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Design and Control Considerations for HighPerformance Series Elastic Actuators

Nicholas Paine, Student Member, IEEE, Sehoon Oh, Member, IEEE, and Luis Sentis, Member, IEEE,

Abstract—This paper discusses design and control of a pris-matic series elastic actuator with high mechanical power outputin a small and lightweight form factor. A design is introduced thatpushes the performance boundary of electric series elastic actu-ators by using high motor voltage coupled with an efficient driv-etrain to enable large continuous actuator force while retainingspeed. Compact size is achieved through the use of a novel piston-style ball screw support mechanism and a concentric compliantelement. Generic models for two common series elastic actuatorconfigurations are introduced and compared. These models arethen used to develop controllers for force and position trackingbased on combinations of PID, model-based, and disturbanceobserver control structures. Finally, our actuator’s performanceis demonstrated through a series of experiments designed tooperate the actuator at the limits of its mechanical and controlcapability.

Index Terms—Series elastic actuators, force control, actuatordesign.

I. INTRODUCTION

SERIES Elastic Actuation (SEA) is a departure from thetraditional approach of rigid actuation commonly used in

factory room automation. Unlike rigid actuators, SEAs containan elastic element in series with the mechanical energy source.The elastic element gives SEAs several unique propertiescompared to rigid actuators including low mechanical outputimpedance, tolerance to impact loads, increased peak poweroutput, and passive mechanical energy storage [1], [2], [3].These properties align with requirements of robustness, highpower output and energy efficiency placed on legged actuationsystems. As a result, SEAs have been widely adopted in thefields of legged robotics and human orthotics [4], [5].

A. SEA Design BackgroundElectric SEAs contain a motor to generate mechanical

power, a speed reduction to amplify motor torque, a compliantelement to sense force, and a transmission mechanism to routemechanical power to the output joint. These components canbe chosen and configured in many different ways, producingdesigns with various trade-offs which affect power output,volumetric size, weight, efficiency, backdrivability, impactresistance, passive energy storage, backlash, and torque ripple.Existing SEA designs can be analyzed to identify such trade-offs based on their choice of speed reduction, compliantelement, and transmission mechanism.

Manuscript received June 21, 2012; revised October 10, 2012, January 23,2013, June 7, 2013.

N. Paine is with the Department of Electrical and Computer Engineering,University of Texas, Austin, TX 78712 USA (e-mail: npaine@utexas.edu).

L. Sentis and S. Oh are with the Department of Mechanical En-gineering, University of Texas, Austin, TX 78712 USA (e-mail: lsen-tis@austin.utexas.edu, sehoon74@gmail.com).

[6], [7], [8] and [9] propose rotary designs based primarilyon commercially available off-the-shelf components, using aplanetary gearbox for speed reduction, rotary or compressionsprings as the compliant element, and power transmissionthrough a bevel gear [8] or chain/cable [6], [7]. Use of off-the-shelf parts make these designs relatively low cost and easyto implement. However, multi-stage planetary gearboxes havepoor efficiency (60-70% for 3-stage) and can be difficult tobackdrive. Additionally, gear teeth introduce torque ripple andbacklash and are easily damaged by impact loads. Bevel gearscompound these effects by adding additional backlash andfriction loss.

A compact rotary SEA design can be achieved using aharmonic drive and a high-stiffness planar spring [10], [11].[12] also uses a harmonic drive but chooses lower stiffnessdie/compression springs. Harmonic drives benefit from havingno backlash and being small in size but suffer from poorefficiency (60-75% depending on ratio, speed, and lubricant),poor backdrivability, torque ripple, and are more expensivethan planetary/spur gears. The high-stiffness planar springs of[10] and [11] deflect only a small amount under load andtherefore store less energy than designs with softer springs.Conversely, stiff springs increase an actuator’s open loopbandwidth which may be desirable for applications with highforce bandwidth requirements.

[12] and [13] use linear springs coupled to rotary shafts andplace the springs between the motor and chassis ground toachieve compact actuator packaging with low spring stiffness.

[14] and [15] place the spring within the reduction phase.This arrangement reduces the torque requirement on the springcompared to designs with the spring at the output. A spring’swire gauge is directly correlated to the amount of torque itcan safely support, which allows the spring in these designsto be smaller. However, because the torque compressing thespring is reduced, the energy stored in the spring is reducedas well. [14] uses a novel worm-gear/rotary-spring/spur-geardesign which allows an orthogonal placement of the motorrelative to the joint axis at the cost of reduced efficiencyand non-backdrivability due to the worm gear. [15] uses twomotors in parallel and has a relatively small reduction througha series of gears and a cable transmission. Two motors inparallel effectively doubles the continuous motor torque whichallows use of a small speed reduction for high actuator outputspeed. This is achieved at the cost of increased weight andcomplexity and is difficult to implement with brushless directcurrent (BLDC) motors due to commutation synchronizationissues.

[16], [17] and [18] propose prismatic designs which useball screws as the primary reduction mechanism followed by

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a cable drive to remotely drive a revolute joint. Ball screws arehighly efficient, even for large speed reductions (85-90%), arebackdrivable, are tolerant to impact loads, and do not introducetorque ripple. However, designs based on ball screws havenot achieved the levels of compactness seen in rotary actuatordesign. [16] includes a belt drive between the motor and theball screw which enables an additional speed reduction due tothe pulley diameter ratio.

[19] uses a ball screw speed reduction and removes theneed for a cable transmission by directly driving the outputjoint with a pushrod mechanism.

Variable stiffness actuators extend the SEA concept byadding an additional degree of freedom which is capableof mechanically adjusting the passive elastic stiffness [20],[21], [22], [23], [24]. Other SEA implementations have exper-imented with non-linear spring stretching to maximize energystorage [25].

