Stabilization for the Compliant Humanoid Robot COMAN Exploiting

Stabilization for the Compliant Humanoid Robot COMAN ExploitingIntrinsic and Controlled Compliance

Zhibin Li, Bram Vanderborght, Nikos G. Tsagarakis, Luca Colasanto, and Darwin G. Caldwell

Abstract— The work presents the standing stabilization of acompliant humanoid robot against external force disturbancesand variations of the terrain inclination. The novel contributionis the proposed control scheme which consists of three strategiesnamed compliance control in the transversal plane, bodyattitude control, and potential energy control, all combinedwith the intrinsic passive compliance in the robot. The physicalcompliant elements of the robot are exploited to react at the firstinstance of the impact while the active compliance control isapplied to further absorb the impact and dissipate the elasticenergy stored in springs preventing the high rate of springrecoil. The body attitude controller meanwhile regulates thespin angular momentum to provide more agile reactions bychanging body inclination. The potential energy control moduleconstrains the robot center of mass (COM) in a virtual slopeto convert the excessive kinetic energy into potential energyto prevent falling. Experiments were carried out with theproposed balance stabilization control demonstrating superiorbalance performance. The compliant humanoid was capable ofrecovering from external force disturbances and moderate oreven abrupt variations of the terrain inclination. Experimentaldata such as the impulse forces, real COM, center of pressure(COP) and the spring elastic energy are presented and analyzed.

I. INTRODUCTION

Humanoids potentially have greater mobility than wheeledsystems over rough/uneven and unstructured terrain due tothe ability to discretely select surfaces in a series of steps.However, this is seldom, if ever, achieved. This is becausehumanoids are permanently at risk of loosing their balancedue to unexpected disturbances, impacts and contacts whichwill occur due to interaction between the robot and theenvironment such as external forces and terrain variations.When such disturbances occur it is desirable that the robotshould have the ability to react and try to recover its bodybalance using different strategies, e.g for low or mediumdisturbances, posture regulation strategies may be enough tomaintain balance while for heavier impacts other strategiesshould be exploited such as taking a step [1].

This paper focuses on the development of a standing sta-bilization scheme to cope with low and medium force impactand terrain inclination disturbances, as shown in Fig. 1. The

This work is supported by the FP7 European project AMARSi (ICT-248311)

Zhibin Li, Nikos G. Tsagarakis, Luca Colasanto, and Darwin G. Caldwellare with the Department of Advanced Robotics, Istituto Italiano di Tec-nologia, via Morego 30, 16163 Genova, Italy [email protected],[email protected], [email protected],[email protected]

Bram Vanderborght is with Department of Mechanical Engineer-ing, Vrije Universiteit Brussel, Pleinlaan 2, Brussel, 1050, [email protected]

cmz 25.6 3.4NF 250max

Fig. 1. Scenarios of various disturbances and uneven terrains

contribution and novelty of the work is on the simplicityof the proposed stabilization control dedicated to positioncontrolled humanoids with simple requirement of sensorfeedbacks, and particularly its application on an intrinsicallycompliant humanoid robot. The stabilization method consistsof a compliance control module in the transversal plane, abody attitude control module, and a potential energy controlmodule. The proposed balance stabilization controller hasbeen successfully applied on the (COmpliant HuMANoid)robot COMAN recently developed at IIT [2] as a compliantextension of the stiff humanoid systems developed previouslyin [3], [4], [5].

Most of the high performance stabilization methods pre-sented in the literature are for humanoids powered by stiffactuation drives. In these systems, the ZMP criterion [6]has been extensively used to keep the robot dynamicallybalanced while walking. The stabilizer in the HRP-1S robotconsists of a ‘Body Inclination Control’, a ‘ZMP Damp-ing Control’ and a ‘Foot Adjusting Control’ [7], [8], [9].Without the stabilizer, the HRP-1S robot tipped although thejoint positions were tracked perfectly. The ‘Body InclinationControl’ regulated the foot position and orientation aroundthe desire ZMP coming from the motion generators, whichin fact created torques around the desire ZMP so the realZMP was modified. Asimo used a similar strategy called‘Ground Reaction Force Control’ to achieve this [10]. The‘ZMP Damping Control’ modulated the horizontal accel-eration of the torso based on ZMP errors measured fromthe force/torque sensor in feet which was the same as the‘Model ZMP Control’ used in Asimo [10]. ‘Foot AdjustingControl’ tracked new desired ZMP computed from the ‘BodyInclination Control’. But for Asimo robot, the ‘Foot LandingPosition control’ modified the position of the upcomingfoothold. With the above control strategies, both HRP-1S

