This paper presents a computational framework for the fast feedback control of musculoskeletal systems using muscle synergies. The proposed motor control framework has a hierarchical structure. A feedback controller at the higher level of hierarchy handles the trajectory planning and error compensation in the task space. This high-level task space controller only deals with the task-related kinematic variables, and thus is computationally efficient. The output of the task space controller is a force vector in the task space, which is fed to the low-level controller to be translated into muscle activity commands. Muscle synergies are employed to make this force-to-activation (F2A) mapping computationally efficient. The explicit relationship between the muscle synergies and task space forces allows for the fast estimation of muscle activations that result in the reference force. The synergy-enabled F2A mapping replaces a computationally heavy nonlinear optimization process by a vector decomposition problem that is solvable in real time. The estimation performance of the F2A mapping is evaluated by comparing the F2A-estimated muscle activities against the measured electromyography (EMG) data. The results show that the F2A algorithm can estimate the muscle activations using only the task-related kinematics/dynamics information with ∼70% accuracy. An example predictive simulation is also presented, and the results show that this feedback motor control framework can control arbitrary movements of a three-dimensional (3D) musculoskeletal arm model quickly and near optimally. It is two orders-of-magnitude faster than the optimal controller, with only 12% increase in muscle activities compared to the optimal. The developed motor control model can be used for real-time near-optimal predictive control of musculoskeletal system dynamics.

References

1.
Bernstein
,
M.
,
1967
,
The Co-Ordination and Regulation of Movements
, 1st ed.,
Pergamon Press
,
New York
.
2.
Morasso
,
P.
,
1981
, “
Spatial Control of Arm Movements
,”
Exp. Brain Res.
,
42
(
2
), pp.
223
227
.
3.
Scholz
,
J.
, and
Schöner
,
G.
,
1999
, “
The Uncontrolled Manifold Concept: Identifying Control Variables for a Functional Task
,”
Exp. Brain Res.
,
126
(
3
), pp.
289
306
.
4.
Georgopoulos
,
A. P.
,
Schwartz
,
A. B.
, and
Kettner
,
R. E.
,
1986
, “
Neuronal Population Coding of Movement Direction
,”
Science
,
233
(
4771
), pp.
1416
1419
.
5.
Georgopoulos
,
A. P.
,
Kettner
,
R. E.
, and
Schwartz
,
A. B.
,
1988
, “
Primate Motor Cortex and Free Arm Movements to Visual Targets in Three-Dimensional Space—II: Coding of the Direction of Movement by a Neuronal Population
,”
J. Neurosci.
,
8
(
8
), pp.
2928
2937
.
6.
Schwartz
,
A. B.
,
Kettner
,
R. E.
, and
Georgopoulos
,
A. P.
,
1988
, “
Primate Motor Cortex and Free Arm Movements to Visual Targets in Three-Dimensional Space—I: Relations Between Single Cell Discharge and Direction of Movement
,”
J. Neurosci.
,
8
(
8
), pp.
2913
2927
.
7.
Lillicrap
,
T. P.
, and
Scott
,
S. H.
,
2013
, “
Preference Distributions of Primary Motor Cortex Neurons Reflect Control Solutions Optimized for Limb Biomechanics
,”
Neuron
,
77
(
1
), pp.
168
179
.
8.
Erdemir
,
A.
,
McLean
,
S.
,
Herzog
,
W.
, and
van den Bogert
,
A. J.
,
2007
, “
Model-Based Estimation of Muscle Forces Exerted During Movements
,”
Clin. Mech.
,
22
(
2
), pp.
131
154
.
9.
Meyer
,
A. J.
,
Eskinazi
,
I.
,
Jackson
,
J. N.
,
Rao
,
A. V.
,
Patten
,
C.
, and
Fregly
,
B. J.
,
2016
, “
Muscle Synergies Facilitate Computational Prediction of Subject-Specific Walking Motions
,”
Front. Bioeng. Biotechnol.
,
4
, p.
77
.
10.
Sharif Shourijeh
,
M.
