Balancing control is important for biped standing. In spite of large efforts, it is very difficult to design balancing control strategies satisfying three requirements simultaneously: maintaining postural stability, improving energy efficiency, and satisfying the constraints between the biped feet and the ground. To implement such a control, inclusion of the actuators' dynamics is necessary, which complicates the overall system, obstructs the control design, and makes stability analysis more difficult. In this paper, a constrained balancing control meeting all three requirements is designed for a standing bipedal robot. The dynamics of the selected actuators has been considered for developing the motion equations of the overall control system, which has usually been neglected in simulations. In addition, stability analysis of such a complex biped control system has been provided using the concept of Lyapunov exponents (LEs), which shows the significance of actuators' dynamics on the stability region. The paper contributes to balancing standing biped in both the theoretical and the practical sense.

References

References
1.
Masani
,
K.
,
Vette
,
A. H.
, and
Popovic
,
M. R.
,
2006
, “
Controlling Balance During Quiet Standing: Proportional and Derivative Controller Generates Preceding Motor Command to Body Sway Position Observed in Experiments
,”
Gait Posture
,
23
(
2
), pp.
164
172
.10.1016/j.gaitpost.2005.01.006
2.
Gatev
,
P.
,
Thomas
,
S.
,
Kepple
,
T.
, and
Hallett
,
M.
,
1999
, “
Feedforward Ankle Strategy of Balance During Quiet Stance in Adults
,”
J. Physiol.
,
514
(
3
), pp.
915
928
.10.1111/j.1469-7793.1999.915ad.x
3.
Pai
,
Y.
, and
Patton
,
J.
,
1997
, “
Center of Mass Velocity-Position Predictions for Balance Control
,”
J. Biomech.
,
30
(
4
), pp.
347
354
.10.1016/S0021-9290(96)00165-0
4.
Yang
,
C.
,
Wu
,
Q.
, and
Joyce
,
G.
,
2007
, “
Effects of Constraints on Bipedal Balance Control During Standing
,”
Int. J. Humanoid Rob.
,
4
(
4
), pp.
753
775
.10.1142/S0219843607001230
5.
Kuo
,
A. D.
,
1995
, “
An Optimal Control Model for Analyzing Human Postural Balance
,”
IEEE Trans. Biomed. Eng.
,
42
(
1
), pp.
87
101
.10.1109/10.362914
6.
Dariush
,
B.
,
Hemami
,
H.
, and
Parnianpour
,
M.
,
2001
, “
Multi-Modal Analysis of Human Motion From External Multi-Modal Analysis of Human Motion From External Measurements
,”
ASME J. Dyn. Syst., Meas., Control
,
123
(
2
), pp.
272
278
.10.1115/1.1370375
7.
Lower
,
M.
,
2008
, “
Simulation Model of Human Individual in Quiet Standing Based on an Inverted Pendulum With Fuzzy Controller
,”
Proceedings of the 7th International Conference on Machine Learning and Cybernetics
, pp.
3418
3422
.
8.
Colbaugh
,
R.
,
Barany
,
E.
, and
Glass
,
K.
,
1997
, “
Global Stabilization of Uncertain Manipulators Using Bounded Controls
,”
Proceedings of the American Control Conference
, Vol.
1
, pp.
86
91
.
9.
Luca
,
A. D.
,
Siciliano
,
B.
, and
Zollo
,
L.
,
2005
, “
PD Control With On-Line Gravity Compensation for Robots With Elastic Joints: Theory and Experiments
,”
Automatica
,
41
(
10
), pp.
1809
1819
.10.1016/j.automatica.2005.05.009
10.
Alvarez-Ramirez
,
J.
,
Jose
,
R.
, and
Cervantes
,
I.
,
2003
, “
Semiglobal Stability of Saturated Linear PID Control for Robot Manipulators
,”
Automatica
,
39
(
6
), pp.
989
995
.10.1016/S0005-1098(03)00035-9
11.
Shen
,
X.
, and
Christ
,
D.
