Abstract

Hybrid functional electrical stimulation (FES) cycling is a method to rehabilitate people with neurological conditions when they are not in and of themselves capable of fully controlling their extremities. To ensure smooth cycling and adequate stimulation to accomplish the rehabilitation task, admittance control is applied between the human and the robotic cycle. The cycle motor is actuated by a dual neural network control structure with an additional robust element tracking the admittance trajectory, while muscles are stimulated with a simple saturated robust controller. The dual neural network structure allows adaptation to separable functions of the dynamic system, in addition to shared adaptation through the admittance filter. A Lyapunov analysis shows that the admittance tracking controller is globally exponentially stable. A passivity analysis shows that the admittance system and cadence tracking error are output strictly passive. A combined analysis shows that the total system is passive. Experiments are performed on eight participants without neurological conditions, on 12 differing protocols including a robust controller for comparison, the addition of noise, and the addition or lack of stimulation. One participant with a neurological condition was evaluated on three different protocols, including a robust controller, a neural network controller, and a game-like mode where the participant was asked to track the trajectory as it appeared on a screen. Statistical analysis of the experiments show that the standard deviation of the tracking error is significantly improved with the adaptive dual neural network control addition when compared to the robust controller, in some instances reducing the magnitude by half.

References

1.
Wallace
,
S. E.
, and
Kimbarow
,
M. L.
,
2016
, “
Traumatic Brain Injury
,”
Cognitive Communication Disorders
,
M. L.
Kimbarow
, ed.,
Plural Publishing
, San Diego, CA, pp.
253
277
.
2.
Benjamin
,
E. J.
,
Blaha
,
M. J.
,
Chiuve
,
S. E.
,
Cushman
,
M.
,
Das
,
S. R.
,
Deo
,
R.
,
de Ferranti
,
S. D.
, et al.,
2017
, “
Heart Disease and Stroke Statistics—2017 Update: A Report From the American Heart Association
,”
Circulation
,
135
(
10
), pp.
e146
e603
.10.1161/CIR.0000000000000485
3.
Rimmer
,
J. H.
, and
Rowland
,
J. L.
,
2008
, “
Health Promotion for People With Disabilities: Implications for Empowering the Person and Promoting Disability-Friendly Environments
,”
Am. J. Lifestyle Med.
,
2
(
5
), pp.
409
420
.10.1177/1559827608317397
4.
Bélanger
,
M.
,
Stein
,
R. B.
,
Wheeler
,
G. D.
,
Gordon
,
T.
, and
Leduc
,
B.
,
2000
, “
Electrical Stimulation: Can It Increase Muscle Strength and Reverse Osteopenia in Spinal Cord Injured Individuals?
,”
Arch. Phys. Med. Rehabil.
,
81
(
8
), pp.
1090
1098
.10.1053/apmr.2000.7170
5.
Ferrante
,
S.
,
Pedrocchi
,
A.
,
Ferrigno
,
G.
, and
Molteni
,
F.
,
2008
, “
Cycling Induced by Functional Electrical Stimulation Improves the Muscular Strength and the Motor Control of Individuals With Post-Acute Stroke
,”
Eur. J. Phys. Rehabil. Med.
,
44
(
2
), pp.
159
167
.https://www.minervamedica.it/en/journals/europamedicophysica/article.php?cod=R33Y2008N02A0159
6.
Mohr
,
T.
,
Pødenphant
,
J.
,
Biering–Sørensen
,
F.
,
Galbo
,
H.
,
Thamsborg
,
G.
, and
Kjær
,
M.
,
1997
, “
Increased Bone Mineral Density After Prolonged Electrically Induced Cycle Training of Paralyzed Limbs in Spinal Cord Injured Man
,”
Calcif. Tissue Int.
,
61
(
1
), pp.
22
25
.10.1007/s002239900286
7.
Bellman
,
M. J.
,
Downey
,
R. J.
,
Parikh
,
A.
