# Safe fall: Humanoid robot fall direction change through intelligent stepping and inertia shaping

**ABSTRACT** Although fall is a rare event in the life of a humanoid robot, we must be prepared for it because its consequences are serious. In this paper we present a fall strategy which rapidly modifies the robot's fall direction in order to avoid hitting a person or an object in the vicinity. Our approach is based on the key observation that during “toppling” the rotational motion of a robot necessarily occurs at the leading edge or the leading corner of its support base polygon. To modify the fall direction the robot needs to change the position and orientation of this edge or corner vis-a-vis the prohibited direction. We achieve it through intelligent stepping as soon as a fall is detected. We compute the optimal stepping location which results in the safest fall. Additional improvement to the fall controller is achieved through inertia shaping techniques aimed at controlling the centroidal inertia of the robot. We demonstrate our results through the simulation of an Asimo-like humanoid robot. To our knowledge, this is the first implementation of a controller that attempts to change the fall direction of a humanoid robot.

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**ABSTRACT:**Purpose – This paper aims to present a step-exchange strategy for balance control of a walking biped robot when a lateral impact acts suddenly. A step-out strategy has been recently proposed for balance control when an unknown lateral force acts to a biped robot during walking. This step-out strategy causes a robot to absorb the impact kinetic energy and efficiently maintain balance without falling down. Nevertheless, it was found that the previous strategies have drawbacks that the two foots should always be on the ground (double-support mode) after being balanced and the authors think it is difficult to continue walking after being balanced. Unlike the existing balance strategies, the proposed step-exchange strategy is to not only maintain balance but also to lift one leg in the air (single-support mode) after being balanced so that it is easy for a biped robot to keep walking after being balanced. Design/methodology/approach – In the proposed step-exchange strategy, forward Newton–Euler equation, angular momentum and energy conservation equation were derived. Hill-climbing algorithm is utilized for numerically finding a solution. To verify the proposed strategy, a biped robot by Open Dynamics Engine was stimulated, and experiments with a real biped robot (LRH-1) were also conducted. Findings – The proposed step-exchange strategy enables a walking biped robot under a lateral impact to keep balance and to keep a single-support mode after exchanging a leg. It is helpful for a biped robot to continue walking without any stop. It is found that the proposed step-exchange strategy can be applicable for maintaining balance even if a biped robot is moving. Even though this proposal seems immature yet, it is the first attempt to exchange the supporting foot itself. This strategy is very straightforward and intuitive because humans are also likely to exchange their supporting foot onto the opposite side when an unexpected force is acting. Research limitations/implications – The proposed step-exchange strategy described in this paper can be applicable in the situation when the external force is applied in the +Y direction, the left leg is the swing leg and the right leg is the stance leg, or it can also be applicable in the situation when the external force is applied in −Y direction, the right leg is the swing leg and the left leg is the stance leg (Figure 2 for ±Y force direction). If an impact force acts to the side of the swing leg, the other step-exchange strategy is needed. The authors are studying this issue as a future work. Originality/value – The authors have originated the proposed step-exchange strategy for balance control of a walking biped robot under lateral impact. The strategy is genuine and superior in comparison with the state-of-the-art strategy because not only can a biped robot be balanced but it can also easily continue walking by using the step-exchange strategy.Industrial Robot 10/2014; 41(5):456-464. · 0.69 Impact Factor - SourceAvailable from: Yeoun-Jae Kim
##### Dataset: IR-03-2014-0311

- SourceAvailable from: Yeoun-Jae Kim
##### Dataset: IR-03-2014-0311

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Safe Fall: Humanoid robot fall direction change

through intelligent stepping and inertia shaping

Seung-kook Yun

Massachusetts Institute of Technology

Cambridge, MA 02139

U.S.A.

yunsk@mit.edu

Ambarish Goswami

Honda Research Institute

Mountain View, CA 94041

U.S.A.

agoswami@honda-ri.com

Yoshiaki Sakagami

Honda Research Institute

Mountain View, CA 94041

U.S.A.

ysakagami@honda-ri.com

Abstract—Although fall is a rare event in the life of a humanoid

robot, we must be prepared for it because its consequences are

serious. In this paper we present a fall strategy which rapidly

modifies the robot’s fall direction in order to avoid hitting a

person or an object in the vicinity. Our approach is based on

the key observation that during “toppling” the rotational motion

of a robot necessarily occurs at the leading edge or the leading

corner of its support base polygon. To modify the fall direction the

robot needs to change the position and orientation of this edge or

corner vis-a-vis the prohibited direction. We achieve it through

intelligent stepping as soon as a fall is detected. We compute

the optimal stepping location which results in the safest fall.

