Abstract

The estimation of human ankle's mechanical impedance is an important tool for modeling human balance. This work presents the implementation of a parameter-estimation approach based on a state-augmented extended Kalman filter (AEKF) to infer the ankle's mechanical impedance during quiet standing. However, the AEKF filter is sensitive to the initialization of the noise covariance matrices. In order to avoid a time-consuming trial-and-error method and to obtain a better estimation performance, a genetic algorithm (GA) is proposed to best tune the measurement noise (Rk) and process noise covariances (Q) of the extended Kalman filter (EKF). Results using simulated data show the efficacy of the proposed algorithm for parameter-estimation of a third-order biomechanical model. Experimental validation of these results is also presented. They suggest that age is an influencing factor in the human balance.

References

1.
Casadio
,
M.
,
Morasso
,
P. G.
, and
Sanguineti
,
V.
,
2005
, “
Direct Measurement of Ankle Stiffness During Quiet Standing: Implications for Control Modelling and Clinical Application
,”
Gait Posture
,
21
(
4
), pp.
410
424
.10.1016/j.gaitpost.2004.05.005
2.
Romero
,
R. C.
,
Cardenas
,
A.
, and
Piovesan
,
D.
,
2014
, “
Viscoelastic Properties of the Ankle During Quiet Standing Via Raster Images and EKF
,”
Signal Processing in Medicine and Biology Symposium
(
SPMB
), IEEE, Philadelphia, PA, Dec. 13, pp.
1
5
.10.1109/SPMB.2014.7002973
3.
Ludvig
,
D.
, and
Perreault
,
E. J.
,
2011
, “
Estimation of Joint Impedance Using Short Data Segments
,”
Annual International Conference of the IEEE Engineering in Medicine and Biology Society
, Boston, MA, Aug. 30–Sept. 3, pp.
4120
4123
.10.1109/IEMBS.2011.6091023
4.
Lee
,
H.
,
Rouse
,
E. J.
, and
Krebs
,
H. I.
,
2016
, “
Summary of Human Ankle Mechanical Impedance During Walking
,”
IEEE J. Transl. Eng. Health Med.
,
4
, pp.
1
7
.10.1109/JTEHM.2016.2601613
5.
Hogan
,
N.
,
1984
, “
Adaptive Control of Mechanical Impedance by Coactivation of Antagonist Muscles
,”
IEEE Trans. Autom. Control
,
29
(
8
), pp.
681
690
.10.1109/TAC.1984.1103644
6.
Ho
,
C. Y.
, and
Bendrups
,
A. P.
,
2002
, “
Ankle Reflex Stiffness During Unperceived Perturbation of Standing in Elderly Subjects
,”
J. Gerontol. Ser. A: Biol. Sci. Med. Sci.
,
57
(
9
), pp.
B344
B350
.10.1093/gerona/57.9.B344
7.
Chavez-Romero
,
R.
,
Cardenas
,
A.
,
Rendon-Mancha
,
J. M.
,
Vernaza
,
K. M.
, and
Piovesan
,
D.
,
2015
, “
Inexpensive Vision-Based System for the Direct Measurement of Ankle Stiffness During Quiet Standing
,”
ASME J. Med. Dev.
,
9
(
4
), p. 041011.10.1115/1.4031060
8.
Cenciarini
,
M.
,
Loughlin
,
P. J.
,
Sparto
,
P. J.
, and
Redfern
,
M. S.
,
2010
, “
Stiffness and Damping in Postural Control Increase With Age
,”
Biomed. Eng., IEEE Trans.
,
57
(
2
), pp.
267
275
.10.1109/TBME.2009.2031874
9.
Bortolami
,
S.
,
DiZio
,
P.
,
Rabin
,
E.
, and
Lackner
,
J.
,
2003
, “
Analysis of Human Postural Responses to Recoverable Falls
,”
Exp. Brain Res.
,
151
(
3
), pp.
387
404
.10.1007/s00221-003-1481-x
10.
Piovesan
,
D.
