This article was downloaded by: [University of Chicago Library]On: 05 October 2014, At: 05:03Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: MortimerHouse, 37-41 Mortimer Street, London W1T 3JH, UK
Intelligent Automation & Soft ComputingPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/tasj20
Omnidirectional Disturbance Rejection for a BipedRobot by Acceleration OptimizationZhangguo Yuab, Fei Menga, Qiang Huangabc, Xuechao Chenab, Gan Maa & Jing Liaa Intelligent Robotics Institute, School of Mechatronical Engineering, BeijingInstitute of Technology, Haidian, Beijing 100081, Chinab Key Laboratory of Biomimetic Robots and Systems (Beijing Institute ofTechnology), Ministry of Education, Chinac Key Laboratory of Intelligent Control and Decision of Complex System, ChinaPublished online: 03 Sep 2014.
To cite this article: Zhangguo Yu, Fei Meng, Qiang Huang, Xuechao Chen, Gan Ma & Jing Li (2014) OmnidirectionalDisturbance Rejection for a Biped Robot by Acceleration Optimization, Intelligent Automation & Soft Computing,20:4, 471-485, DOI: 10.1080/10798587.2014.934587
To link to this article: http://dx.doi.org/10.1080/10798587.2014.934587
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”)contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensorsmake no representations or warranties whatsoever as to the accuracy, completeness, or suitabilityfor any purpose of the Content. Any opinions and views expressed in this publication are the opinionsand views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy ofthe Content should not be relied upon and should be independently verified with primary sources ofinformation. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands,costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly orindirectly in connection with, in relation to or arising out of the use of the Content.
This article may be used for research, teaching, and private study purposes. Any substantial orsystematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution inany form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
OMNIDIRECTIONAL DISTURBANCE REJECTION FOR A BIPED ROBOT BYACCELERATION OPTIMIZATION
ZHANGGUO YU1,2*, FEI MENG
1, QIANG HUANG1,2,3, XUECHAO CHEN
1,2, GAN MA1, AND
JING LI1
1Intelligent Robotics Institute, School of Mechatronical Engineering, Beijing Institute of Technology,
Haidian, Beijing 100081, China2Key Laboratory of Biomimetic Robots and Systems (Beijing Institute of Technology), Ministry of
Education, China3Key Laboratory of Intelligent Control and Decision of Complex System, China
ABSTRACT—Biped robots are expected to keep stability after experiencing unknown disturbances
which often exist in human daily environments. This paper presents a novel method to reject
omnidirectional disturbances by optimizing the accelerations of the floating base of the robot. The
optimized accelerations keep the desired external forces within their constraints and generate
coordinated whole-body motion to reject disturbances from all directions. The effectiveness of the
proposed method is confirmed by simulations with disturbance-rejection scenarios.
Key Words: Biped robot; Disturbance rejection; Acceleration optimization; Inverse dynamics
1. INTRODUCTION
Biped robots are expected to keep stability after experiencing unknown disturbances, which often exist in
human daily environments. Push, one of the very common physical interactions is a typical scenario for
studying recovery from disturbances. Generally, an impulsive push may cause a biped robot to deviate from
its original position and velocity. Researchers have been studying methods to enable robots to recover their
original states [1], [2], [3], [4], [5], [20], [21].
Human-inspired balancing strategies, an ankle strategy and a hip strategy, have been variously
introduced to address stabilization control [6], [7]. To imitate the ankle strategy, most researchers treated
the robot as a Linear Inverted Pendulum Model (LIPM). The LIPM was combined with the flywheel model
to produce the hip strategy, which could control stronger disturbances than the ankle strategy. Yoshikazu
et al. proposed a method for smooth transitions between the ankle and hip strategies [8]. Additionally, the
knee strategy improved the robot’s push-recovery ability [9]. Unfortunately these methods were relatively
conservative because they did not take advantage of whole-body dynamics.
