06776471

IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 19, NO. 6, DECEMBER 2014 1907

Frequency-Shaped Impedance Control forSafe Human–Robot Interaction inReference Tracking Application

Sehoon Oh, Member, IEEE, Hanseung Woo, Student Member, IEEE, and Kyoungchul Kong, Member, IEEE

Abstract—In the control of industrial robots, both safety and ref-erence tracking performance are required. For safe human-robotinteraction, robots should exhibit low mechanical (or controlled)impedance so that they react to the interaction forces in a com-pliant manner. On the other hand, the reference tracking requiresfor the robots to reject exogenous disturbances, which results inan increased impedance. In order to achieve these two conflictingobjectives, a frequency-shaped impedance control (FSIC) methodis proposed in this paper. The proposed method utilizes the twodifferent functionalities of the disturbance observer (DOB): a dis-turbance estimation function as an observer and a disturbancerejection function as a feedback controller. Namely, the DOB isutilized as an observer at the frequencies where the robots interactwith humans, while it is used as a feedback controller (i.e., distur-bance rejection controller) at the frequencies where the referencetracking is required. The proposed approach is realized by shapinga filter of the DOB in the frequency domain so that the impedanceis manipulated to achieve both the compliant interaction and refer-ence tracking. The compromised reference tracking performancein the frequency range, where the impedance is set low, can alsobe supplemented by feedforward control. A typical feedback con-troller and a feedforward controller are designed in addition tothe DOB-controlled system as the whole control system to enhancereference tracking performance and the betterment of stability ro-bustness. The proposed method is verified by experimental resultsin this paper.

Index Terms—Disturbance observer (DOB), force sensorlessimpedance control, frequency-shaped impedance control (FSIC),reference tracking, safe human–robot interaction.

I. INTRODUCTION

FACTORY automation with industrial robots is unavoidablein the modern manufacturing environments. The repeata-

bility and precision of the industrial robots have been dramati-cally improved and overcome those of human workers [1], [2].There are, however, still many nonrepeatable and unexpectedtasks, which cannot be relied on the robots. Also, the dexterous-ness of the human hands is not easy for robotic manipulators

Manuscript received December 11, 2013; accepted February 19, 2014.Date of publication March 20, 2014; date of current version June 13, 2014.Recommended by Technical Editor M. Iwasaki. This work was supportedby the National Research Foundation of Korea (NRF) under Grant NRF-2012R1A1A1008271 funded by the Korea government (MSIP).

The authors are with the Department of Mechanical Engineering, Sogang Uni-versity, Seoul 121-742, Korea (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.2014.2309118

to realize. Consequently, the industrial robots coexist with hu-man workers in the modern manufacturing environments. Dueto the coexistence of robots and humans, the requirements of thecontrol of robotic manipulators have become complicated anddifficult to achieve; the robots are required to show both refer-ence tracking performance and impedance for safe human–robotinteraction.

Not only the industrial robots, but there are also manyother robotic systems that interact with humans. For examples,power steering systems in the modern vehicles, power-assistedwheelchairs [3], and wearable robots [4], [5] are all roboticsystems coexisting with humans.

Both the reference tracking performance and the impedanceof a robotic manipulator are related to and can be explainedby mechanical impedance. The mechanical impedance is aphysical quantity describing the sensitivity from the exter-nally exerted motions to the resistive forces generated bythe robot body. Namely, the safe human–robot interaction re-quires low mechanical impedance so that the robots do notexert a large resistive force to the human in case of a colli-sion [6], [7]. However, it should be noted that the low mechanicalimpedance makes the reference tracking performance vulnera-ble to a disturbance input. Therefore, the mechanical impedanceshould be high enough for the enhancement of reference track-ing performance (i.e., the precision of a controlled roboticmanipulator).

For the reference tracking, various motion control algorithmshave been investigated. For example, many researchers have pro-posed gain tuning processes for the performance enhancement ofa proportional-integral-derivative (PID) controller, which is themost popular and effective control method in industrial robotics.State feedback control methods, such as linear quadratic (LQ)control and H2 /H∞ control, have been modified for the im-proved performance (e.g., frequency-shaped LQ control [8],performance-weighted H∞ control, etc.). Sliding mode con-trol is one of the representative control methods that guaranteethe performance in nonlinear control systems. In the transfer-function approach, a disturbance observer (DOB) is noteworthy.The DOB estimates an exogenous disturbance and rejects it byfeeding the estimated signal back to the system. The DOB alsomakes the physical system follow the mathematical model as-sumed in the design of the DOB by treating the model discrep-ancy as an external disturbance. All of these control methods,however, significantly increase the magnitude of mechanicalimpedance of robotic manipulators, which threatens the safetyof humans in case of a collision.

