Center of Mass Estimator for Humanoids and its Application inModelling Error Compensation, Fall Detection and Prevention

X Xinjilefu, Siyuan Feng, and Christopher G. Atkeson

Abstract— We introduce a center of mass estimator, and itsapplication in full body inverse dynamics control, fall detectionand fall prevention for humanoid robots. We use the LinearInverted Pendulum Model dynamics with an offset to predictthe center of mass motion. This offset can be interpretedas a modelling error on the center of mass position, or anexternal force exerted on the center of mass of the robot,or a combination of both. The center of mass estimator isimplemented on our Atlas humanoid robot. During the DARPARobotics Challenge Finals, it successfully saved our robot fromfalling on two occasions, and made us the only competitiveteam without a fall or human physical intervention among allhumanoid teams.

I. INTRODUCTION

In order to achieve reliable estimation of humanoid robotCenter of Mass (CoM) motion, we need a model that explainshow the CoM moves under external forces. The LinearInverted Pendulum Model (LIPM) model is a natural choicegiven its simplicity [1]. We introduce an additional offsetterm into the LIPM dynamics. This offset can be interpretedas a modelling error on the CoM position, or an externalforce exerted on the CoM of the robot, or a combination ofboth. This paper introduces the CoM estimator, and its appli-cation in inverse dynamics, fall detection, and fall preventionfor humanoid robots. The estimator itself is similar to [2],but the implementation and application are different.

The estimation accuracy of a model-based state estimatorrelies on the model itself. For the Atlas robot, BostonDynamics provides both the kinematic and the dynamicparameters. The kinematic model is useful for manipulationtasks and foot placement during walking. The dynamicmodel is used by the controller to generate desired jointtorques. Both kinematic and dynamic models are used toestimate the full-body states of the robot [3][4].

A. Kinematic Modeling Error

The kinematic model is rooted at the pelvis. We experi-mented on the hand end effector to determine the arm kine-matic error. We put Atlas in double support, and controlledthe hand to follow a predefined trajectory. The trajectory wasa concatenation of manipulation task trajectories, because wecare about the kinematic model accuracy in those situations.We tracked the motion of the hand, feet, and pelvis usingan OptiTrack motion capture system with 8 cameras, andrecorded the marker data and robot data simultaneously at100Hz. We found that the hand end effector had on average

All the authors are with the Robotics Institute, Carnegie Mel-lon University, 5000 Forbes Ave, USA {xxinjile, sfeng,cga}@cs.cmu.edu

an error of about 1cm relative to the pelvis. The error fromthe motion capture system is negligible.

We also tested the leg kinematic error during doublesupport without the motion capture system, because we knowthat both feet are not moving in our test. We control thepelvis of the robot to follow a spiral trajectory in the coronalplane. The average error for the distance between the two feetis within 1cm.

There are several factors contributing to the end effectors’kinematic error. The joint position data we collected was pre-joint transmission (the sensors are on the actuator, not thejoint axis). It is computed based on the linear actuator lengthmeasured by the Linear Variable Differential Transformers(LVDT) which is affected by the loading conditions. Thesole pads beneath the robot’s feet are deformable up to afew millimeters. There are also backlash, play and structuraldeformation on the robot. These effects all contribute to thekinematic error between the two feet.

B. Dynamics Modeling Error

The dynamic model has mass, moments of inertia andcenter of mass location of each link as its parameters. Dy-namic parameters are generally not identified as accuratelyas the kinematic parameters. The error of these parametersis difficult to model individually because the dimension ofthe parameter space is high. We were not allowed to takethe robot apart to measure the inertial parameters. It is hardto account for flexible elements such as oil filled hoses thatcross joints in a rigid body model.

On the other hand, the dynamics of the center of mass ofthe robot can be modeled with a small number of parameters.A widely used control scheme for humanoids is two-levelhierarchical control. The high level controller generates thecenter of mass motion using a simple dynamic model, suchas the LIPM, and the low level controller tries to generate thefull-body motion given the center of mass motion. It is usefulfor the controllers to know accurately the motion of thecenter of mass. Due to modeling error of the link parameters,the center of mass position and velocity computed fromforward kinematics will have modeling error as well.