Additional improvement to the fall controller is achieved through

inertia shaping techniques aimed at controlling the centroidal

inertia of the robot.

We demonstrate our results through the simulation of an

Asimo-like humanoid robot. To our knowledge, this is the first

implementation of a controller that attempts to change the fall

direction of a humanoid robot.

Index Terms—humanoid robot fall, safe fall, fall direction

change, support base geometry, inertia shaping

I. INTRODUCTION

Safety is a primary concern that must be addressed before

humanoid robots can freely exist in human surroundings. Out

of a number of possible situations where safety becomes

an issue, one that involves a fall is particularly worrisome.

Fall from an upright posture can cause damage to the robot,

to delicate and expensive objects in the surrounding or to

a human being. Regardless of the substantial progress in

humanoid robot balance control strategies, the possibility of

a fall remains real, even unavoidable. Yet, a comprehensive

study of humanoid fall and prescribed fall strategies are rare.

A humanoid fall may be caused due to unexpected or

excessive external forces, unusual or unknown slipperiness,

slope or profile of the ground, causing the robot to slip, trip

or topple. In these cases the disturbances that threaten balance

are larger than what the balance controller can handle. Fall

can also result from actuator, power or communication failure

where the balance controller is partially or fully incapacitated.

In this paper we consider only those situations in which the

motor power is retained such that the robot can execute a

prescribed control strategy.

A fall controller can target two major objectives indepen-

dently or in combination: a) fall with a minimum damage

and b) change fall direction such that the robot does not hit

a certain object or person. The present paper introduces a

strategy for fall direction change and describes a controller

which can achieve both objectives.

Fig. 1 shows two cases of a fall caused by a frontward push

on an upright standing humanoid robot (top figure). Without

any fall controller, the robot falls forward and hits a block

located in front of it (bottom, left). In the second case (bottom,

right), the robot takes cognizance of the position of the block

and the proposed controller successfully avoids hitting it.

Fig. 1.

controller. The robot is initially in upright pose and is subjected to a forward

push (top) shown by the green arrow. Without any fall controller the robot

falls on the block object in front of it (bottom, left), potentially damaging or

breaking it. For the same push, the fall controller successfully changes the

fall direction and the robot is able to avoid hitting the object (bottom, right).

Consequence of a humanoid fall without and with the proposed fall

Let us note that a fall controller is not a balance controller.

A fall controller complements, and does not replace, a bal-

ance controller. Only when the default balance controller has

failed to stabilize the robot, the fall controller is activated.

Further, a fall controller is not a push-recovery controller.

A push-recovery controller is essentially a balance controller,

which specifically deals with external disturbances of larger

magnitude. A robot can recover from a push e.g., through an

appropriate stepping strategy[12].

2009 IEEE International Conference on Robotics and Automation

Kobe International Conference Center

Kobe, Japan, May 12-17, 2009

978-1-4244-2789-5/09/$25.00 ©2009 IEEE 781

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II. BACKGROUND AND KEY CONCEPTS

In this section we will review the existing literature and

introduce some of the key concepts used throughout the paper.

A. Related work

Work on humanoid fall is rare. Fujiwara et al. at the Japan

AIST Laboratory has done major work in the area of fall

control of humanoid robots [7], [2], [3], [6], [4], [5]. Although

these papers are concerned with the impact minimization

problem, some important points of general applicability are

established. [3] points out the advantages of a simulator for

fall control research and [4] reports the design and building

of a dedicated hardware (robot) for fall study.

In another work by Ogata et al., a fall detection condition

based on the “degree of abnormality” to distinguish between

fall and no-fall conditions was proposed [11], [10]. The robot

improves fall detection through learning. We have also used

a somewhat similar concept, which we call the Fall Trigger

Boundary (FTB) and is described next.

