Abstract

This paper attempts to address the quandary of flexible-joint humanoid balancing performance augmentation, via the introduction of the Full-State Feedback Variable Impedance Control (FSFVIC), and Model-Free Compliant Floating-base VIC (MCFVIC) schemes. In comparison to rigid-joint humanoid robots, efficient balancing control of compliant bipeds, powered by Series Elastic Actuators (or harmonic drives), requires the design of more sophisticated controllers encapsulating both the motor and underactuated link dynamics. It has been demonstrated that Variable Impedance Control (VIC) can improve robotic interaction performance, albeit by introducing energy-injecting elements that may jeopardize closed-loop stability. To this end, the novel FSFVIC and MCFVIC schemes are proposed, which amalgamate both collocated and non-collocated feedback gains, with power-shaping signals that are capable of preserving the system's stability/passivity during VIC. The FSFVIC and MCFVIC stably modulate the system's collocated state gains to augment balancing performance, in addition to the non-collocated state gains that dictate the position control accuracy. Utilization of arbitrarily low-impedance gains is permitted by both the FSFVIC and MCFVIC schemes propounded herein. An array of experiments involving the COmpliant huMANoid reveals that significant balancing performance amelioration is achievable through online modulation of the full-state feedback gains (VIC), as compared to utilization of invariant impedance control.

References

1.
Vukobratovic
,
M.
, and
Borovac
,
B.
,
2004
, “
Zero-Moment Point—Thirty Five Years of Its Life
,”
Int. J. Human. Robot.
,
1
(
1
), pp.
157
173
. 10.1142/S0219843604000083
2.
Borelli
,
G. A.
,
1989
,
De Motu Animalium (English) Translated by P. Maquet
,
Springer-Verlag
,
Berlin, Heidelberg
.
3.
Sardain
,
P.
, and
Bessonnet
,
G.
,
2004
, “
Forces Acting on a Biped Robot. Center of Pressure—Zero Moment Point
,”
IEEE Trans. Syst. Man Cybern.
,
34
(
5
), pp.
630
637
. 10.1109/TSMCA.2004.832811
4.
Kajita
,
S.
, and
Tani
,
K.
,
1991
, “
Study of Dynamic Biped Locomotion on Rugged Terrain—Derivation and Application of the Linear Inverted Pendulum Mode
,”
IEEE International Conference on Robotics and Automation
,
Sacramento, CA
,
April
, pp.
1405
1411
.
5.
Stephens
,
B.
,
2007
, “
Humanoid Push Recovery
,”
IEEE-RAS International Conference on Humanoid Robots
,
Pittsburgh, PA
,
November
, pp.
589
595
.
6.
Kajita
,
S.
,
Morisawa
,
M.
,
Miura
,
K.
,
Nakaoka
,
S.
,
Kaneko
,
K.
,
Kanehiro
,
F.
, and
Yokoi
,
K.
,
2010
, “
Biped Walking Stabilization Based on Linear Inverted Pendulum Tracking
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Taipei, Taiwan
,
October
, pp.
4489
4496
.
7.
Pratt
,
J.
,
Carff
,
J.
,
Drakunov
,
S.
, and
Goswami
,
A.
,
2006
, “
Capture Point: A Step Toward Humanoid Push Recovery
,”
IEEE-RAS International Conference on Humanoid Robots
,
Genoa, Italy
,
December 2006
.
8.
Lanari
,
L.
,
Hutchinson
,
S.
, and
Marchionni
,
L.
,
2015
, “
Boundedness Issues in Planning of Locomotion Trajectories for Biped Robots
,”
IEEE-RAS International Conference on Humanoid Robots
,
Madrid, Spain
,
November
, pp.
200
207
.
9.
Kajita
,
S.
,
Kanehiro
,
F.
,
Kaneko
,
K.
,
Fujiwara
,
K.
,
Harada
,
K.
,
Yokoi
,
K.
, and
Hirukawa
,
H.
,
2003
, “
Resolved Momentum Control: Humanoid Motion Planning Based on the Linear and Angular Momentum
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Las Vegas, NV
,
October
, pp.