,
Smale
,
K. B.
,
Potvin
,
B. M.
, and
Benoit
,
D. L.
,
2016
, “
A Forward-Muscular Inverse-Skeletal Dynamics Framework for Human Musculoskeletal Simulations
,”
J. Biomech.
,
49
(
9
), pp.
1718
1723
.
11.
Walter
,
J. P.
,
Kinney
,
A. L.
,
Banks
,
S. A.
,
D'Lima
,
D. D.
,
Besier
,
T. F.
,
Lloyd
,
D. G.
, and
Fregly
,
B. J.
,
2014
, “
Muscle Synergies May Improve Optimization Prediction of Knee Contact Forces During Walking
,”
ASME J. Biomech. Eng.
,
136
(
2
), p.
021031
.
12.
Neptune
,
R. R.
,
Clark
,
D. J.
, and
Kautz
,
S. A.
,
2009
, “
Modular Control of Human Walking: A Simulation Study
,”
J. Biomech.
,
42
(
9
), pp.
1282
1287
.
13.
Anderson
,
F. C.
, and
Pandy
,
M. G.
,
2001
, “
Dynamic Optimization of Human Walking
,”
ASME J. Biomech. Eng.
,
123
(
5
), p.
381
.
14.
Sharif Razavian
,
R.
,
Mehrabi
,
N.
, and
McPhee
,
J.
,
2015
, “
A Neuronal Model of Central Pattern Generator to Account for Natural Motion Variation
,”
ASME J. Comput. Nonlinear Dyn.
,
11
(
2
), p.
021007
.
15.
Berniker
,
M.
,
Jarc
,
A.
,
Bizzi
,
E.
, and
Tresch
,
M. C.
,
2009
, “
Simplified and Effective Motor Control Based on Muscle Synergies to Exploit Musculoskeletal Dynamics
,”
Proc. Natl. Acad. Sci. U. S. A.
,
106
(
18
), pp.
7601
7606
.
16.
Jagodnik
,
K. M.
,
Blana
,
D.
,
van den Bogert
,
A. J.
, and
Kirsch
,
R. F.
,
2015
, “
An Optimized Proportional-Derivative Controller for the Human Upper Extremity With Gravity
,”
J. Biomech.
,
48
(
13
), pp.
3701
3709
.
17.
Jagodnik
,
K. M.
, and
van den Bogert
,
A. J.
,
2010
, “
Optimization and Evaluation of a Proportional Derivative Controller for Planar Arm Movement
,”
J. Biomech.
,
43
(
6
), pp.
1086
1091
.
18.
Jagodnik
,
K. M.
,
Thomas
,
P. S.
,
Van Den Bogert
,
A. J.
,
Branicky
,
M. S.
, and
Kirsch
,
R. F.
,
2017
, “
Training an Actor-Critic Reinforcement Learning Controller for Arm Movement Using Human-Generated Rewards
,”
IEEE Trans. Neural Syst. Rehabil. Eng.
,
25
(
10
), pp.
1892
1905
.
19.
Fu
,
K. C. D.
,
Libera
,
F. D.
, and
Ishiguro
,
H.
,
2015
, “
Extracting Motor Synergies From Random Movements for Low-Dimensional Task-Space Control of Musculoskeletal Robots
,”
Bioinspiration Biomimetics
,
10
(
5
), p.
056016
.
20.
Park
,
H.
, and
Durand
,
D. M.
,
2008
, “
Motion Control of Musculoskeletal Systems With Redundancy
,”
Biol. Cybern.
,
99
(
6
), pp.
503
–5
16
.
21.
Blana
,
D.
,
Kirsch
,
R. F.
, and
Chadwick
,
E. K.
,
2009
, “
Combined Feedforward and Feedback Control of a Redundant, Nonlinear, Dynamic Musculoskeletal System
,”
Med. Biol. Eng. Comput.
,
47
(
5
), pp.
533
542
.
22.
Tresch
,
M. C.
, and
Jarc
,
A.
,
2009
, “
The Case for and Against Muscle Synergies
,”
Curr. Opin. Neurobiol.
,
19
(
6
), pp.
601
607
.
23.
Hilt
,
P. M.
,
Delis
,
I.