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1908 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 19, NO. 6, DECEMBER 2014

The control algorithms for safe human–robot interaction havealso been investigated in recent years. Such control methodsinclude the impedance control [9], the natural admittance con-trol [10], and other force control. The impedance control, whichis usually used in rehabilitation robotics, controls robotic ma-nipulators so that the human (i.e., patients) can follow a mo-tion trajectory for rehabilitation. The natural admittance controlis a method to control a responsive force of an end-effectormaintaining its passivity. The natural admittance control isadequate for robotic systems that actively contact an object(e.g., atomic force microscopy). On the other hand, the typ-ical impedance control methods require the measurements ofinteraction forces exerted by the human. Force sensors, suchas strain-gauges and force-sensitive resistors, can be used forthis purpose. For more accurate measurement, a sensor fusionmethod is often accompanied [11]. In recent years, many effortshave been made to develop impedance control methods withoutforce sensors [12]–[16]. For this purpose, the DOB can also beutilized since it estimates the exogenous force without any forcesensor [17].

It should be noted that the DOB is adequate for both ref-erence tracking (when used as a feedback controller) and safehuman–robot interaction (when implemented as an observer).The achievements of such conflicting objectives are possible bydesigning a filter, called Q filter, in different ways. For the ref-erence tracking, the Q filter is to be designed as a low-pass filtersuch that the estimated disturbance is fed back into the systemand rejected. When the DOB is utilized for impedance control,the Q filter may be designed to have a phase shift of 180◦ suchthat the closed-loop system becomes sensitive to the externalforce [18].

In this paper, the Q filter is designed synthesizing these twodifferent approaches such that both the reference tracking andthe safe human–robot interaction with low impedance are guar-anteed in different frequency ranges. With this novel Q filterdesign, a whole control design framework is proposed whichis called frequency-shaped impedance control (FSIC), and thestability criterion of FSIC and the design approaches for thewhole control design framework are introduced. In addition tothe design of Q filter for frequency-shaping of the impedance,a feedforward controller is incorporated to enhance the trackingperformance that is compromised by the low impedance settingfor realizing the compliant interaction.

The proposed frequency-shaping impedance design usingthe Q filter is different from other frequency-shaping designmethodologies, since it takes into consideration the phase char-acteristics of the interaction. Most of the frequency-shapingcontrol methodologies consider only the gain characteristicsand design controllers through optimization processes. Com-pared to those algorithms, the design method proposed in thispaper does not use any optimization algorithm but designs aQ filter intuitively based on the physical interpretation of theimpedance in terms of the frequency characteristics. Moreover,due to the simplicity of the proposed design method, the orderof the controller is very low, while the output of the frequency-shaping controller design based on the optimization tends to bevery high order, which needs reduction of order.

This paper is organized as follows. The basic control frame-work of the FSIC is introduced in Section III. The details ofFSIC is explained and design approach to achieve frequency-shaped low impedance is introduced in Section II. The trackingperformance and robust stability are evaluated and the feedfor-ward control design is discussed in Section IV. Experimentalresults for the verification of the proposed method are given inSection V.

II. STRATEGY FOR FORCE SENSORLESS FREQUENCY-SHAPED

IMPEDANCE CONTROL WITH REFERENCE TRACKING

A. Frequency-Shaped Impedance for Human Safety Issue

The safety issue about robots interacting with humans haslong been discussed and recently formulated in several stan-dards such as ISO 10218 and ISO 13482 [19]–[23]. However,this safety issue is a large and significant problem that requiresa variety of approaches from various perspectives. In this paper,the safety problem is addressed only in terms of the physi-cal interaction between a robot and a human. The interactionbetween the two mainly consists of the interaction forces dueto the interference of motions, and the forces from the robotside against the human’s motion (which is identified with theimpedance) are considered the source of the danger in this in-teraction. Therefore, this paper focuses on characteristics ofreaction forces of the robot that is caused by the human’s mo-tions or the robot itself, and the safe human–robot interactionis achieved by realizing compliant response to the interactionforce and the interference of motions.

The force response of the robot against the human interactionis assessed by the sensitivity function of the feedback control,and in order to make the robot compliant to guarantee safety, thesensitivity function should be designed high (in the case whenno force sensor is utilized). This high sensitivity, however, dete-riorates the reference tracking performance of the robot whichmakes the robot fail to perform any given task. The referencetracking performance and low impedance (or, high compliance)is a tradeoff and cannot be achieved at the same time usingconventional linear time invariant controllers [16].