In order to manage stronger disturbances, many methods used the multi-link model, which described
biped’s physical properties more accurately than the LIPM plus flywheel model to coordinate whole-body
motion. Linear quadratic regulators could serve as controllers for different perturbations [10]. Nevertheless,
these regulators had a significant disadvantage: The necessity of changing the optimization criterion
according the size of the perturbation. Atkeson et al. [11] avoided this problem by employing one
optimization criterion to generate multiple balance strategies, which treated various impulsive
q 2014 TSIw Press
*Corresponding author. Email: [email protected]
Intelligent Automation and Soft Computing, 2014
Vol. 20, No. 4, 471–485, http://dx.doi.org/10.1080/10798587.2014.934587
Dow
nloa
ded
by [
Uni
vers
ity o
f C
hica
go L
ibra
ry]
at 0
5:03
05
Oct
ober
201
4
perturbations uniformly. Later it was extended to solve both impulsive and constant push problems [12]. To
improve the stability robustness of the robot, differential dynamic programming was employed to generate
an optimal trajectory library [13], and robust control based on convex optimization was used to design
push-recovery controllers [14]. However, these methods only considered disturbances typically in sagittal
plane and seldom took disturbances from other directions into account simultaneously.
Balance control in response to disturbances in the frontal plane was studied in [15]. The CoM state was
controlled to reject omnidirectional disturbances by optimizing contact forces in [16] and [17]. However,
these methods ignored some important constraints on the external forces, which could be utilized to
improve robot’s balance capability.
In this study, we present a method which generates coordinated whole-body motion to reject
omnidirectional disturbances. The robot’s balance capability is improved by optimizing the accelerations
of the floating base according to the imposed constraints on the external forces. The relationship between
the accelerations of the floating base and the external forces is established. Imposing constraints on the
external forces yields corresponding constraints on the accelerations. Quadratic Programming (QP) is
employed to acquire optimal accelerations, which are on the boundaries when the desired accelerations
may go beyond the boundaries. The optimal accelerations enhance the robot’s stability. QP is also used to
distribute forces to the feet so that the distributed forces satisfy their own constraints on the feet. The rest of
this paper is organized as follows: Section 2 presents the spatial method to establish a simplified biped
model. The disturbance rejection method is presented in Section 3. Section 4 provides the simulation results
and the conclusions are given in Section 5.
2. WHOLE-BODY DYNAMICS FORMULATION
As seen in Figure 1, a biped model with force-controlled joints is built. The Young’s modulus-coefficient
of restitution element is used instead of the spring-damper model as the contact model between the feet
and the ground. There are six joints in each leg: Two in the hip, one in the knee, one in the shank and
two in the ankle. The symbols qrl [ R6£1 and qll [ R6£1 represent the joint angles of the right leg and
left leg, respectively. Featherstone’s spatial vector method [18], which is an efficient rigid body
dynamics formulation is employed to solve our rigid body dynamics problem. When using it, the frame
for expressing the variables should be specified. In this study, left superscripts denote the reference
frames, and variables with ^ superscripts denote spatial variables. The floating base coordinate frame SR
Figure 1. Simplified Biped Model With Force-Controlled Joints.
Intelligent Automation and Soft Computing472
Dow
nloa
ded
by [
Uni
vers
ity o
f C
hica
go L
ibra
ry]
at 0
5:03
05
Oct
ober
201
4
is located at the center of the pelvis, and the fixed base coordinate frame SW , also known as the world
frame, is fixed on the ground. The floating base is the root of this model, which is built using a kinematic
tree. Six virtual joints are introduced between SW and SR. The first three joints are translational in the x,
y and z directions, and the second three are successively revolute around the x, y and z axes. These
virtual joints are used to express the location of this model in the world frame. qr [ R6£1 represents thepositions and angles of these joints.
