Any articulated system of rigid bodies defines a statically equivalent serial chain (SESC). The SESC is a virtual chain that terminates at the center of mass (CoM) of the original system of bodies. An SESC may be generated experimentally without knowing the mass, CoM, or length of each link in the system given that its joint angles and overall CoM may be measured. This paper presents three developments toward recognizing the SESC as a practical modeling technique. Two of the three developments improve utilizing the technique in practical applications where the arrangement of the joints impacts the derivation of the SESC. The final development provides insight into the number of poses needed to create a usable SESC in the presence of data collection errors. First, modifications to a matrix necessary in computing the SESC are proposed, followed by the experimental validation of SESC modeling. Second, the problem of generating an SESC experimentally when the system of bodies includes a mass fixed in the ground frame are presented and a remedy is proposed for humanoid-like systems. Third, an investigation of the error of the experimental SESC versus the number of data readings collected in the presence of errors in joint readings and CoM data is conducted. By conducting the method on three different systems with various levels of data error, a general form of the function for estimating the error of the experimental SESC is proposed.
Issue Section:
Research Papers
References
1.
Fisher
, O.
, 1902
, “Über die reduzierten systeme und die hauptpunkte der glieder eines gelenkmechanismus
,” Zeitschrift für angewandte Mathematik und Physik
, 47
, pp. 429
–466
.2.
Lowen
, G.
, and Berkof
, R.
, 1968
, “Survey of Investigations Into the Balancing of Linkages
,” J. Mech.
, 3
(4
), pp. 221
–231
.10.1016/0022-2569(68)90001-33.
Espiau
, B.
, and Boulic
, R.
, 1998
, “On the Computation and Control of the Mass Center of Articulated Chains
,” INRIA, Montbonnot St Martin, France, Report No. RR-3479.4.
Cotton
, S.
, Murray
, A.
, and Fraisse
, P.
, 2008
, “Statically Equivalent Serial Chains for Modeling the Center of Mass of Humanoid Robots
,” 8th IEEE-RAS International Conference on Human Robotics
(Humanoids 2008
), Daejeon, South Korea, Dec. 1–3, pp. 138
–144
.10.1109/ICHR.2008.47559585.
Cotton
, S.
, Murray
, A.
, and Fraisse
, P.
, 2009
, “Estimation of the Center of Mass Using Statically Equivalent Serial Chain Modeling
,” ASME
Paper No. DETC2009-86227.10.1115/DETC2009-862276.
Cotton
, S.
, Murray
, A.
, and Fraisse
, P.
, 2009
, “Estimation of the Center of Mass: From Humanoid Robots to Human Beings
,” IEEE/ASME Trans. Mechatronics
, 14
(6
), pp. 707
–712
.10.1109/TMECH.2009.20326877.
Cotton
, S.
, Vanoncini
, M.
, Fraisse
, P.
, Ramdani
, N.
, Demircan
, E.
, Murray
, A.
, and Keller
, T.
, 2011
, “Estimation of the Centre of Mass From Motion Capture and Force Plate Recordings: A Study on the Elderly
,” Appl. Bionics Biomech.
, 8
(1
), pp. 67
–84
.10.3233/ABB-2011-00068.
Gonzalez
, A.
, Hayashibe
, M.
, and Fraisse
, P.
, 2012
, “Three Dimensional Visualization of the Statically Equivalent Serial Chain From Kinect Recording
,” International Conference of the
IEEE Engineering in Medicine and Biology Society (EMBC
), San Diego, CA, Aug. 28–Sept. 1, pp. 4843
–4846
.10.1109/EMBC.2012.63470789.
Dubowsky
, S.
, and Papadopoulos
, E.
, 1993
, “The Kinematics, Dynamics, and Control of Free-Flying and Free-Floating Space Robotic Systems
,” IEEE Trans. Rob. Autom.
, 9
(5
), pp. 531
–543
.10.1109/70.25804610.
Vafa
, Z.
, and Dubowsky
, S.