To observe the modelling error, we conduct a simplequasi-static experiment using our Atlas robot. The robotpelvis follows a spiral trajectory in double support. In anideal situation, where there is neither modeling error in thedynamic model parameters nor forward kinematics, and thefoot force/torque sensors are calibrated, the CoM shouldcoincide with the Center of Pressure (CoP) in the horizontalplane when the robot is static. We observe there is a nearly

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0

0.01

0.02

0.03

0.04

x[m

]

CoM

CoP

CoM − CoP

0 100 200 300 400 500 600 700 800

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

y[m

]

time[s]

Fig. 1. Computed CoM, measured CoP and their difference in the horizontalground plane.

constant offset between the CoM position computed fromkinematics, and the CoP computed from foot force/torquesensors and kinematics. Fig. 1 shows the computed CoM,measured CoP and their differences in the horizontal plane.

We derive the CoM estimator in Section II, and describeits implementation in Section III. In Section IV we discussthe application of the CoM estimator in fall detection andprevention. Section V concludes the paper.

II. THE CENTER OF MASS KALMAN FILTER

We use the following parameterization of the discrete timelinear Kalman filter,

xk+1 = f(xk, uk) = Axk +Buk (1)yk = h(xk) = Cxk +Duk (2)

The LIPM is a simplified model to describe the dynamicsof a humanoid robot. It assumes the CoM is at a constantheight, therefore the total vertical force must be equal to thebody weight at all times. The dynamic equation of LIPM inthe horizontal direction is given by Eq. (3)

xcom = ω2(xcom − ucop) (3)

where ω =√g/zcom is the LIPM eigenfrequency. xcom,

xcom and xcom are the position, velocity and acceleration ofthe CoM in the horizontal plane respectively (both x and ycomponents). ucop is the position of the CoP, g is gravity,and zcom is the CoM height relative to the CoP. In Eq. (3),ucop represents the total CoP.

The error of the LIPM can be modeled by an offset. If weassume the offset is changing relatively slowly, then its firstand second order time derivatives are both close to zero. Weformulate the CoM estimator with offset as a Kalman filter.It predicts the robot CoM position, velocity and offset in thehorizontal plane. The state vector for the CoM estimator isgiven by x = [xcom, xcom, xoffset]

T . We consider the CoPas an input to our state estimator. The process model uses

the LIPM dynamics to predict the CoM acceleration. TheLIPM dynamics with offset is given by Eq. (4)

xcom = ω2(xcom + xoffset − ucop) (4)

xoffset is the LIPM offset. The states are expressed in theworld coordinates. zcom is computed every estimation timestep by forward kinematics. The Kalman filter becomes timevariant due to zcom being a parameter in the state matrix Ain Eq. (5). The process model of the Kalman filter followsEq. (1). It has the following parameters:

A =

I + 12ω

2∆t2I ∆tI 12ω

2∆t2Iω2∆tI I ω2∆tI

0 0 I

,B =

− 12ω

2∆t2I−ω2∆tI

0

(5)

where ∆t is the time step, I is a 2 × 2 identity matrix.The observation model provides predicted measurement

from states. We choose xcom and xcom as predicted mea-surements. The measurement equation can be written as

yk =

[xcomxcom

]

=

[I 0 0ω2I 0 ω2I

] xcomxcomxoffset

+

[0

−ω2I

]ucop (6)

where the output matrix C and feedthrough matrix D inEq. (2) are given by

C =

[I 0 0ω2I 0 ω2I

], D =

[0

−ω2I

](7)

The measurement depends on sensors available to therobot. We use sensed joint position with forward kinematicsto compute CoM position. The root variables are estimatedusing the base state estimator introduced in [3]. For walking,the position error on the base is below 2% (20cm totalerror over a course of 10.12m, 26steps). Our odometryperformance is comparable to that reported in [5]: “over thecourse of the 25 steps our position drifted in XY Z by (0.2,0.0, 0.1) meters”.

Ideally, 6-axis force/torque sensors under the robot feetprovide information about external forces, which can beused to calculate the CoM acceleration in the horizontalplane. However, using the 3-axis (Fz , Mx and My) footforce/torque sensors on the Atlas, we can only compute theCoP in the foot frames. Alternatively, we approximate theCoM acceleration by transforming the acceleration measuredby the Inertial Measurement Unit (IMU) mounted on thepelvis to the location of the CoM. This transformationassumes that the CoM is on the same rigid body (pelvis)as the IMU. The transformation is given by:

acom = aimu + ωimu × (ωimu × r) + ωimu × r (8)

where acom is the approximated CoM acceleration. aimu andωimu are IMU measured acceleration and angular velocityexpressed in the world frame. r is the vector from IMU

to CoM computed using forward kinematics. ωimu is theangular acceleration of the IMU. It can be computed by finitedifferentiating ωimu. We assume a constant angular velocitymodel, so this term is zero. The x and y component of acomare used as measurement.