The approach to tackle this problem adopted in this paperis to utilize different frequency bands for reference trackingand low impedance, respectively. Since the human interactionis the main target of the impedance control, and the frequencyof the human motions is ranged in a certain band (e.g., from 0.5up 5 Hz [24], [25]), the impedance control is achieved in thatfrequency band.

While the frequency for the compliant interaction ranges inthe middle frequency bands, the frequency band where the refer-ence tracking should be achieved is low. Utilizing the differencebetween the frequency bands for two purposes, the proposedcontrol prioritizes the reference tracking performance in thelow frequency band and the impedance against the externalforce in the middle frequency band. In the high frequency bandwhere the modeling error and noises are exhibited dominantly,the controller should be designed mainly to achieve the robuststability.

OH et al.: FREQUENCY-SHAPED IMPEDANCE CONTROL FOR SAFE HUMAN–ROBOT INTERACTION IN REFERENCE TRACKING APPLICATION 1909

Fig. 1. Frequency bands for each control purpose.

Moreover, the control algorithm proposed in this paper incor-porates feedforward control in order to supplement the trackingperformance in the middle frequency bands that is compromisedfor the compliant human interaction. By this compensation, theresponse time of the system output with regard to the referencecan be enhanced. In order to incorporate the DOB and the feed-forward control design at the same time, two-degree-of-freedom(TDOF) control [17] is employed and modified in this paper. Bysynthesizing all these strategies, the proposed controller canachieve both compliant human–robot interaction and referencetracking performance.

B. Q Filter Design for Frequency-Shaped Impedance

In order to achieve these frequency-range-dependent pur-poses, one parameter is adopted: Q filter in the DOB [17].The Q filter which has been used just for the reference trackingand the robust stability, can be used for the impedance designtoo. Fig. 1 illustrates the guideline of the Q filter design for thereference tracking and impedance control; in the low-frequencyrange where the tracking performance should be prioritized,the magnitude of the Q filter should be 1 and its phase should be0◦, while in the middle-frequency range where the impedancecontrol is of the main interest, the phase of Q filter should be180◦. The magnitude of Q filter should be reduced in the high-frequency range to guarantee the robust stability and attenuatethe effect of sensor noises.

This frequency shaping of the impedance control which canalso achieve reference tracking is named FSIC, and the detaileddesign methodology is given in the following section. The ad-vantage of FSIC is its practicalness; the debugging and tuningof the proposed control can be done with ease since the Q filterdesign is the main control parameter.

In this paper, the plant that is considered in the design of theproposed control is limited in the stable second-order systemwhich has one integrator, since this is the most widely usedplant model of one-degree-of-freedom robot arm. However, thedesign methodology and stability criteria proposed in this papercan be extended to more complicated system.

III. FRAMEWORK AND DESIGN PROCEDURE OF

FREQUENCY-SHAPED IMPEDANCE CONTROL BY

TWO-DEGREE-OF-FREEDOM CONTROL

The TDOF control method [17] is often utilized to achievehigh precision tracking performance and disturbance rejection,

Fig. 2. Basic form of two-degree-of-freedom control with disturbanceobserver.

which is due to the robustness and high-gain nature of DOBs.The fundamental TDOF control algorithm consists of 1) a DOBthat detects the exogenous disturbance and the modeling dis-crepancy, which is treated as a lumped disturbance, 2) a feed-back controller to reduce a tracking error, and 3) a feedforwardfilter to enhance the tracking performance by compensating theclosed-loop dynamics.

A. Basic Framework of Two-Degree-of-Freedom Control

Fig. 2 is the basic form of TDOF control where C(s) is thefeedback control, F (s) is the feedforward control, P−1

n (s) isthe nominal inverse model of the plant P (s), and Q(s) is the Qfilter of the DOB. The shaded section is the DOB.

TDOF control has the following features.1) The sensitivity function modified by the DOB is param-

eterized by Q filter; (1 − Q(s)) is the most significantfactor in the sensitivity function, and external disturbanceis eliminated up to the frequency bandwidth of the DOB.

2) The DOB nominalizes the plant P (s) into the nominalmodel Pn (s) in the frequency bandwidth of Q filter. Thefeedback controller C(s) can be designed based on thenominal model.

3) The feedforward control F (s) can be designed based onthe nominal model to improve the response time, whichallows to design the reference tracking performance andthe disturbance elimination performance independently.

The independent design of the tracking and disturbance re-sponses is exploited in the FSIC; FSIC redesigns the responseagainst the external force f to realize compliant motions whilethe tracking performance is not significantly deteriorated.