B. Fall trigger boundary (FTB)

As shown in Fig. 2 the FTB encloses a region in the robot’s

feature space in which the balance controller is able to stabilize

the robot. An exit through the FTB is an indication of a certain

fall and this event is used to activate a switch from the robot’s

balance controller to a fall controller. The parameters that

characterize the feature space can include both sensor data

from and any number of computed variables such as center of

mass (CoM) and center of pressure (CoP) positions, robot lean

angle, angular momentum, etc. The shape and size of the FTB

depends on the nature of the balance controller. Wieber [16]

proposed a similar concept as viability kernel which tracks

all the states as joint angles and velocities of a humanoid

that adapts its motion according to the kernel. We focus not

so much on the interior of the kernel but on the boundary

between balanced and unbalanced regions.

FTB

v1

v2

v3

Balance

control

Certain Fall

Triggers fall control

Fig. 2. Schematic of Fall Trigger Boundary (FTB), a boundary in a humanoid

feature space that surrounds the region where the humanoid is able to maintain

balance. The axes in the figure represent different robot features such as CoM

coordinates, angular momentum components, etc. The FTB represents the

limit beyond which the robot controller must switch to a fall controller.

C. Support base geometry modification

The direction of fall of a humanoid robot is fully determined

by the CoP location with respect to the support base. The

support base can be approximated by a polygonal area which

is the convex hull of all the contact points between the robot

feet and the ground. When the robot starts to topple, its CoP

touches an edge (or corner) of the support base. The robot

rotates about this leading edge (corner). Therefore, a change

in the physical location of the leading edge (corner) of the

support base with respect to the robot CoM exerts influence

on the direction of robot rotation, i.e., the direction of fall.

In Fig. 3 a humanoid robot is subjected to a forward push

as indicated by the red arrow. If the push is strong enough to

topple the robot, the CoP will approach the front edge (red)

of the support base and the robot will begin to rotate about

this leading edge.

P

Q

T

P

Q

T

Fig. 3.

change through support base geometry modification. A forward push is

assumed. P denotes the CoP, and Q is the reference point (explained in

text). The dotted lines show the support base (polygonal convex hull) of the

robot while the polygon edge containing CoP is red dotted.

A schematic diagram showing the basic idea behind fall direction

The direction and magnitude of the toppling motion is

given by PQ where P is the CoP and Q is what we call

a reference point. The reference point indicates the direction

and magnitude of fall. In this paper we have used the capture

point[12] as our reference point1. Although PQ may not be

initially perpendicular to the leading edge of support base, it

becomes so once the toppling motion sets in.

With a different geometry of the support base as in Fig. 3(b),

for the same push, the robot would rotate about a new leading

edge and in the new direction PQ. If the robot is to avoid

falling on an object in front of it, we can effect a change in

the fall direction by changing the support base (specifically,

its leading edge) from Fig. 3(a) to Fig. 3(b).

There are two major challenges that we face. First, the

robot becomes underactuated as soon as it starts toppling.

This creates 1 or 3 additional dofs depending on whether

the robot is toppling about an edge or a corner. Therefore,

we should design a controller very carefully to deal with this

underactuated phase. Second, the CoP and the reference point

continuously move as the robot moves.

The proposed control strategy can be implemented accord-

ing to the following steps:

1We will further describe capture point in Section III-A2.

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1) Compute control duration, the length of time after the

push force has disappeared, during which the controller

is assumed to be active.

2) Estimate reference point location at the end of control

duration, based on inverted pendulum model.

3) Compute optimal stepping location on the ground.

4) Control humanoid legs to step to optimal location.

5) Employ inertia shaping to generate angular momentum

that further diverts the robot away from the obstacle.

III. SUPPORT BASE GEOMETRY MODIFICATION

CONTROLLER

Once the humanoid state exits the fall trigger boundary, the

fall controller estimates the direction and time-to-fall of the

robot. Based on the estimation, it computes the best position

to step and controls the leg accordingly.

The proposed approach sequentially employs two con-

trollers, the support base geometry modification and inertia

shaping, to change the direction of fall. This section describes

the first controller.

A. Robot state estimation through simple humanoid models

To speed up calculations for predicting the robot states we

approximate the robot with an equivalent inverted pendulum,

see Fig. 4. The pendulum connects the CoP and CoM of the

robot and has a point mass equal to the robot mass. If the CoP

is located on an edge of the support base, we model the robot

with a 2D inverted pendulum. If instead, the CoP is located

at a corner, the estimation uses a 3D spherical pendulum

model. The 2D pendulum model has a closed-form solution.

However, since the spherical pendulum does not have closed-

form solutions, we simply simulate its dynamic equations for

the period of control duration. Because the control duration is

typically very short, this simulation can be adequately handled.