III. IMPLEMENTATION AND APPLICATION

We implement the CoM estimator on the Atlas robot.The filter noise parameters are summarized in Table I.The measurement noise parameters for the acceleration aredifferent for walking and for manipulation. Because thewalking motion is more dynamic than manipulation, we filterthe acceleration less in walking.

TABLE ICOM KALMAN FILTER NOISE PARAMETERS.

xcom xcom xoffset

Q 1e−10 1e−4 1e−10

Walking xcom xcom

R 1e−6 1e−3

Manipulation xcom xcom

R 1e−6 1e−2

*Q and R are process and measurement noise covariances.

The estimated offset plays several roles in the controlof the robot. The first application is to translate it into anexternal force acting on the robot CoM, and to apply theforce while solving the inverse dynamics using quadraticprogramming (QP) [6]. During early development, the offsetwas also used to bias the target CoM location while solvingInverse Kinematics (IK) for walking [7], IK is no longer usedin our walking controller. The second application of the offsetis to detect and prevent robot falling. In this case, the offsetis interpreted as a position offset of the robot CoM, and thenused to compute a corrected capture point. The details willbe discussed in Section. IV.

A. Kinematic Modelling Error Compensation

Due to pre-transmission joint position sensing and back-lash, play and compliance in the mechanism, the forwardkinematics model for Atlas is not very accurate. For station-ary single support stance, there can be up to 3cm offsetsbetween the model CoM from forward kinematics and mea-sured CoP. A simple linear torque dependant heuristic toreduce the effects of joint compliance is proposed by [8],which is also employed in our controller for the leg joints.

In addition to the pre-transmission joint position sens-ing, the shoulder and elbow joints are also equipped withincremental encoders that measure position changes. Theencoders provide more accurate joint position measurementbecause they are after the transmission. They can only beused after calibration. Our calibration procedure is to driveall the joints to the known mechanical joint limits and fitparameters to the offsets and scale factors. A very similarprocedure provided by Boston Dynamics is used to calibratethe electric forearms.

Fig. 2. Plot of the estimated CoM offset, and the difference between CoMand CoP after applying CoM offset during a static walk. The shaded greenregion is double support, the unshaded region is single support.

B. Dynamic Modelling Error Compensation

The estimated CoM offset xoffset can be interpreted as avirtual force fext = mω2xoffset applied at the CoM of therobot. Given the equation of motion of the full body floatingbase dynamics of a humanoid robot,

M(q)q + h(q, q) = Sτ + JTc (q)f (9)

where M is the mass matrix, h is the nonlinear vector ofgravity, Coriolis and centrifugal forces, Jc is the contactJacobian, f is the contract force, S is a selection matrix,and τ is the actuator torque. We add the estimated virtualforce fext to the right-hand side of Eq. (9) pre-multiplied bythe CoM Jacobian transpose JT

com,

M(q)q + h(q, q) = Sτ + JTc (q)f + JT

com(q)fext (10)

so that the modelling error can be handled properly by theinverse dynamics.

We demonstrate the effectiveness of our modelling errorcompensation approach in a forward walking experiment. InFig. 2, we show the estimated CoM offset, and the differencebetween CoM and CoP considering the CoM offset. If therobot is under a static configuration, the difference betweencorrected CoM and CoP should be zero. When the CoMis accelerating, LIPM dynamics explains the difference. Weobserve near zero difference in single support, and largedifferences during double support when the robot is shiftingits weight distribution across its supporting feet.

Fig. 3 is a plot of the CoM velocity from the Kalmanfilter, and from forward kinematics. The CoM velocity fromforward kinematics has noise injected from the measuredIMU angular velocity, and occasional spikes from the leftshoulder and wrist pitch joints. The estimated CoM velocityhas a lower noise level compared to that computed fromforward kinematics.

