottlecap back on. Five such trials were conducted with the thumband first finger in addition to the thumb and little finger withthe same 30-mm diameter bottle cap used by the human testsubjects.

The measured Shadow Hand joint angle data from these ex-periments were also used in conjunction with the forward kine-matics (see Appendix I) to calculate the Cartesian coordinates ofthe Shadow Hand thumb tip and fingertips produced by the sinu-soidal joint angle trajectories. Based on these data, the averageabsolute difference in Cartesian space between the fingertips andthumb tip of the physical Shadow Hand and the fingertips andthumb tip of the skeletal structure based on the measured Cy-berGlove data was calculated. This error analysis is performedto indicate how well the Shadow Hand fingertip motions withthe sinusoidal joint angle approximations match the measuredhuman fingertip and thumb tip motions in Cartesian space.

Based on the joint angle parameterization with object diame-ter (see Fig. 11), five additional screwing and unscrewing exper-iments were done with the thumb and first finger and also withthe thumb and little finger. The bottle cap diameter was 40 mmwith the thumb and first finger while the bottle cap diameter was72 mm with the thumb and little finger. Specific joint angle off-sets for these different diameters are shown in Fig. 11. Screwingand unscrewing experiments were also performed with a 30-mmdiameter cylinder attached to a potentiometer to illustrate howthe sinusoidal joint trajectories produce rotational motion at the

Fig. 13. Sample joint angle data for joint xF 1b and xF 2 while unscrewingand screwing and the potentiometer (angular position β is depicted in Fig. 12).Note the mirror symmetry of the data.

Fig. 14. Photo sequence of CyberGlove and Shadow Hand unscrewing andscrewing the bottle caps. Note the rotation of the black stripe on the bottle caps.Scripts a,b = unscrewing with CyberGlove and ShadowHand; c,d = screwingwith CyberGlove and Shadow Hand; e = Screwing the 40-mm bottle cap usingthe Shadow Hand with the first finger and thumb; f = unscrewing the 72-mmbottle cap using the Shadow Hand with the little finger and thumb.


Fig. 15. (a) Shadow Hand input to thumb joint (xD 1 ) while unscrew-ing/screwing. (b) Thumb joint data (x1 ) while unscrewing and screwing the30-mm bottle cap. (c) First finger joint (xF 1b ) data while unscrewing andscrewing the 40-mm bottle cap. (d) Little finger joint (xL 1b ) data while un-screwing and screwing the 72-mm bottle cap.

Fig. 16. Joint angle frequencies increase and decrease while increasing anddecreasing the sinusoidal synergy frequency ω. Note the mirror symmetry.

fingertips. This experiment also shows how increasing and thendecreasing the time vector within the family of sinusoids createsa transition from unscrewing to screwing.

Finally, another experiment was performed with a variablesinusoidal synergy frequency to show how the speed of thesynergies comprised of multiple DOFs can be controlled througha single parameter: the frequency of the family of sinusoids ω.

X. SHADOW HAND SYNERGY RESULTS

A. Cartesian Space Error Analysis

The comparison of the fingertip and thumb tip positions inCartesian space shows a close correlation between the humandata and the physical Shadow Hand using the sinusoidal jointangle approximations (see Fig. 12). Results of the error analysis(see Table IV) show that the created sinusoidal joint trajectories

of the Shadow Hand closely replicate the fingertip position ofthe human test subjects. The magnitudes of the average errorwhen using the first finger and thumb are 2.12 and 2.84 mm,respectively. The magnitudes of the average error while usingthe little finger and thumb are 1.92 and 4.83 mm, respectively.The slightly larger error between the human and robotic thumbsin each case (in comparison to the fingers) was expected becauseof the difficulty to formulate a universal biomechanical modelof the human thumb [32], [33]. This is in contrast to the humanfirst finger which is less complex and has been modeled quitewell in the past [35].

B. Unscrewing and Screwing Results

Sample joint angle data from the Shadow Hand while un-screwing and screwing a 30-mm diameter cylinder attached toa potentiometer are shown to illustrate the mirror-symmetricnature of this control concept (see Fig. 13). Simply by increas-ing and then decreasing the time vector within the family ofsinusoids, the transition from unscrewing to screwing can bemade.

Using the developed sinusoidal inputs, the Shadow Hand suc-cessfully screwed and unscrewed the 30-, 40-, and 72-mm bottlecaps in all five trials for each case (see Fig. 14). Sample jointangle data are presented for each condition (see Fig. 15). Thereis a delay present in the recorded joint angle data with respectto the input signals due to the time constants of the motors.

