Abstract

For practical applications of interactive manipulation, active contact control is one of the fundamental functions that flexible-link parallel mechanisms (FLPMs) should be equipped with. In this paper, a force control approach is proposed for FLPMs to make active adjustment toward their payload, which cannot be directly achieved by their intrinsic passive compliance. To begin with, at a starting configuration the Jacobian matrix is accurately calculated with the finite difference method, while at non-starting configurations it is deduced with an increment-based approach. The compliance model is derived through mapping from the joint stiffness within each elastic rod. On this basis, the differential relation among pose, payload, and actuation variables is constructed to form the control logic, whose correctness and feasibility are then verified with simulations. Finally, interaction experiments under fixed environment and cooperative motion are carried out, and the results demonstrate that force control for a quasi-translational FLPM can be accomplished with enough pose accuracy.

References

1.
Howell
,
L. L.
,
2001
,
Compliant Mechanisms
,
Wiley
,
New York, NY
.
2.
Orekhov
,
A. L.
,
Bryson
,
C. E.
,
Till
,
J.
,
Chung
,
S.
, and
Rucker
,
D.
,
2015
, “
A Surgical Parallel Continuum Manipulator With a Cable-Driven Grasper
,” 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Milan, Italy, Aug. 25–29, pp.
5264
5267
.
3.
Orekhov
,
A. L.
,
Black
,
C. B.
,
Till
,
J.
,
Chung
,
S.
, and
Rucker
,
D. C.
,
2016
, “
Analysis and Validation of a Teleoperated Surgical Parallel Continuum Manipulator
,”
IEEE Rob. Autom. Lett.
,
1
(
2
), pp.
828
835
.
4.
Hogan
,
N.
,
1985
, “
Impedance Control: An Approach to Manipulation: Part I — Theory
,”
ASME J. Dyn. Syst. Meas. Contr.
,
107
(
1
), pp.
1
7
.
5.
Whitney
,
D. E.
,
1977
, “
Force Feedback Control of Manipulator Fine Motions
,”
ASME J. Dyn. Syst. Meas. Contr.
,
99
(
2
), pp.
91
97
.
6.
Salisbury
,
J. K.
,
1980
, “
Active Stiffness Control of a Manipulator in Cartesian Coordinates
,” 1980 19th IEEE Conference on Decision and Control Including the Symposium on Adaptive Processes, Albuquerque, NM, Dec. 10–12, pp.
95
100
.
7.
Kazerooni
,
H.
,
Sheridan
,
T. B.
, and
Houpt
,
P. K.
,
1986
, “
Robust Compliant Motion for Manipulators, Part I: the Fundamental Concepts of Compliant Motion
,”
IEEE J. Rob. Autom.
,
2
(
2
), pp.
83
92
.
8.
Kazerooni
,
H.
,
Houpt
,
P. K.
, and
Sheridan
,
T. B.
,
1986
, “
Robust Compliant Motion for Manipulators, Part II: Design Method
,”
IEEE J. Rob. Autom.
,
2
(
2
), pp.
93
105
.
9.
Seraji
,
H.
, and
Colbaugh
,
R.
,
1993
, “
Force Tracking in Impedance Control
,” [1993] Proceedings IEEE International Conference on Robotics and Automation, Atlanta, GA, Dec. 10–12, pp.
499
506
.
10.
Wang
,
L.
,
Chen
,
Z.
,
Chalasani
,
P.
,
Yasin
,
R. M.
,
Kazanzides
,
P.
,
Taylor
,
R. H.
, and
Simaan
,
N.
,
2017
, “