Manuscript for research circulation only, please find official paper from IEEE

and Honda Asimo robot can walk on a level ground withcertain variations of uneven surfaces.

Although the previous stabilization techniques have beensuccessfully applied on stiff humanoid systems, the recentdevelopments of compliant humanoid platforms pose newchallenges on the balance stabilization. This is mainly dueto the increased complexity in modeling the dynamics ofthe system including the passive elasticity and its inducedoscillations characteristics. For the conventional stiff robots,the existence of passive compliance could cause instabilityif it is not effectively modeled and considered in the controlsystem of these robots.

However, there are several though advantages in havingphysically compliant elements in humanoids in terms ofadaptability to interaction uncertainties, shock absorption toimpacts and collisions. Compliance allows instantaneouslyresponse to impacts in contrast to solely active compliancecontrol which may not react sufficiently fast especially atthe first instance of the force impulse due to delays inthe impact detection, signal processing and reaction control[11]. Particularly humanoids are exposed to impacts andshocks during normal operation but also during accidentalconditions (falling down or during unexpected collisions witha hard environment). In such situation, the inherent elasticmechanical properties provide impact magnitude reductionto protect the robot. Another significant reason of havingpassive compliance is the possibility of improving the energyefficiency by storing and releasing energy into the elasticelements [12], [13], [14], [15] through the exploitation ofthe natural dynamics of the robot [16], [17], [18].

Inspiration for adding passive compliance can be alsotaken from biological systems where tendons and ligamentsact like passive compliant components. These compliantfeatures prevent the force peaks becoming too high duringthe foot ground impact and act as energy storage elementsin locomotion [19].

We therefore propose a stabilization control scheme whichutilizes the self-adaptation of the passive compliance forforce impact absorption and an active stabilization controllerfor dissipating the stored elastic energy. In this way, thecontrol system takes the advantage of the inherent compli-ance property to cope with impacts, and reduce the controlcomplexity.

The paper is structured as follows. Section II presents theprinciples of the stabilization control. Section III introducesextensive experimental results from trials executed with thecompliant humanoid COMAN. Finally, Section IV presentsthe conclusions and reports on future developments.

II. PRINCIPLES OF STABILIZATION CONTROL

This section introduces the principle of the proposedstabilization method which is based on the compliancemodulation of the humanoid body to buffer its disturbedmotion. It is resembled to the soft martial art reactiontechnique. When a person is encountering a punch, he/shedodges in the same direction of the punch in order toavoid hurt instead of moving against the punch. In this

des

cop

des

cop

y

x

cop

cop

y

x

comcomcomzyx ,,

,

des

pelvis

des

pelvis

des

com

des

com

des

comzyx ,,,,

+

+

- +

COM based Inverse

Kinematics

F/T sensor measurement

q

Force impact

Active Compliance

Control

real

cop

real

copyx ,

ref

pelvis

ref

pelvis

ref

com

ref

com

ref

com

z

y

x

Fig. 2. Stabilization control scheme

F

z

x

real

copx des

copx

F

real

copx des

copx

F

real

copx des

copx

0com

x

kk '0

comx

kk '

0com

x

kk 'Referential

COM

Real

COM

Fig. 3. Compliance control by regulating referential COM motion

control framework, the physical compliant elements play therole of instantaneous impulse force absorption and providemore time for the active compliance control to effectivelyexecute. The passive oscillations introduced by springs areeliminated by the active control to improve stability. Thecontrol diagram shown in Fig. 2 explains how the jointangles are updated based on feedback. The sensor feedbackis the overall center of pressure (COP) computed from theforce/torque measurements installed at feet.