Imposing kinematic constraints
d
dtWJrf _q� � ¼ 0 and
d
dtWJlf _q� � ¼ 0 ð1Þ
which result from the contact between the feet and the ground. The dynamics of this model is written as
MðqÞ€qþ Cðq; _qÞ ¼ tþW JTrfWfrf þW JTlf
Wflf ð2Þ
where q ¼qr
qrl
qll
2664
3775, M [ R18£18 is the inertia matrix, C [ R18£1 is a vector containing the Coriolis,
centrifugal and gravitational terms, and t ¼ 06£1trltll½ �. trl [ R6£1 and tll [ R6£1 are torque inputs for
the right leg and left leg, respectively. WJrf [ R6£18 is the Jacobian from the right foot coordinate frame to
SW , andWJlf [ R6£18 is the Jacobian from the left foot to SW .
Wfrf [ R6£1 is the external force acting on theright foot expressed in SW , and
Wflf [ R6£1 is that of the left foot.We introduce some variables which will be used later. WPr ¼ ½ux; uy; uz; px; py; pz�T consists of the
attitude and position of SR with respect to SR.Rvr ¼ ½vx;vy;vz; vx; vy; vz�T is the spatial velocity of the
floating base expressed in SR.WPr is used to obtain the coordinate transformation matrix RXW , which
transforms spatial velocity, acceleration or force from SW to SR.
The spatial acceleration of the floating base War and the angular acceleration of the virtual joints are
related by
€qr ¼W J21R
War 2W _JR _qr
� � ð3Þwhere WJr is the Jacobian from SR to SW .
Due to the kinematic constraints expressed by (1), €qrl, €qll and €qr have the following relationships
€qrl ¼W J21rf2 2W_Jrf _q2
WJrf1 €qr� � ð4Þ
and
€qll ¼W J21lf3 2W_Jlf _q2
WJlf1 €qr� � ð5Þ
where WJrf ¼ WJrf1;WJrf2;
WJrf3� �
and WJlf ¼ WJlf1;WJlf2;
WJlf3� �
. WJrf1,WJrf2,
WJrf3,WJlf1,
WJlf2, andWJlf3 [ R6£6.
The spatial acceleration War is related to conventional acceleration as
War ¼RX21W ac 2
03£1Rvr £Rvr
" # !ð6Þ
where ac ¼R_vr
Rv_r
" #is the conventional acceleration of the floating base in SR.
As long as ac is given, the angular accelerations of all joints €q can be calculated by (3), (4), (5) and (6).
Omnidirectional Disturbance Rejection for a Biped Robot by Acceleration Optimization 473
Dow
nloa
ded
by [
Uni
vers
ity o
f C
hica
go L
ibra
ry]
at 0
5:03
05
Oct
ober
201
4
3. DISTURBANCE REJECTION
3.1 Constraints on the Accelerations of the Floating Base
The contact constraint between the feet and the ground is unilateral, so we should impose constraints on the
external forces, which cause corresponding constraints on the accelerations of the floating base.
First, the relationship between the accelerations of the floating base and their corresponding external
forces is deduced. Rewrite MðqÞ as MðqÞ ¼M11 M12 M13
M21 M22 M23
M31 M32 M33
2664
3775. Each element of this matrix is a R6£6
matrix. The following equation is obtained by (2).
M11 €qr þM12 €qrl þM13 €qll þ C1 ¼WJTM1
MXTW
Mfm ð7Þ
where MXW is the coordinate transformation matrix from SW to frame SM. As shown in Figure 2, SM
locates on the margin of the Supporting Convex Hull (SCH). M fm is the external force expressed in this
frame.
Equation (7) is simplified as follows by using (4) and (5):
H €qr þ D ¼ WMfm ð8Þ
Figure 2. Supporting Convex Hull.
Intelligent Automation and Soft Computing474
Dow
nloa
ded
by [
Uni
vers
ity o
f C
hica
go L
ibra
ry]
at 0
5:03
05
Oct
ober
201
4
where
W ¼WJTM1
MXTW ð9Þ
H ¼ M11 2MW12J
21rf2
WJrf1 2MW
13J21lf3
WJlf1 ð10Þ
D ¼ C1 2MW12J
21rf2
W_Jrf _q2MW13J
21rf3
W_Jlf _q ð11ÞThe following equation is obtained by (3), (6) and (8).