B. SEA Control Background

Many different control architectures have been proposed forseries elastic actuators. Some of the variation in controllerdesign is rooted in differences imposed by hardware. Forexample, force can be observed either by measuring changein resistance, as is accomplished using strain gauges in [1],or by measuring spring deflection and applying Hooke’s law,as shown in [26]. A control strategy for hardware designsusing spring deflection sensors may treat a motor as a ve-locity source, and transform desired spring forces into desiredspring deflections. However, for hardware designs using straingauges, the force sensor does not output an intermediatedisplacement value, but maps change in resistance directly toapplied force. For such a system, modeling the motor as aforce source is more convenient.

Further classification of SEA control strategies may be madebased on the types and combinations of control structuresused. [27], [28], [9] measure spring force and control motorforce using some subset of PID control structures (P, PD,etc). If friction and backlash are too large then a pure high-gain PID approach can suffer from stability issues. To remedythis issue, [29] suggests using position feedback as the inner-most control structure for force control. This idea has beenadopted and carried on by many others, treating force controlas a position or velocity tracking problem [25], [10], [30],[31]. Another class of controllers use PID control but alsoconsider the dynamics of the mechanical system to improvethe frequency response of force control [1], [20]. [8], [14]use PID, model-based, and disturbance observer structurestogether to achieve impressive torque tracking performance.In this paper, we build on the force controller presented in [8]by proposing a simple method for obtaining the closed-loopmodel used by the disturbance observer.

C. Actuator Performance

In this paper we define actuator performance by a com-bination of metrics which include measured power-to-weightratio, force tracking accuracy and bandwidth, position trackingaccuracy and bandwidth, and actuation efficiency.

These metrics are heavily influenced by decisions made atthe design phase. For example, heat is generated when torqueis produced by an electric motor. Therefore, continuous poweroutput of electric actuators directly depends on the motor’sthermal properties. However, a motor is able to generatetorques greater than the thermally permissible continuous limitif done so for short periods of time. These intermittent torquesoften far exceed those which the speed reduction mechanismcan support. Because of this discrepancy, the speed reductionmechanism is commonly the component which determines thepeak output power capability of the actuator, not the motor.Additionally, the speed reduction mechanism is often a largesource of loss in an electric actuator, so its selection criticallyinfluences efficiency as well.

For actuators with a fixed range of motion, the performancemetrics also depend on actuator control strategies. Actuatorpower output is maximized when applying large torques athigh velocities. Obtaining high velocities within a fixed rangeof motion requires short bursts of acceleration to and fromrest. This requirement differs from those of continuous travelactuation schemes, whose maximum power output may beachieved simply with a viscous load and a step or ramp indesired torque. For actuators with a fixed range of motion,the boundary conditions placed on high power experimentsnecessitates the use of automatic control strategies to ensurethe actuator operates within its permissible range of motion. Itis then the combined performance of the hardware design andthe control design which determines usable power-to-weightratio of the actuator.

Detailed data on these performance metrics is not currentlypublicly available for most existing electric SEAs. [4] providesexperimental data for peak power output for the actuatordescribed in [19] and is able to achieve 64 W/kg. [32] providesthe power exerted during a hop for the knee joint of [12] (closeto 60 W), but because the actuators are integrated into a threedegree-of-freedom leg, the actuator power-to-weight ratio isdifficult to calculate.

D. Contributions and Paper Structure

This paper highlights research in development of the Uni-versity of Texas Series Elastic Actuator (UT-SEA), a compact,light-weight, high-power electric actuator (Figure 1). Ourcontributions include 1) a novel mechanical design that ismore compact and lightweight than previous ball screw SEAdesigns, 2) a study of the theoretical limitations imposed bythe dynamics of two common SEA design configurations,3) an improvement on controller design and implementa-tion methodology for force and position control of SEAs,4) achievement of leading experimental results in the fieldof electric SEA performance (94 W/kg, 77% mechanicalefficiency) which we believe may serve as a performancebenchmark for other fixed-range-of-motion, passively cooled,high force electric actuators.

We first describe the design motivation behind the electricalpower system and motor operation, followed by explanationof the actuator drivetrain and mechanical design. We thengeneralize our discussion to generic models for SEAs which

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Fig. 1. UT-SEA operation for a fixed-displacement variable-force scenario.Actuator displacement is defined as the distance between points A and B.This distance remains constant while spring deflection (x) depends on actuatorforce.

are used to build controllers for actuator force and position.Finally, we validate the entire system in hardware through aseries of experiments demonstrating actuator speed, power, andefficiency.

II. DESIGN

Nature provides many examples of well designed actuators.An average human adult male can produce 1500 watts ofmechanical power during pedaling exercises, which corre-sponds to a whole-body power-to-weight ratio of 19.5 wattsper kilogram [33]. To achieve similar performance in man-made machines, great care must be taken during the actuatordesign phase to maximize mechanical power output whilekeeping actuator size and weight small. Excess actuator weightreduces the whole-body power-to-weight ratio while large sizelimits a modular actuator’s applicability in dense high-degree-of-freedom robot designs. Hydraulic actuation is one approachwhich achieves these goals but suffers from inefficient opera-tion as discussed in [34].

We began the design process with a set of loose performancespecifications for a robotic knee actuator (peak joint torques of70Nm and maximum velocities of 15 rad/sec). These specifi-cations were obtained from simulations of legged locomotionof a 15kg robot in rough terrain. However, it is important tonote that the design goal of this particular actuator was notfor use in any specific robot, only for experimental study ofmechanical power output.