A. Horizontal Compliance Control

Fig. 3 illustrates an inverted pendulum with torsion springconnected to a foot which represents the compliant robot,where k is an equivalent physical stiffness of the overallcenter of mass (COM) around the ankle and k′ is the resultantstiffness observed from the COM’s behavior. The real COMis marked black, the referential COM is marked red, and thecolliding obstacle is drawn in light blue. Fig. 3 shows howthe stiffness observed from contact interface can be regulatedby controlling the referential COM position. For example,when the real COM is disturbed backward due to the impact,the COP moves in the same direction. If the referential COMis regulated to move to the same direction as the COP, theobserved stiffness k′ reduces, in other words, the robot ismore compliant. Contrarily, if the desired COM moves inthe opposite direction as the COP, the observed stiffness k′

increases.The horizontal compliance control module is responsible

for regulating the compliance of the robot body along thetransversal plane based on the error of the COP. The com-pliance regulation is done through positional modificationof the COM based on the COP error. This is in analogywith the admittance control techniques where position per-turbations computed from the applied forces are added tothe reference position of a stiff position controlled robotto mimic compliant behavior. Let define the desired COMand COP at the static equilibrium xdescom, xdescop respectively,


and COM modification ∆xcom as the controller output, and∆xcop = xrealcop −xdescop is the error of control input. The samenotation applies for the y coordinate. The simple control lawsare expressed in a PID manner

∆xcom = kxp∆xcop − kxd∆xcop + kxi

∫(xdescop − xcop)∆t

(1)

∆ycom = kyp∆ycop − kyd∆ycop + kyi

∫(ydescop − ycop)∆t

(2)

, where kp, kd, and ki are the proportional, derivative, andintegral gains respectively, and ∆t is the sampling time.

Gain kp determines how much the desired COM shouldmove in the same direction as COP, therefore tuning ofthis parameters affects the resultant compliance observedfrom the COM behavior. Gain kd instead applies a dampingaction on the COM motion. In certain circumstances such aswhen the robot is standing still in flat, inclined or uneventerrain, the real COP will have an error compared to adesired one due to the spring compression. As the controlaction in the actuators of COMAN is on the motor sidebefore the compliant element, the link is passively deflectedunder the external load. Therefore, the integral term is usedto counterbalance the COP offset. As COP is related toCOM acceleration, its frequency spectrum is high. We areinterested here to eliminate only the static offset of COP. Forthis purpose, a low-pass filter (fc = 0.6Hz−0.8Hz) is usedto extract the low frequency component of the COP signalfor the integral term. The integral windup is addressed byusing a limited time window for integration and setting theupper and lower bound limits. xcop and ycop hereby denotethe low frequency component of the measured COP signal.

B. Body Attitude Control

Note that the COM based inverse kinematics has multiplesolutions given different orientation inputs. All solutionscan produce joint trajectories to realize the desire COMposition. However, the rotational dynamics of the COM alsosignificantly influences the robot response to the externaldisturbances.

The body attitude control utilizes the rotational dynamicsof the pelvis to minimize the spin angular momentum. Thetotal angular momentum of the robot consists of two terms:one is the orbital term caused by the linear momentum of theoverall COM about the pivot, which is unavoidable; the otheris the spin angular momentum caused by all the segmentsspinning around the overall COM. So zero spin angularmomentum means that the entire robot behaves as a pointmass and the moment of inertia felt by the external load isonly that of a point mass around the pivot mr2. The torquearound the COM of the entire rigid body would be zero,compensating inertia Ic as depicted in the right schema inFig. 4(a). Without controlling the spin angular momentum,the apparent inertia tensor will also include Ic, left schemein Fig. 4(a), resulting in slower reaction.

Pivot

CImr ,2

F

2mr

F

(a) (b)

Fig. 4. Influence of rotational dynamics (a) spin angular momentum shapesthe exhibited inertia (b) body attitude control.

