In this paper, we introduce two robust adaptive controllers for the human shank motion tracking problem that is inherent in neuromuscular electrical stimulation (NMES) systems. The control laws adaptively compensate for the unknown parameters that appear nonlinearly in the musculoskeletal dynamics while providing robustness to additive disturbance torques. The adaptive schemes exploit the Lipschitzian and/or the concave/convex parameterizations of the model functions. The resulting control laws are continuous and guarantee practical tracking for the shank angular position. The performance of the two robust adaptive controllers is demonstrated via simulations.
Issue Section:
Research Papers
References
1.
Sharma
, N.
, Gregory
, C.
, and Dixon
, W.
, 2011
, “Predictor-Based Compensation for Electromechanical Delay During Neuromuscular Electrical Stimulation
,” IEEE Trans. Neural Syst. Rehab. Eng.
, 19
(6
), pp. 601
–611
.2.
Ferrarin
, M.
, and Pedotti
, A.
, 2000
, “The Relationship Between Electrical Stimulus and Joint Torque: A Dynamic Model
,” IEEE Trans. Rehab. Eng.
, 8
(3
), pp. 342
–352
.3.
Hausdorff
, J.
, and Durfee
, W.
, 1991
, “Open-Loop Position Control of the Knee Joint Using Electrical Stimulation of the Quadriceps and Hamstrings
,” Med. Biol. Eng. Comput.
, 29
(3
), pp. 269
–280
.4.
Jezernik
, S.
, Wassink
, R.
, and Keller
, T.
, 2004
, “Sliding Mode Closed Loop Control of FES: Controlling the Shank Movement
,” IEEE Trans. Biomed. Eng.
, 51
(2
), pp. 263
–272
.5.
Schauer
, T.
, Negard
, N.
, Previdi
, F.
, Hunt
, K.
, Fraser
, M.
, Ferchland
, E.
, and Raisch
, J.
, 2005
, “Online Identification and Nonlinear Control of the Electrically Stimulated Quadriceps Muscle
,” Control Eng. Pract.
, 13
(9
), pp. 1207
–1219
.6.
Crago
, P.
, Lan
, N.
, Veltink
, P.
, Abbas
, J.
, and Kantor
, C.
, 1996
, “New Control Strategies for Neuroprosthetic Systems
,” J. Rehab. Res. Dev.
, 33
(2
), pp. 158
–172
.7.
Hill
, A.
, 1938
, “The Heat of Shortening and the Dynamic Constants of Muscle
,” Proc. R. Soc. London B
, 126
(843
), pp. 136
–195
.8.
Dorgan
, S.
, and O'Malley
, M.
, 1997
, “A Nonlinear Mathematical Model of Electrically Stimulated Skeletal Muscle
,” IEEE Trans. Rehab. Eng.
, 5
(2
), pp. 179
–194
.9.
Edrich
, T.
, Riener
, R.
, and Quintern
, J.
, 2000
, “Analysis of Passive Elastic Joint Moments in Paraplegics
,” IEEE Trans. Biomed. Eng.
, 47
(8
), pp. 1058
–1065
.10.
Franken
, H.
, Veltink
, P.
, and Henk
, R.
, 1993
, “Identification of Passive Knee Joint and Shank Dynamics in Paraplegics Using Quadriceps Stimulation
,” IEEE Trans. Rehab. Eng.
, 1
(3
), pp. 154
–164
.11.
Hatze
, H.
, 1977
, “A Myocybernetic Control Model of Skeletal Muscle
,” Biol. Cybern.
, 25
(2
), pp. 103
–119
.12.
Kearney
, R.
, and Hunter
, I.
, 1990
, “System Identification of Human Joint Dynamics
,” Critical Rev. Biomed. Eng.
, 18
(1
), pp. 57
–88
.13.
Levy
, M.
, Mizrahi
, J.
, and Susak
, Z.
, 1990
, “Recruitment, Force and Fatigue Characteristics of Quadriceps Muscles of Paraplegics, Isometrically Activated by Surface FES
,” J. Biomed. Eng.
, 12
(2
), pp. 150
–156
.14.
Riener
, R.
, Quintern
, J.
, and Schmidt
, G.
, 1996
, “Biomechanical Model of the Human Knee Evaluated by Neuromuscular Stimulation
,” J. Biomech.
, 29
(9
), pp. 1157
–1167
.15.
Schutte
, L.
, Rodgers
, M.
, Zajac
, F.
, and Glaser
, R.
, 1993
, “Improving the Efficacy of Electrical Stimulation-Induced Leg Cycle Ergometry: An Analysis Based on a Dynamic Musculoskeletal Model
,” IEEE Trans. Rehab. Eng.
, 1
(2
), pp. 109
–125
.16.
Ferrarin
, M.
, Palazzo
, F.
, Riener
, R.
, and Quintern
, J.
, 2001
, “Model-Based Control of FES-Induced Single Joint Movements
,” IEEE Trans. Neural Syst. Rehab. Eng.
, 9
(3
), pp. 245
–257
.17.