, and
Dixon
,
W. E.
,
2017
, “
Automatic Control of Cycling Induced by Functional Electrical Stimulation With Electric Motor Assistance
,”
IEEE Trans. Autom. Sci. Eng.
,
14
(
2
), pp.
1225
1234
.10.1109/TASE.2016.2527716
8.
Del-Ama
,
A. J.
,
Gil-Agudo
,
Á.
,
Pons
,
J. L.
, and
Moreno
,
J. C.
,
2014
, “
Hybrid FES-Robot Cooperative Control of Ambulatory Gait Rehabilitation Exoskeleton
,”
J. Neuroeng. Rehabil.
,
11
(
1
), pp.
1
15
.10.1186/1743-0003-11-27
9.
Hunt
,
K. J.
,
Hosmann
,
D.
,
Grob
,
M.
, and
Saengsuwan
,
J.
,
2013
, “
Metabolic Efficiency of Volitional and Electrically Stimulated Cycling in Able-Bodied Subjects
,”
Med. Eng. Phys.
,
35
(
7
), pp.
919
925
.10.1016/j.medengphy.2012.08.023
10.
Haddadin
,
S.
,
Albu-Schaffer
,
A.
,
De Luca
,
A.
, and
Hirzinger
,
G.
,
2008
, “
Collision Detection and Reaction: A Contribution to Safe Physical Human-Robot Interaction
,”
Proceedings of the 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems
, Nice, France, Sept. 22–26, pp.
3356
3363
.10.1109/IROS.2008.4650764
11.
Haddadin
,
S.
,
Albu-Schäffer
,
A.
, and
Hirzinger
,
G.
,
2010
, “
Safety Analysis for a Human-Friendly Manipulator
,”
Int. J. Soc. Rob.
,
2
(
3
), pp.
235
252
.10.1007/s12369-010-0053-z
12.
Poon
,
C. S.
,
2004
, “
Sensorimotor Learning and Information Processing by Bayesian Internal Models
,”
Proceedings of the 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society
, San Francisco, CA, Sept. 1–5, pp.
4481
4482
.10.1109/IEMBS.2004.1404245
13.
Rossini
,
P. M.
, and
Dal Forno
,
G.
,
2004
, “
Integrated Technology for Evaluation of Brain Function and Neural Plasticity
,”
Phys. Med. Rehabil. Clin.
,
15
(
1
), pp.
263
306
.10.1016/S1047-9651(03)00124-4
14.
Stein
,
J.
,
Krebs
,
H. I.
,
Frontera
,
W. R.
,
Fasoli
,
S. E.
,
Hughes
,
R.
, and
Hogan
,
N.
,
2004
, “
Comparison of Two Techniques of Robot-Aided Upper Limb Exercise Training After Stroke
,”
Am. J. Phys. Med. Rehabil.
,
83
(
9
), pp.
720
728
.10.1097/01.PHM.0000137313.14480.CE
15.
Del-Ama
,
A. J.
,
Koutsou
,
A. D.
,
Moreno
,
J. C.
,
De-Los-Reyes
,
A.
,
Gil-Agudo
,
Á.
, and
Pons
,
J. L.
,
2012
, “
Review of Hybrid Exoskeletons to Restore Gait Following Spinal Cord Injury
,”
J. Rehabil. Res. Dev.
,
49
(
4
), pp.
497
514
.10.1682/JRRD.2011.03.0043
16.
Anaya
,
F.
,
Thangavel
,
P.
, and
Yu
,
H.
,
2018
, “
Hybrid FES–Robotic Gait Rehabilitation Technologies: A Review on Mechanical Design, Actuation, and Control Strategies
,”
Int. J. Intell. Rob. Appl.
,
2
(
1
), pp.
1
28
.10.1007/s41315-017-0042-6
17.
Hogan
,
N.
,
1985
, “
Impedance Control: An Approach to Manipulation Part I, II, III
,”
ASME J. Dyn. Syst., Meas., Control
,
107
(
1
), pp.
1
7
.10.1115/1.3140702
18.