Finally, speed control of every DOF involved in the synergycan be controlled through a single parameter: ω. Sample jointangle data showed that the synergy frequency increased andthen decreased as the ω vector increased and then decreased(see Fig. 16).

XI. CONCLUSION

In this paper, the Shadow Hand has been used for the complextask of unscrewing and screwing different sized objects with a100% success rate. This problem has been addressed in thepast; however, there are significant contributions presented inthis study. Because the finger joint motions are based on humantest subject data, this represents an anthropomorphic solutionthat is well suited to a prosthetic hand. The application of thisapproach to prostheses of the future is also facilitated by thefact that the entire synergy can be driven by a single input. Thishas been accomplished by approximating with high accuracythe joint angle data from human test subjects with sinusoidalfunctions. Thus, a family of sinusoids can be used to accom-plish a complex task. Furthermore, the speed of screwing orunscrewing can be easily controlled through a single parameter:the frequency of the family of sinusoids. Because the synergyis mirror-symmetric, the same joint trajectories can be used forscrewing as are used for unscrewing by simply increasing ordecreasing the time vector within the family of sinusoids.

Additionally, this technique has been shown to be useful forobjects with a wide range of diameter by relating joint angleoffsets to the diameter of the object to be screwed or unscrewed.The kinematics of the hand have been presented in generic formso that they can be applied to any finger of the Shadow Hand.


This is important to help spur the improved design of dexterousartificial hands because if there is no provision to intelligentlycontrol each digit of the robotic hand, there is no need for a dex-terous design. This has also been facilitated by the human handstudy of the little finger in this paper, an area that has not beendeeply explored in the past. Finally, the anthropomorphic sinu-soidal synergies have been implemented within a sliding modecontroller to guarantee system stability within certain bounds.

This sinusoidal synergy control technique would be partic-ularly useful to control multi-DOF prosthetic hands. This isbecause the ability to obtain multiple independent control chan-nels from amputees is difficult [36]. Since only one or twocontrol channels are typically utilized by amputees with pow-ered upper limb prostheses [24], this research is relevant to thecontrol of prosthetic hands [37], [38] as the synergies describedherein can be driven by a single input. Electromyogram controlwith these synergies for application to prostheses is currentlyunderway [39]. This research is also being broadened to thegeneral case where the artificial hand can have any orientationwith respect to the object to be screwed or unscrewed [40].

The PCA of the nine human test subjects will also be usefulto manufacturers of artificial hands and prostheses of the futureto indicate which human hand DOFs are the most useful forscrewing and unscrewing motions.

APPENDIX I

FORWARD KINEMATICS OF THE SHADOW HAND

The forward kinematics in Appendix I have been presentedin generic form so that they can be applied to any finger of theShadow Hand or human hand skeletal structure. The Cartesiancoordinate system and link length definitions used for the for-ward kinematics are given in Fig. 1(c), with ai1 = ai1a + ai1b .Link lengths are in millimeters and joint positions are in ra-dians. This assumes that both the first and little fingers are inconfiguration (2).

The Cartesian coordinates for the thumb are (xT , yT , zT ):

xT =√

22

[aT 1 [cx1 x2 [cx3 x4 − sx3 x4 sx5 ] + sx1 x2 cx5 ]

− aT 2 [cx2 [sx3 x4 sx5 − cx3 x4 ] − sx2 cx5 ]

− aT 3 [sx4 sx5 − cx4 ]] (12)

yT = aT 3sx4 cx5 + aT 2 [sx2 sx5 + cx2 sx3 x4 cx5 ]

+ aT 1 [sx1 x2 sx5 + cx1 x2 sx3 x4 cx5 ] + yT H (13)

zT =√

22

[aT 1 [cx1 x2 [cx3 x4 + sx3 x4 sx5 ] − sx1 x2 cx5 ]

+ aT 2 [cx2 [sx3 x4 sx5 + cx3 x4 ] − sx2 cx5 ]

+ aT 3 [sx4 sx5 + cx4 ]] (14)

where yT H = 8.5 mm.The Cartesian coordinates for the first, middle, or ring finger

(i = F/M/R) are given by (xi, yi , zi):

xi = ai3 + ai1acxi 1 a xi 1 b xi 2 cxi 3 + ai1bcxi 1 b xi 2 cxi 3

+ ai2cxi 2 cxi 3 (15)

yi = ai1asxi 1 a xi 1 b xi 2 + ai1bsxi 1 b xi 2 + ai2sxi 2 (16)

zi = −ai1acxi 1 a xi 1 b xi 2 sxi 3 − ai1bcxi 1 b xi 2 sxi 3

− ai2cxi 2 sxi 3 − bi (17)

where bF = 0, bM = a, and bR = a + b [see Fig. 1(a)].The Cartesian coordinates for the little finger are given by

