Disturbance Observer based Linear Feedback Controllerfor Compliant Motion of Humanoid Robot

Mingon Kim1, Jung Hoon Kim2, Sanghyun Kim1, Jaehoon Sim1, and Jaeheung Park1,3

Abstract— Actuator modules of humanoid robots have rel-atively higher joint elasticity than those of industrial robots.Such joint elasticity could lead to negative effects on boththe tracking performance and stability for walking. Especially,unstable contact between the foot and ground caused by jointelasticity is a critical problem, as it decreases the stability ofposition-controlled humanoid robots. To address this problem,this paper introduces a novel control scheme for position-controlled humanoid robots by which we can obtain not onlyenhance compliance capability for unknown contact but alsosuppress the vibration caused by joint elasticity. To estimatethe disturbance caused by external forces and modeling errorsbetween the actual system and nominal system, a disturbanceobserver based estimator is designed at each joint. Furthermore,a linear feedback controller for the flexible joint model anda gravity compensator is considered to reduce vibration anddeflection due to the joint elasticity. The proposed controlscheme was implemented on our humanoid robot, DYROS-JET,and its performance was demonstrated by improved stabilityduring dynamic walking and stepping on objects.

I. INTRODUCTIONHumanoid robots have been widely developed to provide

the capability of mobility in human-centered environment.Especially, many studies have been focused on robust bipedalwalking because a humanoid should be able to traversenot only flat ground but also uneven terrain. However, asshown at the DARPA Robotics Challenge (DRC) Finals2015, bipedal walking remains one of the most difficult tasksin humanoid research [1].

One of the main reasons for instability in walking isthe difference between the actual robot and the estimatedmodel [2]. In particular, joint elasticity could exist at thegear transmission of the actuator in the real system. Ingeneral, the joint compliance of industrial robots is negligiblysmall, because actuator modules with heavy and strongmaterials have been extensively used to minimize vibrationand tracking errors. However, the actuator modules of ahumanoid are lighter and smaller than those of an industrialrobot because a humanoid robot must walk and manipulate

*This work was supported by the National Research Foundation ofKorea (NRF) grant funded by the Korea government (MSIP) (No.NRF-2015R1A2A1A10055798) and the Technology Innovation Program(10060081) funded by the Ministry of Trade, industry & Energy (MI,Korea).

1Mingon Kim, Sanghyun Kim, Jaehoon Sim, and Jaeheung Park are withGraduate School of Convergence Science and Technology, Seoul NationalUniversity, Suwon, Republic of Korea (mingonkim, ggory15,simjeh, park73)@snu.ac.kr

2Jung Hoon Kim is with the Center for Robotics Research,Korea Institute of Science and Technology (KIST), Seoul, Korea.j.h.kim@kist.re.kr

3Jaeheung Park is also with Advanced Institutes of Convergence Tech-nology(AICT), Suwon, Korea. He is a corresponding author of this paper.

objects under low power consumption [3]. For this reason,the actuator modules in a humanoid have relatively higherjoint elasticity than those in an industrial robot.

Because the aforementioned joint elasticity brings aboutunexpected vibrations and deflections of joints in a hu-manoid, it can lead to not only a walking performanceproblem but also an instability of the robot [4], [5]. Indeed,our previous work shows that joint elasticity can negativelyinfluence on the Zero Moment Point (ZMP) tracking, becausethe pelvis of our position-controlled humanoid, DYROS-JET,is tilted toward the direction of gravity during walking [6].

There are several researches to overcome the deflectionand vibration caused by joint elasticity. In [5], pelvis tiltingis compensated for by measuring the distance between thepelvis and ground using laser range finder. However, thismethod has the limitation that it cannot measure the deflec-tion of each joint. In our previous work [6], the deflection ofeach joint is compensated for by estimating gravity torquein a quasi-static system. Thus, the stability of a robot withthis algorithm could decrease during dynamic walking. Toreduce the vibration of ZMP during walking, a dampingcontroller with a linear inverted pendulum model is alsodesigned in [7]. In [8], a feed-forward controller based onan input shaping method is implemented. However, thesemethods ensure only the vibration suppression of ZMP, notthat of joints. The decentralized state feedback controller wasdeveloped to minimize vibration of each joint [9], [10]. Inthis controller, the input torque of the system is calculatedby using not only motor’s position and velocity but also jointtorque which is estimated by the elastic deformation betweenmotor and link position. However, in practice, it is difficultto obtain accurate joint torque because of low resolution ofthe encoder.