Koo
, B.
, and Leonessa
, A.
, 2011
, “An Adaptive Block Backstepping Control Design for Functional Electrical Stimulation of Agonist-Antagonist Muscles,” ASME
Paper No. DSCC2011-6143.18.
Yang
, R.
, and de Queiroz
, M.
, 2016
, “Adaptive Control of the Nonlinearly Parameterized Limb Dynamics With Application to Neuromuscular Electrical Stimulation
,” American Control Conference
(ACC
), Boston, MA, July 6–8, pp. 4871
–4876
.19.
Kobravi
, H.-R.
, and Erfanian
, A.
, 2009
, “Decentralized Adaptive Robust Control Based on Sliding Mode and Nonlinear Compensator for Control of Ankle Movement Using Functional Electrical Stimulation of Agonist-Antagonist Muscles
,” J. Neural Eng.
, 6
(4
), pp. 2818
–2827
.20.
Cheng
, T.-H.
, Wang
, Q.
, Kamalapurkar
, R.
, Dinh
, H. T.
, Bellman
, M.
, and Dixon
, W. E.
, 2016
, “Identification-Based Closed-Loop NMES Limb Tracking With Amplitude-Modulated Control Input
,” IEEE Trans. Cybern.
, 46
(7
), pp. 1679
–1690
.21.
Giuffrida
, J.
, and Crago
, P.
, 2005
, “Functional Restoration of Elbow Extension After Spinal-Cord Injury Using a Neural Network-Based Synergistic FES Controller
,” IEEE Trans. Neural Syst. Rehab. Eng.
, 13
(2
), pp. 147
–152
.22.
Riess
, J.
, and Abbas
, J.
, 2000
, “Adaptive Neural Network Control of Cyclic Movements Using Functional Neuromuscular Stimulation
,” IEEE Trans. Neural Syst. Rehab. Eng.
, 8
(1
), pp. 42
–52
.23.
Sharma
, N.
, Gregory
, C.
, Johnson
, M.
, and Dixon
, W.
, 2012
, “Closed-Loop Neural Network-Based NMES Control for Human Limb Tracking
,” IEEE Trans. Control Syst. Technol.
, 20
(3
), pp. 712
–725
.24.
Wang
, Q.
, Sharma
, N.
, Johnson
, M.
, Gregory
, C. M.
, and Dixon
, W.
, 2013
, “Adaptive Inverse Optimal Neuromuscular Electrical Stimulation
,” IEEE Trans. Cybern.
, 43
(6
), pp. 1710
–1718
.25.
Sharma
, N.
, Stegath
, K.
, Gregory
, C.
, and Dixon
, W.
, 2009
, “Nonlinear Neuromuscular Electrical Stimulation Tracking Control of a Human Limb
,” IEEE Trans. Neural Syst. Rehab. Eng.
, 17
(6
), pp. 576
–584
.26.
Karafyllis
, I.
, Malisoff
, M.
, de Queiroz
, M.
, Krstic
, M.
, and Yang
, R.
, 2015
, “Predictor-Based Tracking for Neuromuscular Electrical Stimulation
,” Int. J. Rob. Nonlinear Control
, 25
(14
), pp. 2391
–2419
.27.
Merad
, M.
, Downey
, R. J.
, Obuz
, S.
, and Dixon
, W. E.
, 2016
, “Isometric Torque Control for Neuromuscular Electrical Stimulation With Time-Varying Input Delay
,” IEEE Trans. Control Syst. Technol.
, 24
(3
), pp. 971
–978
.28.
Downey
, R. J.
, Cheng
, T.-H.
, Bellman
, M.
, and Dixon
, W. E.
, 2015
, “Closed-Loop Asynchronous Electrical Stimulation Prolongs Functional Movements in the Lower Body
,” IEEE Trans. Neural Syst. Rehab. Eng.
, 23
(6
), pp. 1117
–1127
.29.
Ortega
, R.
, 1996
, “Some Remarks on Adaptive Neuro-Fuzzy Systems
,” Int. J. Adapt. Control Signal Process.
, 10
(1
), pp. 79
–83
.30.
Annaswamy
, A.
, Skantze
, F.
, and Loh
, A.
, 1998
, “Adaptive Control of Continuous Time Systems With Convex/Concave Parameterization
,” Automatica
, 34
(1
), pp. 33
–49
.31.
Kojic
, A.
, Annaswamy
, A. M.
, Loh
, A.-P.
, and Lozano
, R.
, 1999
, “Adaptive Control of a Class of Nonlinear Systems With Convex/Concave Parameterization
,” Syst. Control Lett.
, 37
(5
), pp. 267
–274
.32.
Loh
, A.
, Annaswamy
, A.
, and Skantze
, F.
, 1999
, “Adaptation in the Presence of a General Nonlinear Parameterization: An Error Model Approach
,” IEEE Trans. Autom. Control
, 44
(9
), pp. 1634
–1652
.33.
Netto
, M.
, Annaswamy
, A. M.
, Ortega
, R.
, and Moya
, P.