Uac þ V ¼M fm ð12Þ
U ¼ W 21HWJ21R
RX21W ð13Þ
V ¼ W 21 D2 HWJ21R
RX21W
03£1Rvr £Rnr
" #þW _JR _qr
! !: ð14Þ
Equation (12) shows a clear relationship between the conventional acceleration and the external force.
The variablesU and V are functions of q and_q, which means that different poses and velocities may result in
different U and V. Thus, U and V are updated in every control period.
The variable M fm is a spatial vector which has six elements, M fm ¼ ½tx; ty; tz; f x; f y; f z�T. The forceconstraints can be further explained through the following inequalities.
. f z . 0. The ground can only push the feet.
. f x=f z , m=ffiffiffi2
p, f y=f z , m=
ffiffiffi2
pand tz=f z , mS. No slipping happens. Where, M is the coefficient of
friction and S is related to the area of the SCH.
. ty . or , 0 guarantees the ZMP within the SCH in the x direction. Choosing . or , depends on
where the coordinate frame is. For instance, if the frame is at the front side of the SCH, . is
selected; if the frame is at the back side of the SCH, , is selected.
. tx . or , 0 guarantees the ZMP within the SCH in the y direction. If the frame is at the left side of
the SCH, , is selected; if the frame is at the right side of the SCH, . is selected.
There are two constrained M fm which are expressed in SM1 and SM2, respectively. According to
the force constraints and (12), we can obtain 12 inequalities for each ac. These 12 inequalities are related to
U and V. We rewrite them into matrix form as
Aac , b: ð15Þwhere A [ R12£6 and b [ R12£1 are functions of U and V, respectively.
3.2 Desired Accelerations
PD (Proportional-Derivative) algorithm yields desired conventional accelerations acdes; which enable the
robot to recover its original state.
acdes ¼ KRPRW
Wprefr 2Wpr� �
2 KRd vr ð16Þ
where KP and Kd are PD gain matrices, RRW ¼I3£3 03£303£3 R21
" #, R is the posture matrix of the floating base
inSW ,Wprefr represents desired positions and attitudes of the floating base. However, the robot cannot move
Omnidirectional Disturbance Rejection for a Biped Robot by Acceleration Optimization 475
Dow
nloa
ded
by [
Uni
vers
ity o
f C
hica
go L
ibra
ry]
at 0
5:03
05
Oct
ober
201
4
with these desired accelerations unless they satisfy their constraints expressed by (15).We need to find
optimal accelerations which meet the constraints.
3.3 Acceleration Optimization
When the desired acceleration acdesis obtained through (16), QP is used to find optimal ones to satisfy the
constraints of the external forces exerted on the robot’s feet. The cost function is
f ða cÞ ¼ ða c 2 acdesÞTWaðac 2 acdesÞ ð17Þwhere Wa is a weight matrix.
Finally, f ðacÞ is minimized as
mina c
f ðacÞ; s:t: Aac # b ð18Þ
to obtain optimal accelerations which replace acdes to perform inverse dynamics.
3.4 Desired External Forces
The desired external forces which can drive the robot with the optimized accelerations is formulated as
follows. For simplification, the model is regarded as a fixed base model without external forces. Joint
torques are calculated by
tr
trl
tll
2664
3775 ¼ M €qþ C ð19Þ
where tr is the joint torques of the virtual joints. These torques result from virtual external forces acting on
the floating base. The external forces are derived through
W fext ¼WJ2TR tr ð20Þ
where W fest is the total external force provided by the feet.
3.5 Forces Distribution
It is very vital to distribute forces to each foot to satisfy their own individual constraints. First, an equality
constraint can be obtained:
W frf þW flf ¼W fext ð21ÞThen, inequality constraints similar to (15) are obtained. There are four constrained Mfm, which are
expressed in SM2, SM3
, SM4and SM1
respectively. The first two are for the right foot and the other two are
for the left foot. Thus, inequality constraints on the distributed forces are found as follows.