, 1990
. “The Kinematics and Dynamics of Space Manipulators—The Virtual Manipulator Approach
,” Int. J. Rob. Res.
, 9
(4
), pp. 3
–21
.10.1177/02783649900090040111.
Vafa
, Z.
, and Dubowsky
, S.
, 1990
, “On the Dynamics of Space Manipulators Using the Virtual Manipulator, With Applications to Path Planning
,” J. Astronaut. Sci.
, 38
(4
), pp. 441
–472
10.1007/978-1-4615-3588-1_3.12.
Papadopoulos
, E.
, and Dubowsky
, S.
, 1991
, “On the Nature of Control Algorithms for Free-Floating Space Manipulators
,” IEEE Trans. Rob. Autom.
, 7
(6
), pp. 750
–758
.10.1109/70.10538413.
Agrawal
, S.
, Gardner
, G.
, and Pledgie
, S.
, 2001
, “Design and Fabrication of an Active Gravity Balanced Planar Mechanism Using Auxiliary Parallelograms
,” ASME J. Mech. Des.
, 123
(4
), pp. 525
–528
.10.1115/1.141377114.
Hasan
, S. S.
, Robin
, D. W.
, Szurkus
, D. C.
, Ashmead
, D. H.
, Peterson
, S. W.
, and Shiavi
, R. G.
, 1996
, “Simultaneous Measurement of Body Center of Pressure and Center of Gravity During Upright Stance. Part I: Methods
,” Gait Posture
, 4
(1
), pp. 1
–10
.10.1016/0966-6362(95)01030-015.
Winter
, D.
, 1995
, “Human Balance and Posture Control During Standing and Walking
,” Gait Posture
, 3
(4
), pp. 193
–214
.10.1016/0966-6362(96)82849-916.
Winter
, D.
, 2009
, Biomechanics and Motor Control of Human Movement
, 4th ed., Wiley
, New York
.10.1002/978047054914817.
Leva
, P.
, 1996
, “Adjustments to Zatsiorsky–Seluyanov's Inertia Parameters
,” J. Biomech.
, 29
(9
), pp. 1223
–1230
.10.1016/0021-9290(95)00178-618.
Zatsiorsky
, V.
, and Seluyanov
, V.
, 1983
, “The Mass and Inertia Characteristics of the Main Segments of the Human Body
,” Biomechanics
, VIII
(B
), pp. 1152
–1159
.19.
Cavagna
, G. A.
, 1975
, “Force Platforms as Ergometers
,” J. Appl. Physiol.
, 39
(1
), pp. 174
–179
.20.
Shimba
, T.
, 1984
, “An Estimation of Center of Gravity From Force Platform Data
,” J. Biomech.
, 17
(1
), pp. 53
–60
.10.1016/0021-9290(84)90080-021.
King
, D.
, and Zatsiorsky
, V.
, 1997
, “Extracting Gravity Line Displacement From Stabilographic Recordings
,” Gait Posture
, 6
(1
), pp. 27
–38
.10.1016/S0966-6362(96)01101-022.
Brenière
, Y.
, 1996
, “Why We Walk the Way We Do?
,” J. Mot. Behav.
, 28
(4
), pp. 291
–298
.10.1080/00222895.1996.1054459823.
Caron
, O.
, Faure
, B.
, and Brenière
, Y.
, 1997
, “Estimating the Centre of Gravity of the Body on the Basis of the Centre of Pressure in Standing Posture
,” J. Biomech.
, 30
(11–12
), pp. 1169
–1171
.10.1016/S0021-9290(97)00094-824.
Schepers
, H. M.
, van Asseldonk
, E. H. F.
, Buurke
, J. H.
, and Veltink
, P. H.
, 2009
, “Ambulatory Estimation of Center of Mass Displacement During Walking
,” IEEE Trans. Biomed. Eng.
, 56
(4
), pp. 1189
–1195
.10.1109/TBME.2008.201105925.
Betker
, A.
, Moussaviand
, Z.