A. Motor

The motor in an electric actuator is the source of mechanicalenergy and therefore must be chosen and integrated carefullyto achieve optimal performance. Motors convert electricalvoltage and current into mechanical velocity and torque. The

Fig. 2. Motor operating range for Maxon EC-powermax 30 as taken from thedatasheet. A motor is capable of operating inside of the area below the speed-torque curve for a given applied voltage. Increasing voltage to 80V greatlyincreases the operating range of the motor, particularly in the continuousoperating region.

higher the applied voltage, the greater the obtainable veloci-ties and torques become. All motor windings have electricalresistance, which produce heat when current flows throughthem. Because motor torque is proportional to winding current,motor torque is limited by the heat generated in its windings.High temperatures can damage the motor by depolarizingmagnets, melting bonding agents, or damaging windings, ifbrought above certain manufacturer-supplied values.

A Pulse-Width-Modulated (PWM) signal is used to effi-ciently modulate voltage applied to the motor. Due to theresistor-inductor (R-L) circuit behavior of the motor windings,their current response to the PWM voltage signal takes theshape of a first order exponential signal which rises when thePWM signal is high and falls when the PWM signal is low.The maximum absolute value of this transient current signaldepends on 1) PWM frequency (how long the signal has torise or fall), 2) the L/R time constant of the motor circuit, and3) the amplitude of the PWM signal, which corresponds to thevoltage used to drive the motor (bus voltage). If the maximumabsolute value of the transient current is too large, motorheating will occur simply due to the PWM signal without anyuseful motor torque being produced.

High bus voltage is desirable to maximize achievable motorvelocity and torque. Motor manufacturers typically provide a”rated voltage” for each motor which keeps transient motorcurrent within reasonable values for common PWM frequen-cies (10 to 20kHz). However, larger voltages and thus greatermechanical power is possible as long as transient current islimited. For the UT-SEA we chose a Maxon EC-powermax30 BLDC motor with a rated voltage of 48V. To increasemechanical power, we instead supply the motor with 80V(see Figure 2). Transient motor current is regulated by us-ing a 32kHz PWM servo drive (Elmo Ocarina 15/100) andby adding high-current inductors in series with the motor.Calculations provided by the drive manufacturer indicatedthat a series inductance of 0.082mH would keep transientcurrent within reasonable values. The small added mass of theinductors is justified in that they allow the continuous force ofthe actuator to be increased by 66% without sacrificing outputspeed.

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Fig. 3. Cross section of the UT-SEA showing drivetrain components including a) Maxon EC-4pole 30 200W BLDC motor, b) 3:1 pulley speed reduction,c) low backlash timing belt, d) angular contact bearings, e) piston-style ball screw support, f) high compliance springs, g) miniature ball bearing guides, h)absolute encoder, and i) incremental encoder. The compression load path is depicted as well.

The high motor speed produced by high bus voltage enablesthe use of a large speed reduction which increases bothintermittent and continuous torque capability compared todesigns with lower voltages and lower speed reductions. Forthis motor, the gain in output power by using 80V comparedto 48V is less pronounced due to the diminished continuoustorque at very high motor speed. The final motor outputcharacteristics indicated that a design using a speed reductionof approximately 175:1 would allow the actuator to meet thespecified torque and speed requirements.

B. Drivetrain

To maximize mechanical power at the joint, energy mustbe transmitted from the motor to the joint with as few lossesas possible. We chose a pulley/ball-screw speed reductiondesign similar to [16] for several reasons. A pulley/ball-screwreduction is efficient (typically above 90%), impact resistant,and backdrivable while the pulley ratio reduces the high motorspeed to a speed more suitable for driving the ball screw.

Unlike [16] and other ball screw SEA designs, our designdrives the ball nut instead of the ball screw ([35] uses asimilar ball-nut-driven design but is a non-series-elastic cable-driven actuator). Driving the ball nut enables two key featureswhich reduce the size and weight of the UT-SEA. First, ballscrew support is incorporated directly into the actuator housingusing an innovative piston-style guide (see Figure 3). Thisfeature replaces the long, bulky rails used to support the outputcarriage in conventional prismatic SEA designs. Secondly,the compliant element is placed concentrically around thepiston-style ball screw support which gives series elasticitywithout adding to the length of the actuator. These two featurescombine together to define the compact form factor of the UT-SEA.

The ball nut is supported by dual angular contact bearingswhich allow the ball nut to rotate within the housing whiletransmitting axial force from the ball nut to the housing.Custom preloaded die springs (manufactured by DiamondWire Spring Co.) transmit force from the actuator housingto the chassis ground. The die springs are supported by fourminiature ball bearing guide rails (Misumi) which are mountedto the housing using grommets that allow for slight misalign-ment during operation. The miniature ball bearing guides offerboth lower friction and higher tolerance to torsional loads than

Fig. 4. Range of motion comparison between prismatic (a) FSEAs and (b)RFSEAs. For simplification, we assume that springs are fully compressible,spring plates have zero thickness, and the FSEA carriage travel is constrainedto the length of the ball screw. The notations represent B: ball screw length,C: carriage length, N: ball nut length. Range of motion is then B − C forthe FSEA and B + C −N for the RFSEA.

bushing style guides. Force is sensed using a 20,000 count-per-revolution incremental encoder (Avago AEDA 3300) alongwith an absolute sensor (Novotechnik Vert-X 1302) to removethe need for startup calibration. A low stretch, low creepVectran cable is attached to the chassis ground and is routedaround the two spring deflection sensors using pulleys andan idler. Overall actuator position is measured combiningreadings from the motor encoder and the spring encoders. Anabsolute rotary sensor on the driven joint is used to initializeactuator position.

C. Spring Placement and Stiffness

There are two common arrangements of components foundin SEA designs. The first arrangement, which we will refer toin this paper as Force Sensing Series Elastic Actuator (FSEA),places the compliant element between the gearbox output andthe load. The second arrangement, which we will refer toas Reaction Force Sensing Series Elastic Actuator (RFSEA),places the spring between the motor housing and the chassisground.