AWrf frf , 012£1 ð22Þ
and
AWrf flf , 012£1 ð23Þ
where Arf and Arf [ R12£6.
Intelligent Automation and Soft Computing476
Dow
nloa
ded
by [
Uni
vers
ity o
f C
hica
go L
ibra
ry]
at 0
5:03
05
Oct
ober
201
4
Rewrite (21)–(23) as
Aeq f feet ¼W fext ð24Þ
Aineq f feet , 024£1 ð25Þ
where f feet ¼W frf
W flf
24
35, Aineq ¼
Arf 012£6012£6 Alf
" #, Aeq ¼ ½ I6£6 I6£6 �.
The cost function is
gðf feetÞ ¼ f TfeetWf f feet ð26Þ
where Wf is a weight matrix.
Finally, f feet is obtained by
minf feet
gðf feetÞ; s:t: Aeqf feet ¼W fext;Aineq f feet , 024£1 ð27Þ
3.6 Inverse Dynamics
The variable €q is obtained by (3), (4), (5), (6) and (18). The variables W frf andW flf are obtained through (27).
So joint torques are calculated through
06£1trl
tll
2664
3775 ¼ M €qþ C 2WJTrf
Wfrf 2
WJTlfWflf ð28Þ
Note that the first six torques at the left side of (28) are zeros since the first six joints are virtual joints
which do not have kinematic constraints on the floating base.
Figure 3. Screenshot in the Side View After Experiencing a Disturbance in the Sagittal Plane.
Omnidirectional Disturbance Rejection for a Biped Robot by Acceleration Optimization 477
Dow
nloa
ded
by [
Uni
vers
ity o
f C
hica
go L
ibra
ry]
at 0
5:03
05
Oct
ober
201
4
4. SIMULATION
To validate the effectiveness of proposed method to reject omnidirectional disturbances, we applied
interference forces/torques on the torso in the sagittal plane, the lateral plane and the transverse plane,
respectively. No matter where the push is applied on the torso, the force is converted to a force and a torque
expressed in SR. So a force and a torque in SR is exerted to imitate a disturbance. All forces in the
simulations lasted for 0.1s.
The robot stands in place and keeps its torso upright. The total mass of the robot is 97kg. The length of
the forefoot is 0.182m. The distance between the center of the feet and the right side of the right foot is
0.15m. The height of the CoM is 0.883m.
4.1 Disturbance Rejection in the Sagittal Plane
A force of 300N in the x direction and 100 N�m around the y axis were exerted simultaneously to the robot
to simulate a disturbance in the sagittal plane. Figure 3 is the screenshot of the robot in the side view. The
Figure 4. Motion on the Floating Base When Experiencing a Disturbance in the Sagittal Plane.
Figure 5. Screenshot in the Front View After Experiencing a Disturbance in the Lateral Plane.
Intelligent Automation and Soft Computing478
Dow
nloa
ded
by [
Uni
vers
ity o
f C
hica
go L
ibra
ry]
at 0
5:03
05
Oct
ober
201
4
Figure 7. Screenshot in the Vertical View after a Disturbance in the Transverse Plane.
Figure 6. Motion on the Floating Base When Experiencing a Disturbance in the Lateral Plane.
Figure 8. Motion on the Floating Base When Experiencing a Disturbance in the Transverse Plane.
Omnidirectional Disturbance Rejection for a Biped Robot by Acceleration Optimization 479
Dow
nloa
ded
by [
Uni
vers
ity o
f C
hica
go L
ibra
ry]
at 0
5:03
05
Oct
ober
201
4
Figure 9. Screen Shot of the Robot Recovering From a Push with 800N.
Figure 10. Motion of the Floating Base When Experiencing Different Pushes in the x Direction. (a)Roll, (b)Pitch, (c)Yaw, (d)
Position in the x direction, (e) Position in the y direction, (f) Position in the z direction.