On the other hand, there are some researches to enhancecompliance capability of the humanoid, because an unex-pected contact force due to joint elasticity can cause therobot to lose balance. Impedance control [11] and dampingcontrol [12] methods have been proposed to adjust the footposition using measured contact forces. However, these con-trollers require accurate system model and can only changethe impedance of the foot. Also, adaptive neural impedancecontrol has been proposed to overcome model inaccuracyin [13], [14]. No prior information of the robot model isrequired because unknown system dynamics is estimatedby using neural network. However, the torque sensor isneeded to measure contact forces between the robot and theenvironment. Also, the disturbance observer [15] is designedto estimate the contact force and enhance the performance

2018 IEEE International Conference on Robotics and Automation (ICRA)May 21-25, 2018, Brisbane, Australia

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of force control. Furthermore, inverse dynamics control [16]and whole-body control [17] enhance the compliant perfor-mance of each joint and task. However, these methods cannotbe easily adopted to existing position-controlled robots.

In this paper, we propose a novel control scheme forposition-controlled humanoids not only to enhance compli-ance capability for unknown contact but also to suppress vi-bration caused by joint elasticity. To estimate the disturbancecaused by external forces and the modeling error between theactual system and nominal system, a disturbance observer(DOB) based estimator is designed at each joint. A linearfeedback controller with a flexible joint model and a gravitycompensator is also implemented to reduce vibration anddeflection due to joint elasticity.

The main contribution of the paper is as follows: First, thedisturbance from the modeling errors and unexpected contactforces can be observed using our DOB based estimatorequipped with the encoders and motor model. Thus, oursystem can estimate the disturbance by using the motormodel, even if the measured elastic deformation is noisy.Furthermore, no additional sensor such as a force/torquesensor is required for the proposed framework. Second,the DOB based linear feedback controller can not onlyminimize vibration but also ensure compliant motion ofeach joint. This controller moves each joint of the robot inthe direction of estimated disturbance. Finally, the proposedalgorithm is applied to the human-sized humanoid robot andits performance was demonstrated by experiments. We couldensure compliant motion for stable walking of the humanoidrobot despite unexpected contact forces between its foot andother objects.

This paper is organized as follows. In Section II, webriefly introduce the actuator model with joint elasticity. Wenext propose the DOB-based estimator for compliant motiontogether with the linear feedback controller to reduce vibra-tion in Section III. Section IV describes the experimentalprocedure and validates the effectiveness of the proposedcontrol scheme by using a 1-DoF testbed system and ahumanoid. Concluding remarks are given in Section V. Inthis paper, bold upper letter A, bold lower letter a, andlower/upper letter a/A indicate a matrix, vector, and scalar,respectively.

II. MODELING WITH FLEXIBLE JOINTS

To deal with the negative effects caused by high jointelasticity in humanoid robots, each joint of a humanoid robotis modeled to have a spring and damper as shown in Fig. 1.The dynamic model of an n-DoF humanoid robot in contactwith the ground is described by,

τ j =K(θm−θ j)+D(θm− θ j), (1)

Jmθm = τm−τ j, (2)

M(θ)θ+b(θ, θ)+g(θ)+JTc fc = S

T τ j, (3)

where θm ∈ Rn, θ j ∈ Rn, τm ∈ Rn, and τ j ∈ Rn denotethe motor angles, joint angles, motor torque, and joint

K

D

jθjτ

mθmτ

M

mJ

< Motor >< Link >

Fig. 1: Dynamic model of humanoid flexible joint

LinearFeedbackController

Humanoid Robot

Gravity Compensator

Disturbance Observer

Based Estimator

Fig. 2: Control flow of proposed method with gravity com-pensator, DOB based estimator, and LQR based controller

torque vector, respectively. K ∈Rn×n and D ∈Rn×n are thediagonal matrices for the spring and damping coefficientsof the motor’s gear, and θ = [θv θ j]

