To understand how humans perform non-ballistic movements, we have developed an optimal control model to simulate rising from a chair. The human body was modeled as a three-segment, articulated, planar linkage, with adjacent links joined together by frictionless revolutes. The skeleton was actuated by eight musculotendinous units with each muscle modeled as a three-element entity in series with tendon. Because rising from a chair presents a relatively ambiguous performance criterion, we chose to evaluate a number of different performance criteria, each based upon a fundamental dynamical property of movement: muscle force. Through a quantitative comparison of model and experiment, we found that neither a minimum-impulse nor a minimum-energy criterion is able to reproduce the major features of standing up. Instead, we introduce a performance criterion based upon an important and previously overlooked dynamical property of muscle: the time derivative of force. Our motivation for incorporating such a quantity into a mathematical description of the goal of a motor task is founded upon the belief that non-ballistic movements are controlled by gradual increases in muscle force rather than by rapid changes in force over time. By computing the optimal control solution for rising from a static squatting position, we show that minimizing the integral of a quantity which depends upon the time derivative of muscle force meets an important physiological requirement: it minimizes the peak forces developed by muscles throughout the movement. Furthermore, by computing the optimal control solution for rising from a chair, we demonstrate that multi-joint coordination is dictated not only by the choice of a performance criterion but by the presence of a motion constraint as well.

1.
Anderson
F. C.
, and
Pandy
M. G.
, “
Storage and Utilization of Elastic Strain Energy During Jumping
,”
J. Biomechanics
, Vol.
26
,
1993
, pp.
1413
1427
.
2.
Pandy
M. G.
, and
Zajac
F. E.
, “
Optimal Muscular Coordination Strategies for Jumping
,”
J. Biomechanics
, Vol.
24
,
1991
, pp.
1
10
.
3.
Marshall
R. N.
,
Wood
G. A.
, and
Jennings
L. S.
, “
Performance Objectives in Human Movement: A Review and Application to the Stance Phase of Normal Walking
,”
Human Movement Science
, Vol.
8
,
1989
, pp.
571
594
.
4.
Oguztoreli
M. N.
, and
Stein
R. B.
, “
Optimal Task Performance of Antagonistic Muscles
,”
Biol. Cybern.
, Vol.
64
,
1990
, pp.
87
94
.
5.
Stein, R. B., Oguztoreli, M. N., and Capaday, C., “What is Optimized in Muscular Movements?,” Jones, N. L., McCartney, N., and McComas, A. J., eds., Human Muscle Power, Human Kinetics Publishers, Champaign, IL, 1986 pp. 131–150.
6.
Uno
Y.
,
Kawato
M.
, and
Suzuki
R.
, “
Formation and Control of Optimal Trajectory in Human Multijoint Arm Movement
,”
Biol. Cybern.
, Vol.
61
,
1989
, pp.
89
101
.
7.
Nelson
W. G.
, “
Physical Principles for Economies of Skilled Movements
,”
Biol. Cybern.
, Vol.
46
,
1983
, pp.
135
147
.
8.
Seif-Naraghi, A. H., and Winters, J. M., “Optimized Strategies for Scaling Goal-Directed Dynamic Limb Movements,” Winters, J. M., and Woo, S. L-Y. (ed.): Multiple Muscle Systems: Biomechanics and Movement Organization, Springer-Verlag, New York, 1990 pp. 312–334.
9.
Flash
T.
, and
Hogan
N.
, “
The Coordination of Arm Movements: An Experimentally Confirmed Mathematical Model
,”
J. Neurosci.
, Vol.
7
,
1985
, pp.
1688
1703
.
10.
Pandy
M. G.
,
Zajac
F. E.
,
Sim
E.
, and
Levin
W. S.
, “
An Optimal Control Model for Maximum-Height Human Jumping
,”
J. Biomechanics
, Vol.
23
,
1990
, pp.
1185
1198
.
11.
Zajac, F. E., “Muscle and Tendon: Properties, Models, Scaling, and Application to Biomechanics and Motor Control,” CRC Critical Rev. Biomed. Engng, J. R. Bourne, ed., Vol. 17, 1989, pp. 359–411.
12.
Pandy
M. G.
,
Anderson
F. C.
, and
Hull
D. G.
, “
A Parameter Optimization Approach for the Optimal Control of Large-Scale Musculoskeletal Systems
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
114
,
1992
, pp.
450
460
.
13.
Khang
G.
, and
Zajac
F. E.
, “
Paraplegic Standing Controlled by Functional Neuromuscular Stimulation: Part I—Computer Model and Control-System Design
,”
IEEE Transactions on Biomedical Engng.
, Vol.
36
,
1989
, pp.
873
884
.
14.
Mirka
G. A.
, “
The Quantification of EMG Normalization Error
.”
Ergonomics
, Vol.
34
, No.
3
,
1991
, pp.
343
352
.
15.
Wickiewicz
T. L.
,
Roy
R. R.
,
Powell
P. L.
, and
Edgerton
V. R.
, “
Muscle Architecture of the Human Lower Limb
,”
Clin. Orthop. Rel. Res.
, Vol.
179
,
1983
, pp.
275
283
.
16.
Brand
R. A.
,
Pedersen
D. R.
, and
Friederich
J. A.
, “
The Sensitivity of Muscle Force Predictions to Changes in Physiological Cross-Sectional Area
,”
J. Biomechanics
, Vol.
19
,
1986
, pp.
589
596
.
17.