From a design standpoint there are several trade-offs be-tween the two arrangements. RFSEA style actuators havethe advantage of being more compact since the compliantelement does not have to travel with the load but may beplaced statically behind the actuator (or it can be remotelylocated as shown in [12], [13]). Prismatic RFSEAs also havegreater range of motion for a given ball screw travel lengthcompared to prismatic FSEAs as shown in Figure 4. Theprimary drawbacks of RFSEAs are less direct force sensing,reduced force tracking performance, and decreased protection

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TABLE IUT-SEA SPECIFICATIONS

from impact loads as described in Section III-B. An RFSEAstyle design was chosen to minimize the bounding volume ofthe UT-SEA. However, this design decision was heavily in-fluenced by the selection of the pushrod/ball-screw drivetrain.The drivetrain exhibited strong radial symmetry and possessedlong, narrow ball screw support structure which allowed diesprings to be integrated without excess bulk. Additionally, thedecreased protection from impact loads of an RFSEA designis somewhat, though not completely, mitigated by the impact-tolerance of the ball screw drivetrain in the UT-SEA.

Spring stiffness for UT-SEA was chosen to maximize energystorage. For a given force, soft springs are able to storemore energy than stiff springs. Peak force, desired deflection(maximum possible deflection to minimize stiffness), and thegeometric constraints of the actuator were given as designspecifications to Diamond Wire Spring Co. They then designedand manufactured a spring with a stiffness rate of 138 N/mmwhich effectively doubles to 277 N/mm for the actuator springconstant because two springs are used with precompression.

D. Design Summary

The end result of the design process is a pushrod RFSEA-style actuator that is compact and modular enough to beintegrated into dense mechanical designs. Rotary joint designsusing linear actuators can benefit from the nonlinear linkagekinematics created at the joint at the cost of a fixed rangeof motion (refer to Figure 12). Torque generated by such alinkage has an angle-dependent moment arm which can beused to provide high torque and high speed capability wherethey are needed. A summary of the design parameters for theactuator can be seen in Table I.

III. MODELING AND CONTROL

This paper discusses two main control objectives for theUT-SEA. First, when operated in force control mode, the UT-SEA should be capable of closely approximating an idealforce source. An ideal force source is able to accurately tracka desired force signal both in steady state and for higherbandwidth, rapidly changing desired force signals. An idealforce source is the common building block for several higherlevel control strategies, including: Operational Space Control[36], Virtual Model Control [37], impedance control [38], and

classical model-based control, among others. In this paper,we only consider classical model-based position control asan extension to a near-ideal force source. We create this near-ideal force source by developing a force control strategy whichattempts to minimize measured force error by sending desiredcurrent commands to the motor servo drive.

The second control objective discussed in this paper is stableand accurate tracking of joint position for high joint velocities.As discussed in Section I-C, this objective is made difficultdue to the fixed-range-of-motion requirement, and thereforerequires accurate tracking of large accelerations. We achievethis objective using a model-based control strategy whichrelies on the near-ideal force source developed for the firstcontrol objective.

Because both control objectives require excellent dynamicresponse, it is essential to understand the basic dynamics of theUT-SEA. We begin discussion of the controller developmentprocess by defining a simple model of the UT-SEA. Thismodel is generic and may be applied to other RFSEA style ac-tuators. In parallel, we also present a FSEA actuator model andcompare it against the RFSEA model to understand inherentdifferences between the two SEA arrangements. Then, usingthe RFSEA model, we develop force and position controllersfor the UT-SEA.

A. Modeling

Figure 5 shows simple models for both FSEA and RFSEAstyle actuators. In the FSEA model (Figure 5c), generalizedmotor force (Fm) is generated between chassis ground anda lumped sprung mass (mk) which includes rotor inertia, thegearbox reduction, and transmission inertia. If the motor isunpowered and backdriven, a viscous backdriving friction (bb)is felt from transmission friction and motor friction. The springis between the transmission output and output mass (mo) andhas stiffness (k) and viscous friction (bk) generated by thespring support mechanism. In the RFSEA model the springand force generation elements are switched. In addition, thedistribution of sprung mass and output mass is different foran RFSEA. mo in the RFSEA model includes rotor inertia,the gearbox reduction, and transmission inertia. mk varies bydesign. For the UT-SEA, mk includes the mass of the actuatorhousing and mass of the motor, including rotor mass.

A high output impedance model is useful for simplifyingthe force controller design problem (Figure 5d). It assumesthat the actuator output is rigidly connected to an infinitemass, which cannot be moved. For the high output impedancemodels, the sprung mass feels a summation of forces from1) the motor (Fm), 2) the spring (Fk), 3) lumped viscousfriction (Fbeff

) where beff = bb + bk, and 4) from otherdisturbances that are difficult to model (Fd) such as torqueripple from commutation, torque ripple from gearboxes due toteeth engaging and disengaging, backlash, and various formsof friction such as stiction, and coulomb friction.

B. FSEAs vs RFSEAs

The force sensing challenge is to calculate force felt at theactuator output (Fo) given measurement of spring deflection

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Fig. 5. Models for FSEA and RFSEA style actuators. The notations representFm: motor force, Fo: output force, bb: viscous backdriving friction, bk:viscous spring friction, k: spring constant, x: spring deflection, mk: lumpedsprung mass, mo: output mass, beff : lumped damping which equals bb+bk ,Fd: disturbance forces and forces which are difficult to model.

(x). For both FSEAs and RFSEAs, the spring acts as the forcesensor. The difference between the two is where the spring islocated relative to the output force. This discrepancy does notaffect low frequency force measurement but must be taken intoaccount to measure high frequency forces accurately.

For FSEAs with high output impedance (Figure 5d), Fo =Fk+Fbeff

. If Fbeffis small, which can be accomplished with

careful mechanical design, then Fo can be closely approxi-mated by measuring Fk alone. This simplification removesthe need to measure or calculate time derivatives of x.

FoFSEA= Fk = kx (1)

For RFSEAs with high output impedance, Fo = Fm+Fd =Fmk

+ Fbeff+ Fk. Here, measurement or calculation of time

derivatives of x is critical in considering the large forces ofFmk

and Fbeff. Output force can be observed as follows.