B. Impedance Q Filter Design for Frequency-ShapedCompliant Motion

As explained above, Q filter is the key design factor in TDOFcontrol. Q filter is usually designed using a low-pass filter. Afirst-order low-pass filter in (1) is used as Q filter here for thesake of the simplicity

Qconv(s) =1

τq s + 1(1)

where τq determines the frequency bandwidth of the sensitivityfunction.

The analysis of force sensorless power assist control(FSPAC) [16], which we have proposed previously, revealed


Fig. 3. Frequency characteristic of the proposed impedance Q filter.

that the Q filter of FSPAC has negative phase characteristics forimproving the sensitivity of the closed-loop system in a positivefeedback manner. Taking this characteristic into consideration,a novel Q filter is designed here as

Qimp(s) =−τus + 1τls + 1

1τq s + 1

(2)

which has three parameters: τq , τu , and τl .τq works the same as the τq of the conventional Q filter

in (1) which determines the high cut-off frequency. τu is setlarger than τl so that the phase starts to shift toward 180◦ from1τu

rad/s. The ratio of τu

τlis the amount of the gain increase in

the frequency range from 1τu

(rad/s) to 1τq

(rad/s) where the phaseis set near 180◦. This novel Q filter to achieve the frequency-shaped impedance is called impedance filter in this paper.

Fig. 3 is the frequency characteristic of the Q filters, whereτq = 1

2π×3 , τl = 12π×0.7 , τu = 1

2π×0.5 . The curves labeled with“filter for assistance” represent the frequency response of a fil-ter −τu s+1

τl s+1 in the impedance Q filter. In the figure, the gainincreases from 1/τu (rad/s) and it reaches 20 log τu

τldB. The

phase characteristic also exhibits a large difference; the phaseof the conventional Q filter remains between 0◦ and 90◦, whilethe phase of the proposed impedance Q filter is shifted from0◦ to 180◦ around 1

τlrad/s. This is to bring the negative phase

characteristic into the proposed FSIC system as in [16].The impedance Q filter is designed as follows. First, the

frequency at which the compliant motion starts is determined byτu . Then, the desired gain increase (i.e., τu

τl) is designed, which

determines τl . Lastly, τq is designed to determine the bandwidthof the sensitivity function in the high-frequency range, in thesame way the conventional Q filter is designed.

C. Frequency Response of the Proposed Control

Impedance against the external force can be evaluated by thetransfer function from the force f to the output y in Fig. 2.This external force sensitivity function is calculated as (3) and

Fig. 4. Frequency responses against external force.

(4). The comparison between two force sensitivity functionsreveals that the filter (1 − Q) is the most important factor in theproposed impedance design

Tf.f b = Sf bP =P

1 + CP(3)

Tf.tdof = StdofP =P (1 − Q)1 + CP

. (4)

Fig. 4 is the force sensitivity functions with and without DOB,where the inertia J is set to 0.00892, and the damping B is set to0.0625. (Notice that the nominal model of a plant is assumed tobe the same as the actual dynamics of the plant in this discussion.The modeling error issues will be discussed in Section IV.)

P (s) =1

Js2 + Bs. (5)

The position feedback controller C is designed using the PDcontrol with the proportional gain set to 3 and the derivativegain set to 1. The feedback controller C should be designedtaking into consideration the novel Q filter design, i.e., the plantdynamics is nominalized only in the low-frequency range wherethe phase of Q filter is set to 0◦. The parameters of Q filters arethe ones used in Fig. 3.

In Fig. 4, the proposed impedance Q filter increases the forcesensitivity in a certain frequency range while the conventional Qfilter in DOB lowers the force sensitivity far below the feedback-only case. However, the force sensitivity by the impedance Qfilter is lower than the feedback case in the low-frequency range.

The compliant motion achieved by the proposed algorithmis different from FSPAC [16] which can design the mechani-cal impedance of the plant in the whole frequency range; theproposed control can achieve the compliant motion only in acertain frequency band while it rejects external forces in the low-frequency range, which can be useful for the reference tracking.

D. Impedance Control by the All Pass Filter

All pass filter which changes the phase characteristic at acertain frequency point without changing the gain characteristiccan be used for the Q filter for compliant motions. Equation (6)is the Q filter with an all-pass filter

Q(s) =−τas + 1τas + 1

1τq s + 1

. (6)


Fig. 5. Q filter with all pass filter.

Fig. 6. Frequency responses against external force with all pass filter.