,
Pozzo
,
T.
, and
Berret
,
B.
,
2018
, “
Space-By-Time Modular Decomposition Effectively Describes Whole-Body Muscle Activity During Upright Reaching in Various Directions
,”
Front. Comput. Neurosci.
,
12
, pp.
1
19
.
24.
Sharif Shourijeh
,
M.
,
Flaxman
,
T. E.
, and
Benoit
,
D. L.
,
2016
, “
An Approach for Improving Repeatability and Reliability of Non-Negative Matrix Factorization for Muscle Synergy Analysis
,”
J. Electromyography Kinesiology
,
26
, pp.
36
43
.
25.
Smale
,
K. B.
,
Sharif Shourijeh
,
M.
, and
Benoit
,
D. L.
,
2016
, “
Use of Muscle Synergies and Wavelet Transforms to Identify Fatigue During Squatting
,”
J. Electromyography Kinesiology
,
28
, pp.
158
166
.
26.
Kutch
,
J. J.
,
Kuo
,
A. D.
,
Bloch
,
A. M.
, and
Rymer
,
W. Z.
,
2008
, “
Endpoint Force Fluctuations Reveal Flexible Rather Than Synergistic Patterns of Muscle Cooperation
,”
J. Neurophysiol.
,
100
(
5
), pp.
2455
2471
.
27.
D'Avella
,
A.
,
Portone
,
A.
,
Fernandez
,
L.
, and
Lacquaniti
,
F.
,
2006
, “
Control of Fast-Reaching Movements by Muscle Synergy Combinations
,”
J. Neurosci.
,
26
(
30
), pp.
7791
–7
810
.
28.
Ivanenko
,
Y. P.
,
Poppele
,
R. E.
, and
Lacquaniti
,
F.
,
2004
, “
Five Basic Muscle Activation Patterns Account for Muscle Activity During Human Locomotion
,”
J. Physiol.
,
556
(
1
), pp.
267
282
.
29.
Berger
,
D. J.
,
Gentner
,
R.
,
Edmunds
,
T.
,
Pai
,
D. K.
, and
D'Avella
,
A.
,
2013
, “
Differences in Adaptation Rates After Virtual Surgeries Provide Direct Evidence for Modularity
,”
J. Neurosci.
,
33
(
30
), pp.
12384
12394
.
30.
Dominici
,
N.
,
Ivanenko
,
Y. P.
,
Cappellini
,
G.
,
D'Avella
,
A.
,
Mond
,
V.
,
Cicchese
,
M.
,
Fabiano
,
A.
,
Silei
,
T.
,
Di Paolo
,
A.
,
Giannini
,
C.
,
Poppele
,
R. E.
, and
Lacquaniti
,
F.
,
2011
, “
Locomotor Primitives in Newborn Babies and Their Development
,”
Science
,
334
(
6058
), pp.
997
999
.
31.
Zariffa
,
J.
,
Steeves
,
J.
, and
Pai
,
D. K.
,
2012
, “
Changes in Hand Muscle Synergies in Subjects With Spinal Cord Injury: Characterization and Functional Implications
,”
J. Spinal Cord Med.
,
35
(
5
), pp.
310
318
.
32.
Clark
,
D. J.
,
Ting
,
L. H.
,
Zajac
,
F. E.
,
Neptune
,
R. R.
, and
Kautz
,
S. A.
,
2010
, “
Merging of Healthy Motor Modules Predicts Reduced Locomotor Performance and Muscle Coordination Complexity Post-Stroke
,”
J. Neurophysiol.
,
103
(
2
), pp.
844
857
.
33.
Steele
,
K. M.
,
Rozumalski
,
A.
, and
Schwartz
,
M. H.
,
2015
, “
Muscle Synergies and Complexity of Neuromuscular Control During Gait in Cerebral Palsy
,”
Dev. Med. Child Neurol.
,
57
(12), pp. 1176–1182.
34.
Overduin
,
S. A.
,
D'Avella
,
A.
,
Roh
,
J.
, and
Bizzi
,
E.