FoRFSEA= Fmk

+ Fbeff+ Fk = mkx+ beff x+ kx (2)

These equations tell us that force sensing for RFSEA styleactuators should possess models of sprung mass and viscousdamping and should be able to measure or calculate both x andx for accurate force sensing across the frequency spectrum.

An additional drawback of RFSEAs is revealed when con-sidering internal forces required to generate a desired outputforce. For a FSEA, the relationship between Fk and Fo isgiven by:

Fk(s)

Fo(s)=

k

sbeff + k(3)

Whereas for a RFSEA the same relationship is given by:

Fig. 6. Relation of internal actuator forces to output force. The four linesrepresent equations (3), (4), (5), and (6). As the figure shows, RFSEA springforce exceeds output force for resonant frequencies. Parameters are selectedto match the UT-SEA design.

Fk(s)

Fo(s)=

k

s2mk + sbeff + k(4)

Similarly, the relation between Fm and Fo for FSEAs (5)and RFSEAs (6) are as follows:

Fm(s)

Fo(s)=s2mk + sbeff + k

sbeff + k(5)

Fm(s)

Fo(s)=

s2mk + sbeff + k

s2mk + s(beff + bb) + k(6)

Plotting the frequency response of (3), (4), (5), and (6)yields the results shown in Figure 6. Each line representsan internal force relative to the actuator output force acrossthe frequency spectrum. A magnitude greater than one (0 dB)indicates that, at the represented frequency, the internal forcevalue is greater than output force. Motor force for both theFSEA and RFSEA remain less than or equal to the outputforce below the resonant frequency. Motor force for the FSEAincreases for frequencies greater than the resonant frequencybecause the motor force must counteract the low-pass filtercreated by the mass-spring system. The RFSEA is able toproduce high frequency forces without an increased burden tothe motor force. The problem regarding the RFSEA design liesin the spring force, which is the only internal force to increaseabove output force for resonant frequencies and below. Theresonant peak for spring force is about 15 dB (a factor ofaround five) for the UT-SEA, meaning spring force is fivetimes greater than output force. The mechanical design ofUT-SEA assumes peak forces occur at the output, meaninglarge forces from resonance could easily result in mechanicalfailure. We address this issue with our force control strategyby choosing to regulate spring force rather than output force.

To summarize key differences between FSEAs and RF-SEAs:

1) Accurate force sensing for RFSEAs requires knowledgeof k, beff , mk, x, x, and x whereas FSEAs only requirek and x for a close approximation of output force.

2) FSEA output force can safely track a reference forcesignal up to and past resonant frequencies but willrequire large motor effort at high frequencies. RFSEAs

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cannot safely track references force signals close to theirresonant frequencies due to large resonant spring forces,but can track high frequency force signals with lowmotor effort.

3) FSEAs place a mechanical low-pass filter between theoutput and the gearbox, making them more tolerant toimpact forces than RFSEAs.

Based on these observations FSEAs are better suited forforce control applications. However, as discussed in sectionII-C, the excellent size and packaging characteristics of RF-SEAs outweigh the trade-offs in force controllability for ourapplication and this configuration was therefore chosen for theUT-SEA. Accurate force sensing is achieved in our implemen-tation by using high precision encoder data processed with astandard model-based infinite impulse response (IIR) filter.

C. Force Control

Our proposed force controller uses a structure similar to[8] but differs in that the disturbance observer is not designedbased on an analytical model of the inner PID control loop,but is designed using a model obtained from experimentalsystem identification. In this section we provide a simplifiedexplanation of the force control structure, and describe thesystem identification process used to obtain the model used inthe disturbance observer.

The goal of force control is to make measured actuatoroutput force (Fo) track a desired force profile (Fd) usingmotor current (im) as the plant input and spring deflection(x) as the output. However, as discussed in Section III-B,because the UT-SEA is a RFSEA style actuator Fo cannotsafely track Fd for all frequencies. Instead, our force controlapproach regulates spring force (Fk). This decision sacrificesforce tracking of Fo near resonant frequencies but guaranteessafe and oscillation free force tracking at all frequencies.Additionally, because Fk is the control target, this approachapplies equally to both FSEA and RFSEA designs. The effectsof this decision on the tracking accuracy of Fo will be shownlater in the paper (see Figure 11 for frequency response andFigure 15 for time domain response).

For a given output force, the motor current required toproduce this force can be approximately calculated withknowledge of the motor torque constant (kτ ), actuator speedreduction (Nbs), and drivetrain efficiency (η). For the UT-SEA,the mapping from motor torque (τ ) to ball screw force (F )results from a pulley reduction (Np) and a ball screw, whichis parameterized by ball screw lead (l).

Nbs =F

τ=

2πNpl

(7)

The inverse of Nbs, η, and kτ can be used as a feedforwardterm in a force control scheme (Figure 7).

Without feedback compensation, unmodelled actuator fric-tion will reduce force tracking accuracy. A PID compensator(Kp = 0.072, Ki = 0, Kd = 0) addresses this problem byproducing control effort as a function of measured force errore = Fd−kx, where kx represents measured force as calculatedusing Hooke’s Law.

Fig. 7. PID force controller used for closed-loop system identification. Thephysical actuator is denoted by the ”UT-SEA” block, which takes an inputof motor current and produces spring deflection as an observable output. Thenotations represent Nbs: ball screw speed reduction, η: drivetrain efficiency,kτ : motor torque constant, k: spring constant, Pc: the closed-loop transferfunction from Fd to Fk .