Therefore, the idea of the upper body attitude control isto rotate the upper body in an opposite direction to that ofthe lower limbs, as shown in Fig. 4(b). In this way the spinangular momentum created by the upper body cancels outthe one generated by the legs, thus the net spin angularmomentum is minimized, Lx,y ≈ 0. This creates a moreagile reaction since the exhibited inertia is smaller.

The Tait−Bryan convention is used to denote the upperbody pitch θ and roll ϕ angles. The modification of thesereferential angles are computed by the following equations.

∆θ = −(kθp∆xcop − kθd∆xcop) + kθi

∫(xdescop − xcop)∆t

(3)

∆ϕ = kϕp∆ycop − kϕd∆ycop − kϕi

∫(ydescop − ycop)∆t (4)

Note that the expressions of ∆θ and ∆ϕ have oppositesign due to coordinate definition following right-hand rule asshown in Fig. 3. It should be noted that this control strategyis only suitable when combined with the compliance controlstrategy. Without the compliance control, solely modulatingthe upper body according to (3) only moves against theexternal perturbation and increases the contact forces.

The control law used in this work has no formulation of thespin angular momentum, thus its implementation is simple.However, in turn it relies on the numerical tuning of thegain values. Small gains wouldn’t be effective, and over largegains would cause self-oscillation. In addition, as the controlstrategy finally results in joint modifications at the motorside, the real Lx,y would be a small value fluctuating aroundzero instead of being a perfect zero value.

C. Potential Energy Control

In the single inverted pendulum model, the COM heightdecreases when moves away from the vertical position andthe potential energy converts into kinetic energy making thesystem unstable. In the case of the linear inverted pendulummodel, the vertical GRF has the same magnitude as gravityto keep the COM height constant. Consequently there is noconversion from potential energy into the kinetic energy.

The potential energy control stabilization strategy, pro-posed here, constrains the COM on a virtual slope surfacewith ascending gradient with respect to the desired static


Fig. 5. COM height modification ∆zcom with Dz = 0.01m

F/T sensor

for impact

measurement

Fig. 6. Experimental step-up of COMAN robot

equilibrium. When the COM is perturbed from the equilib-rium, it moves up this virtual slope thus the excessive kineticenergy partly converts into potential energy. This strategybecomes useful especially when the impact energy is closeto the absorption limit of the previous two strategies.

The formula to construct the virtual slope is given by:

∆zcom = kzpZ + kzdZ (5)

Z = Dz

2 − 2∆x2

cop+∆y2cop(Sx−xdes

cop)2+(Sy−ydescop)2+ 1

(6)

, where Sx = 0.1m,Sy = 0.13m are the distance fromthe center of support polygon to the edge in x, y coor-dinate respectively. The reference coordinate origin is themidpoint between the two ankle joints projections on thecontact surface. Dz is a scaling coefficient used to tunethe incremental height. Fig. 5 gives an example where thedesired COP locates at the center of the support polygon(xdescop = 0.04m, ydescop = 0m). The preset value of Dz dependson how much the COM height can still be increased usingthe leg extension. The more the knees bend, the bigger theDz can be. The construction of the virtual slope can havevarious formulations as long as the slope gradient is zero andcontinuous at the equilibrium.

III. EXPERIMENTS

The COMAN humanoid robot has compliant actuators atthe knee and ankle sagittal joints with a torsional spring stiff-ness of 120Nm/rad. More details of the mechanical designand specifications can be referred in [2]. Fig. 6 shows theexperimental set-up. A F/T sensor was installed just abovethe torso joint for monitoring the applied disturbance forces.

t=0s t=0.2s t=0.4s t=0.6s t=0.8s

Fig. 7. Snapshots spaced by 0.2s of stabilization against impact forces.

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rce

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]

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PeriodicPush withDifferentFrequencies

BackwardImpact

PushForward

ForwardImpact

30.9 30.95 31 31.05 31.1

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-50

0

40 ms

Fig. 8. Various force disturbances in x direction

Two 6-DOF F/T sensors located at the ankles measured thereal COP which is used as the feedback signal in the threestabilization strategies. The control loop runs at 1kHz. Toshow the effectiveness of the proposed control scheme, thefollowing experiments were conducted:

1) Application of various disturbance forces, includingstatic forces, periodic forces, and impulsive forces;

2) Slow and abrupt changes of the terrain inclination.