0 5 10 15 20 25

−0.1

−0.05

0

0.05

0.1

0.15xd

[m/s

]

KinematicsEstimator

0 5 10 15 20 25

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

yd[m

/s]

time[s]

Fig. 3. Plot of the estimated CoM velocity, from the CoM offset estimator,and from full body kinematics starting at the root.

IV. FALL DETECTION AND PREVENTION

Compared to wheeled and multilegged robots, humanoidsusually have a higher CoM and a smaller support region.This means a higher risk of hardware damage when fallingand a smaller stability margin. In a real world scenariowhere humanoid robots have to interact with the environmentwithout a safety belay system, fall prevention and recoverybehaviors are necessary. A good example is the DARPARobotics Challenge (DRC), where robots have to performdisaster response related tasks involving physical contactwith the environment. What we observed during the contestwas that most humanoids fell down. We will discuss ourimplementation of fall detection and prevention algorithmsusing the CoM estimator.

A. Background

Fujiwara’s group in JAIST has worked on fall controlof humanoid robots [9][10][11][12][13][14]. Their work fo-cused on minimizing impact during fall. Another line ofwork deals with fall detection. The general idea is to detectabnormality in sensor measurements or computed quantitiessuch as CoM and CoP. The methods differ in what featuresto use and how they are parameterized, whether the modelis built online or offline, and what algorithms are usedto detect abnormality. Sensor measurements are comparedwith sensor models in humanoid walking to determine thedynamic instability of the gait. The sensor model is builtoffline in [15], and a heuristic is used online in [16]. Ogataet al. detect abnormality through discriminant analysis andlearning [17][18], similarly, pattern classification is usedin [19]. Yun et al. introduced the concept of “Fall triggerboundary” which encloses a region in the robot’s featurespace where the balance controller is able to stabilize therobot [20].

B. Capture Point

The Capture Point (CP), introduced in [21], is the pointon the ground where a humanoid must step to in orderto come to a complete stop. If the humanoid dynamics isapproximated using the LIPM, the CP has a very simpleexpression as a linear combination of the CoM position andvelocity in the horizontal plane. We can derive the CP byanalysing the LIPM orbital energy [21], or by solving theLIPM ODE Eq. (3) and posing boundary conditions [22].We briefly derive the CP expression by solving Eq. (3). TheCoM has the following solution

xcom(t) =1

2

[xcom(0) − ucop +

xcom(0)

ω

]eωt

+1

2

[xcom(0) − ucop −

xcom(0)

ω

]e−ωt + ucop (11)

The CP xcp is defined as the point where the CoM comesto a complete stop, which can be written as

xcp = limt→∞

xcom(t) = limt→∞

ucop (12)

In order for Eq. (12) to be finite, the divergent componentof Eq. (11) eωt has to have zero coefficient, which translatesto

xcom(0) +xcom(0)

ω= xcp (13)

Given that Eq. (13) has to be satisfied all the time, the timeindex can be dropped and the CP is defined as

xcp = xcom +xcomω

(14)

Because the simple CP expression Eq. (14) is derivedfrom the LIPM dynamics, it is only an approximation ofthe real CP when the robot motion can be explained bythe LIPM dynamics. More complicated approximations suchas the Angular Momentum Pendulum Model lead to morecomplicated expressions for the CP. Refer to [21] for adetailed discussion. We use the simplest CP on the Atlasrobot because the LIPM is a good enough approximation fortasks our robot performs.

C. Fall detection and prevention

Our fall detection algorithm is based on whether the CPis within the robot’s polygon of support. The CoM estimatoris used to compute the CP, and the key of our algorithm isto use a “Corrected Capture Point (CCP)”, where the LIPMoffset is used as a CoM position offset. The CCP xcp isdefined by

xcp = xcom +xcomω

+ xoffset (15)

The xcp is readily available since every quantity in Eq. (15) isa state estimated by the CoM filter. xcp can handle modellingerror and relatively small dynamics forces, such as dragfrom the tether. It is especially helpful in estimating theunplanned quasi-static external forces applied at unknownlocations on the robot, which happens quite often duringmanipulation tasks. We are making the assumption that any

Safe Region Support Polygon

Capture Point Corrected Capture Point

Force

Fig. 4. For the manipulation controller, the robot is in double support andpushed back by an external force. The modelled CP is maintained at thecenter of support polygon by the controller. The CCP is pushed back andclose to the boundary of the safe region. The controller will freeze the robotas soon as the CCP is outside of the safe region. In our implementation, thesafe region is the convex hull of the shrunk foot corners, where the shrunkfoot has the following dimension: 4.5cm to the front and side, 5cm to theback of the physical foot.

external force is caused by the robot’s action, and that is whywe freeze/stop, to stop the force from increasing, moving theCP outside the polygon of support, and forcing a steppingresponse on fall.