T ∈ R6+n consistsof virtual joints (θv ∈ R6) for the floating base robot andjoint angles, while M(θ) ∈ R(6+n)×(6+n), b(θ, θ) ∈ R6+n,and g(θ) ∈ R6+n are the joint space inertia matrix, thevector of Coriolis and centrifugal torques, and the vector ofgravitational torques, respectively. Jc ∈ Rm×(6+n) and fc ∈Rm are the contact Jacobian and contact wrench, respectively.Finally, S = [0n×6 In×n] ∈ Rn×(6+n) is the selection matrixwith the first 6 virtual joints.

Because position-controlled actuators have lower band-width than torque-controlled actuators, we can approximate(2) as the first order system with the command angles u∈Rn

and the motor angles θm ∈ Rn

θm =Kp(u−θm), (4)

where Kp ∈Rn×n is the proportional gain matrix of motors.Then, the dynamic model of a position-controlled humanoidrobot can be described using (1), (3), and (4).

III. CONTROL METHODOLOGY

This section is devoted to providing a control method forcompliant motion and vibration suppression in the systemmodel with flexible joints discussed in the previous section.More precisely, we consider control inputs consisting of

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three parts as shown in Fig. 2: the DOB based estimatorfor external force and the linear quadratic regulator (LQR)based trajectory tracking controller together with the gravitycompensator. The aim of these controllers is to achieve com-pliant motion of the humanoid robot and reduce vibration.

In the next subsections, we first describe the gravity com-pensator. The details of the proposed framework includingthe DOB based estimator and the linear feedback trajectorytracking controller are then presented in Section III-B andIII-C.

A. Gravity Compensator Design

Gravity torque in (3) can be estimated by using a systemmodeling of the robot. Thus, we design the gravity com-pensator with feed-forward action to compensate for gravitytorque. This concept was used in our previous research [6]and its effectiveness was validated through experiments withhumanoids.

Given contact forces of the right foot (fr ∈ R3) and leftfoot (fl ∈ R3), the estimated gravity torque (τg ∈ Rn) iscalculated by

τg = JTr fr +J

Tl fl , (5)

where Jr ∈ R3×n and Jl ∈ R3×n are the right and leftJacobian from the Center of Mass (CoM) to the contactpoints, respectively [12], [18].

Contact forces of the right and left foot can be obtainedby considering the total weight of the humanoid f ∈R3 andthe relative CoM position with respect to feet, as below:

fr = µf ,

fl = (1−µ)f ,(6)

whereµ = |pcom−pl

pr−pl|. (7)

In (6), pcom ∈ R3, pr ∈ R3, and pl ∈ R3 are the positionvectors in the global frame of the CoM, right foot, and leftfoot, respectively. Note that gravity torque in (5) is uniquelyobtained during a single support phase, because µ is 0 (leftsupport case) or 1 (right support case).

Finally, for the position-controlled robot, the estimatedtorque in (5) is compensated for by the feed-forward ac-tion [6],

ug =K−1τg, (8)

where ug ∈ Rn×n is the control input for gravity compensa-tion and K−1 is the inverse of spring coefficients in (1).

B. DOB Based Estimator Synthesis for Compliant Motion ofHumanoid

This section presents the estimator synthesis method forcompliant motion of humanoids using the concept of theDOB. The modeling errors between the real system andour proposed nominal system and external force betweenthe robot and the environment can be estimated using theDOB based estimator, and its connection to the real system isconsidered to achieve compliance capability. Here, it shouldbe remarked that even though most of the conventional

Disturbance Observer Based Estimator

Fig. 3: Structure of proposed DOB based estimator

studies [19], [20] relevant to the DOB based estimator is toreduce the effects caused by the disturbance, the proposedmethod can be interpreted as a new concept to achievecompliance capability.