1) Estimation of the control duration: Time-to-fall is a

critical parameter for the evaluation and formulation of a fall

response strategy. The biomechanics literature gives us a few

data on the time-to-fall of human. A simple forward fall of

an adult starting from a stationary 15◦inclination takes about

0.98s, whereas that for a backward fall starting from stationary

5◦inclination takes 0.749s (for a flexed knee fall) and 0.873s

(for an extended knee fall)[14].

The fall controller remains active until the lean angle θ

between the humanoid CoP-CoM line and the vertical axis

crosses a certain threshold θthreshold. We assume that all

external forces have disappeared when the robot starts to use

the fall controller. The control duration is obtained through

an incomplete elliptic integral of the first kind of the 2D

pendulum model [13] when the lean angle goes over the

threshold. For the spherical pendulum model, we simulate its

dynamic equations.

2) Estimation of reference point: As mentioned before, we

have used the capture point as the reference point in this work.

Capture point is the point on the ground where a humanoid

must step to in order to come to a complete stop after an

external disturbance[12]. The location of the capture point is

proportional to the linear velocity of the robot’s CoM. Capture

mg

P

threshold

Fig. 4.

CoP, m is the humanoid mass, and θ is the lean angle between the CoP-CoM

line and the vertical. We use this model for the fast estimation of time duration

and other parameters of the robot.

Simple model of an inverted pendulum falling under gravity. P is

point (xQ, yQ) for an inverted pendulum approximation of the

robot is computed as follows:

xQ= xG+

?zG

?zG

g

˙ xG

(1)

yQ= yG+

g

˙ yG

(2)

where (xG,yG,zG) and (˙ xG, ˙ yG, ˙ zG= 0) are the robot CoM

position and velocity, as estimated from the dynamic equations

of the pendulum models.

Suppose the control duration is ΔT. In the 2D pendulum

model, the velocity after ΔT is computed from the energy

equation as follow:

?

I

˙θ(ΔT) =

2E

−2mgLcos(θ(ΔT))

I

(3)

where E is the total energy (constant) of the pendulum, I is

the moment of inertia with respect to CoP and L is the distance

between CoP and CoM. Simulation of the dynamic equations

yields the velocity of the spherical pendulum.

B. Definition of the optimal step location

Fig. 5 shows a robot that is about to topple. The old CoP P1

has reached an edge of the support base, and the support base

has shrunk to a line. Approximating the robot as a rigid body

instantaneously, the trajectory of the CoM is parallel to P1Q1.

T is the target object to avoid. Our goal is to find a point P2

within the allowable stepping zone of the robot such that the

robot is maximally diverted away from T, i.e., to maximize

α2.

Assuming that the humanoid is in double support phase, the

optimal CoP is selected among the following 5 cases:

1) No change, i.e., robot does not react

2) (2 cases) Lifting (and not re-planting) left or right foot

3) (2 cases) Taking left or right step

We use a brute-force search for each case to find the

optimal new CoP. The allowable stepping zone on the floor

where the robot’s swing foot can reach within the control

duration is denoted by D, shown as the green dotted polygon

in Fig. 5. This area is divided into cells of x, y and β, the

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P1

P1

P2

P2

Q1

Q1

TT

?1

?1

?2

?2

Q2

Q2

Fig. 5.

and Q1is the reference point when the controller starts, and the robot will fall

in the direction P1Q1. T is the target to avoid. The support base is shown in

blue dotted lines. The green dotted lines enclose the allowable stepping zone,

the region where a new CoP can be placed through proper foot placement.

P2 is a candidate for the new CoP by stepping. Q2 is the estimated new

reference point when the step is taken. αi is the avoidance angle between

PiQiand PiT. The fall controller will try to maximize α2.

Schematic of a biped robot subject to a fall. P1is the current CoP,

angular displacement (of foot). We re-locate the non-support

foot according to (x,y,β) of each cell, and estimate a new

reference point and CoP.

The avoidance angle α is computed for each case and the

optimal CoP is selected as follows:

P2= argmax

P2∈CoP(D)

angle(Q2P2T)

(4)

We assume a rectangular foot sole and the support polygon

can be computed with a finite number of points. The reference

point needs to be estimated at the time the non-support foot

touches the ground.