Due to stability limitations, PID gains can only be increasedup to certain values. To improve force tracking performancefurther and to remove steady state error another controlapproach is required. As demonstrated by [39], a disturbanceobserver (DOB) may be used to 1) measure and compensatefor error from disturbances and 2) reduce the effect of plantmodeling error. To use a DOB a nominal plant model isrequired. For this application, the DOB plant is the closed-loop transfer function (Pc) created by the PID controller shownin Figure 7. To obtain an accurate representation of Pc, weimplement the controller shown in Figure 7 in hardware,fix the actuator output (mo) to ground to match the highoutput impedance model of Figure 5d, and perform systemidentification of Pc using an exponential chirp signal for Fd.Plotting the frequency response of the magnitude and phaseof Fk/Fd (Figure 8) identifies a second-order system, whichwe model as the mass-spring-damper of Figure 5d. With kmeasured before actuator assembly, the only unknowns are thesprung mass and effective damping. Fitting the mass-spring-damper model to the experimental data results in mk = 18 kgand beff = 250 Ns/m and a damped resonant frequency of19.2Hz. This model is shown as the dashed line in Figure 8.

Pc =Fk(s)

Fd(s)=

k

s2mk + sbeff + k(8)

With the nominal DOB plant model identified, the DOB isincorporated into the force controller as shown in Figure 9.Measuring the frequency response of the controller with theDOB added shows improved tracking performance comparedto PD control (Figure 8). In fact, low frequency force trackingerror is reduced 98.4% by adding the DOB to the PD controller(Figure 10). The DOB forces the closed-loop response to fitclosely to the mass-spring-damper model. The DOB includes afilter (Qτd) which is required to make the inverse plant modelrealizable and to attenuate high frequency disturbances. Qτd,with the rest of the Q functions depicted in Figures 9, and 13,is implemented as a low-pass Butterworth filter and has thefollowing transfer function:

Q(s) =1

(s/ωc)2 + 1.4142(s/ωc) + 1(9)

The cutoff frequency of each filter (ωc) was determinedempirically (Qτd = 60Hz, QFF = 20Hz, Qm = 20Hz)and in general should be set higher than the desired closed-loop control bandwidth of the application. For a more detailed

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Fig. 8. Measured frequency response of two force control strategies. Theproposed controller (Figure 9) improves upon PD control (Figure 7) by 1)removing the resonant peak (occurring at 19.2 Hz), 2) increasing bandwidthto 60Hz, and 3) reducing force tracking error (see Figure 10).

Fig. 9. Block diagram of the proposed force control structure. The physicalactuator is denoted by the ”UT-SEA” block. The Q functions are low-passfilters defined by (9).

description on Q filter design and for discussions on controllerstability, refer to [8] and [14].

Ideally, the magnitude of the closed-loop transfer functionof the force controller should be close to one (0 dB) oversome desired bandwidth. As can be seen in Figure 8, thePD controller amplifies spring force by 20 dB (a factor of10) for excitation signals close to the resonant frequency.To remove this resonance, a feedforward filter is introducedwhich is created using the inverse nominal plant dynamics(Pc−1 in Figure 9). A low-pass filter (QFF ) is again used tomake the inverse transfer function realizable. Finally, althoughit is not used in the force feedback loop, a filter is usedto generate an estimate of output force (Foest ) from springdeflection measurement (Pc−1Qm in Figure 9) which is used

Fig. 10. Measured force tracking error versus frequency for two force controlstrategies. The proposed control technique reduces error at low frequenciesby 98.4% (36dB) compared to PD control.

Fig. 11. Closed loop force tracking performance of spring force (Fk) andestimated output force (Foest ) for the UT-SEA.

for observation purposes. A comparison between trackingperformance of Fk and Foest is shown in Figure 11. The dip inthe Foest signal around the resonant frequency is intentionaland maintains Fk below Fd to ensure structural integrity ofthe actuator.

D. Position ControlIn this section we develop a position controller which builds

upon the force controller. However, for position control, weno longer assume that the actuator is in a high impedanceconfiguration. While moving from a high impedance configu-ration changes the plant of the force controller, experimentaltests of the position controller show high tracking accuracyand large bandwidth. We believe there are three reasons whythis is the case: 1) Output inertia is coupled to motor rotorinertia through a large speed reduction (175:1 at θa = 90◦)which reduces the inertia seen at the motor by the squareof the reduction. This significantly reduces the effect of loadinertia on the resonant frequencies of the actuator. 2) Theforce control DOB is designed to reduce the sensitivity ofthe controller to modeling error. Any change in the plant thatoccurs from the reduced output impedance is attenuated bythe DOB. 3) The combined effects of 1) and 2) help maintainthe effectiveness of the feedforward inverse dynamics block ofthe force controller so that actuator resonance is suppressed.The small force error that does develop in Section IV can beattributed to this difference in plant model.

By using the aforementioned force controller as the inner-most component of the position controller, we are able totreat the actuator as a nearly ideal force source. This forcesource generates a torque through a mechanical linkage witha moment arm (L) as depicted in Figure 12. Actuator force(F ) generates arm torque (τa) depending on arm angle (θa)according to the following equation.

τa = FL(θa) = Fcb sin θa√

b2 + c2 − 2bc cos θa(10)

The dynamics relating τa to θa with arm inertia (Ja) andjoint friction (Ba) are:

9

Fig. 12. UT-SEA mounted on a test bench with the prismatic linkagegeometry shown. The notations represent: L: linkage moment arm, c: distancebetween the actuator pivot and the arm pivot, b: distance between the arm pivotand the pushrod pivot, F : actuator force, τa: torque exerted on the output arm,θa: output arm angle, Ja: inertia of the output arm, φ: offset angle. Valuesused during testing of the actuator are: b = 0.025 [m], c = 0.125 [m]. Speedreduction from motor output to arm output is 175:1 at θa = 90◦.

Fig. 13. Block diagram of the control structure used for position control. Thenotations represent: τg : gravity compensation torque, L: nonlinear linkagekinematics, Fcntrl: the force control block shown in Figure 9. The Qfunctions are low-pass filters defined by (9).