Fig. 5 is the frequency characteristics of this Q filter withτa = 1

2π×0.5 and τq = 12π×3 where the gain characteristics of

the conventional Q filter and the proposed Q filter show thesame magnitude. On the other hand, the phase characteristicchanges from 0◦ to 180◦. Comparing with Fig. 3, the Q filterwith the all pass filter does not have any gain increase in themiddle-frequency range; there is only a phase change.

Fig. 6 is the force sensitivity of this Q filter, and the gain ina certain frequency range is increased to lower the impedance.This clarifies that the low impedance by the impedance Q filter isnot due to the gain increase τu

τlin (2), but the phase characteristic

of 180◦. This implies that the gain increase in the Q filter designis a tuning option, not the requirement; as long as the phaseis set to 180◦, the gain can be tuned to meet other controlrequirements such as robust stability which will be discussed inthe next section.

IV. TRACKING PERFORMANCE AND ROBUSTNESS

ANALYSIS OF FSIC

While impedance realized by the impedance Q filter is ana-lyzed in the previous section, the tracking performance and therobustness of FSIC against modeling error should be analyzedfor the proposed control to be practical enough.

Fig. 7. Robust stability analysis using multiplicative model uncertainty.

A. Tracking Performance of the Proposed Algorithm

Since the impedance Q filter affects the sensitivity functiononly in a certain frequency range, the overall tracking perfor-mance is not deteriorated significantly. Moreover, the sensitivityby FSIC is low in the low-frequency range, which results in smallor no steady-state error.

Basically, the proposed control is two-degree-of-freedomcontrol which has a feedforward control to design the track-ing performance independently from the disturbance rejectionperformance. Due to this feature, the tracking performance canbe kept the same even though the impedance Q filter changesthe disturbance rejection performance.

The tracking performance of the proposed control is validatedby the experiments in the following section.

B. Robustness Stability Analysis

Since the impedance against external forces by FSIC is basedon the DOB which uses a nominal model of the target plant,the robustness against the modeling error should be provided.Usually the robustness is evaluated using the small gain theoremto guarantee the robust stability [26].

When the plant with the uncertainty is given as (7), the closedloop system is stable when it meets the criterion of (8), wherePn (s) is a nominal plant model, Δ(s) is the uncertainty, andT (s) is the complementary sensitivity function

P (s) = Pn (s) (1 + Δ(s)) (7)

‖T (s)Δ(s)‖∞ < 0. (8)

In order to apply the small gain theorem, the complimentarysensitivity function in FSIC control is derived using Fig. 7. Thecomplimentary sensitivity function here is defined as the transferfunction from the input right after the uncertainty Δ(s) to theoutput to the uncertainty.

The derived complimentary sensitivity function is given in(10). Compared with the complimentary sensitivity functionwith the usual feedback control which is given in (9), Q fil-ter is added in the numerator in the FSIC case. Notice thatthis complimentary sensitivity function is the same with that ofTDOF control since FSIC has the same controller frameworkwith TDOF control

Tr.f b =CPn

1 + CPn(9)

Tr.tdof =CPn + Q

1 + CPn. (10)


Fig. 8. Complimentary sensitivity function for robust stability analysis.

Fig. 9. Robust stability analysis using complimentary sensitivity function.

The change in this complimentary sensitivity function by theimpedance Q filter is shown in Fig. 8. At first, the complimen-tary sensitivity function without the DOB is shown, and thecomplimentary sensitivity functions with three different typesof DOB are shown: the first is with the conventional Q filterdesign shown in Fig. 3, the second is with the impedance Qfilter shown in Fig. 3, and the last is with the all pass impedanceQ filter shown in Fig. 5.

TDOF control with the conventional DOB raises the gainof the complimentary sensitivity function compared with thefeedback-only case. The gain of FSIC is larger than the gainof TDOF control in the frequency range that is designed to becompliant against the external forces.

This fits to the general knowledge that the sensitivity to theexternal forces is also the sensitivity to the modeling error, whichleads to the fact that there are limits to the impedance that canbe achieved by FSIC due to this robust stability problem.

The complimentary sensitivity function of FSIC with the allpass impedance Q filter does not have large increase in the gain,which means the Q filter with an all pass filter does not sacrificethe robust stability significantly while it has a wide range andlow impedance as illustrated in Fig. 6.

In order to check the derived robust stability, simulationswith modeling errors are conducted. Fig. 9 is the relationshipbetween the complimentary sensitivity function with FSIC andthe simulated modeling error, where the dynamics of the plantis as (5) with J = 0.00892 and B = 0.0625 (which are fromthe dynamic model of the robot arm that will be used for thefollowing experiments), and the position feedback controller

Fig. 10. Step response with various modeling errors.