C. Estimation of the allowable stepping zone

Given the control duration, the allowable stepping zone is

estimated using leg Jacobians. Suppose the robot has a firm

support on the ground. With two legs, we have the following

equations:

˙PL−˙Pbody= JL˙θL

˙PR−˙Pbody= JR˙θR,

(5)

(6)

where PLand PRare the positions of the left and right feet,

respectively, with respect to the support foot PL, and Pbody

is the location of the body frame, θLand θRare 6 × 1 joint

angle vectors of the robot legs, and JL and JR are the leg

Jacobian matrices.

Performing (Eq. 6)-(Eq. 5):

˙PR−˙PL= [JR − JL]

?˙θR˙θL

?T

(7)

where we have used the (6×12) foot-to-foot Jacobian matrix

asˆJ = [JR

− JL].

The size of the allowable stepping zone is estimated by the

Jacobian as shown in Fig. 6.

Dk(x,y,β)= ΔT

12

?

i=1

???ˆJki˙θMAX

i

??? ≈ γΔT

12

?

i=1

???ˆJki

???

(8)

?

?

??

??

??

?

Fig. 6.

left foot is the support foot. P is the CoP with the single support and Q is the

reference point. The allowable stepping zone is the upper part of the rectangle

(above the blue separatrix) with edges Dx and Dy. Dβdenotes amount of

rotation of the swing foot.

In this figure the allowable stepping zone is shown in yellow. The

where˙θMAX

constant included to approximate˙θMAX

same for all joints.

We use only the upper half of the region cut by the

separatrix line which is perpendicular to PQ and goes through

the center of the moving foot. This is because a robot that is

falling along PQ can hardly place its foot on the other side.

i

is the maximum velocity of a leg joint. γ is a

i

, which is assumed

D. Step controller for a toppling humanoid

Once the optimal step location is computed one can expect

to simply control the joint angles through an invers kinematics.

However, taking a successful step to the optimal step location

is not trivial because inverse kinematics solution will not be

precise for a toppling robot. The main problem is that the

support foot of the robot is not flat with the ground, i.e., it is

underactuated, and robot is not likely to step as expected.

To compensate for this we need to know the foot rotation

angle of the robot. Assuming that the robot possesses a gyro

sensor in the trunk, the foot rotation angle can be estimated

by noting the mismatch between the trunk orientation angle

as computed by the gyro and by the robot joint angle sensors.

With this information, we implement a leg controller to ensure

that the swing foot is flat as it touches down on the ground.

Since we assume that the CoP does not change during fall,

the CoP is modeled as passive rotational joint at which the

support foot rotates, as shown in Fig. 7.

P

Q

Ts

Tn

P

Ts

Tn

Fig. 7.

CoP, P, towards the reference point Q. We model a free joint at P. Without

external forces, the joint angle should increase. (right) desired landing posture

(Left) For a robot that is falling, the support foot rotates about the

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Although we cannot actuate the passive joint, the support

foot is expected to rotate as estimated in the pendulum models

without control. A transformation matrix from the support foot

to the non-support foot Ts

nis:

Ts

n= T0

s

−1T0

n

(9)

where T0

already fixed in optimizing the CoP.

If the joints are controlled according to Ts

support foot hits the ground as in Fig. 7 (Left), the robot is

expected to step on the desired location by gravity, Fig. 7

(Right). Note that the pre-computed T0

posture, Fig. 7(b).

We can compute joint velocities to move the swing leg as.

nis the transformation of the non-support foot and

nbefore the non-

sis for the landed

˙θ =ˆJ

#(˙PR−˙PL)

(10)

whereˆJ

#is the least damped-square pseudo-inverse ofˆJ.

IV. WHOLE-BODY FALLING MOTION CONTROL THROUGH

INERTIA SHAPING

The humanoid can attempt to change the fall direction

further, after the step is taken. Since a falling robot is nor-

mally underactuated, direct control of the CoM would not be

effective. However, we can indirectly change the fall direction

by generating angular momentum against the direction to the

target. For this we can employ the inertia shaping technique [8]

In inertia shaping we control the centroidal composite rigid

body (CRB) inertia [15] or the locked-inertia of the robot.

Cenroidal CRB inertia is the instantaneous rotational inertia

of the robot if all its joints are locked. Unlike linear inertia

the CRB inertia is a function of the robot configuration and

varies continuously.