τa = Jaθa +Baθa + τg(θa) (11)

where τg is the torque due to gravity and is parameterizedby the mass of the output link (ma), the distance from thepoint of rotation to the center of mass (lm) and an angle (φ)to correct for c in Figure 12 not being orthogonal to the gravityvector.

τg(θa) = −maglm cos (θa + φ) (12)

Combining (10) (11) and (12) the full dynamics from F toθa are then represented by the following nonlinear differentialequation.

(13)F =

√b2 + c2 − 2bc cos θa

cb sin θa

[Jaθa

+Baθa −maglm cos (θa + φ)]

Our position control approach first considers the problem ofcontrolling θa given τa, assuming no gravity is present. Therelation between τa and θa in this case is given as:

θaτa

=1

s2Ja + sBa(14)

Inverting (14) provides a desired arm torque (τades ) given adesired arm angle (θd) and is used as the initial block in the

position controller (Figure 13). Because (14) does not considergravity, the desired arm torque signal must be summed witha gravity compensation torque (12) to produce the expectedmotion. The resulting torque value is then converted intodesired actuator force by multiplying by the inverse of thenonlinear kinematics (L−1 from (10)). This desired force isthen passed to the force controller.

Without some form of feedback the position controllerwould not be able to track a desired position due to modelingerror and external disturbances. A DOB is placed in an outerloop around the model-based position controller to resolvethese issues. The DOB treats modeling error and exogenousinput as a disturbance and counteracts this disturbance withinput to the model-based position controller. Qp (fc = 10Hz)in Figure 13 is a feedforward low-pass filter to smooth positionresponse, thus reducing required torques. Qpd (fc = 35Hz) isa low-pass filter that attenuates high frequency disturbancesignals of the DOB.

IV. PERFORMANCE EXPERIMENTS AND ENERGETICS

Our goal was to design hardware and controllers that wouldmaximize performance, but how do we know if we have beensuccessful? One way of measuring the success of the controldesign is to attempt to reach the mechanical limits of actuatorcomponents in a safe and controlled manner. To this end weperformed an experiment to push actuator speed to the limitsof mechanical and control capabilities. A 5th order splinewas used to generate a smooth position reference signal forhigh speed transitions between a large angle displacement (60degrees). Figure 14 shows the experimental results. The armis able to track the reference position closely and achieves avelocity of 15 rad/sec which is the mechanical limit of theball screw. In this test, the motor reached a speed of 22,600rpm which is 3,000 rpm below the maximum possible motorspeed. Acceleration from rest, to maximum speed, and backto rest occurs within less than 0.2 seconds.

A critical metric for performance is power output. Tomaximize achievable power we designed an experiment which

High Speed Test

5060708090

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Arm

TAng

leT(

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-10

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Arm

TVel

ocity

T(d

eg)

TimeT(sec)

ArmTVelocity(rad/sec)

Fig. 14. High speed position tracking test. The actuator output followsa reference signal that changes 60 degrees in less than 0.2 seconds. Theactuator is able to track the reference signal closely and reaches the maximummechanical speed of the ball screw of 15 rad/sec. The torque moment arm(L) rotates through its largest length at θa = 90◦.

10

Time (sec)

(position control w/ 4.5kg weight on 0.23m moment arm)

High Power Test

120

130

ArmtAngletWdeg)

Des

iredt

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tAng

leWd

eg)

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letW

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cetW

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iredt

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ceWN

)S

prin

gtF

orce

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uato

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orc

eWN

)

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cetW

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DesiredtForceWN)SpringtForceWN)

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cetE

rror

tWN

)

ActuatortForcetErrortWN)SpringtForcetErrortWN)

-200-150-100

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cetE

rror

tWN

)

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uato

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orc

etE

rror

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prin

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orce

tErr

ort

WN)

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han

ical

tPow

ertW

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Mec

han

ical

tPow

ertW

W)

MotortPowerWW)ArmtPowerWW)

Mot

ortP

ower

WW)

Arm

tPow

erWW

)

Fig. 15. Data from the high power test. Accuracy of both position andforce tracking can be seen in the top two graphs. The third graph showsforce error of both spring force and output force (see Section III-A). Thebottom graph shows power measured at the motor (desired torque time motorvelocity) and at the output (measured torque times measured velocity). Thefollowing variable mappings are used: Desired Arm Angle (θd), Arm Angle(θa), Desired Force (Fd), Spring Force (Fk), Actuator Force (Foest ).

would require high speed and high torque simultaneously. Thedesign of the output arm which the actuator is attached toallows for additional weight to be added. For the experiment,we fixed a 4.5 kg weight to the arm with a 0.23 meter momentarm. The experiment requires the arm to track a referenceposition which is again generated using splines. The motionis not symmetrical. When the weight is being lowered thereference signal changes slowly and when the weight is beingraised the reference signal changes quickly. The combinationof fast motion and the fact that the motion is directed upwardsagainst gravity makes this test require very high actuator poweroutput. Figure 15 shows the experimental results. On thebottom graph power at the motor and power at the arm can beseen. Output power is measured as output torque times outputvelocity. The actuator generates peak mechanical output powerof approximately 110 watts, which corresponds to a power-to-weight ratio of 94 watts per kilogram. Comparing with [4]this represents a 47% improvement over previous attempts.While these are strong results, we believe that the actuator iscapable of much higher output. We plan to test this hypothesisin future design iterations.