A. Experiments with Various Force Disturbances

Fig. 7 shows the snapshots of the stabilization against im-pulsive forces demonstrating the effectiveness of stabilizingthe compliant robot within 0.8s after the impacts. Fig. 8displays the different types of force disturbances applied; themaximum allowable forces in the backward direction that therobot can withstand without loosing balance were as high as250N with a duration of 40ms. This peak force was 137%of the robot overall weight (total mass 18.6kg). Fig. 9 showsthe responses of the real COM, COP and the reference COMposition xrefcom during the whole experiment.

In a micro time scale, Fig. 10 reveals the time delayof active compliance control during the impact starting at30.98s (Fig. 8). For a better comparison, the variables arescaled, and the time is reset zero. Fig. 10 indicates thatthe real COM position started to change when the impactapplied. However, the control output which is the referenceposition xrefcom, started to respond approximately 20ms afterthe impact applied. The first reason is that the COP feedbackwas under the feet and the impact went through all the


10 15 20 25 30 35 40 45−0.06

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0.1

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0.14

Time [s]

Pos

ition

[m]

xcomref

xcomreal

xcopreal

Fig. 9. Responses of xrefcom, xrealcom, and xrealcop

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

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−150

−100

−50

0

Time [s]

Impact Force

xcomreal

xcomref

Fig. 10. Responses of xrealcom and xrefcom after an impulsive impact

mechanism coupled by elastic joints. The springs in kneesand ankles acted as low-pass filters and introduced delay.Therefore the change of COP measured in feet occurredslightly later then the direct force measurement at the impactplace. The second reason is that the 6-DOF F/T sensor datahas been filtered to eliminate noises and this introducedsignal processing delay. Since the impulse force has aduration of 40ms (Fig. 8), this delay means that the activecompliance control started to react when the impulse forcealmost reached its maximum. The reaction of the robot at theinitial phase of the impulse was mainly due to the physicalelasticity integrated in the joints.

The reaction of the passive elasticity to the applied forcecan be also confirmed by observing the energy state in thesprings. As shown in Fig. 11 the initial elastic potentialenergy in all springs is 0.2J due to the compression causedby gravity, and it increases up to 1.71J when the impactforce is applied. The sharp increase of the elastic potentialenergy reveals the deflection of the spring and the energystored during the passive reaction phase, while the elasticenergy decay after the peak indicates the effective dissipationperformed during the active control phase.

Fig. 12 presents the waist pitch angle during stabilization.Fig. 13 compares the modified reference COM height zrefcom

and the measured one. It can be seen that this control modulewas more effective when robot was pushed backward ratherthan forward. This is because the desired COP was set atthe center of support area so gravity creates a torque offsetaround ankle. The gravitational torque became bigger whenCOM ground projection was more far away from ankle.Since the front foot section (14cm) was longer than the

5 10 15 20 25 30 35 40 45 500

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time [s]

Spr

ing

Ela

stic

Ene

rgy

[J]

Fig. 11. Total elastic energy in springs during stabilization

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−2

0

2

4

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8

Time [s]

Pel

vis

Pitc

h A

ngle

[deg

]

Fig. 12. Measured body pitch angle θ under sagittal perturbation

rear foot section (6cm), the gravitational torque affects morewhen the robot was pushed forward.

There are several interesting features found in lateralstabilization because lateral joints are stiff without passivecompliant components. In Fig. 14, it can be seen that a forceof approximately 250N was the maximum force that therobot could withstand without lifting one support foot underthe stabilization control. In Fig. 15, the modified yrefcom hada faster response to yrealcop compared to the sagittal case (Fig.9). Also the COM height control demonstrates good trackingunder the disturbances in both left and right direction. Thepelvis roll angle had fewer oscillations after disturbance asshown in Fig. 16 compared to the one in Fig. 12.