Fig. 11. Experimental setup. (a), (b), (c) are joints with actuators and (d), (e),(f) are robot frames.

C is a PD controller with the proportional gain of 3 and thederivative gain of 1. The nominal plant for the DOB is set toJn = 0.00892, Bn = 0.0625. In the simulation several valuesof J and B that are different from the nominal plant are used,and the stability is evaluated.

The result reveals that the system can be unstable when theinertia and damping of the nominal plant are set too larger thanthose of the real plant. Fig. 10 is the simulation of the timeresponse to the stepwise external force with the magnitude of10. The result shows the same result with the analysis in Fig. 9;the system becomes unstable when the inertia of the real plantis too smaller than that of the nominal plant. However, theproposed control can work stable with other several modelingerrors which meet the criteria of (8).

V. EXPERIMENTAL STUDY ON FREQUENCY-SHAPED

IMPEDANCE CONTROL

A. Robot Arm as an Experimental Setup

The proposed method is verified by experimental results witha three-link robot shown in Fig. 11. Each frame is driven by anac motor of 400 W. The joints and the motors are connectedby a belt. The belt introduces large nonlinearity due to its fric-tion and backlash, while the motor has inherent nonlinearityin the current-torque relationship. Such nonlinearities are to berejected by the DOB in the experiment.

In order to focus on the validation of the effectiveness of theproposed controller design, only the second joint is controlledand other two joints are locked in order not to affect the motionof the second joint. Extension of the proposed algorithm to themulti-input multi-output system will be the future work.


The parameters of the Q filters are set to τq = 12π×3 , τl =

12π×0.7 , τu = 1

2π×0.5 . The feedback controller in Fig. 2 is de-signed as a PD control with the gains Kp = 3 and Kd = 1.The nominal model of the arm is set to Jn = 0.00892 andBn = 0.0625.

B. Two Types of Human–Robot Interaction

FSIC addresses the safety problem in terms of the interactionbetween a robot and a human, where the interaction can be ledfrom either the robot side or a human, or both of them. TheQ filter should be designed based on the characteristics of thisinteraction. In the case when a human leads this interaction, theimpedance in the frequency band of human motions needs tobe set low by an appropriate Q filter. It is studied that there is alimitation in human motions in terms of frequency band, whichcan be assumed to be from 0.5 to 5 Hz [24], [25]. τu and τl in (2)can be set based on these studies, and the Q filter that is utilizedin the following experiments are set based on this too.

In this human-driven interaction case, the interaction oftenstarts from the zero velocity, which is the case of the experimentspresented in Section V-C; several types of external forces whichrepresent human interaction forces are applied to a robot whenthe robot is at rest, and the response of the robot against theexternal forces are evaluated in terms of compliance. This kindof interaction can guarantee the safety when a human body (orany part of it) is clamped or stuck by a robot; the human canexert his/her force to escape from the robot since the proposedcontrol can make the robot compliant against the human’s forceto escape from the robot and thus reduce the criteria such asviscosity criterion and compression criterion [27].

The interaction which is driven by a robot is the other type ofthe human–robot interaction. Large impact/contact force whichis one of the most significant danger factors in the human–robotinteraction belongs to this case, and it is usually evaluated usingcriteria such as head injury criterion [28]. Since the impact is avery fast dynamic process, the frequency band associated withthe impact is different from the frequency band of human mo-tions, which means the Q filter needs to be designed differentlyfrom the human-driven interaction case. Experiments to vali-date how FSIC can change the impact force in this interactionis given in Section V-E, and the results show that the frequencybandwidth of the low impedance should be set high by Q filterdesign to reduce the impact force.

C. Low Impedance Against Human Interaction Force

First, the impedance against human interaction forces is ver-ified. The response against external forces, which is consideredas human interaction forces, is evaluated. In order to apply theregulated external forces, additional motor torques with differentfrequencies are added as external forces. The output positionsof the robot arm are evaluated to examine how the impedanceof the robot arm changes according to the frequency by theproposed FSIC.

Fig. 12 shows the angles of the robot arm when the externalforces with the frequencies of 0.1, 0.5, 1, and 2 Hz are applied.

Fig. 12. Angle output against the external force. External forces are with 0.1,0.4, 0.7, 1, and 2 Hz.

Fig. 13. Comparison of the frequency response against the human interactiveforce with and without FSIC.

The input magnitudes are all set to 2 and the amplitudes ofthe angle represent the response of the robot arm against theexternal force. The result shows that the robot arm moves morecompliantly responding human interactive forces under FSIC.