The estimator discussed in this paper does not involve aforce/torque sensor, but it is designed using information fromthe motor’s encoders. More precisely, the disturbance frommodeling errors and external forces in the treatment of (4)could be estimated by designing the DOB based estimatorfor each joint as shown in Fig. 3, where P(s), Pn(s), Q(s)and Kdist denote the real system, the nominal system, the firstorder low pass filter and the weighting gain, respectively.

The dynamics of the real system P(s) is given by

θm = P(s)(u′+d), (9)

where u′ denotes the plant input consisting of the controlinput uc and the estimated disturbance d i.e.,

u′ = uc + d. (10)

Here, the estimated disturbance d is obtained by

d = KdistQ(s)(P−1n (s)θm−u′)

= KdistQ(s)(P−1n (s)P(s)(u′+d)−u′)

= KdistQ(s)((P−1n (s)P(s)−1)u′+P−1

n (s)P(s)d), (11)

where the first and second terms on the right-hand-side(RHS) in (11) correspond to the modeling error and thedisturbance caused by external forces, respectively. As wecan see in (11), the value of Kdist determines how muchmodeling error and the disturbance caused by external forceswill be reflected as the estimated disturbance in the proposedcontrol framework.

As a preliminary step to deal with the effect of Kdist , wefirst note from (10) together with (11) that

u′ =(1−KdistQ(s)(P−1n (s)P(s)−1))−1uc+

(1−KdistQ(s)(P−1n (s)P(s)−1))−1KdistQ(s)P−1

n (s)P(s)d(12)

Here, let us assume that the modeling error between P(s)and Pn(s) can be described by

P−1n (s)P(s) = 1+∆(s) (13)

405

where

|∆(s)|s= jω ≤ δ << 1 (∀ω ∈ (−∞,∞)) (14)

This assumption means the boundedness of the modelingerror in the frequency-domain and has been naturally dealtwith in several studies on control engineering [21]. Combin-ing (9), (10), (12) and (13) leads to

θm =P(s)(1−KdistQ(s)∆(s))−1uc+

P(s)((1−KdistQ(s)∆(s))−1KdistQ(s)(1+∆(s))d +d)(15)

If we note for a quite small KdistQ(s)∆(s) that

(1−KdisdtQ(s)∆(s))−1 =1+KdistQ(s)∆(s)+

(KdistQ(s)∆(s))2 + · · · (16)

then (1−KdistQ(s)∆(s))−1 can be almost equivalently treatedby

(1−KdistQ(s)∆(s))−1 ≈ 1+KdistQ(s)∆(s) (17)

Thus, (15) can be further simplified by

θm ≈P(s)(1+KdistQ(s)∆(s))uc+

P(s)(1+KdistQ(s)∆(s))KdistQ(s)(1+∆(s))d +P(s)d

≈P(s)uc +P(s)(1+KdistQ(s))d (18)

Hence, we can see from (18) that the gain of Kdist playsan important role in ensuring compliance of the system. Forexample, as the gain becomes larger, the motor angle rotatesmore in the direction of the disturbance. Thus, the robotsystem is to be more compliant to the disturbance causedby the modeling errors and external forces. It would beworthwhile to note that such a compliant motion could allowus to obtain stability against external force disturbances suchas an unexpected collision between a foot and an object. Forexample, a negative value of Kdist would make the robotkeep to proceed with the collision direction, while a positivevalue of Kdist could let the robot avoid proceeding such adirection. In this sense, the value of this gain can be decideddepending on the task of the robot system considering (18).

C. LQR based Trajectory Tracking Controller Synthesis

With respect to tracking performance for an arbitrarydesired angle trajectory, this section considers the LQR basedcontrol scheme. Because we assume that the gravity torqueis totally compensated by the gravity compensator whichis discussed in Sec. III-A and the Coriolis and centrifugaltorques are ignored by assuming a slow walking motion in(3), we obtain the simple relation given by

θ j = Sθ = SM(θ)−1(I−Pc)STτ j =: Smτ j, (19)

where Pc = JcT Jc

T . The Matrix Jc is the dynamicallyconsistent inverse of contact Jacobian Jc [17]. Note thatcontact Jacobian Jc is the Jacobian of a supporting foot,which is either left or right foot depending on the state of

the robot. The contact Jacobian is changed to the Jacobian ofthe other foot at the midpoint of the Double Support Phase.