Approximating the robot as a reaction mass pendulum,

RMP[8], or an inverted pendulum with inertial mass, and

assuming no slip at the ground, its CoM velocity can be

computed as (see Fig. 8):

VG= ωP

G× PG

(11)

where G and ωP

of the pendulum. For best results, we want VG= −c PT for

some scalar c. This can be achieved by setting the desired

angular velocity ωdas follows

Gare the CoM location and the angular velocity

ωd= −ez×PT,

(12)

where ez×PTis a unit vector along the cross product between

by z and PT. The desired locked inertia is obtained as Id=

RIR−1, where I is the current locked inertia and R is the

rotation matrix obtained with an exponential map[9] from ωd.

To implement inertia shaping we string out the 6 unique

elements of the CRB inertia matrix in the form of a vector:

I(3×3)→s?I(6×1). Next we obtain the CRB inertia Jacobian

sponding changes ins?I, i.e.,

δs?I = JIδθ.

JIwhich maps changes in the robot joint angles into corre-

(13)

P

T

G

z

VG

Q

D

P

T

G

z

VG

Q

D

Fig. 8.

CoM should be away from T. For this the robot should overall rotate around

an axis obtained by the cross product of PT and the vertical, where P is

the CoP.

To avoid falling on the block, VG, the linear velocity of the robot

To attain Id, the desired joint velocities are:

˙θ = J#

I(Id− I)

(14)

where J#

The humanoid can recruit all the joints to attain Id. The

effect of inertia shaping might not always be big enough to

obtain the desired VG, however, even a modest change is very

useful.

Iis the pseudo-inverse of JI.

V. SIMULATION RESULTS

We have performed the simulations using Webots [1], a

commercial mobile robot simulation software developed by

Cyberbotics Ltd. The humanoid fall is simulated with an sharp

push of small duration. We have tested two initial conditions

of the humanoid: standing and walking.

A. Standing humanoid

The humanoid stands on both feet, and is subjected to a

push on its trunk for 0.1s. The push has a magnitude of 200N

forward and 50N to the right. The target for the humanoid

to avoid is located 1.2m in front of it, and the head of the

humanoid would hit it without control. The fall controller starts

0.05s after the push has ended. Inertia shaping, if used, begins

to work as soon as the swinging foot contacts the ground. We

present results with support base change only and with both

of inertia shaping and support base change.

Fig. 9 shows snapshots of the simulation. The support base

changes from a rectangle to a point, then to a quadrilateral

and back to a rectangle. The direction of fall changes, as

expected, according to support base geometry change. When

the humanoid is on double support, it topples forward and

rotates about the front edge of the support base for which the

CoP is located roughly in the middle. Once the robot lifts

the right leg to take a step, it starts toppling around the right

top corner of the left foot and the support base shrinks to a

point (9(b)). Taking a step makes the support base polygon a

quadrilateral (9(c)), and the direction of fall goes to the right

since the reference point is at the right of the support polygon.

Finally the humanoid achieves the rightward fall direction.

Fig. 10 shows the motion of a falling humanoid with

both the support base geometry controller and inertia shaping

controller. After taking a step (10(b)), the humanoid appears

to change the falling direction by rolling the upper body

backward (10(c)).

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−0.2

0

0.2

0.4

0.6

0.8

1

1.2

−0.8−0.6−0.4−0.20 0.2 0.40.60.8

t=0.004

X (m)

Y (m)

convex hull of ASIMO

(a)

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

−0.8−0.6−0.4−0.20 0.2 0.4 0.60.8

t=0.804

X (m)

Y (m)

convex hull of ASIMO

(b)

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

−0.8−0.6−0.4−0.20 0.20.40.60.8

t=1.04

X (m)

Y (m)

convex hull of ASIMO

(c)

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

−0.8−0.6−0.4−0.200.20.40.60.8

t=1.484

X (m)

Y (m)

convex hull of ASIMO

(d)

Fig. 9.

points. The yellow region is the support polygon. The green square is the target object (to avoid). The small red square is CoP, and the cross mark is the

reference point. These two points are connected by the blue line to show the estimated direction of fall. (a) The humanoid gets a forward push. Direction of

the push is shown as the red line. The support polygon is a rectangle formed by the two feet. (b) The humanoid has lifted the right foot to take a step. The

support polygon is simply a point, and it is coincident with the CoP. The reference point implies that the falling direction is toward left. (c) The humanoid

has taken a step. The support polygon is a quadrilateral formed by three points of the right foot and one point of the left foot. (d) The humanoid is falling

leftwards, rotating about the rightmost edge of the right foot.