(xL , yL , zL )

xL = aL1 a[cxL 1 a xL 1 b xL 2 ΩLx − cαsxL 1 a xL 1 b xL 2 sxL 4 ]

+ aL1 b[cxL 1 b xL 2 ΩLx − cαsxL 1 b xL 2 sxL 4 ] + aL2 [cxL 2 ΩLx

− cαsxL 2 sxL 4 ] + aL3[s2

α + c2αcxL 4

]+ aL4 (18)

yL = aL1 a[cα−xL 3 cxL 1 a xL 1 b xL 2 sxL 4 + sxL 1 a xL 1 b xL 2 cxL 4 ]

+ aL1 b[cα−xL 3 cxL 1 b xL 2 sxL 4 + sxL 1 b xL 2 cxL 4 ]

+ aL2 [cα−xL 3 cxL 2 sxL 4 + sxL 2 cxL 4 ] + aL3cαsxL 4 (19)

zL = aL1 a[cxL 1 a xL 1 b xL 2 ΩLz + sαsxL 1 a xL 1 b xL 2 sxL 4 ]

+ aL1 b[cxL 1 b xL 2 ΩLz + sαsxL 1 b xL 2 sxL 4 ] + aL2 [cxL 2 ΩLz

+ sαsxL 2 sxL 4 ] + aL3 [cαsα (1 − cxL 4 )] − c (20)

where ΩLx =(cαcα−xL 3 cxL 4 +sαsα−xL 3 ),ΩLz =(cαsα−xL 3 −sαcα−xL 3 cxL 4 ), and α = 0.96 rad.

APPENDIX II

INVERSE KINEMATICS

The two-link inverse kinematics solution is presented forF/M/R/L fingers of the Shadow Hand using (15)–(20) as

D=(xi − xiJ 2)2 + (yi − yiJ 2)2 + (zi − ziJ 2)2 − a2

i1 − a2i2

2ai1ai2

(21)

xi1b = atan2(D,√

1 − D2) (22)

xi2 = atan2(√

(xi − xiJ 2)2 + (yi − yiJ 2)2 , (zi − ziJ 2))

− atan2(ai2 + ai1cX 1 b, (ai1sX 1 b

)) (23)

where xiJ 2 = ai3 and yiJ 2 = 0. ziJ 2 = 0, a, a + b arefor first, middle, and ring fingers, respectively. For the littlefinger, xLJ 2 = aL3

[s2

α + c2αcxL 4

]+ aL4 , yLJ 2 = aL3cαsxL 4 ,

and zLJ 2 = aL3 [cαsα (1 − cxL 4 )] − c due to the CMC jointLFJ4 (xL4).

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[40] N. Karnati, B. Kent, and E. Engeberg, “Adaptive synergy control for adexterous hand based on grasped object orientation,” presented at theICCAS Conf., Jeju Island, Korea, Oct. 2012.

Nareen Karnati (S’12) received the B.E. degreefrom Maturi Venkata Subha Rao Engineering Col-lege, Osmania University, Hyderabad, India, and theM.S degree from The University of Akron, Akron,OH, in 2009 and 2012, respectively, both in mechan-ical engineering.

He is currently a Project Engineer at Tipton De-sign and Engineering, Inc. Solon, OH. His currentresearch interests include bioinspired robotics andmechanical design.

Dr. Karnati received the National Award for hispresentation on mechanical design at Jawaharlal Nehru Technological Univer-sity, India, in 2009.

Benjamin A. Kent (S’11) received the B.S. degreein mechanical engineering from The University ofAkron, Akron, OH in 2010, where he is currentlyworking toward the Ph.D. degree.

He has coauthored 15 peer-reviewed publications.He has also coauthored a paper with Dr. Engebergthat won the Outstanding Paper Award at the 2012ICCAS Conference. His current research interestsinclude biomimetic control algorithms, bioinspiredrobotics, grasping, and the design and control of dex-terous hands.

Erik D. Engeberg (S’08–M’09) received the B.S.degree from Walla Walla University, College Place,WA, and the Ph.D. degree from the University ofUtah, Salt Lake City, in 2003 and 2008, respectively,both in mechanical engineering.

He is currently an Assistant Professor with ajoint appointment in the Mechanical Engineeringand Biomedical Engineering Departments at TheUniversity of Akron, Akron, OH. He has authoredor coauthored more than 30 peer-reviewed journaland conference papers. He has three patents pend-

ing. His current research interests include biologically inspired control algo-rithms, upper-limb prosthetics, dexterous robotic hands, energy harvesting, andelectrophysiology.

Dr. Engeberg received an NSF I-Corps Team award.

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