If we define the state variable, output, and control inputas x(t) = [θm θ j θ j]

T ∈ R3n, y(t) = [θ j] ∈ Rn, and uc ∈Rn, respectively, the associated state-space representation isdescribed by combining (1), (4), and (19), as below.

x(t) =Ax(t)+Buc(t)

y(t) =Cx(t),(20)

where

A=

−Kp 0n×n 0n×n0n×n 0n×n In×n

Sm(K−DKp) −SmK −SmD

∈ R3n×3n,

B =

Kp0n×n

SmDKp

∈ R3n×n,

C =[0n×n In×n 0n×n

]∈ Rn×3n,

Next, we derive an augmented error system to transformthe tracking problem into a regulator problem, as below.

ddt

[e(t)x(t)

]︸ ︷︷ ︸

x

=

[0n×n C03n×n A

]︸ ︷︷ ︸

A

[e(t)x(t)

]+

[0n×nB

]︸ ︷︷ ︸

B

uc(t)

−[In×n03n×n

]θd(t),

(21)

where, e(t) = y(t)−θd(t)∈Rn is tracking error and θd(t)∈Rn is the desired angle of the robot.

Because we generate the reference trajectory θd(t) withθd(t) ≈ 0, we deal with the following LQR problem byassuming θd(t) = 0 in (21):

J =∫

∞

t=t0(eT (t)Qee(t)+ xT (t)Qxx(t)+ uT

c (t)Ruc(t))dt

(22)On the RHS of (24), the first term denotes a quadratic

cost of tracking error. Further, the second and third termsmean the regularization cost for the derivative state variable,and derivative control input, respectively. Furthermore, thestate cost-weighting matrices Qe ∈ Rn×n and R ∈ Rn×n aresymmetric positive definite matrices, and Qx ∈ R3n×3n is asymmetric non-negative definite matrix.

Locally optimal policy is obtained by solving the algebraicRiccati equation for the matrix, S:

ATS+SA−SBR−BTS+Q= 0, (23)

where Q ∈ R4n×4n is a block-diagonal matrix with Qe

and Qx. The derivative of optimal control input of linearfeedback control is as follow.

uc(t) =−Kx(t), (24)

where K =R−1BTS.

406

1

2

4

2

1

3

Actuator with external encoder Load

Obstacle

4 FT sensor

3

(a)

(b)

Roll

Pitch

Yaw

370

373

96839

795

(c)

Fig. 4: Experimental system overview: (a) 1-DoF testbed, (b)DYROS-JET, (c) configuration of joint of DYROS-JET

Consequently, as shown in Fig. 2, the final control inputfor the proposed framework u(tk) can be calculated by

u(tk) = uc(tk)+ d(tk)+ug(tk)

= uc(tk−∆ t)+∫ tk

t=tk−∆ tuc(t)dt + d(tk)+ug(tk),

(25)

where ∆ t is the control period of our system. In (25), thefinal control input for tracking the desired angle, u(tk), canbe calculated by previous control input, uc(tk − ∆ t), theincremental control input, uc(t), that minimizes the costfunction, and the disturbance caused by external force, d(tk).Therefore, our control input is helpful to not only decreasevibrations of the robot but also ensure compliant motion.

IV. EXPERIMENTS

The proposed algorithm was verified through experimentswith a 1-DoF testbed and our humanoid robot, DYROS-JET.First, we performed experiments using the 1-DoF system tovalidate compliance capability and vibration suppression of

Object contact Overload protection

(a)

Overload protection

Object contact

(b)

Fig. 5: Experimental results when unexpected object inter-feres with the motion of robot: (a) measured joint angle, (b)measured force of the proposed algorithm (red dash-dot line)and PID Controller (blue dot line)

our proposed algorithm when external forces were applied.Second, experiments with the humanoid were performed toverify that the proposed algorithm shows better performanceand stability compared with our previous walking con-troller [22] when the robot walks on a flat terrain and stepson un recognized objects. The subsections below describe thedetails of our experimental systems and validation results.

