Inverse dynamics analysis as well as the generation of an optimal goal oriented human motion both lead to the problem of finding suitable activations of the redundant muscles involved. This paper employs an iterative feedback tuning approach to perform the forward dynamics simulation of the human musculoskeletal system during level walking. A modified form of the proportional-integral-derivative (PID) controller is proposed to stabilize the movement and provide tracking of problems of the desired lower extremity joint profiles. Controller parameters were determined iteratively using an optimization algorithm to minimize tracking errors during forward dynamics simulation. Static optimization was employed simultaneously to compute a set of desired musculotendon forces in the closed-loop simulation to resolve muscle redundancy. Quantitative comparisons of the simulation results with the gait experimental measurements and the reference muscle activity show the accuracy and efficiency of the proposed method to provide a stable gait.
SeiregA.ArvikarR. J.‘The prediction of muscular load sharing and joint forces in the lower extremities during walking.’J. Biomechanics8 (1975): 89–102
2.
PatriarcoA. G.MannR. W.SimonS. R.MansourJ. M.‘An evaluation of the approaches of optimization models in the prediction of muscle forces during human gait.’J. Biomechanics14 (1981): 513–525
3.
CrowninshieldR. D.BrandR. A.‘A physiologically based criterion of muscle force prediction in locomotion.’J. Biomechanics14 (1981): 793–801
4.
BrandR. A.PedersenD. R.FriederichJ. A.‘The sensitivity of muscle force predictions to changes in physiologic cross-sectional area.’J. Biomechanics19 (1986): 589–596
5.
GlitschU.BaumannW.‘The three-dimensional determination of internal loads in the lower extremity.’J. Biomechanics30 (1997): 1123–1131
6.
PedersenD. R.BrandR. A.DavyD. T.‘Pelvic muscle and acetabular contact forces during gait.’J. Biomechanics30 (1997): 959–965
7.
DavyD. T.AuduM. L.‘A dynamic optimization technique for predicting muscle forces in the swing phase of gait.’J. Biomechanics20 (1987): 187–201
8.
YamaguchiG. T.ZajacF. E.‘Restoring unassisted natural gait to paraplegics via functional neuromuscular stimulation: A computer simulation study.’IEEE Trans. on Biomed. Engng37 (1990): 886–902
9.
NeptuneR. R.KautzS. A.ZajacF. E.‘Contributions of the ankle plantar flexors to support, forward progression and swing initiation during walking.’J. Biomechanics34 (2001): 1387–1398
10.
HappeeR.‘Inverse dynamic optimization including muscular dynamics, a new simulation method applied to goal directed movements.’J. Biomechanics27 (1994): 953–960
11.
ThelenD. G.AndersonF. C.DelpL. S.‘Generating dynamic simulations of movement using computed muscle control.’J. Biomechanics36 (2003): 321–328
12.
PeasgoodM.KubicaE.McPheeJ.‘Stabilization of a dynamic walking gait simulation.’J. Computat. Nonlinear Dynamics2 (2007): 65–72
13.
ListerS. J.JonesN. B.SpurgeonS. K.ScottJ. J. A.‘Simulation of human gait and associated muscle activation strategies using sliding-mode control techniques.’Simul. Modeling Pract. Theory14 (5) (2006): 586–596
14.
HägglundT.ÅströmK. J.‘Method and an apparatus in tuning a PID regulator.’ US Patent 4549123, 1985.
15.
ZieglerJ. G.NicholsN. B.‘Optimum setting for automatic controllers.’Trans. ASME64 (1942): 759–768
16.
ÅströmK. J.HägglundT.PID controllers: theory, design, and tuning, (Instrument Society of America, Research Triangle Park, North Carolina1995)
MarchettiG.ScaliC.‘Use of modified relay techniques for the design of model-based controllers for chemical processes.’Ind. Engng Chem. Res.39 (2000): 3325–3334
19.
ChenJ.HuangT. C.‘Applying neural networks to on-line updated PID controllers for nonlinear process control.’J. Process Control14 (2004): 211–230
20.
HjalmarssonH.GunnarssonS.GeversM.‘A convergent iterative restricted complexity control design scheme.’In Proceedings of the 33rd IEEE Conference on Decision and control, Orlando, Florida, 1994, pp. 1735–1740.
21.
HjalmarssonH.GunnarssonS.GeversM.‘Model-free tuning of a robust regulator for a flexible transmission system.’Eur. J. Control1 (2) (1995): 148–156
22.
LequinO.‘Optimal closed loop PID tuning in the process industry with the iterative feedback tuning scheme.’ In CD-ROM of European Control Conference, Brussels, Belgium, 1997, paper TH-A-H6.
23.
HjalmarssonH.GeversM.GunnarssonS.LequinO.‘Iterative feedback tuning: Theory and applications.’IEEE Control Systems Mag.18 (4) (1998): 26–41
24.
YamaguchiG. T.ZajacF. E.‘A planar model for the knee joint to characterize the knee extensor mechanism.’J. Biomechanics22 (1989): 1–10
25.
ZajacF. E.‘Muscle and tendon: Properties, models, scaling, and application to biomechanics and motor control.’CRC Critical Rev. in Biomed. Engng19 (1989): 359–411
26.
AndersonF. C.PandyM. G.‘A dynamic optimization solution for vertical jumping in three dimensions.’Computer Methods in Biomech. Biomed. Engng2 (1999): 201–231
27.
AlkjaerT.SimonsenE. B.Dyhre-PoulsenP.‘Comparison of inverse dynamics calculated by two- and three-dimensional models during walking.’Gait and Posture13 (2001): 73–77
28.
JaniceJ.WinterD. A.‘Kinetic analysis of the lower limbs during walking: What information can be gained from a three-dimensional model?’J. Biomechanics28 (6) (1995): 753–758
29.
GhafariSelk A.MeghdariA.VossoughiG. R.‘Modeling of human lower extremity musculoskeletal structure using bond graph approach.’ In CD-ROM Proceedings of ASME International Mechanical Engineering and Exposition, Seattle, Washington, 2007.
30.
BrandR. A.CrowninshieldR. D.WittstockC. E.PedersonD. R.ClarkC. R.van KriekenF. M.‘A model of lower extremity muscular anatomy.’J. Biomech. Engng104 (1982): 304–310
31.
WinterD. A.International Society of Biomechanics, Biomechanical Data Resources, Gait Data; available at www.isbweb.org/data.
32.
ZajacF. E.NeptuneR. R.KautzS. A.‘Biomechanics and muscle coordination of human walking. Part I: Introduction to concepts, power transfer, dynamics, and simulations.’Gait and Posture16 (2002): 215–232
33.
ZajacF. E.NeptuneR. R.KautzS. A.‘Biomechanics and muscle coordination of human walking. Part II: Lessons from dynamical simulations and clinical implications.’Gait and Posture17 (2003): 1–17