Ranatunga
,
I.
,
Lewis
,
F. L.
,
Popa
,
D. O.
, and
Tousif
,
S. M.
,
2017
, “
Adaptive Admittance Control for Human–Robot Interaction Using Model Reference Design and Adaptive Inverse Filtering
,”
IEEE Trans. Control Syst. Technol.
,
25
(
1
), pp.
278
285
.10.1109/TCST.2016.2523901
19.
Herrnstadt
,
G.
, and
Menon
,
C.
,
2016
, “
Admittance-Based Voluntary-Driven Motion With Speed-Controlled Tremor Rejection
,”
IEEE/ASME Trans. Mechatron.
,
21
(
4
), pp.
2108
2119
.10.1109/TMECH.2016.2555811
20.
Wu
,
Q.
,
Wang
,
X.
,
Chen
,
B.
, and
Wu
,
H.
,
2018
, “
Development of a Minimal-Intervention-Based Admittance Control Strategy for Upper Extremity Rehabilitation Exoskeleton
,”
IEEE Trans. Syst., Man, Cybern.: Syst.
,
48
(
6
), pp.
1005
1016
.10.1109/TSMC.2017.2771227
21.
Cousin
,
C. A.
,
Rouse
,
C. A.
,
Duenas
,
V. H.
, and
Dixon
,
W. E.
,
2019
, “
Controlling the Cadence and Admittance of a Functional Electrical Stimulation Cycle
,”
IEEE Trans. Neural Syst. Rehabil. Eng.
,
27
(
6
), pp.
1181
1192
.10.1109/TNSRE.2019.2914579
22.
Cousin
,
C. A.
,
Deptula
,
P.
,
Rouse
,
C. A.
, and
Dixon
,
W. E.
,
2019
, “
Cycling With Functional Electrical Stimulation and Adaptive Neural Network Admittance Control
,” Proceedings of the 2019 American Control Conference (
ACC
), Philadelphia, PA, July 10–12, pp.
1742
1747
.10.23919/ACC.2019.8814619
23.
Duenas
,
V. H.
,
Cousin
,
C. A.
,
Ghanbari
,
V.
, and
Dixon
,
W. E.
,
2018
, “
Passivity-Based Learning Control for Torque and Cadence Tracking in Functional Electrical Stimulation (FES) Induced Cycling
,” Proceedings of the 2018 Annual American Control Conference (
ACC
), Milwaukee, WI, June 27–29, pp.
3726
3731
.10.23919/ACC.2018.8431421
24.
Duenas
,
V. H.
,
Cousin
,
C. A.
,
Rouse
,
C. A.
, and
Dixon
,
W. E.
,
2019
, “
Extremum Seeking Control for Power Tracking Via Functional Electrical Stimulation
,”
IFAC-PapersOnLine
,
51
(
34
), pp.
164
169
.10.1016/j.ifacol.2019.01.060
25.
Duenas
,
V. H.
,
Cousin
,
C. A.
,
Ghanbari
,
V.
,
Fox
,
E. J.
, and
Dixon
,
W. E.
,
2020
, “
Torque and Cadence Tracking in Functional Electrical Stimulation Induced Cycling Using Passivity-Based Spatial Repetitive Learning Control
,”
Automatica
,
115
, p.
108852
.10.1016/j.automatica.2020.108852
26.
Cousin
,
C. A.
,
Duenas
,
V. H.
,
Rouse
,
C. A.
,
Bellman
,
M. J.
,
Freeborn
,
P.
,
Fox
,
E. J.
, and
Dixon
,
W. E.
,
2020
, “
Closed-Loop Cadence and Instantaneous Power Control on a Motorized Functional Electrical Stimulation Cycle
,”
IEEE Trans. Control Syst. Technol.
,
28
(
6
), pp.
2276
2291
.10.1109/TCST.2019.2937725
27.
Cousin
,
C. A.
,
Rouse
,
C. A.
, and
Dixon
,
W. E.
,
2021
, “
Split-Crank Functional Electrical Stimulation Cycling: An Adapting Admitting Rehabilitation Robot
,”
IEEE Trans. Control Syst. Technol.