,
2011
, “
Design and Control of Chemomuscle: A Liquid-Propellant-Powered Muscle Actuation System
,”
ASME J. Dyn. Syst., Meas., Control
,
133
(
2
), p.
021006
.10.1115/1.4003208
12.
Ghorbani
,
R.
,
Wu
,
Q.
, and
Wang
,
G. G.
,
2007
, “
Nearly Optimal Neural Network Stabilization of Bipedal Standing Using Genetic Algorithm
,”
Eng. Appl. Artif. Intell.
,
20
(
4
), pp.
473
480
.10.1016/j.engappai.2006.09.007
13.
Sun
,
Y.
, and
Wu
,
C. Q.
,
2012
, “
Stability Analysis via the Concept of Lyapunov Exponents: A Case Study in Optimal Controlled Biped Standing
,”
Int. J. Control
,
85
(
12
), pp.
1952
1966
.10.1080/00207179.2012.713985
14.
Chevallereau
,
C.
, and
Aoustin
,
Y.
,
2001
, “
Optimal Reference Trajectories for Walking and Running of a Biped Robot
,”
Robotica
,
19
, pp.
557
569
.10.1017/S0263574701003307
15.
Bertec, Co.
,
2014
,
Bertec Instrumented-Treadmills
, http://bertec.com/products/instrumented-treadmills.html
16.
Stefanski
,
A.
,
2000
, “
Estimation of the Largest Lyapunov Exponent in Systems With Impacts
,”
Chaos Solitons Fractals
,
11
(
15
), pp.
2443
2451
.10.1016/S0960-0779(00)00029-1
17.
Dingwell
,
J. B.
, and
Cusumano
,
J. P.
,
2000
, “
Nonlinear Time Series Analysis of Normal and Pathological Human Walking
,”
Chaos
,
10
(
4
), pp.
848
863
.10.1063/1.1324008
18.
Kinsner
,
W.
,
2006
, “
Characterizing Chaos Through Lyapunov Metrics
,”
IEEE Trans. Syst., Man Cybern., Part C
,
36
(
2
), pp.
141
151
.10.1109/TSMCC.2006.871132
19.
Polo
,
M. P.
,
Albertos
,
P.
, and
Galiano
,
J. A. B.
,
2008
, “
Tuning of a PID Controlled Gyro by Using the Bifurcation Theory
,”
Syst. Control Lett.
,
57
(
1
), pp.
10
17
.10.1016/j.sysconle.2007.06.007
20.
Zribi
,
M.
,
Oteafy
,
A.
, and
Smaoui
,
N.
,
2009
, “
Controlling Chaos in the Permanent Magnet Syschronous Motor
,”
Chaos, Solitons Fractals
,
41
(
3
), pp.
1266
1276
.10.1016/j.chaos.2008.05.019
21.
Oseledec
,
V. I.
,
1968
, “
A Multiplicative Ergodic Theorem: Lyapunov Characteristic Numbers for Dynamical System
,”
Trans. Moscow Math. Soc.
,
19
, pp.
197
231
.
22.
Wolf
,
A.
,
Swift
,
J. B.
,
Swinney
,
H. L.
, and
Vastano
,
J. A.
,
1985
, “
Determining Lyapunov Exponents From a Time Series
,”
Physics D
,
16
, pp.
285
317
.10.1016/0167-2789(85)90011-9
23.
Brown
,
R.
,
Bryant
,
P.
, and
Abarbanel
,
H. D. I.
,
1991
, “
Computing the Lyapunov Spectrum of a Dynamical System From an Observed Time Series
,”
Phys. Rev. A
,
43
, pp.
2787
2806
.10.1103/PhysRevA.43.2787
24.
Williams
,
G. P.
,
1997
,
Chaos Theory Tamed
,
Joseph Henry Press
,
Washington, DC
.
25.
Slotine
,
J.-J. E.
, and
Li
,
W.
,
1991
,
Applied Nonlinear Control
,
Prentice Hall
,
New York
.
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