,
Morasso
,
P.
,
Giannoni
,
P.
, and
Casadio
,
M.
,
2013
, “
Arm Stiffness During Assisted Movement After Stroke: The Influence of Visual Feedback and Training
,”
Neural Syst. Rehabil. Eng., IEEE Trans.
,
21
(
3
), pp.
454
465
.10.1109/TNSRE.2012.2226915
11.
Piovesan
,
D.
,
Kennett
,
C. J.
,
Chavez-Romero
,
R.
,
Panza
,
M. J.
, and
Cárdenas
,
A.
,
2015
, “
Stiffness Boundary Conditions for Critical Damping in Balance Recovery
,”
ASME Paper No. IMECE2015-50564
.10.1115/IMECE2015-50564
12.
van der Kooij
,
H.
,
Donker
,
S.
,
de Vrijer
,
M.
, and
van der Helm
,
F.
,
2004
, “
Identification of Human Balance Control in Standing
,”
IEEE International Conference on Systems, Man and Cybernetics
, Vol.
3
,
IEEE
,
The Hague, The Netherlands
, Oct. 10–13, pp.
2535
2541
.10.1109/ICSMC.2004.1400711
13.
Vlutters
,
M.
,
Boonstra
,
T.
,
Schouten
,
A.
, and
van der Kooij
,
H.
,
2015
, “
Direct Measurement of the Intrinsic Ankle Stiffness During Standing
,”
J. Biomech.
,
48
(
7
), pp.
1258
1263
.10.1016/j.jbiomech.2015.03.004
14.
Melendez-Calderon
,
A.
,
Piovesan
,
D.
,
Patton
,
J. L.
, and
Mussa-Ivaldi
,
F. A.
,
2014
, “
Enhanced Assessment of Limb Neuro-Mechanics Via a Haptic Display
,”
Rob. Biomimetics
,
1
(
1
), pp.
1
10
.10.1186/s40638-014-0012-5
15.
Olinsky
,
A. D.
,
Quinn
,
J. T.
,
Mangiameli
,
P. M.
, and
Chen
,
S. K.
,
2004
, “
A Genetic Algorithm Approach to Nonlinear Least Squares Estimation
,”
Int. J. Math. Educ. Sci. Technol.
,
35
(
2
), pp.
207
217
.10.1080/00207390310001638331
16.
Tomioka
,
S.
,
Nisiyama
,
S.
, and
Enoto
,
T.
,
2007
, “
Nonlinear Least Square Regression by Adaptive Domain Method With Multiple Genetic Algorithms
,”
IEEE Trans. Evol. Comput.
,
11
(
1
), pp.
1
16
.10.1109/TEVC.2006.876363
17.
Piovesan
,
D.
,
Pierobon
,
A.
,
DiZio
,
P.
, and
Lackner
,
J. R.
,
2012
, “
Measuring Multi-Joint Stiffness During Single Movements: Numerical Validation of a Novel Time-Frequency Approach
,”
PLoS One
,
7
(
3
), p.
e33086
.10.1371/journal.pone.0033086
18.
Piovesan
,
D.
,
Pierobon
,
A.
, and
Ivaldi
,
F. A. M.
,
2013
, “
Critical Damping Conditions for Third Order Muscle Models: Implications for Force Control
,”
ASME J. Biomech. Eng.
,
135
(
10
), p.
101010
.10.1115/1.4025110
19.
Kistemaker
,
D. A.
, and
Rozendaal
,
L. A.
,
2011
, “
In Vivo Dynamics of the Musculoskeletal System Cannot Be Adequately Described Using a Stiffness-Damping-Inertia Model
,”
PLoS One
,
6
(
5
), p.
e19568
.10.1371/journal.pone.0019568
20.
Crevecoeur
,
F.
, and
Scott
,
S. H.
,
2014
, “
Beyond Muscles Stiffness: Importance of State-Estimation to Account for Very Fast Motor Corrections
,”
PLoS Comput. Biol.