Intelligent Automation and Soft Computing480
Dow
nloa
ded
by [
Uni
vers
ity o
f C
hica
go L
ibra
ry]
at 0
5:03
05
Oct
ober
201
4
robot can keep its balance and recovery to its original position after a while. Figure 4 is the motion of the
floating base after the robot experiences the disturbance. Besides the motion in the same direction as the
disturbance, the robot also made use of motion in other directions to reject the disturbance, especially the
movement in the z direction. It is similar to the result in our previous work [19].
4.2 Disturbance Rejection in the Lateral Plane
A force of 300N in the y direction and a torque with 100 N�m around the x axis were applied
simultaneously to simulate a disturbance in the lateral plane. Figure 5 is the screenshot of the robot in the
front view. The robot can keep its stability and recovery to its original position as well. From Figure 6, the
disturbance in the lateral plane also resulted in motion in other planes to stabilize the robot.
4.3 Disturbance Rejection in the Transverse Plane
We applied 300N in the x direction 100 N�m around the z axis simultaneously to simulate a disturbance in
the transverse plane. Figure 7 is the screenshot of the robot in the vertical view and Figure 8 is the motion of
the floating base. Analogously, the disturbance in the transverse plane also resulted in motion in sagittal and
lateral planes to reject the disturbance.
Figure 11. ZMP, Friction Constraints and Vertical Force When Experiencing Disturbance. (a) ZMP in the x direction, (b) ZMP in the
y direction, (c) Friction constraint in the x direction, (d) Friction constraint in the y direction, (e) Friction constraint around the z axis,
(f) Vertical force.
Omnidirectional Disturbance Rejection for a Biped Robot by Acceleration Optimization 481
Dow
nloa
ded
by [
Uni
vers
ity o
f C
hica
go L
ibra
ry]
at 0
5:03
05
Oct
ober
201
4
The above three simulations show that a push in/around a direction will induce the torso motion in/
around other axes. This demonstrates our method exploits coordinated whole-body motion for stabilization.
Furthermore, we need not change any rules of the stabilization controller to reject different disturbances.
4.4 Comparison of Different Disturbances in the Same Direction
We did a group of simulations with increasing forces applied in the x direction. Figure 10 shows the motion
of the floating base after the robot suffers 400N, 600N and 800N, respectively. If the push is small, the robot
recovers quickly. If the push is large, the robot recovers slowly.
When it is over 800N, it is hard for the robot to recover its original position. Figures 9 and 10 shows the
screen shots of the robot after experiencing 800N. Figure 11 shows the external forces.
We set m ¼ 0:1 and S ¼ 0:1. f r ¼ ½0; 0; tzr; f xr; f yr; f zr�T and f l ¼ ½0; 0; tzl; f xl; f yl; f zl�T are the ground
reaction forces expressed in the frames located on the right foot and left foot respectively. In order to have
stability margin, the size of the feet was set to be 1 cm shorter in each side than the actual feet. Figure 11(a),
(b) show the actual ZMP trajectories are within their own margin. Figure 11(c)–(e) shows that the friction
constraints are satisfied. The ground only provides push forces to the feet according to Figure 11(f). The
desired and optimal accelerations are compared in Figure 12. The optimal accelerations are not equal to the
Figure 12. Desired and Optimized Accelerations. (a) Angular acceleration around the x axis, (b) Angular acceleration around the y
axis, (c) Angular acceleration around the z axis, (d) Acceleration in the x direction, (e) Acceleration in the y direction, (f) Acceleration
in the z direction.
Intelligent Automation and Soft Computing482
Dow
nloa
ded
by [
Uni
vers
ity o
f C
hica
go L
ibra
ry]
at 0
5:03
05
Oct
ober
201
4
desired ones after the disturbance is exerted because the desired accelerations go beyond the boundaries.
When the deviations become small enough so that the desired accelerations satisfy the constraints, the
desired and optimal accelerations converge.
5. CONCLUSION AND DISCUSSION
This study presents a method to reject omnidirectional disturbances by acceleration optimization. The
robot’s stability capability was improved by optimizing the accelerations of the floating base according to
the imposed constraints on the external forces. The effectiveness of the proposed method was demonstrated
by simulations.
