Abstract

Achieving coordinated motion between transfemoral amputee patients and powered prosthetic joints is of paramount importance for powered prostheses control. In this article, we propose employing an algebraic curve representation of nominal human walking data for a powered knee prosthesis controller design. The proposed algebraic curve representation encodes the desired holonomic relationship between the human and the powered prosthetic joints with no dependence on joint velocities. For an impedance model of the knee joint motion driven by the hip angle signal, we create a continuum of equilibria along the gait cycle using a variable impedance scheme. Our variable impedance-based control law, which is designed using the parameter-dependent Lyapunov function framework, realizes the coordinated hip-knee motion with a family of spring and damper behaviors that continuously change along the human-inspired algebraic curve. In order to accommodate variability in the user's hip motion, we propose a computationally efficient radial projection-based algorithm onto the human-inspired algebraic curve in the hip-knee plane.

References

1.
Sup
,
F.
,
Bohara
,
A.
, and
Goldfarb
,
M.
,
2008
, “
Design and Control of a Powered Transfemoral Prosthesis
,”
Int. J. Robot. Res.
,
27
(
2
), pp.
263
273
.
2.
Liu
,
M.
,
Zhang
,
F.
,
Datseris
,
P.
, and
Huang
,
H. H.
,
2014
, “
Improving Finite State Impedance Control of Active-Transfemoral Prosthesis Using Dempster-Shafer Based State Transition Rules
,”
J. Intell. Robot. Syst.
,
76
(
3–4
), pp.
461
474
.
3.
Zhang
,
F.
,
Liu
,
M.
, and
Huang
,
H.
,
2015
, “
Investigation of Timing to Switch Control Mode in Powered Knee Prostheses During Task Transitions
,”
PLoS One
,
10
(
7
), p.
e0133965
.
4.
Zhang
,
F.
,
Liu
,
M.
, and
Huang
,
H.
,
2015
, “
Effects of Locomotion Mode Recognition Errors on Volitional Control of Powered Above-Knee Prostheses
,”
IEEE Trans. Neural Syst. Rehabil. Eng.
,
23
(
1
), pp.
64
72
.
5.
Simon
,
A. M.
,
Ingraham
,
K. A.
,
Fey
,
N. P.
,
Finucane
,
S. B.
,
Lipschutz
,
R. D.
,
Young
,
A. J.
, and
Hargrove
,
L. J.
,
2014
, “
Configuring a Powered Knee and Ankle Prosthesis for Transfemoral Amputees Within Five Specific Ambulation Modes
,”
PLoS One
,
9
(
6
), p.
e99387
.
6.
Fite
,
K.
,
Mitchell
,
J.
,
Sup
,
F.
, and
Goldfarb
,
M.
,
2007
, “
Design and Control of an Electrically Powered Knee Prosthesis
,”
IEEE Tenth International Conference on Rehabilitation Robotics
(
ICORR
),
Noordwijk, The Netherlands
,
June 13–15
, pp.
902
905
.
7.
Huang
,
H.
,
Crouch
,
D. L.
,
Liu
,
M.
,
Sawicki
,
G. S.
, and
Wang
,
D.
,
2016
, “
A Cyber Expert System for Auto-Tuning Powered Prosthesis Impedance Control Parameters
,”
Annals Biomed. Eng.
,
44
(
5
), pp.
1613
1624
.
8.
Wen
,
Y.
,
Liu
,
M.
,
Si
,
J.
, and
Huang
,
H. H.
,
2016
, “
Adaptive Control of Powered Transfemoral Prostheses Based on Adaptive Dynamic Programming
,”
IEEE 38th Annual International Conference Engineering Medicine Biology Society
(
EMBC
),
Orlando, FL
,
Aug. 16–20
, pp.
5071
5074
.
9.
Gregg
,
R. D.
,
Lenzi
,
T.
,
Hargrove
,
L. J.
, and
Sensinger
,
J. W.
,
2014
, “
Virtual Constraint Control of a Powered Prosthetic Leg: From Simulation to Experiments With Transfemoral Amputees
,”
IEEE Trans. Robot.
,
30
(
6
), pp.
1455
1471
.
10.