,
10
(
10
), p.
e1003869
.10.1371/journal.pcbi.1003869
21.
McGinnis
,
P.
,
2013
,
Biomechanics of Sport and Exercise
,
Human Kinetics
,
Champaign, IL
.
22.
Åström
,
K. J.
,
1980
, “
Maximum Likelihood and Prediction Error Methods
,”
Automatica
,
16
(
5
), pp.
551
574
.10.1016/0005-1098(80)90078-3
23.
Mehra
,
R. K.
,
Stepner
,
D. E.
, and
Tyler
,
J. S.
,
1974
, “
Maximum Likelihood Identification of Aircraft Stability and Control Derivatives
,”
J. Aircr.
,
11
(
2
), pp.
81
89
.10.2514/3.60327
24.
Peyada
,
N. K.
,
Sen
,
A.
, and
Ghosh
,
A. K.
,
2008
, “
Aerodynamic Characterization of HANSA-3 Aircraft Using Equation Error, Maximum Likelihood and Filter Error Methods
,”
Proceedings of the International MultiConference of Engineers and Computer Scientists (IMECS)
, Vol.
2
, Hong Kong, Mar. 19–21.https://www.researchgate.net/publication/44261880_Aerodynamic_Characterization_of_HANSA-3_aircraft_using_Equation_Error_Maximum_Likelihood_and_Filter_Error_Methods
25.
Balakrishnan
,
A.
,
1968
, “
Stochastic System Identification Techniques
,”
Stochastic Optimization and Control
,
H. F.
Karreman
, ed.,
Wiley
,
New York
.
26.
Mehra
,
R. K.
,
1971
, “
Identification of Stochastic Linear Dynamic Systems Using Kalman Filter Representation
,”
AIAA J.
,
9
(
1
), pp.
28
31
.10.2514/3.6120
27.
Kopp
,
R. E.
, and
Orford
,
R. J.
,
1963
, “
Linear Regression Applied to System Identification for Adaptive Control Systems
,”
AIAA J.
,
1
(
10
), pp.
2300
2306
.10.2514/3.2056
28.
Simon
,
D.
,
2006
,
Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches
,
Wiley
,
New York
.
29.
Raol
,
J. R.
,
Girija
,
G.
, and
Singh
,
J.
,
2004
, “
Modelling and Parameter Estimation of Dynamic Systems
,”
IET
,
London, UK
, Vol.
65
.
30.
Chan
,
Z. S.
,
Ngan
,
H.
,
Fung
,
Y.
, and
Rad
,
A.
,
2001
, “
An Advanced Evolutionary Algorithm for Parameter Estimation of the Discrete Kalman Filter
,”
Comput. Phys. Commun.
,
142
(
1–3
), pp.
248
254
.10.1016/S0010-4655(01)00332-0
31.
Wenzel
,
T.
,
Burnham
,
K.
,
Williams
,
R.
, and
Blundell
,
M.
,
2004
, “
Hybrid Genetic Algorithms/Extended Kalman Filter Approach for Vehicle State and Parameter Estimation
,”
Proceedings of the International Conference Control
, Palo Alto, CA, Sept., pp.
104
109
.http://ukacc.group.shef.ac.uk/proceedings/control2004/Papers/124.pdf
32.
Chan
,
T.-F.
, and
Shi
,
K.
,
2011
, “
GA-Optimized Extended Kalman Filter for Speed Estimation
,”
Applied Intelligent Control Induction Motor Drives
,
Wiley-IEEE Press
,
New York
, pp.
243
271
.10.1002/9780470825587.ch9
33.
Tofiq
,
L. N.
, and
Aula
,
F. T.
,
2016
, “
Real Time Estimation of Kalman Filter Parameters Using the Genetic Algorithm for Optimum Balancing Controller of Two-Wheel Robotic System
,”
ZANCO J. Pure Appl. Sci.
,
28
(
2
), pp.
s539
s544
.10.21271/zjpas.v28i2.866
34.
Ting
,
T.
,
Man
,
K. L.
,
Lim
,
E. G.
, and
Leach
,
M.