In Fig. 12, the amplitude becomes the largest when the fre-quency of the applied force is around 0.4 Hz. In order to evaluatethe frequency characteristic of the impedance achieved by FSIC,the frequency response of the system is examined in detail; theangle responses against external forces with 12 different fre-quencies are measured. The ratio between the root mean squarevalues of the angle outputs and the input torques are calculatedfrom the experimental results as the frequency response of thecontrolled robot arm.

Three types of experiments are conducted: one is with FSIC,the second is without FSIC, and the last is without any feedbackcontrol. Fig. 13 is the obtained frequency responses.


Fig. 14. Response against a stepwise external force.

In the low-frequency range, the impedance of the case withFSIC is the largest, and in the high-frequency range, theimpedance with FSIC becomes smaller leading to the compli-ant response against the external forces. The feedback controllerwithout the impedance Q filter increases the impedance so thatthe system moves less compliantly compared to the case with-out the feedback. The impedance with FSIC becomes smalleraround 0.4 Hz than in other frequency ranges, which is the resultas designed in Fig. 4, and this verifies that FSIC can design thefrequency-shaped impedance using the impedance Q filter.

This frequency response shows that FSIC with an ade-quate design of the impedance Q filter can design the desiredimpedance according to the frequency range of the human in-teractive forces.

D. Reference Tracking Performance Evaluation

In FSIC, the sensitivity function is designed to provide smallimpedance in a certain frequency range, and the tracking per-formance can be guaranteed in other ranges. For example, thehuman interaction forces are in the moderately high-frequencyrange, while the friction force that should be rejected is in thelow-frequency range. FSIC can distinguish these two forcesbased on their frequency ranges and effectively reject the fric-tion force to achieve good tracking performance while it movescompliantly when the human force is applied.

In the following experiment, the robot arm is regulated to keepits original position and the stepwise external torque is added toexamine how FSIC reacts to this stepwise torque and keeps itsoriginal angle. Fig. 14 is the result which shows the applied ex-ternal torque (which is applied by the additional motor torque),the estimated external torque, the output of the impedance Qfilter, the output of PD control, and the angle value.

Soon after the step torque is applied, the applied torque isobserved by the DOB, and the impedance Q filter generates theopposite directional torque to make the robot arm compliantagainst the applied torque. As time goes on, however, the signof the output of the impedance Q filter reverses and increases.The output goes up to the value of the sum of the applied torque(which is 3) and the friction force of the robot arm (which is 1.3).This output is subtracted in the control input as in Fig. 2 and theangle of the robot arm comes back to the original position by thisoutput. The PD controller plays a role to suppress the deviation

Fig. 15. Angle output with the sinusoidal reference signal with the frequenciesof 0.1, 0.4, 0.7, and 1 Hz.

of the angle in the early phase of control, and the output of theimpedance filter becomes the dominant control input in the latephase of control.

This result shows that FSIC exhibits a good tracking per-formance same as the conventional DOB in the low-frequencyrange. However, in the moderately high or middle frequencyrange where the system becomes compliant, the performancemay be deteriorated. The feedforward control in Fig. 2 can re-cover this deterioration.

Additional experiments are conducted to verify the effective-ness of the feedforward control in the reference tracking. Anglereferences with different frequencies are applied to the robotarm and the tracking performance is evaluated. Two cases arecompared: one with the feedforward control and the other iswithout the feedforward control.

Fig. 15 is the result with the references of four different fre-quencies. Tracking performance without the feedforward con-trol is deteriorated at 0.4 and 0.7 Hz, where the small impedanceis generated by the impedance Q filter. With the feedforwardcontrol, however, the performance is recovered. This experi-ment verifies that the feedforward control in FSIC achieveshigh tracking performance in spite of the compromised highsensitivity for the low impedance.

E. Impact Force Reduction by FSIC

Experiments measuring the impact force during the interac-tion are conducted to evaluate how FSIC changes the impactforce. Fig. 16 illustrates the conducted experiments, where arobot arm is controlled to rotate at a constant angular velocityand makes an impact with an acrylic plate. The impact force


Fig. 16. Experiment of impact force measurement.

TABLE IEXPERIMENTAL RESULTS OF IMPACT/CONTACT FORCE REDUCTION

between the robot arm and the plate is measured using a loadcell which is located 10 cm away from the center of joint axis.

Three types of experiments are conducted, which are1) without the Q filter and only with the feedback control

C(s) and the feedforward control F (s) in Fig. 2,2) C(s) and F (s) with the Q filter (τl = 1

2π×0.7 , τu =1

2π×0.5 ),3) C(s) and F (s) with the Q filter (τl = 1

2π×1 , τu = 12π×0.5 ).