A. System Overview

As shown in Fig. 4(a), our testbed consists of an actuatormodule with an external encoder for measuring the deflectionof joints. A commercial actuator module, Dynamixel Pro(H54-200-S500-R, ROBOTIS Co., Ltd), is used as the actu-ator module of the system, and the rotary magnetic encoder(RLC2ICA13BK00A00 with MR075E060A120B00, RLS Co.)is attached to the outside of the actuator module.

Also, Figure 4(b) and 4(c) present our humanoid robot,DYROS-JET, and its joint configuration. Our hardware, JET,is an upgraded THORMANG model to increase manipulabil-ity and workspace [23]. Compared with the original platform,DYROS-JET is taller and lighter. The height, weight, andwingspan are 1.63m, 48kg, and 2.12m, respectively. JETconsists of a total of 32 DoFs: eight in each arm (with thegripper), six in each leg, two in the waist, and two in theneck. Each actuator module with an external encoder used in

407

Fig. 6: Experimental results when the impact force is applied.Measured joint angle of the proposed algorithm with highgain (Kdist = 1, red dash-dot line), that of the proposedalgorithm with middle gain (Kdist = 0.5, green dash line),and that of PID controller (blue dot line).

JET is identical to that of the testbed. The control frequencyis 200Hz.

In all experiments, the actuator’s spring coefficient K,damping coefficient D, and the proportional gain Kp in (4)were 2000, 100, and 10, respectively. And the cost state-weighting matrix Q and R for the LQR controller are thediagonal matrix of 10 and 1, respectively.

B. Experiment Using Testbed

We conducted two experiments with the testbed to verifythe effectiveness of the DOB based estimator and LQRcontroller. First, to demonstrate the compliance capabilityof the proposed algorithm, an experiment was conducted inwhich the object (in Fig. 4(a)) interferes with the motion ofthe load attached to the actuator. Figure 5(a) and 5(b) showthe desired and measured joint angle, and the contact forceat the end of the link during the experiment, respectively.The actuator with the proposed algorithm was compliant to asmall contact force (20N∼40N) at 2.3 s when it encounteredunexpected contact, as in Fig 4(a). However, in the sameexperiment, the actuator with the PID Controller turned offafter 1.5 s of contact because the contact force was too large(≥ 70N).

Next, a momentary external force was applied to theload of the testbed to validate the performance for vibrationsuppression. Figure 6 shows the measured joint angle of theLQR controller with the proposed DOB and a PID controller,when an impact force of 80N was applied. Although thepeak of first oscillation of the proposed algorithm withthe gain of 1.0 (0.079rad) is larger than that of the PIDcontroller (0.038rad), the vibration is then quickly reducedin the proposed algorithm. This is because the LQR basedcontroller with the flexible model in Sec. III-C is used tocompensate for the vibration due to joint elasticity.

Further, as shown in Fig. 6, the result of the proposed

algorithm with high gain (Kdist = 1.0) shows more compliantmotion than that of the proposed algorithm with middle gain(Kdist = 0.5). However, the steady state error (0.0021rad) ofthe proposed method with high gain (Kdist = 1.0) is relativelyhigher than that with the middle gain (0.0012rad). As men-tioned in Sec. III-B, the estimated disturbance includes notonly the disturbance due to external force but also modelingerror. Thus, the steady state error due to modeling error mayincrease when Kdist is high.

Overall, the use of our proposed algorithm could greatlyenhance compliance and reduce vibration by external forces.

C. Experiment Using Humanoid

Based on our walking control scheme including theinverse kinematic controller and the trajectory generatorfor ZMP and CoM [22], the proposed algorithm with thegravity compensator and the DoB based LQR controller(GC+LQR+DOB) is implemented on the legs of the hu-manoid to validate stability and performance during lo-comotion. Likewise, three algorithms are implemented forcomparison experiment, as below: our default walking con-troller [22], the walking controller with only the proposedgravity compensator (GC), the walking controller with thegravity compensator and LQR controller (GC+LQR).