Consider the following example: the robot is standing stilland pushing on the wall slowly with one hand until it tipsover, see Fig. 4. Even though the modelled CP xcp is kept atthe center of the support polygon by the balance controller,the CCP xcp is pushed back and out of the support polygononce the robot is tipped over. Without estimating the LIPMoffset, the modelled CP can not predict falling.

Even though we assume the total external force appliedto the robot is slow and quasi-static, so that xoffset haszero derivative which is consistent with Eq. (5), the CoMestimator formulation is not limited by this assumption. Byincreasing Q (the expected process noise) on the xoffset,and decreasing R (expected measurement noise) on the CoMacceleration, we can essentially tune how fast the xoffsetis estimating the total external force. The adaptive Kalmanfilter is a good candidate to handle different situationsautomatically.

The implementation of the fall detection and preventionalgorithm on the robot is controller dependent. There aretwo full body controllers implemented on the robot, onefor manipulation and one for walking. Details of thesecontrollers can be found in [6].

1) Manipulation: For the manipulation controller, therobot is always assumed to be in double support, and thesupport polygon is computed by finding the convex hullof the foot corner points using Andrew’s monotone chain2D convex hull algorithm [23]. The foot corner points arecomputed using forward kinematics. To prevent the robotfrom falling during manipulation, we require the CCP to liewithin a subset of the support polygon called the safe region(Fig. 4). The moment the CCP escapes the safe region, a

Fig. 5. The CCP motion during the drill task on the second day of the DRCFinals. The black trace started from the center of support polygon and movedtowards the back, corresponding to the robot pushing itself backwards. Oncethe CCP exceeds the boundary of the safe region (the yellow circle), thearm motion is stopped and the robot went into freeze mode. The red traceshowed the corrected CP motion during the freeze. It went outside of supportpolygon briefly and had oscillations. The blue trace was when the operatorunfroze the robot and it released the drill.

freeze signal is sent to the manipulation controller, and itclears all running joint trajectories and freezes the robot atthe current pose (the balance controller is still running).

During our second run in the DRC finals, the right electricforearm mechanically failed when the cutting motion wasinitiated during the drill task. The uncontrolled forearmwedged the drill into the drywall and pushed the robotbackwards. The controller froze and saved the robot fromfalling. The operator was able to recover from an otherwisecatastrophic scenario. Fig. 5 is a plot of the CCP in the footground plane.

The time plot in Fig. 6 shows candidate fall predictorsduring this event. We can eliminate some candidate fallpredictors easily. The CoM (and a corrected CoM (notshown)) usually provide a fall warning too late, becausethe CoM velocity is not included. The CP does not includeinformation about external forces. The CoP can warn of foottipping, but it is less reliable about warning about robotfalling, which is not the same thing as foot tipping in a forcecontrolled robot or if there are non-foot contacts and externalforces. In this plot, we see that the CoP moves away fromthe safe region during recovery, predicting that the robot isgoing to fall, while the CCP moves towards the interior ofthe safe region.

The fall detection algorithm for the walking controller issimilar to that of the manipulation controller and will bediscussed next.

2) Walking: Compared to the manipulation tasks wherethe robot is always in double support, the support polygonundergoes constant change during walking, and is deter-mined by contact state. The contact state is computed by

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−2.6

−2.55

−2.5

−2.45

−2.4

time[s]

X[m

]

Corrected CP

CP

model CoM

measured CoP

Left Foot

Right Foot

Fig. 6. Plots of candidate fall predictors in the fore/aft direction duringthe drill task. The black vertical dashed lines mark the freeze time and thestart of manual recovery.

thresholding the 3-axis foot force/torque sensor readings.The strain gages on the robot are not perfect even aftercalibration. Often a nonzero value up to ±50N is measuredon the swing foot. Sometimes a much bigger value canbe observed during swing. This value can change fromstep to step (see Fig. 7), which makes robust contact statedetection difficult. We implemented a simple Schmitt triggerfor contact state detection. Instead of a single threshold, aSchmitt trigger has both low and high thresholds. If the footis in contact and the force/torque sensor reading drops belowthe low threshold, the contact state of that foot switchesto swing. If the foot is in swing and the sensed force isabove the high threshold, the contact state changes to stance.We choose the low and high thresholds to be 80N and100N respectively. The Schmitt trigger eliminates a lot oferror compared to a single threshold. Even with the Schmitttrigger, the contact detection can go wrong sometimes due tobad sensor readings. We suspect the strain gage fluctuationis due to thermal effects, and a possible change in the straingage bonding with the substrate.