1644
1650
.
10.
Lee
,
S.-H.
, and
Goswami
,
A.
,
2012
, “
A Momentum-Based Balance Controller for Humanoid Robots on Non-level and Non-stationary Ground
,”
Auton. Robots
,
33
(
4
), pp.
399
414
. 10.1007/s10514-012-9294-z
11.
Lee
,
S.-H.
, and
Goswami
,
A.
,
2007
, “
Reaction Mass Pendulum (RMP): An Explicit Model for Centroidal Angular Momentum of Humanoid Robots
,”
IEEE International Conference on Robotics and Automation
,
Rome, Italy
,
April
, pp.
4667
4672
.
12.
Papadopoulos
,
E.
, and
Dubowsky
,
S.
,
1991
, “
On the Nature of Control Algorithms for Free-Floating Space Manipulators
,”
IEEE Trans. Rob. Autom.
,
7
(
6
), pp.
1102
1108
. 10.1109/70.105384
13.
Dubowsky
,
S.
, and
Papadopoulos
,
E.
,
1993
, “
The Kinematics, Dynamics, and Control of Free-Flying and Free-Floating Space Robotic Systems
,”
IEEE Trans. Rob. Autom.
,
9
(
5
), pp.
531
543
. 10.1109/70.258046
14.
Sentis
,
L.
, and
Khatib
,
O.
,
2005
, “
Control of Free-Floating Humanoid Robots Through Task Prioritization
,”
IEEE International Conference on Robotics and Automation
,
Barcelona, Spain
,
April
, pp.
1718
1723
.
15.
Park
,
J.
, and
Khatib
,
O.
,
2006
, “
Contact Consistent Control Framework for Humanoid Robots
,”
IEEE International Conference on Robotics and Automation
,
Orlando, FL
,
May
, pp.
1963
1969
.
16.
Nakanishi
,
J.
,
Mistry
,
M.
, and
Schaal
,
S.
,
2007
, “
Inverse Dynamics Control With Floating Base and Constraints
,”
IEEE International Conference on Robotics and Automation
,
Rome, Italy
,
April
, pp.
1942
1947
.
17.
Hyon
,
S.-H.
,
2009
, “
Compliant Terrain Adaptation for Biped Humanoids Without Measuring Ground Surface and Contact Forces
,”
IEEE Trans. Robot.
,
25
(
1
), pp.
171
178
. 10.1109/TRO.2008.2006870
18.
Mistry
,
M.
,
Buchli
,
J.
, and
Schaal
,
S.
,
2010
, “
Inverse Dynamics Control of Floating Base Systems Using Orthogonal Decomposition
,”
IEEE International Conference on Robotics and Automation
,
Anchorage, AK
,
May
, pp.
3406
3412
.
19.
Righetti
,
L.
,
Buchli
,
J.
,
Mistry
,
M.
, and
Schaal
,
S.
,
2011
, “
Control of Legged Robots With Optimal Distribution of Contact Forces
,”
IEEE-RAS International Conference on Humanoid Robots
,
Bled, Slovenia
,
October
, pp.
318
324
.
20.
Hogan
,
N.
,
1984
, “
Impedance Control: An Approach to Manipulation
,”
American Control Conference
,
San Diego, CA
,
June
, pp.
304
313
.
21.
Park
,
J. H.
,
2001
, “
Impedance Control for Biped Robot Locomotion
,”
IEEE Trans. Rob. Autom.
,
17
(
6
), pp.
870
882
. 10.1109/70.976014
22.
Kim
,
Y.
,
Lee
,
B.
,
Ryu
,
J.
, and
Kim
,
J.
,
2007
, “
Landing Force Control for Humanoid Robot by Time-Domain Passivity Approach
,”
IEEE Trans. Robot.
,
23
(
6
), pp.
1294
1301
. 10.1109/TRO.2007.906250
23.
Wang
,
Y.
,
Xiong
,
R.
,
Zhu
,
Q.
, and
Chu
,
J.