As mentioned in Sec. IV-A, the matrices, Kp, K, D, Q,and R in experiments with the humanoid, were the sameas those in the previous experiments because the actuatormodules in the testbed are the same as those of the humanoidrobot. However, the feedback gain for accommodating ex-ternal forces Kdist has different values, depending on thewalking phase. In our experiments, Kdist was set to 0.2 tominimize the trajectory tracking error always except for thelanding period. During the landing phase, the gain of thelanding leg was changed to 1.0 to overcome the unexpectedcontact with objects. As mentioned in Section. III-B, one ofthe advantage of our algorithm is that the feedback gain canbe changed depending on the situation.

In the first experiment, the robot walked on a very flat sur-face with a quasi-static motion (0.8 s of single support timeand, 3.2 s of double support time). As shown in Fig. 7(a),when the robot walked with low speed, the ZMP trackingperformances of the walking controller with GC+LQR andGC+LQR+DOB were obviously better than those of the othercontrollers. This is because the proposed LQR controlleralone can suppress the small vibration, during slow walking.

Next, Fig. 7(b) shows the measured ZMP and the desiredZMP in the lateral direction when the robot walked on thesame flat surface with dynamic walking. We set the singlesupport time and double support time were 0.8 s and 0.3 s,respectively. As shown in Fig. 7(b), the result of the proposedalgorithm shows better tracking performance and vibrationsuppression than those of the walking controller with GCand GC+LQR. This is because DOB based estimator andLQR based controller in the proposed framework ensuresthe compliance to absorb impact force when the leg of therobot landed on the ground. In case of other controllers, the

408

Double Support Phase

Single Support Phase

(a) (b)

Fig. 7: Desired and measured ZMP positions: (a) when the single support time and the double support time are 0.8 s and3.2 s, (b) when the single support time and the double support time are 0.8 s and 0.3 s. GC, GC+LQR, and GC+DOB+LQRindicate walking controller with gravity compensator walking controller with gravity compensator and LQR based controller,and walking controller with the gravity compensator, DOB based estimator, and LQR based controller, respectively. Thepurple box denotes foot placement of the humanoid.

7.2s 7.6s 8.3s 8.8s 9.4s

Fig. 8: Snapshots of DYROS-JET stepping on objects with the proposed algorithm.

measured ZMP trajectory was sometimes on the edge of thefoot. Even, the robot with the default algorithm could notwalk.

Finally, the robot with the proposed algorithm steppedon unexpected objects to verify the compliance capacity ofthe robot. Figure 8 shows the sequence snapshots, whenDYROS-JET stepped on an unknown object. Although ex-ternal force was applied on the landing foot by unexpectedcontact between the foot and obstacle, walking stabilitywas preserved because our controller could estimate andaccommodate the disturbance with our proposed controllers.

Consequently, overall results from experiments with thehumanoid show that the stability of walking is dramaticallyimproved by the proposed algorithm. The video clips of theexperiments described in this paper are available in [24].

V. CONCLUSIONSIn this paper, a novel DOB based control framework for

compliant motion of humanoid robots is proposed. The DOBbased estimator in each joint is designed to estimate theexternal force and modeling error between the real systemand nominal system. Also, LQR-based trajectory trackingcontroller with the gravity compensator is implemented toaccount for minimizing vibrations caused by joint elasticity.The main contributions of this work are summarized as fol-lows. First, the DOB-based estimator is designed to enhancecompliance capability by actuating joints in the direction ofthe estimated disturbance. The compliance performance ofthe estimator is validated by several experiments with thetestbed and the humanoid. Second, the proposed observer-based estimator can estimate disturbances without additionalsensors. Third, LQR-based controller with a flexible jointmodel can suppress the vibration caused by joint elasticity.

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Finally, and most importantly, the walking stability of thehumanoid robot is dramatically enhanced using the proposedframeworks. Especially, the proposed framework works notonly in dynamic walking with a 1.1 s single step time, butalso in stepping on objects. The ZMP tracking error waswithin 2cm from the reference ZMP trajectory. Our futurework will involve the extension of the proposed algorithmto the whole-body of the robot to enhance stability duringwhole-body contact.

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