, and Szturm
, T.
, 2004
, “Center of Mass Function Approximation
,” 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society
(IEMBS '04
), San Francisco, CA, Sept. 1–5, pp. 687
–690
.10.1109/IEMBS.2004.140325126.
Betker
, A.
, Szturm
, T.
, and Moussaviand
, Z.
, 2003
, “Application of Feedforward Backpropagation Neural Network to Center of Mass Estimation for Use in a Clinical Environment
,” 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society
(IEMBS
), Cancun, Mexico, Sept. 17–21, pp. 2714
–2717
.10.1109/IEMBS.2003.128047727.
Eames
, M.
, Cosgrove
, A.
, and Baker
, R.
, 1999
, “Comparing Methods of Estimating the Total Body Centre of Mass in Three-Dimensions in Normal and Pathological Gaits
,” Hum. Mov. Sci.
, 18
(5
), pp. 637
–646
.10.1016/S0167-9457(99)00022-628.
Gard
, S. A.
, Miff
, S. C.
, and Kuo
, A. D.
, 2004
, “Comparison of Kinematic and Kinetic Methods for Computing the Vertical Motion of the Body Center of Mass During Walking
,” Hum. Mov. Sci.
, 22
(6
), pp. 597
–610
.10.1016/j.humov.2003.11.00229.
Gutierrez-Farewik
, E. M.
, Bartonek
, A.
, and Saraste
, H.
, 2006
, “Comparison and Evaluation of Two Common Methods to Measure Center of Mass Displacement in Three Dimensions During Gait
,” Hum. Mov. Sci.
, 25
(2
), pp. 238
–256
.10.1016/j.humov.2005.11.00130.
Thirunarayan
, M. A.
, Kerrigan
, D. C.
, Rabuffetti
, M.
, Croce
, U. D.
, and Saini
, M.
, 1996
, “Comparison of Three Methods for Estimating Vertical Displacement of Center of Mass During Level Walking in Patients
,” Gait Posture
, 4
(4
), pp. 306
–314
.10.1016/0966-6362(95)01058-031.
Lafond
, D.
, Duarte
, M.
, and Prince
, F.
, 2004
, “Comparison of Three Methods to Estimate the Center of Mass During Balance Assessment
,” J. Biomech.
, 37
(9
), pp. 1421
–1426
.10.1016/S0021-9290(03)00251-332.
Nigg
, B. M.
, and Herzog
, W.
, 1999
, Biomechanics of the Musculo-Skeletal System
, Vol. 192
, Wiley
, New York
.33.
Lee
, S.-H.
, and Terzopoulos
, D.
, 2008
, “Spline Joints for Multibody Dynamics
,” 35th International Conference and Exhibition on Computer Graphics and Interactive Techniques (SIGGRAPH 2008
), Los Angeles
, CA
, Aug. 11–15, Paper No. 22.10.1145/1399504.136062134.
Zatsiorsky
, V.
, 1998
, Kinematics of Human Motion
, Human Kinetics
, Champaign, IL.35.
Shao
, W.
, and Ng-Thow-Hing
, V.
, 2003
, “A General Joint Component Framework for Realistic Articulation in Human Characters
,” Proceedings of the 2003 Symposium on Interactive 3D Graphics
(I3D ’03
), Monterey, CA, Apr. 27–30, pp. 11
–18
.10.1145/641485.64148636.
Gonzalez
, A.
, Hayashibe
, M.
, and Fraisse
, P.
, 2013
, “Online Identification and Visualization of the Statically Equivalent Serial Chain Via Constrained Kalman Filter
,” IEEE International Conference on Robotics and Automation
(ICRA
), Karlsruhe, Germany, May 6–10, pp. 5323
–5328
.10.1109/ICRA.2013.663133937.
McCarthy
, J.
, 1990
, An Introduction to Theoretical Kinematics
, MIT Press
, Cambridge, MA.38.
Copyright © 2015 by ASME
You do not currently have access to this content.