Alexander
R. McN
, and
Vernon
A.
, “
The Dimensions of Knee and Ankle Muscles and the Forces They Exert
,”
J. Hum. Mvmt. Stud.
, Vol.
1
,
1975
, pp.
115
123
.
18.
Woo
S. L.-Y.
,
Gomez
M. A.
,
Woo
Y.
, and
Akeson
W. H.
, “
Mechanical Properties of Tendons and Ligaments. II. The Relationships of Immobilization and Exercise on Tissue Remodeling
,”
Biorheology
, Vol.
19
,
1982
, pp.
397
408
.
19.
Butler
D. L.
,
Grood
E. S.
,
Noycs
F. R.
,
Zernicke
R. F.
, and
Brackett
K.
, “
Effects of Structure and Strain Measurement Technique on the Material Properties of Young Human Tendons and Fascia
,”
J. Biomechanics
, Vol.
17
,
1984
, pp.
579
596
.
20.
Brand
R. A.
,
Crowninshield
R. D.
,
Wittstock
C. E.
,
Pedersen
D. R.
,
Clark
C. R.
, and
van Krieken
F. M.
, “
A Model for Lower Extremity Muscular Anatomy
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
104
,
1982
, pp.
304
310
.
21.
Garner, B. A., “A Dynamic Musculoskeletal Computer Model for Rising from a Squatting or Sitting Position: A Study of Performance Criteria for Optimal Control of Non-Ballistic Human Movements,” Masters Thesis, Department of Mechanical Engineering, University of Texas at Austin, Austin, TX, 1992.
22.
Powell, M. J. D., “A Fast Algorithm for Nonlinearly Constrained Optimization Calculations,” Numerical Analysis: Lecture Notes in Mathematics, G. A. Matson, ed., Springer-Verlag, Vol. 630, 1978, pp. 144–157.
23.
Russel, D., and Hogan, N., “How Humans Perform Constrained Motions,” Stein, J. L., Ashton-Miller, J. A., and Pandy, M. G., eds., Issues in the Modeling and Control of Biomechanical Systems, DSC-Vol. 17, 1989, ASME, New York.
24.
Zajac
F. E.
, and
Gordon
M. E.
, “
Determining Muscle’s Force and Action in Multi-Articular Movement
,”
Exer. and Sport Sci. Rev.
, Williams and Wilkins, Baltimore, Vol.
17
,
1989
, pp.
187
230
.
25.
Daigle, K. E., “The Effect of Muscle Strength on the Coordination of Rising from a Chair in Minimum Time: Predictions of an Optimal Control Model,” Masters Thesis, Department of Kinesiology, University of Texas at Austin, Austin, TX 78712.
26.
Seireg
A.
, and
Arvikar
R. J.
, “
Mathematical Model for Evaluation of Forces in Lower Extremities of the Musculoskeletal System
,”
J. Biomechanics
, Vol.
6
,
1973
, pp.
313
326
.
27.
Pedotti
A.
,
Krishnan
V. V.
, and
Stark
L.
, “
Optimization of Muscle-Force Sequencing in Human Locomotion
,”
Math. Biosciences
, Vol.
38
,
1978
, pp.
57
76
.
28.
Crowninshield
R. D.
, and
Brand
R. A.
, “
A Physiologically Based Criterion for Muscle Force Prediction in Locomotion
,”
J. Biomechanics
, Vol.
14
,
1981
, pp.
793
801
.
29.
Patriarco
A. G.
,
Mann
R. W.
,
Simon
S. R.
, and
Mansour
J. M.
, “
An Evaluation of the Approaches of Optimization Models in the Prediction of Muscle Forces During Human Gait
,”
J. Biomechanics
, Vol.
14
,
1981
, pp.
513
525
.
30.
Hardt
D. E.
, “
Determining Muscle Forces in the Leg During Normal Human Walking—An Application and Evaluation of Optimization Methods
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
100
,
1978
, pp.
72
78
.
31.
Davy
D. T.
, and
Audu
M. L.
, “
A Dynamic Optimization Technique for Predicting Muscle Forces in the Swing Phase of Gait
,”
J. Biomechanics
, Vol.
20
,
1987
, pp.
187
201
.
32.
MacConaill, M. A., “The Ergonomic Aspects of Articular Mechanics,” Evans, F. G., ed., Studies on the Anatomy and Function of Bones and Joints, 1967, pp. 69–80, Springer, Berlin.
33.
Alexander
N. B.
,
Schultz
A. B.
, and
Warwick
D. N.
, “
Rising from a Chair: Effects of Age and Functional Ability on Performance Biomechanics
,”
J. Gerontology
, Vol.
46
,
1991
, pp.
91
98
.
34.
Schultz
A. B.
, “
Mobility Impairment in the Elderly: Challenges for Biomechanics Research
,”
J. Biomechanics
, Vol.
25
,
1992
, pp.
519
528
.
35.
Riley
P. O.
,
Schenkman
M. L.
,
Mann
R. W.
, and
Hodge
W. A.
, “
Mechanics of a Constrained Chair Rise
,”
J. Biomechanics
, Vol.
24
,
1991
, pp.
77
85
.
36.
Kelley, D. L., Dainis, A., and Wood, G. K., “Mechanics and Muscular Dynamics of Rising from a Seated Position,” Komi, P. V., ed.: Biomechanics V-B, University Park Press, Baltimore, 1976, pp. 127–133.
This content is only available via PDF.
You do not currently have access to this content.