Our method enables the biped robot to reject disturbances by controlling the torso. So it can be
extended to balance a quadruped robot as well. In our future work, we will confirm our method by
experiments on a real biped robot. Moreover, we will extend our method to endure greater disturbances by
using step strategy.
ACKNOWLEDGEMENTSThis work was supported by the National Natural Science Foundation of China under Grants 61273348, 61320106012, 61375103,
60925014, and 61175077, “111 Project” under Grant B08043, “863” Project under Grant 2014AA041602, and Beijing Municipal
Science and Technology Project.
REFERENCES[1] Urata, J., Nshiwaki, K., Nakanishi, Y., Okada, K., Kagami, S., & Inaba, M. (2012). Online walking pattern generation for push
recovery and minimum delay to commanded change of direction and speed. Proceedings of IEEE/RSJ International Conference
on Intelligent Robots and Systems, 3411–3416.
[2] Adiwahono, A. H., Chew, C. M., & Huang, W. (2010). Humanoid robot push recovery through walking phase modification.
Proceedings of IEEE International Conference on Robotics and Automation, 569–574.
[3] Morisawa, M., Kanehiro, F., Kaneko, K., Mansard, N., Sola, J., Yoshida, E., & Laumond, J. P. (2010). Combining suppression of
the disturbance and reactive stepping for recovering balance. Proceedings of IEEE/RSJ International Conference on Intelligent
Robots and Systems, 3150–3156.
[4] Huang, Q., & Nakamura, Y. (2005). Sensory reflex Control for Humanoid Walking. IEEE Transactions on Robotics, 21,
977–984.
[5] Pratt, J., Carff, J., Drakunov, S., & Goswami, A. (2006). Capture point: A step toward humanoid push recovery. Proceedings of
IEEE-RAS International Conference On Humanoid Robots, 200–207.
[6] Yi, S. J., Zhang, B. T., Hong, D., & Lee, D. D. (2012). Active stabilization of a humanoid robot for impact motions with unknown
reaction forces. Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, 4034–4039.
[7] Stephens, B. (2007). Humanoid push recovery. Proceedings of IEEE-RAS International Conference on Humanoid Robots,
589–595.
[8] Kanamiya, Y., Ota, S., & Sato, D. (2010). Ankle and hip balance control strategies with transitions. Proceedings of IEEE
International Conference on Robotics and Automation, 3446–3451.
[9] Mahani, M. A. N., Jafari, S., & Rahmatkhah, R. (2011). Novel humanoid push recovery using knee joint. Proceedings of IEEE/
RAS International Conference on Humanoid Robots, 446–451.
[10] Kuo, A. (1995). An optimal control model for analyzing human postural balance. IEEE Transactions on Biomedical Engineering,
42, 87–101.
[11] Atkeson, C. G., & Stephens, B. (2007). Multiple balance strategies from one optimization criterion. Proceedings of IEEE
International Conference on Humanoid Robots, 57–64.
[12] Xing, D. P., & Liu, X. (2010). Multiple balance strategies for humanoid standing control. Acta Automatica Sinica, 37, 228–233.
[13] Liu, C. G., & Atkeson, C. G. (2009). Standing balance control using a trajectory library. Proceedings of IEEE/RSJ International
Conference on Intelligent Robots and Systems, 3031–3036.
[14] Wang, J. (2012). Humanoid push recovery with robust convex synthesis. Proceedings of IEEE/RSJ International Conference on
Intelligent Robots and Systems, 4354–4359.
[15] Yoshida, Y., Takeuchi, K., Sato, D., & Nenchev, D. (2011). Balance control of humanoid robots in response to disturbances in the
frontal plane. Proceedings of IEEE International Conference on Robotics and Biomimetics, 2241–2242.