The error during high acceleration shown in Figure 15may be attributed to the following factors. First, the highoutput impedance model assumed for system identificationdoes not consider motion of the load. Depending on theamount of tolerable error, this system identification model

0

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cal P

ower

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)

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Motor Power(W)Arm Power(W)

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Ang

le (

deg)

Time (sec)

Arm Angle(deg)

η = 77%η = 70% f

b

Actuator Efficiency (motor power vs arm power)(position control of 9kg weight on 0.23m moment arm)

Fig. 16. Test to measure actuator mechanical efficiency. The arm is trackinga sinusoidal position reference with weight added. Motor power is calculatedfrom desired motor torque times measured motor velocity while arm power iscalculated from measured arm torque times measured arm velocity. ηf and ηbrepresent forward and backward efficiency, respectively. On upward swings,motor power is greater than arm power because the actuator must work againstgravity. On downward swings, arm power is greater than motor power due togravity backdriving the actuator.

may be extended to include dynamics of the load side of theactuator. Although, it should be noted that doing so reducesthe modularity of the actuation system in general and requiresthe control law to be tailored to load characteristics. Second,as depicted in Figure 11, the UT-SEA is not able to trackforce accurately near its resonant frequency. Using an FSEAstyle actuator would improve this aspect of force tracking atthe cost of increased actuator size and weight, as discussed inSection II-C.

We present one final experiment aimed at measuring ac-tuator efficiency. There are several places for loss to occuras energy is transferred through an actuation system. Wedesigned an experiment to measure the efficiency of powertransfer from the output of the motor to the output of theactuator. The experiment was performed by fixing a 9 kgweight to the arm and tracking a sinusoidal position referenceand measuring power at each location. Figure 16 shows theexperimental results. Interestingly, peak arm power remainsthe same regardless of direction of travel while motor powerdoes not. This indicates that the transfer of power reversesdirection depending on whether the arm is rising or falling.When the arm is rising, the motor is injecting power intothe system and there is a loss from the motor to the output.When the arm is falling, gravity is injecting power into thesystem and there is a loss in the opposite direction, from theoutput to the motor. Motor data is not as clean as the outputdata because desired torque values are changing rapidly dueto automatic control. To calculate efficiency, we fit a 4th ordercurve to each phase of motor data. Efficiency in the forwarddirection from the motor to the output (ηf ) was measured tobe 77% while efficiency in the reverse direction (ηb) was 70%.This experiment does not consider the efficiency of convertingelectrical power into mechanical power of the motor. However,efficiency of the motor drive’s H-bridge and the efficiency of

11

the motor can be very high, mostly depending on motor load.We plan to measure this efficiency in future work.

Experiments were performed on a PC-104 form factorcomputer from Advanced Digital Logic (ADLS15PC) runningUbuntu Linux with an RTAI patched kernel to enable realtime computation. Data was passed to and from the actuatorusing analog and quadrature signals which pass through acustom signal conditioning board. Both force and positioncontrol were performed at a servo frequency of 1kHz. Allcontinuous time control structures and signal time derivativeswere converted to discrete time using a bilinear (Tustin)transform and were implemented in C.

V. CONCLUSIONS

This paper introduced the UT-SEA, a compact, light-weight,high-power actuator designed to empower the next genera-tion of electrically actuated machines. Unlike other prismaticSEAs, the UT-SEA features a tightly integrated pushrod designwhich allows the actuator to be housed within a robotic limband use a nonlinear mechanical linkage to drive a rotaryjoint. High motor voltage and current filtering enable theuse of a large speed reduction which significantly increasesboth continuous and peak torque capabilities. Placement ofthe elastic element between the actuator housing and chassisground creates a design with increased range of motion andsmall size.

We presented methods for modeling both FSEA and RFSEAstyle actuators which revealed fundamental differences be-tween the two in terms of controller design and force trackingcapability. Although RFSEA style actuators present difficul-ties, we proposed a control design based on model-based, PID,and disturbance observer structures and validated the controllerin hardware. The proposed force controller was able to trackforces with 98.4% less error than conventional PD-basedcontrol for low frequency signals and removed harmful springresonance associated with RFSEA designs. We also presenteda model-based position controller which includes the proposedforce controller as the innermost loop. We performed highspeed tracking experiments with this controller and achievedspeeds of 15 rad/sec which is the mechanical limit of thehardware. Additional tests showed peak actuator power outputof 110 watts and mechanical efficiency of 77%.

VI. ACKNOWLEDGMENTS

The authors would like to thank members of the UT MEMachine Shop, especially Scott Allen, for their valuable inputduring the design and fabrication phase. We would also liketo thank Alan Kwok for helping with spring support guideexperiments.

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Nicholas Paine (S’12) received B.S and M.S. de-grees in Electrical Engineering from The Universityof Texas at Austin, USA in 2008 and 2010, respec-tively. He is currently working toward a Ph.D. degreein Electrical Engineering at the University of Texasat Austin.

His research interests include design and controlof actuators and systems for dynamic legged robots.Mr. Paine is the recipient of the Virginia & ErnestCockrell, Jr. Fellowship in Engineering since 2008.

Sehoon Oh (S’05-M’06) received B.S., M.S., andPh.D. degrees in electrical engineering from theUniversity of Tokyo, Tokyo, Japan, in 1998, 2000,and 2005, respectively.

He worked as an assistant professor in the De-partment of Electrical Engineering at The Universityof Tokyo until 2012, and was a visiting researcherat the University of Texas at Austin from 2010 to2011. He is currently a Research Professor at SogangUniversity, South Korea. His research fields includethe development of human-friendly motion control

algorithms and assistive devices for people.Dr. Oh is a member of IEEE and the Institute of Electrical Engineers of

Japan.

Luis Sentis (S’04-M’07) is an Assistant Professorat the University of Texas at Austin where he di-rects the Human Centered Robotics Laboratory. Hisresearch focuses on foundations for the compliantcontrol of humanoid robots, algorithms to generateextreme dynamic locomotion, and building robotsfor educating students in mechatronics. He holdsPhD and MS degrees in Electrical Engineering fromStanford University where he developed leadingwork in theoretical and computational methods forthe compliant control of humanoid robots. Prior to

that, he worked in Silicon Valley in the area of clean room automation.