Upper pictures are the top views of falling humanoid with changing support polygon. The lower figures show the support polygon and significant

Fig. 10.

Fig. 9. Inertia shaping starts after taking a step in the third picture. The humanoid appears to lean its body backwards as if it does limbo. After inertia shaping,

the humanoid has fallen almost backwards.

Snapshots of falling humanoid which uses both the support base geometry controller and inertia shaping controller. The push is the same as in

Comparison of the CoM trajectories for the cases - no

control, support polygon change, and support polygon change

plus inertia shaping - are shown in Fig. 11. The figure clearly

shows that the trajectory of the full controller diverges from the

trajectory of the support polygon change and goes backwards.

0 0.20.40.60.81 1.2

0

0.2

0.4

0.6

0.8

1

1.2

Y of CoM (m)

X of CoM (m)

No control

Geometry control

Geometry control + Inertia shaping

0.40.60.811.2 1.41.61.8

0

20

40

60

80

100

120

140

160

180

time (sec)

angle from the target (deg)

No control

Geometry control

Geometry control + Inertia shaping

Estimated fall angle

Fig. 11.

(Right) of a falling humanoid which was pushes during upright standing. The

humanoid falls on the target without any control, which corresponds to a

0◦avoidance angle. Intelligence footstep control improves this to 100◦and

inertia shaping further improves to 180◦.

Simulation plots of CoM trajectories (Left) and avoidance angles

B. Walking Humanoid

The humanoid is subjected to a forward push during forward

walking. The push is 150N for 0.1 second. Snapshots of the

simulation are shown in Fig. 12. After the push, the humanoid

takes a step on the front right of the ground by the swinging

right leg, and the direction of fall changes to left forward.

Inertia shaping yields a larger angle of falling direction from

the target as shown in Fig. 13.

VI. DISCUSSION AND CONCLUSIONS

We have presented a humanoid robot fall controller, the

objective of which is to rapidly modify the fall direction in

order to avoid hitting an object or a person in the vicinity. The

approach taken by us is to modify the support base geometry

of the robot which indirectly, but strongly, modifies the fall

direction of the robot. The shape of the support base should

be carefully adjusted such that it does not possess any leading

edge facing the object to avoid.

We have implemented the controller through an intelligent

foot placement strategy of the robot, which triggers as soon

as a fall is detected. We have shown how an optimal stepping

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Page 7

Fig. 12.

change the direction of fall. After the step, it does inertia shaping and tries to move away from the target. Inertia shaping is not efficient enough to change

the direction completely backwards, however the direction deviates a little more compared to a case of changing the support polygon only.

Humanoid gets a forward push while walking. It was supposed to take a step forward, however it has changed the plan and steps right-forward to

−1.2−1−0.8 −0.6−0.4

Y of CoM (m)

−0.20 0.2

0

0.2

0.4

0.6

0.8

1

1.2

X of CoM (m)

No control

Geometry control

Geometry control + Inertia shaping

2.533.54

0

20

40

60

80

100

120

140

160

180

time (sec)

angle from the target (deg)

No control

Geometry control

Geometry control + Inertia shaping

Estimated fall angle

Fig. 13.

(Right) of a falling humanoid which was pushed while walking. Intelligence

footstep control results in a 50◦avoidance angle and inertia shaping further

improves to 120◦.

Simulation plots of CoM trajectories (Left) and avoidance angles

location can be computed, one that maximally diverts the

avoidance angle, the angle between the fall direction and the

direction to avoid. Additionally, we have applied inertia shap-

ing controller to further divert the robot. We have demonstrated

our results through the simulation of an Asimo-like humanoid

robot.

To our knowledge, this is the first implementation of a

controller that attempts to change the fall direction of a

humanoid robot.

Falling is an unstable motion in nature, and it is hard

to tightly control it. Estimation errors can accumulate in

our method especially because we have used approximate

inverted pendulum models for predicting the robot states at

a future time. Currently, our controller has two distinct phases

including the modification of the support base polygon and

inertia shaping. However, they can be blended together in a

control scheme.

ACKNOWLEDGMENTS

Seung-kook was supported by a Honda Research Institute

USA summer internship. Important help from Dr. Kankang

Yin as a summer intern is also gratefully acknowledged.

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