Villarreal
,
D. J.
,
Poonawala
,
H. A.
, and
Gregg
,
R. D.
,
2017
, “
A Robust Parameterization of Human Gait Patterns Across Phase-Shifting Perturbations
,”
IEEE Trans. Neural Syst. Rehabil. Eng.
,
25
(
3
), pp.
265
278
.
11.
Holgate
,
M. A.
,
Sugar
,
T. G.
, and
Bohler
,
A. W.
,
2009
, “
A Novel Control Algorithm for Wearable Robotics Using Phase Plane Invariants
,”
IEEE International Conference on Robotics and Automation
(
ROBOT
),
Kobe, Japan
,
May 12–17
, pp.
3845
3850
.
12.
Quintero
,
D.
,
Villarreal
,
D. J.
,
Lambert
,
D. J.
,
Kapp
,
S.
, and
Gregg
,
R. D.
,
2018
, “
Continuous-Phase Control of a Powered Knee–Ankle Prosthesis: Amputee Experiments Across Speeds and Inclines
,”
IEEE Trans. Robot.
,
34
(
3
), pp.
686
701
.
13.
Quintero
,
D.
,
Villarreal
,
D. J.
, and
Gregg
,
R. D.
,
2016
, “
Preliminary Experiments With a Unified Controller for a Powered Knee-Ankle Prosthetic Leg Across Walking Speeds
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
),
Daejeon, South Korea
,
Oct. 9–14
, pp.
5427
5433
.
14.
Shultz
,
A. H.
, and
Goldfarb
,
M.
,
2018
, “
A Unified Controller for Walking on Even and Uneven Terrain With a Powered Ankle Prosthesis
,”
IEEE Trans. Neural Syst. Rehabil. Eng.
,
26
(
4
), pp.
788
797
.
15.
Quintero
,
D.
,
Martin
,
A. E.
, and
Gregg
,
R. D.
,
2018
, “
Toward Unified Control of a Powered Prosthetic Leg: A Simulation Study
,”
IEEE Trans. Control Syst. Technol.
,
26
(
1
), pp.
305
312
.
16.
Villarreal
,
D. J.
,
Quintero
,
D.
, and
Gregg
,
R. D.
,
2017
, “
Piecewise and Unified Phase Variables in the Control of a Powered Prosthetic Leg
,”
IEEE International Conference on
Rehabilitation Robotics (
ICORR
),
London, UK
,
July 17–20
, pp.
1425
1430
.
17.
Martin
,
A. E.
, and
Gregg
,
R. D.
,
2017
, “
Stable, Robust Hybrid Zero Dynamics Control of Powered Lower-Limb Prostheses
,”
IEEE Trans. Autom. Control
,
62
(
8
), pp.
3930
3942
.
18.
Quintero
,
D.
,
Lambert
,
D. J.
,
Villarreal
,
D. J.
, and
Gregg
,
R. D.
,
2017
, “
Real-Time Continuous Gait Phase and Speed Estimation From a Single Sensor
,”
IEEE Conference on Control Technology and Applications
(
CCTA
),
Mauna Lani, HI
,
Aug. 27–30
, pp.
847
852
.
19.
Kumar
,
S.
,
Mohammadi
,
A.
,
Gans
,
N.
, and
Gregg
,
R. D.
,
2017
, “
Automatic Tuning of Virtual Constraint-Based Control Algorithms for Powered Knee-Ankle Prostheses
,”
IEEE
Conference on Control Technology and Applications
,
Mauna Lani, HI
,
Aug. 27–30
, pp.
812
818
.
20.
Blane
,
M. M.
,
Lei
,
Z.
,
Çivi
,
H.
, and
Cooper
,
D. B.
,
2000
, “
The 3 L Algorithm for Fitting Implicit Polynomial Curves and Surfaces to Data
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
22
(
3
), pp.
298
313
.
21.
Mohammadi
,
A.
, and
Gregg
,
R. D.
,
2018
, “
Human-Inspired Algebraic Curves for Wearable Robot Control
,”
ASME
Paper No. DSCC2018-9061.
22.
Martínez
,
A.
,
Lawson
,
B.
, and
Goldfarb
,
M.
,
2018
, “
A Controller for Guiding Leg Movement During Overground Walking With a Lower Limb Exoskeleton
,”
IEEE Trans. Robot.