,
2014
, “
Compliance Control for Standing Maintenance of Humanoid Robots Under Unknown External Disturbances
,”
IEEE International Conference on Robotics and Automation
,
Hong Kong, China
,
May
, pp.
2297
2304
.
24.
Kronander
,
K.
, and
Billard
,
A.
,
2016
, “
Stability Considerations of Variable Impedance Control
,”
IEEE Trans. Robot.
,
32
(
5
), pp.
1298
1305
. 10.1109/TRO.2016.2593492
25.
Spyrakos-Papastavridis
,
E.
,
Childs
,
P. R. N.
, and
Dai
,
J. S.
,
2020
, “
Passivity Preservation for Variable Impedance Control of Compliant Robots
,”
IEEE/ASME Trans. Mechatron.
,
25
(
5
), pp.
2342
2353
. 10.1109/TMECH.2019.2961478
26.
Spyrakos-Papastavridis
,
E.
, and
Dai
,
J. S.
,
2020
, “
Minimally Model-Based Trajectory Tracking and Variable Impedance Control of Flexible-Joint Robots
,”
IEEE Tran. Ind. Electron.
, p.
1
. 10.1109/tie.2020.2994886
27.
Spyrakos-Papastavridis
,
E.
, and
Dai
,
J. S.
,
2020
, “
A Model-Free Solution for Stable Balancing and Locomotion of Floating-Base Legged SystemsSystems
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Las Vegas, NV, USA (Virtual)
,
October
, pp.
3816
3822
.
28.
Tsagarakis
,
N. G.
,
Li
,
Z.
,
Saglia
,
J.
, and
Caldwell
,
D. G.
,
2011
, “
The Design of the Lower Body of the Compliant Humanoid Robot “Ccub”
,”
IEEE International Conference on Robotics and Automation
,
Shanghai, China
,
May
, pp.
2035
2040
.
29.
Mazumdar
,
A.
,
Spencer
,
S.
,
Salton
,
J.
,
Hobart
,
C.
,
Love
,
J.
,
Dullea
,
K.
,
Kuehl
,
M.
,
Blada
,
T.
,
Quigley
,
M.
,
Smith
,
J.
,
Bertrand
,
S.
,
Wu
,
T.
,
Pratt
,
J.
, and
Buerger
,
S.
,
2015
, “
Using Parallel Stiffness to Achieve Improved Locomotive Efficiency With the Sandia STEPPR Robot
,”
IEEE International Conference on Robotics and Automation
,
Seattle, WA
,
May 2015
, pp.
835
841
.
30.
Enoch
,
A.
,
Sutas
,
A.
,
Nakaoka
,
S.
, and
Vijayakumar
,
S.
,
2012
, “
BLUE: A Bipedal Robot With Variable Stiffness and Damping
,”
IEEE-RAS International Conference on Humanoid Robots
,
Osaka, Japan
,
November
, pp.
487
494
.
31.
Pratt
,
G. A.
, and
Williamson
,
M. M.
,
1995
, “
Series Elastic Actuators
,”
International Conference on Intelligent Robots and Systems
,
Pittsburgh, PA
,
August
, pp.
1208
1213
.
32.
Tomei
,
P.
,
1991
, “
A Simple PD Controller for Robots With Elastic Joints
,”
IEEE Trans. Autom. Control
,
36
(
10
), pp.
1208
1213
. 10.1109/9.90238
33.
De Luca
,
A.
,
Siciliano
,
B.
, and
Zollo
,
L.
,
2005
, “
PD Control With On-line Gravity Compensation for Robots With Elastic Joints: Theory and Experiments
,”
Automatica
,
41
(
10
), pp.
1809
1819
. 10.1016/j.automatica.2005.05.009
34.
Albu-Schäffer
,
A.
,
Ott
,
C.
, and
Hirzinger
,
G.
,
2007
, “
A Unified Passivity-Based Control Framework for Position, Torque and Impedance Control of Flexible Joint Robots
,”
Int. J. Robot. Res.
,
26
(
1
), pp.