Omnidirectional Disturbance Rejection for a Biped Robot by Acceleration Optimization 483
Dow
nloa
ded
by [
Uni
vers
ity o
f C
hica
go L
ibra
ry]
at 0
5:03
05
Oct
ober
201
4
[16] Hyon, S., Osu, R., & Otaka, Y. (2009). Integration of multi-level postural balancing on humanoid robots. Proceedings of IEEE
International Conference on Robotics and Automation, 1549–1556.
[17] Ott, C., Roa, M. A., & Hirzinger, G. (2011). Posture and balance control for biped robots based on contact force optimization.
Proceedings of IEEE-RAS International Conference on Humanoid Robots, 26–33.
[18] Featherstone, R. (2010). A beginner’s guide to 6-d vectors (part 1). IEEE Robotics & Automation Magazine, 17, 83–94.
[19] Chen, X., Huang, Q., Yu, Z., Lu, Y. (2014) Robust push recovery by whole-body dynamics control with extremal accelerations.
Robotica, 32, 467–476. doi:10.1017/S0263574713000829.
[20] Shi, W., Wang, K., & Yang, S. X. (2009). A fuzzy-neural network approach to multisensor integration for obstacle avoidance of a
mobile robot. Intelligent Automation and Soft Computing, 15, 289–301.
[21] Yan, M., Zhu, D., & Yang, S. X. (2013). A novel 3-D bio-inspired neural network model for the path planning of an AUV in
underwater environments. Intelligent Automation and Soft Computing, 19, 555–566.
NOTES ON CONTRIBUTORS
Zhangguo Yu received B.S. degree in Electronics Engineering and M.S. degree in Control Engineering
from Southwest University of Science and Technology and Ph.D. degree in Mechatronics Engineering
from Beijing Institute of Technology, China, in 1997, 2005, and 2009. Currently, he is with Beijing
Institute of Technology, China. His research interests include humanoid robots, and motion planning and
control. Email: [email protected].
Fei Meng received B.S. and M.S. degrees in 2008 and 2010 from Beijing Institute of Technology. He is
currently working towards a Ph.D. degree at Beijing Institute of Technology, China. His research interests
include control and planning for biped robots.
Qiang Huang received B.S. and M.S. degrees from Harbin Institute of Technology, China, and Ph.D.
degree from Waseda University, Tokyo, Japan, in 1986, 1989, and 1996, respectively. He joined the
Mechanical Engineering Laboratory (MEL), AIST, Tsukuba, Japan, as a research fellow in 1996, and was
a researcher at the Department of Mechano-Informatics, University of Tokyo from 1999 to 2000. Since
2001, he has been with Beijing Institute of Technology (BIT), China. Currently he is a professor and the
director of the Intelligent Robotics Institute, BIT, China. His research interests include humanoid robots,
space robots and intelligent mechatronics.
Intelligent Automation and Soft Computing484
Dow
nloa
ded
by [
Uni
vers
ity o
f C
hica
go L
ibra
ry]
at 0
5:03
05
Oct
ober
201
4
Xuechao Chen received B.S. and Ph.D. degrees in Mechatronics Engineering from Beijing Institute of
Technology (BIT), China in 2007 and 2013, respectively. Currently he is a lecturer at the School of
Mechatronics Engineering, BIT. He was a visiting student in Robotics Institute, Carnegie Mellon
University in 2012. His research interests include biped locomotion, humanoid robotics, and dynamics
simulation.
Gan Ma received B.S. degree in Mechanical Engineering from Sichuan University, China, in 2009. He
became a Ph.D. candidate at Beijing Institute of Technology, China in 2009. His research focuses on
development of humanoid robots and stability control.
Jing Li received B.S. degree at Shandong University of Technology, China, in 2007. Currently he is a Ph.D. candidate at Intelligent Robotics Institute, Beijing Institute of Technology, China. His research
interests include biped locomotion and motion planning.
Omnidirectional Disturbance Rejection for a Biped Robot by Acceleration Optimization 485
Dow
nloa
ded
by [
Uni
vers
ity o
f C
hica
go L
ibra
ry]
at 0
5:03
05
Oct
ober
201
4
Recommended