,
29
(
5
), pp.
2153
2165
.10.1109/TCST.2020.3032474
28.
Khalil
,
H. K.
,
2002
,
Nonlinear Systems
, 3rd ed.,
Prentice Hall
,
Upper Saddle River, NJ
.
29.
Khalil
,
H. K.
, and
Esfandiari
,
F.
,
1993
, “
Semiglobal Stabilization of a Class of Nonlinear Systems Using Output Feedback
,”
IEEE Trans. Autom. Control
,
38
(
9
), pp.
1412
1415
.10.1109/9.237658
30.
Cousin
,
C. A.
,
Deptula
,
P.
,
Rouse
,
C. A.
, and
Dixon
,
W. E.
,
2022
, “
A Switched Lyapunov-Passivity Approach to Motorized FES Cycling Using Adaptive Admittance Control
,”
IEEE Trans. Control Syst. Technol.
,
30
(
2
), pp.
740
754
.10.1109/TCST.2021.3076934
31.
Behal
,
A.
,
Dixon
,
W. E.
,
Dawson
,
D. M.
, and
Xian
,
B.
,
2009
,
Lyapunov-Based Control of Robotic Systems
, Vol.
36
,
CRC Press
, Boca Raton, FL.
32.
Marchal-Crespo
,
L.
, and
Reinkensmeyer
,
D. J.
,
2009
, “
Review of Control Strategies for Robotic Movement Training After Neurologic Injury
,”
J. Neuroeng. Rehabil.
,
6
(
1
), pp.
1
15
.10.1186/1743-0003-6-20
33.
Tee
,
K. P.
,
Yan
,
R.
, and
Li
,
H.
,
2010
, “
Adaptive Admittance Control of a Robot Manipulator Under Task Space Constraint
,”
Proceedings of the 2010 IEEE International Conference on Robotics and Automation
, Anchorage, AK, May 3–7, pp.
5181
5186
.10.1109/ROBOT.2010.5509874
34.
Li
,
Y.
, and
Ge
,
S. S.
,
2014
, “
Impedance Learning for Robots Interacting With Unknown Environments
,”
IEEE Trans. Control Syst. Technol.
,
22
(
4
), pp.
1422
1432
.10.1109/TCST.2013.2286194
35.
Lewis
,
F. L.
,
2008
, “
Nonlinear Network Structures for Feedback Control
,”
Asian J. Control
,
1
(
4
), pp.
205
228
.10.1111/j.1934-6093.1999.tb00021.x
36.
Lewis
,
F. L.
,
Campos
,
J.
, and
Selmic
,
R.
,
2002
,
Neuro-Fuzzy Control of Industrial Systems With Actuator Nonlinearities
,
Society for Industrial and Applied Mathematics
,
Philadelphia, PA
.
37.
Dixon
,
W. E.
,
Behal
,
A.
,
Dawson
,
D. M.
, and
Nagarkatti
,
S. P.
,
2003
,
Nonlinear Control of Engineering Systems: A Lyapunov-Based Approach
,
Springer Science & Business Media
, New York.
38.
Kamalapurkar
,
R.
,
Rosenfeld
,
J. A.
,
Parikh
,
A.
,
Teel
,
A. R.
, and
Dixon
,
W. E.
,
2019
, “
Invariance-Like Results for Nonautonomous Switched Systems
,”
IEEE Trans. Autom. Control
,
64
(
2
), pp.
614
627
.10.1109/TAC.2018.2838055
39.
Clarke
,
F. H.
,
1990
,
Optimization and Nonsmooth Analysis
,
Society for Industrial and Applied Mathematics
, Philadelphia, PA.
40.
Filippov
,
A. F.
,
2013
,
Differential Equations With Discontinuous Righthand Sides: Control Systems
, Vol.
18
,
Springer Science & Business Media
, New York.
You do not currently have access to this content.