,
2014
, “
Tuning of Kalman Filter Parameters Via Genetic Algorithm for State-of-Charge Estimation in Battery Management System
,”
Sci. World J.
,
2014
, pp.
1
11
.10.1155/2014/176052
35.
Thede
,
S. M.
,
2004
, “
An Introduction to Genetic Algorithms
,”
J. Comput. Sci. Coll.
,
20
(
1
), pp.
115
123
.https://dl.acm.org/doi/10.5555/1040231.1040247
36.
Holland
,
J. H.
,
1992
, “
Genetic Algorithms
,”
Sci. Am.
,
267
(
1
), pp.
66
72
.10.1038/scientificamerican0792-66
37.
Boyd
,
S.
, and
Vandenberghe
,
L.
,
2004
,
Convex Optimization
,
Cambridge University Press
,
Cambridge, GB
.
38.
Coronado
,
E.
,
Chavez-Romero
,
R.
,
Maya
,
M.
,
Cardenas
,
A.
, and
Piovesan
,
D.
,
2015
, “
Combining Genetic Algorithms and Extended Kalman Filter to Estimate Ankle's Muscle-Tendon Parameters
,”
ASME Paper No. DSCC2015-9781
.10.1115/DSCC2015-9781
39.
Segura
,
M. E.
,
Coronado
,
E.
,
Cardenas
,
A.
, and
Piovesan
,
D.
,
2014
, “
Time-Based Identification of Human Ankle Impedance Via Microsoft Kinect
,”
Signal Processing in Medicine and Biology Symposium (SPMB)
,
IEEE
,
Philadelphia, PA
, Dec. 12, pp.
1
5
.10.1109/SPMB.2015.7405424
40.
Fortin
,
F.-A.
,
De Rainville
,
F.-M.
,
Gardner
,
M.-A.
,
Parizeau
,
M.
, and
Gagné
,
C.
,
2012
, “
DEAP: Evolutionary Algorithms Made Easy
,”
J. Mach. Learn. Res.
,
13
(
1
), pp.
2171
2175
.https://dl.acm.org/doi/abs/10.5555/2503308.2503311
41.
Shemmell
,
J.
,
2015
, “
Interactions Between Stretch and Startle Reflexes Produce Task-Appropriate Rapid Postural Reactions
,”
Front. Integr. Neurosci.
,
9
(
2
).10.3389/fnint.2015.00002
42.
Pardes
,
A.
,
Beach
,
Z.
,
Raja
,
H.
,
Rodriguez
,
A.
,
Freedman
,
B.
, and
Soslowsky
,
L.
,
2017
, “
Aging Leads to Inferior Achilles Tendon Mechanics and Altered Ankle Function in Rodents
,”
J. Biomech.
,
60
(
06
), pp.
30
38
.10.1016/j.jbiomech.2017.06.008
43.
Lamontagne
,
A.
,
Malouin
,
F.
, and
Richards
,
C. L.
,
2000
, “
Contribution of Passive Stiffness to Ankle Plantarflexor Moment During Gait After Stroke
,”
Arch. Phys. Med. Rehabil.
,
81
(
3
), pp.
351
358
.10.1016/S0003-9993(00)90083-2
44.
Marusiak
,
J.
,
Kisiel-Sajewicz
,
K.
,
Jaskólska
,
A.
, and
Jaskólski
,
A.
,
2010
, “
Higher Muscle Passive Stiffness in Parkinson's Disease Patients Than in Controls Measured by Myotonometry
,”
Arch. Phys. Med. Rehabil.
,
91
(
5
), pp.
800
802
.10.1016/j.apmr.2010.01.012
45.
Sinkjær
,
T.
,
Andersen
,
J. B.
, and
Nielsen
,
J. F.
,
1996
, “
Impaired Stretch Reflex and Joint Torque Modulation During Spastic Gait in Multiple Sclerosis Patients
,”
J. Neurol.
,
243
(
8
), pp.
566
574
.10.1007/BF00900943
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