For dynamic walking, the CP naturally goes beyond thesupporting polygon during swing phase and is captured bythe touchdown foot. One way to predict a fall is to use theswing foot time to touchdown and predict if the currentCP is within the support polygon of possible or desiredfootholds. This approach is complicated because it dependson the controller. Our simpler solution is to use a heuristicthat detects a fall only if the CP is outside of the supportpolygon for a continuous period of time. The time is set to0.6 seconds after extensive testing. As soon as the fall isdetected, there are several things the humanoid can do, suchas using angular moment to maintain balance, or taking astep as presented in [22]. We have implemented a simplestep recovery controller that works in single support wherethe robot puts down the swing foot right away given thereis no self collision.

If none of the aforementioned approaches can stop therobot from falling down, then a safe fall behavior should betriggered. In testing, there happened to be a false positivedue to false contact detection during one of our terrain taskpractice runs two days before the DRC Finals, so we turnedoff the fall detection in the walking controller in the finalcontest.

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−20

0

20

40

time[s]

Fz[

N]

left footright foot

Fig. 7. The force/torque sensor readings during swing for several steps,the sensors are calibrated in the air before taking steps. Ideally the flat partshould read near zero and equal for both feet, but we observe measurementsranging from -40N to 40N and they are not constant or repeatable.

Fig. 8. Successful sidestepping through the door (left, middle) and thefailure in the DRC rehearsal (right) in which the protective cage (blackpadding) for the head is against the white door frame.

On the DRC rehearsal day, the robot was caught on thedoor frame when sidestepping through (Fig 8). The walkingcontroller detected that the CoP had not moved as expected,delayed liftoff and remained in double support, and stoppedthe current behavior for manual recovery. Data from thisexperiment is plotted in Fig 9.

V. CONCLUSIONS

In the paper, we introduced a CoM estimator for humanoidrobots and its applications in modeling error compensationand fall detection and prevention. A better estimate ofthe CoM motion improves the controller performance andstability of the robot. Essentially, it uses the LIPM dynamicswith variable height to approximate the dynamics of the CoMof the robot. The modeling error on each link is lumped asthe CoM offset. It makes state estimation simple and robust,and saves us from tuning mass models of the robot. Moreimportantly, it serves as an observer of unexpected externalforces. This enables fall being detected and sometimes pre-vented. During DRC Finals, the CoM estimator successfullysaved our robot from falling in two cases, and made us theonly competitive team that attempted all tasks, and did notfall or require human physical assistance. Its limitations comefrom the limitation of the LIPM model, which does not takeinto account angular momentum.

ACKNOWLEDGMENT

This material is based upon work supported in part bythe US National Science Foundation (ECCS-0824077, and

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1.6

1.7

1.8

1.9

Time [s]

X [m

]

measured CoPmodel CoMestimated CoMleft footright foot

659 660 661 662 663 664 665 666 667 6680.08

0.1

0.12

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0.2

Time [s]

Y [m

]

measured CoPmodel CoMestimated CoMleft footright foot

659 660 661 662 663 664 665 666 667 668−80

−60

−40

−20

0

20

Time [s]

Ext

erna

l for

ce [N

]

estimated external Fxestimated external Fy

Fig. 9. Atlas was caught on the door frame when sidestepping throughit during the rehearsal at the DRC Finals. The walking controller delayedliftoff and remained in double support when the CoM estimator detecteda large offset. Single support phase is shown by the shaded area, and theblack dashed lines indicate the planned liftoff time. The estimated CoM isthe sum of the model CoM and the estimated CoM offset.

IIS-0964581) and the DARPA M3 and Robotics Challengeprograms under DRC Contract No. HR0011-14-C-0011.

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