,
2008
, “
Modulation of Muscle Synergy Recruitment in Primate Grasping
,”
J. Neurosci.
,
28
(
4
), pp.
880
892
.
35.
Bizzi
,
E.
,
Cheung
,
V. C. K.
,
D'Avella
,
A.
,
Saltiel
,
P.
, and
Tresch
,
M. C.
,
2008
, “
Combining Modules for Movement
,”
Brain Res. Rev.
,
57
(
1
), pp.
125
133
.
36.
Cheung
,
V. C. K.
,
D'Avella
,
A.
,
Tresch
,
M. C.
, and
Bizzi
,
E.
,
2005
, “
Central and Sensory Contributions to the Activation and Organization of Muscle Synergies During Natural Motor Behaviors
,”
J. Neurosci.
,
25
(
27
), pp.
6419
6434
.
37.
Hart
,
C. B.
, and
Giszter
,
S. F.
,
2004
, “
Modular Premotor Drives and Unit Bursts as Primitives for Frog Motor Behaviors
,”
J. Neurosci.
,
24
(
22
), pp.
5269
5282
.
38.
Saltiel
,
P.
,
Wyler-Duda
,
K.
,
D'Avella
,
A.
,
Tresch
,
M. C.
, and
Bizzi
,
E.
,
2001
, “
Muscle Synergies Encoded Within the Spinal Cord: Evidence From Focal Intraspinal NMDA Iontophoresis in the Frog
,”
J. Neurophysiol.
,
85
(
2
), pp.
605
619
.
39.
Tresch
,
M. C.
,
Saltiel
,
P.
, and
Bizzi
,
E.
,
1999
, “
The Construction of Movement by the Spinal Cord
,”
Nat. Neurosci.
,
2
(
2
), pp.
162
167
.
40.
Sohn
,
M. H.
, and
Ting
,
L. H.
,
2016
, “
Suboptimal Muscle Synergy Activation Patterns Generalize Their Motor Function Across Postures
,”
Front. Comput. Neurosci.
,
10
, p. 7.
41.
Ting
,
L. H.
, and
McKay
,
J. L.
,
2007
, “
Neuromechanics of Muscle Synergies for Posture and Movement
,”
Curr. Opin. Neurobiol.
,
17
(
6
), pp.
622
628
.
42.
Torres-Oviedo
,
G.
,
Macpherson
,
J. M.
, and
Ting
,
L. H.
,
2006
, “
Muscle Synergy Organization is Robust Across a Variety of Postural Perturbations
,”
J. Neurophysiol.
,
96
(
3
), pp.
1530
1546
.
43.
Ting
,
L. H.
, and
Macpherson
,
J. M.
,
2004
, “
Ratio of Shear to Load Ground-Reaction Force May Underlie the Directional Tuning of the Automatic Postural Response to Rotation and Translation
,”
J. Neurophysiol.
,
92
(
2
), pp.
808
823
.
44.
Lockhart
,
D. B.
, and
Ting
,
L. H.
,
2007
, “
Optimal Sensorimotor Transformations for Balance
,”
Nat. Neurosci.
,
10
(
10
), pp.
1329
1336
.
45.
Sharif Razavian
,
R.
,
Mehrabi
,
N.
, and
McPhee
,
J.
,
2015
, “
A Model-Based Approach to Predict Muscle Synergies Using Optimization: Application to Feedback Control
,”
Front. Comput. Neurosci.
,
9
, p. 121.
46.
Kargo
,
W. J.
,
Ramakrishnan
,
A.
,
Hart
,
C. B.
,
Rome
,
L. C.
, and
Giszter
,
S. F.
,
2010
, “
A Simple Experimentally Based Model Using Proprioceptive Regulation of Motor Primitives Captures Adjusted Trajectory Formation in Spinal Frogs
,”
J. Neurophysiol.
,
103
(
1
), pp.
573
590
.
47.
Alessandro
,
C.
,
Carbajal
,
J. P.
, and
D'Avella
,
A.
,
2014
, “
A Computational Analysis of Motor Synergies by Dynamic Response Decomposition
,”
Front. Comput. Neurosci.
,
7
, pp.
1
20
.
48.