Since the characteristics of the impact process are determinedby the impact velocity, four different impact velocities are se-lected for each set of experiments, i.e., 3.49 (rad/s), 2.32(rad/s),1.74(rad/s) and 1.40 (rad/s). Each experiment is conducted tentimes, and the mean value and the standard deviation value ofthe peak impact forces are calculated. Table I is the experimentalresult of the experiments. Fig. 17 shows two sets of the exper-imental results in the time domain with two different impactvelocities.

The result shows that FSIC can reduce the impact force at lowangular velocities, while it cannot reduce the impact force at highangular velocities. The impact force at high impact velocity is avery fast dynamic process, which leads to the large magnitudeof the impact force in a short rising time as shown in Fig. 17(a).In order to reduce this fast impact force, the system needs toexhibit large compliance up to high-frequency range, whichrequires large τu

τland small τq in Q filter design. The results in

Table I and Fig. 17 show that the larger τu

τlcan perform better

in the impact force reduction.However, the large compliance in the high-frequency range

can cause the robust stability problem which is shown in Fig. 9,since there is unmodeled dynamics in the high-frequency range.Q filter design to reduce the impact force should take into con-sideration this tradeoff between the compliance and robust sta-bility. The analysis provided in Sections III-C and IV-B canbe a guideline for this design to reduce the impact force; Qfilter should be designed considering (4) and (10) to meet therequirements of compliance and robust stability.

(a)

(b)

Fig. 17. Measured impact forces at two different velocities. (a) Measuredimpact force at the velocity of 3.49 rad/s (b) Measured impact force at thevelocity of 1.40 rad/s.

VI. CONCLUSION

Frequency-shaped impedance control (FSIC) is proposed inthis paper. FSIC can reduce the impedance of a system in thefrequency range where the human interactive force is dominantand increase the impedance in the low-frequency range wherethe friction force is dominant. This frequency-shaped impedancecan be achieved by the DOB design framework and the proposedimpedance Q filter.

FSIC has feedback controller and feedforward controller toguarantee high tracking performance. The deterioration in thesensitivity function to lower impedance is compensated for bythe feedforward control. The low impedance and the trackingperformance of FSIC are verified by various experiments.

The proposed FSIC is a key technology for human-friendlymotion control that can make the motions of robots safe forhuman. It also can be applied to any assistive device wherethe shared control between the reference tracking and the hu-man force assistance is required at the same time. Even thoughthe experiments were conducted with one actuator, FSIC canbe applied to a multidegree-of-freedom robot arm taking intoconsideration the dynamics and kinematics of the arm.

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Sehoon Oh (S’05–M’06) received the B.S., M.S.,and Ph.D. degrees in electrical engineering from TheUniversity of Tokyo, Tokyo, Japan, in 1998, 2000,and 2005, respectively.

He was an Assistant Professor at TheUniversity of Tokyo until 2012 and a Senior Re-searcher at Samsung Heavy Industries from 2012 to2013. He was a Visiting Researcher at The Univer-sity of Texas at Austin from 2010 to 2011. He iscurrently a Research Professor at Sogang University,Seoul, Korea. His research interests include the de-

velopment of human-friendly motion control algorithms and assistive devicesfor people.

Hanseung Woo (S’12) received the B.S. and M.S.degrees in mechanical engineering from Sogang Uni-versity, Seoul, Korea, in 2012 and 2014, respectively,where he is currently working toward the Ph.D. de-gree in mechanical engineering.

His current interests include mechanical design,sensing, and control of active ankle-foot prostheses.

Kyoungchul Kong (S’04–M’09) received the B.Eng.degree (summa cum laude) in mechanical engineer-ing, the B.S. degree in physics in 2004, and theM.S. degree in mechanical engineering in 2006 fromSogang University, Seoul, Korea, and the Ph.D. de-gree in mechanical engineering from the Universityof California at Berkeley, Berkeley, CA, USA, in2009, where he later became a Postdoctoral ResearchFellow until 2011.

In 2011, he joined the Department of Mechani-cal Engineering, Sogang University, as an Assistant

Professor. He has authored or coauthored more than 80 technical articles injournals and conference proceedings in the area of control systems and mecha-tronics. His current research interests include design, modeling, and controlof mechatronic systems with emphasis on locomotion and mobility of human-centered robotic systems.

Dr. Kong received the Best Student Paper Award at the IEEE Conferenceon Advanced Intelligent Mechatronics in 2008 and the Best Paper Award in theDivision of Dynamic Systems and Control at the Korean Society of MechanicalEngineers Annual Conference in 2005.