B. Experiments with Slow and Abrupt Terrain Disturbances

To demonstrate the robustness with the same controllaw, we tested the robot on a platform with slow andabrupt inclination variations. The slow inclination changewas shown previously in Fig. 1. Fig. 18 shows the snapshotsof the abrupt fall of the surface where the robot stood. Thefall created inclination of 4.3◦ in both sagittal and lateralscenarios. Fig. 19 illustrates the impact energy absorbed bythe springs when robot landed on the suddenly fallen surface.In the sagittal fall, the elastic energy reached up to 2.2J anddissipated within 4s − 5s. In the lateral fall, the absorbedenergy had a maximum of 1.8J , and decayed within 2.5s.

IV. CONCLUSIONS

This work presented a novel stabilization method for acompliant humanoid robot. The proposed method consistsof three main strategies referring as horizontal compliancecontrol, body attitude control and potential energy control.


10 15 20 25 30 35 40 45

0.414

0.416

0.418

0.42

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Time [s]

CO

M H

eigh

t Var

iatio

n [m

]

Desired COM HeightMeasured COM Height

Fig. 13. COM height zcom under sagittal perturbation

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]

Push toLeft

Push toRight

PeriodicPush withDifferentFrequencies

Impactto Left

Impactto Right

Fig. 14. Various force disturbances in y direction

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−0.04

−0.02

0

0.02

0.04

0.06

Time [s]

Pos

ition

[m]

ycomref

ycomreal

ycopreal

Fig. 15. Responses of yrefcom, yrealcom , and yrealcop

10 15 20 25 30 35−6

−4

−2

0

2

4

6

Time [s]

Pel

vis

Rol

l Ang

le [d

eg]

Fig. 16. Measured body roll angle ϕ under lateral perturbation

Extensive experimental trials with the compliant humanoidplatform COMAN successfully assessed and demonstratedthe superior stabilization performance achieved by the syn-ergetic combination of this active stabilization techniqueand the inherent passive stabilization properties of the robothardware. During these experiments, it was demonstratedthat the robot could withstand horizontal pushes, adapt to

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0.42

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Time [s]

CO

M H

eigh

t Var

iatio

n [m

]

Desired COM HeightMeasured COM Height

Fig. 17. COM height zcom under lateral perturbation

t=0s t=0.16s t=0.32s t=0.48s t=0.64s

t=0s t=0.08s t=0.16s t=0.24s t=0.32s

Fig. 18. Abrupt change of terrain inclination 4.3◦

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0.5

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1.5

2

Ela

stic

Ene

rgy

[J]

Abrupt Fall in Sagittal Plane

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0.5

1

1.5

2

Time [s]

Ela

stic

Ene

rgy

[J]

Abrupt Fall in Lateral Plane

Fig. 19. Elastic energy stored in spring during abrupt terrain test

slow or even sudden changes of the terrain inclination, andstand on rugged terrain. The experimental results confirmedthat passive compliance plays an essential role in stabilitybecause springs can react to instantaneous impulsive forces.This fast reaction to impacts and the absorption of the impactenergy permits more time for the active controller to react.In this way, during the first instance of the impulse, energyis stored in springs and subsequently dissipated by the activestabilization control preventing the spring recoil. In additionto the benefits related to the control performance, passiveelastic components filter the peaks of the impact forces,


protecting the hardware components such as bearings andgears, and improving the overall system robustness.

The sensory feedback in the presented work was solelybased on the force/torque measurement from feet. The robotis able to endure impact forces up to 250N in horizontalplane, and also adapt to the slope changes of 4.3◦ for abruptinclination and 6.5◦ for static inclination. To improve theadaptation to inclination and also for the case when the robotstarts to rotate around the foot edge, an inertia measurementunit is necessarily required. Future work will integrate theinertia measurements (IMU) together with the F/T sensordata to further extend the stabilization scheme and providemore agility for the disturbance rejection.

V. ACKNOWLEDGMENT

This work is supported by the FP7 European projectAMARSi (ICT-248311).

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[19] R. Alexander, Principles of animal locomotion. Princeton UniversityPress, 2003.


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Stabilization for the Compliant Humanoid Robot COMAN Exploiting