Sharif Razavian
,
R.
,
2017
, “
A Human Motor Control Framework Based on Muscle Synergies
,”
Ph.D thesis
, University of Waterloo, Waterloo, ON, Canada.http://hdl.handle.net/10012/12180
49.
Sharif Razavian
,
R.
, and
McPhee
,
J.
,
2016
, “
A Motor Control Framework for the Fast Control of a 3D Musculoskeletal Arm Motion Using Muscle Synergy
,”
Fourth Joint International Conference on Multibody System Dynamics
, Montreal, QC, Canada, May 29–June 2.https://uwaterloo.ca/motion-research-group/publications/motor-control-framework-fast-control-3d-musculoskeletal-arm
50.
Boettcher
,
C. E.
,
Ginn
,
K. A.
, and
Cathers
,
I.
,
2008
, “
Standard Maximum Isometric Voluntary Contraction Tests for Normalizing Shoulder Muscle EMG
,”
J. Orthop. Res.
,
26
(
12
), pp.
1591
1597
.
51.
Lee
,
D. D.
, and
Seung
,
H. S.
,
2001
, “
Algorithms for Non-Negative Matrix Factorization
,”
Adv. Neural Inf. Process. Syst.
,
13
(
1
), pp.
556
562
.https://dl.acm.org/citation.cfm?id=3008829
52.
Tresch
,
M. C.
,
Cheung
,
V. C. K.
, and
D'Avella
,
A.
,
2006
, “
Matrix Factorization Algorithms for the Identification of Muscle Synergies: Evaluation on Simulated and Experimental Data Sets
,”
J. Neurophysiol.
,
95
(
4
), pp.
2199
–2
212
.
53.
Roh
,
J.
,
Rymer
,
W. Z.
, and
Beer
,
R. F.
,
2012
, “
Robustness of Muscle Synergies Underlying Three-Dimensional Force Generation at the Hand in Healthy Humans
,”
J. Neurophysiol.
,
107
(
8
), pp.
2123
2142
.
54.
de Rugy
,
A.
,
Loeb
,
G. E.
, and
Carroll
,
T. J.
,
2013
, “
Are Muscle Synergies Useful for Neural Control?
Front. Comput. Neurosci.
,
7
, p. 19.
55.
Mehrabi
,
N.
,
Sharif Razavian
,
R.
, and
McPhee
,
J.
,
2015
, “
Steering Disturbance Rejection Using a Physics-Based Neuromusculoskeletal Driver Model
,”
Veh. Syst. Dyn.
,
53
(
10
), pp.
1393
1415
.
56.
Thelen
,
D. G.
,
2003
, “
Adjustment of Muscle Mechanics Model Parameters to Simulate Dynamic Contractions in Older Adults
,”
ASME J. Biomech. Eng.
,
125
(
1
), p.
70
.
57.
Mehrabi
,
N.
,
Sharif Razavian
,
R.
,
Ghannadi
,
B.
, and
McPhee
,
J.
,
2017
, “
Predictive Simulation of Reaching Moving Targets Using Nonlinear Model Predictive Control
,”
Front. Comput. Neurosci.
,
10
, p. 143.
58.
Sartori
,
M.
,
Gizzi
,
L.
,
Lloyd
,
D. G.
, and
Farina
,
D.
,
2013
, “
A Musculoskeletal Model of Human Locomotion Driven by a Low Dimensional Set of Impulsive Excitation Primitives
,”
Front. Comput. Neurosci.
,
7
, p.
79
.
59.
Moran
,
D.
, and
Schwartz
,
A. B.
,
1999
, “
Motor Cortical Representation of Speed and Direction During Reaching
,”
J. Neurophysiol.
,
82
(
5
), pp.
2676
2692
.
60.
Boline
,
J.
, and
Ashe
,
J.
,
2005
, “
On the Relations Between Single Cell Activity in the Motor Cortex and the Direction and Magnitude of Three-Dimensional Dynamic Isometric Force
,”
Exp. Brain Res.
,
167
(
2
), pp.
148
159
.
61.