, 2000
, “Adaptive Control of a Class of Nonlinearly Parameterized Systems Using Convexification
,” Int. J. Control
, 73
(14
), pp. 1312
–1321
.34.
Fradkov
, A.
, Ortega
, R.
, and Bastin
, G.
, 2001
, “Semi-Adaptive Control of Convexly Parametrized Systems With Application to Temperature Regulation of Chemical Reactors
,” Int. J. Adapt. Control Signal Process.
, 15
(4
), pp. 415
–426
.35.
Netto
, M.
, and Annaswamy
, A. M.
, 2012
, “Adaptive Control of a Class of Multilinearly Parameterized Systems by Using Noncertainty Equivalence Control
,” IEEE Conference on Decision and Control
(CDC
), Maui, HI, Dec. 10–13, pp. 4829
–4834
.36.
Hung
, N. V. Q.
, Tuan
, H. D.
, Apkarian
, P.
, and Narikiyo
, T.
, 2002
, “General Adaptive Controls for Nonlinearly Parameterized Systems Under Generalized Matching Condition
,” 15th Triennial World Congress
(IFAC
), Barcelona, Spain, July 21–26, pp. 840
–846
.37.
de Queiroz
, M. S.
, Dawson
, D. M.
, Nagarkatti
, S.
, and Zhang
, F.
, 2000
, Lyapunov-Based Control of Mechanical Systems
, Birkhäuser
, Cambridge, MA
.38.
Yang
, R.
, and de Queiroz
, M.
, 2016
, “Adaptive Control With Concave/Convex Parameterization for an Electrically Stimulated Human Limb
,” IFAC Conference on Cyber-Physical and Human-Systems
, Florianopolis, Brazil, Dec. 7–9, pp. 194
–199
.39.
Yokoi
, K.
, Hung
, N.
, Tuan
, H.
, and Hosoe
, S.
, 2007
, “Adaptive Control Design for Nonlinearly Parameterized Systems With a Triangular Structure
,” Asian J. Control
, 9
(2
), pp. 121
–132
.40.
Polycarpou
, M.
, and Ioannou
, P.
, 1996, “A Robust Adaptive Nonlinear Control Design
,” Automatica
, 32
(3
), pp. 423
–427
.41.
Davy
, D.
, and Audu
, M.
, 1987
, “A Dynamic Optimization Technique for Predicting Muscle Force in the Swing Phase of Gait
,” J. Biomech.
, 20
(2
), pp. 187
–201
.42.
Mansour
, J.
, and Audu
, M.
, 1986
, “The Passive Elastic Moment at the Knee and Its Influence on Human Gait
,” J. Biomech.
, 19
(5
), pp. 369
–373
.43.
Qiu
, T.
, Alibeji
, N.
, and Sharma
, N.
, 2016
, “Robust Compensation of Electromechanical Delay During Neuromuscular Electrical Stimulation of Antagonistic Muscles
,” American Control Conference
(ACC
), Boston, MA, July 6–8, pp. 4871
–4876
.44.
Narendra
, K. S.
, and Annaswamy
, A. M.
, 2005
, Stable Adaptive Systems
, Dover
, Mineola, NY
.45.
Qian
, C.
, and Lin
, W.
, 2002
, “Practical Output Tracking of Nonlinear Systems With Uncontrollable Unstable Linearization
,” IEEE Trans. Autom. Control
, 47
(1
), pp. 21
–36
.46.
Winter
, D. A.
, 2009
, Biomechanics and Motor Control of Human Movement
, Wiley
, Hoboken, NJ
.47.
Gao
, F.
, de Queiroz
, M. S.
, and Dawson
, D. M.
, 2007
, “A New Tuning Function-Based Robust Adaptive Controller for Parametric Strict-Feedback Systems
,” IEEE Conference Decision and Control
(CDC
), New Orleans, LA, Dec. 12–14, pp. 3543
–3548
.48.
Qu
, Z.
, and Xu
, J. X.
, 2002
, “Model-Based Learning Controls and Their Comparisons Using Lyapunov Direct Method
,” Asian J. Control
, 4
(1
), pp. 99
–110
.49.
Xian
, B.
, Dawson
, D.
, de Queiroz
, M.
, and Chen
, J.
, 2004
, “A Continuous Asymptotic Tracking Control Strategy for Uncertain Nonlinear Systems
,” IEEE Trans. Autom. Control
, 49
(7
), pp. 1206
–1211
.50.
Krstić
, M.
, 1996
, “Invariant Manifolds and Asymptotic Properties of Adaptive Nonlinear Stabilizers
,” IEEE Trans. Autom. Control
, 41
(6
), pp. 817
–829
.51.
Anderson
, D.
, Madigan
, M.
, and Nussbaum
, M.
, 2007
, “Maximum Voluntary Joint Torque as a Function of Joint Angle and Angular Velocity: Model Development and Application to the Lower Limb
,” J. Biomech.
, 40
(14
), pp. 3105
–3113
.Copyright © 2018 by ASME
You do not currently have access to this content.