,
34
(
1
), pp.
183
193
.
23.
Mohammadi
,
A.
,
Horn
,
J.
, and
Gregg
,
R. D.
,
2017
, “
Removing Phase Variables From Biped Robot Parametric Gaits
,”
IEEE Conference on Control Technology and Applications
(
CCTA
),
Mauna Lani, HI
,
Aug. 27–30
, pp.
834
840
.
24.
Silverman
,
J. H.
,
2009
,
The Arithmetic of Elliptic Curves
, Vol.
106
,
Springer Science and Business Media
, Dordrecht, The Netherlands.
25.
Unel
,
M.
, and
Wolovich
,
W. A.
,
2000
, “
On the Construction of Complete Sets of Geometric Invariants for Algebraic Curves
,”
Adv. Appl. Math.
,
24
(
1
), pp.
65
87
.
26.
Winter
,
D. A.
,
1991
,
Biomechanics and Motor Control of Human Gait: Normal, Elderly and Pathological
, 2nd ed.,
University of Waterloo Press
, Waterloo, ON, Canada.
27.
Lei
,
Z.
,
Blane
,
M. M.
, and
Cooper
,
D. B.
,
1996
, “
3 L Fitting of Higher Degree Implicit Polynomials
,”
Third IEEE Workshop Applications Computer Vision
(
ACV
),
Sarasota, FL
,
Dec. 2–4
, pp.
148
153
.
28.
Wolovich
,
W.
,
Albakri
,
H.
, and
Yalcin
,
H.
,
2002
, “
The Precise Measurement of Free-Form Surfaces
,”
ASME J. Manuf. Sci. Eng.
,
124
(
2
), pp.
326
332
.
29.
Wolovich
,
W. A.
,
2001
, “
On the Structure of Algebraic Curves and Their Relation to Dynamical Systems
,”
IFAC Proc.
,
34
(
13
), pp.
13
19
.
30.
Winter
,
D. A.
,
2009
,
Biomechanics and Motor Control of Human Movement
,
Wiley
, New York.
31.
Rugh
,
W. J.
, and
Shamma
,
J. S.
,
2000
, “
Research on Gain Scheduling
,”
Automatica
,
36
(
10
), pp.
1401
1425
.
32.
Teel
,
A.
, and
Praly
,
L.
,
1995
, “
Tools for Semiglobal Stabilization by Partial State and Output Feedback
,”
SIAM J. Control Optim.
,
33
(
5
), pp.
1443
1488
.
33.
Gahinet
,
P.
,
Apkarian
,
P.
, and
Chilali
,
M.
,
1996
, “
Affine Parameter-Dependent Lyapunov Functions and Real Parametric Uncertainty
,”
IEEE Trans. Autom. Control
,
41
(
3
), pp.
436
442
.
34.
Khalil
,
H. K.
,
2002
,
Nonlinear Systems
,
Prentice Hall
,
Upper Saddle River, NJ
.
35.
Mohammadi
,
A.
,
2016
, “
Virtual Holonomic Constraints for Euler-Lagrange Control Systems
,” Ph.D. thesis, University of Toronto, Toronto, ON, Canada.
36.
Westervelt
,
E. R.
,
Chevallereau
,
C.
,
Choi
,
J. H.
,
Morris
,
B.
, and
Grizzle
,
J. W.
,
2007
,
Feedback Control of Dynamic Bipedal Robot Locomotion
,
CRC Press
, Boca Raton, FL.
37.
Westervelt
,
E. R.
,
Grizzle
,
J. W.
, and
Koditschek
,
D. E.
,
2003
, “
Hybrid Zero Dynamics of Planar Biped Walkers
,”
IEEE Trans. Autom. Control
,
48
(
1
), pp.
42
56
.
38.
Atkinson
,
K. E.
,
2008
,
An Introduction to Numerical Analysis
,
Wiley
, New York.
39.
Martin
,
A. E.
,
Villarreal
,
D. J.
, and
Gregg
,
R. D.
,
2016
, “
Characterizing and Modeling the Joint-Level Variability in Human Walking
,”
J. Biomech.
,
49
(
14
), pp.
3298
3305
.
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