Kettner
,
R. E.
,
Schwartz
,
A. B.
, and
Georgopoulos
,
A. P.
,
1988
, “
Primate Motor Cortex and Free Arm Movements to Visual Targets in Three-Dimensional Space—III: Positional Gradients and Population Coding of Movement Direction From Various Movement Origins
,”
J. Neurosci.
,
8
(
8
), pp.
2938
2947
.
62.
Ashe
,
J.
, and
Georgopoulos
,
A. P.
,
1994
, “
Movement Parameters and Neural Activity in Motor Cortex and Area 5
,”
Cerebral Cortex
,
4
(
6
), pp.
590
600
.
63.
Todorov
,
E.
, and
Jordan
,
M. I.
,
2002
, “
A Minimal Intervention Principle for Coordinated Movement
,”
Advances in Neural Information Processing Systems Conference
, Vancouver, BC, Canada, Dec. 8–13, pp.
27
34
.https://papers.nips.cc/paper/2195-a-minimal-intervention-principle-for-coordinated-movement.pdf
64.
de Rugy
,
A.
,
Loeb
,
G. E.
, and
Carroll
,
T. J.
,
2012
, “
Muscle Coordination Is Habitual Rather Than Optimal
,”
J. Neurosci.
,
32
(
21
), pp.
7384
7391
.
65.
Krishnamoorthy
,
V.
,
Scholz
,
J. P.
, and
Latash
,
M. L.
,
2007
, “
The Use of Flexible Arm Muscle Synergies to Perform an Isometric Stabilization Task
,”
Clin. Neurophysiol.
,
118
(
3
), pp.
525
537
.
66.
Steele
,
K. M.
,
Tresch
,
M. C.
, and
Perreault
,
E. J.
,
2013
, “
The Number and Choice of Muscles Impact the Results of Muscle Synergy Analyses
,”
Front. Comput. Neurosci.
,
7
, p.
105
.
67.
Gentner
,
R.
,
Edmunds
,
T.
,
Pai
,
D. K.
, and
D'Avella
,
A.
,
2013
, “
Robustness of Muscle Synergies During Visuomotor Adaptation
,”
Front. Comput. Neurosci.
,
7
, p.
120
.
68.
Loeb
,
G. E.
,
2012
, “
Optimal Isn't Good Enough
,”
Biol. Cybern.
,
106
(
11–12
), pp.
757
765
.
69.
Sharif Razavian
,
R.
,
Ghannadi
,
B.
, and
McPhee
,
J.
,
2017
, “
Feedback Control of Functional Electrical Stimulation for Arbitrary Upper Extremity Movements
,”
2017 IEEE International Conference on Rehabilitation Robotics
(
ICORR
), London, July 17–20, pp.
1451
1456
.
70.
Sharif Razavian
,
R.
,
Ghannadi
,
B.
,
Mehrabi
,
N.
,
Charlet
,
M.
, and
McPhee
,
J.
, 2018, “
Feedback Control of Functional Electrical Stimulation for 2-D Arm Reaching Movements
,”
IEEE Trans. Neural Syst. Rehabil. Eng.
,
26
(10), pp. 2033–2043.
71.
Berger
,
D. J.
, and
D'Avella
,
A.
,
2014
, “
Effective Force Control by Muscle Synergies
,”
Front. Comput. Neurosci.
,
8
, p.
46
.
72.
Jiang
,
N.
,
Rehbaum
,
H.
,
Vujaklija
,
I.
,
Graimann
,
B.
, and
Farina
,
D.
,
2014
, “
Intuitive, Online, Simultaneous, and Proportional Myoelectric Control Over Two Degrees-of-Freedom in Upper Limb Amputees
,”
IEEE Trans. Neural Syst. Rehabil. Eng.
,
22
(
3
), pp.
501
510
.
73.
Muceli
,
S.
,
Jiang
,
N.
, and
Farina
,
D.
,
2014
, “
Extracting Signals Robust to Electrode Number and Shift for Online Simultaneous and Proportional Myoelectric Control by Factorization Algorithms
,”
IEEE Trans. Neural Syst. Rehabil. Eng.
,
22
(
3
), pp.
623
633
.
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