23
39
. 10.1177/0278364907073776
35.
Tian
,
L.
, and
Goldenberg
,
A.
,
1995
, “
Robust Adaptive Control of Flexible Joint Robots With Joint Torque Feedback
,”
IEEE International Conference on Robotics and Automation
,
Nagoya, Japan
,
May
, pp.
1229
1234
.
36.
Nicosia
,
S.
, and
Tomei
,
P.
,
1993
, “
Design of Global Tracking Controllers for Flexible-Joint Robots
,”
J. Robot. Syst.
,
10
(
6
), pp.
835
846
. 10.1002/rob.4620100604
37.
Keppler
,
M.
,
Lakatos
,
D.
,
Ott
,
C.
, and
Albu-Schaeffer
,
A.
,
2018
, “
Elastic Structure Preserving (ESP) Control for Compliantly Actuated Robots
,”
IEEE Trans. Robot.
,
23
(
5
), pp.
317
335
. 10.1109/TRO.2017.2776314
38.
Spyrakos-Papastavridis
,
E.
,
Dai
,
J. S.
,
Childs
,
P. R. N.
, and
Tsagarakis
,
N. G.
,
2018
, “
Selective-Compliance-Based Lagrange Model and Multilevel Noncollocated Feedback Control of a Humanoid Robot
,”
ASME J. Mech. Rob.
,
10
(
3
), p.
031009
. 10.1115/1.4039394
39.
Spyrakos-Papastavridis
,
E.
,
Kashiri
,
N.
,
Childs
,
P. R. N.
, and
Tsagarakis
,
N. G.
,
2018
, “
Online Impedance Regulation Techniques for Compliant Humanoid Balancing
,”
Robot. Autonom. Syst.
,
104
, pp.
85
98
. 10.1016/j.robot.2018.03.001
40.
Spyrakos-Papastavridis
,
E.
,
Childs
,
P. R. N.
, and
Tsagarakis
,
N. G.
,
2017
, “
Variable Impedance Walking Using Time-Varying Lyapunov Stability Margins
,”
IEEE-RAS International Conference on Humanoid Robots
,
Birmingham, UK
,
November
, pp.
318
323
.
41.
Barkana
,
I.
,
2014
, “
Defending the Beauty of the Invariance Principle
,”
Int. J. Control
,
87
(
1
), pp.
186
206
. 10.1080/00207179.2013.826385
42.
Slotine
,
J. E.
, and
Li
,
W.
,
1987
, “
On the Adaptive Control of Robot Manipulators
,”
Int. J. Robot. Res.
,
6
(
3
), pp.
49
59
. 10.1177/027836498700600303
43.
van der Schaft
,
A.
,
2000
,
L2-Gain and Passivity Theorem Techniques in Nonlinear Control
,
Springer-Verlag
,
Berlin, Germany
.
44.
Spyrakos-Papastavridis
,
E.
,
Caldwell
,
D. G.
, and
Tsagarakis
,
N. G.
,
2016
, “
Balance and Impedance Optimization Control for Compliant Humanoid Stepping
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Daejeon, South Korea
,
October
, pp.
1349
1355
.
45.
Spyrakos-Papastavridis
,
E.
,
Perrin
,
N.
,
Tsagarakis
,
N. G.
,
Dai
,
J. S.
, and
Caldwell
,
D. G.
,
2014
, “
Lyapunov Stability Margins for Humanoid Robot Balancing
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Chicago, IL
,
September
, pp.
945
951
.
46.
Bryson
,
A. E.
, and
Ho
,
Y.
,
1975
,
Applied Optimal Control: Optimization, Estimation, and Control
,
Taylor & Francis
,
New York
.
47.
Herzog
,
A.
,
Righetti
,
L.
,
Grimminger
,
F.
,
Pastor
,
P.
, and
Schaal
,
S.
,
2014
, “
Balancing Experiments on a Torque-Controlled Humanoid With Hierarchical Inverse Dynamics
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Chicago, IL
,
September
, pp.
981
988
.
You do not currently have access to this content.