Force-Controlled Exploration for Updating Virtual Fixture Geometry in Model-Mediated Telemanipulation
,”
ASME J. Mech Rob.
,
9
(
2
), p.
021010
.
11.
Roveda
,
L.
,
Iannacci
,
N.
,
Vicentini
,
F.
,
Pedrocchi
,
N.
,
Braghin
,
F.
, and
Tosatti
,
L. M.
,
2016
, “
Optimal Impedance Force-Tracking Control Design With Impact Formulation for Interaction Tasks
,”
IEEE Rob. Autom. Lett.
,
1
(
1
), pp.
130
136
.
12.
Jung
,
S.
, and
Hsia
,
T. C.
,
2000
, “
Robust Neural Force Control Scheme Under Uncertainties in Robot Dynamics and Unknown Environment
,”
IEEE Trans. Ind. Electron.
,
47
(
2
), pp.
403
412
.
13.
Mallapragada
,
V.
,
Erol
,
D.
, and
Sarkar
,
N.
,
2006
, “
A New Method of Force Control for Unknown Environments
,” 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, China, Oct. 09–15, pp.
4509
4514
.
14.
Sun
,
Y.
,
Liu
,
H.
, and
Cui
,
D.
,
2008
, “
Study on the Neural Network Impedance Force Control for Inner-Wall Grinding Robot
,” International Conference on Modelling, Identification and Control, Shanghai, China, June 29.
15.
Deng
,
Z.
,
Jin
,
H.
,
Hu
,
Y.
,
He
,
Y.
,
Zhang
,
P.
,
Tian
,
W.
, and
Zhang
,
J.
,
2016
, “
Fuzzy Force Control and State Detection in Vertebral Lamina Milling
,”
Mechatronics
,
35
, pp.
1
10
.
16.
Kormushev
,
P.
,
Calinon
,
S.
, and
Caldwell
,
D. G.
,
2010
, “
Robot Motor Skill Coordination With EM-Based Reinforcement Learning
,” 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan, Oct. 18–22, pp.
3232
3237
.
17.
Buchli
,
J.
,
Stulp
,
F.
,
Theodorou
,
E.
, and
Schaal
,
S.
,
2011
, “
Learning Variable Impedance Control
,”
Int. J. Rob. Res.
,
30
(
7
), pp.
820
833
.
18.
Rombokas
,
E.
,
Malhotra
,
M.
,
Theodorou
,
E.
,
Matsuoka
,
Y.
, and
Todorov
,
E.
,
2012
, “
Tendon-Driven Variable Impedance Control Using Reinforcement Learning
,” Proceedings of the 8th Annual Robotics: Science and Systems (RSS) Conference, Sydney, Australia, July 9–12.
19.
Calinon
,
S.
,
Sardellitti
,
I.
, and
Caldwell
,
D. G.
,
2010
, “
Learning-Based Control Strategy for Safe Human-Robot Interaction Exploiting Task and Robot Redundancies
,” 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan, Dec. 10–12, pp.
249
254
.
20.
Kronander
,
K.
, and
Billard
,
A.
,
2012
, “
Online Learning of Varying Stiffness Through Physical Human-Robot Interaction
,” 2012 IEEE International Conference on Robotics and Automation, Saint Paul, MN, May 14–18, pp.
1842
1849
.
21.
Duan
,
J.
,
Gan
,
Y.
,
Chen
,
M.
, and
Dai
,
X.
,
2018
, “
Adaptive Variable Impedance Control for Dynamic Contact Force Tracking in Uncertain Environment
,”
Rob. Auton. Syst.
,
102
, pp.
54
65
.
22.
Raibert
,
M. H.
, and
Craig
,
J. J.
,
1981
, “
Hybrid Position/Force Control of Manipulators
,”
ASME J. Dyn. Syst. Meas. Contr.
,
103
(
2
), pp.
126
133
.
23.
Kiguchi
,
K.
, and
Fukuda
,
T.
,
2000
, “
Position/Force Control of Robot Manipulators for Geometrically Unknown Objects Using Fuzzy Neural Networks
,”
IEEE Trans. Ind. Electron.
,
47
(
3
), pp.
641
649
.
24.
Baigzadehnoe
,
B.
,
Rahmani
,
Z.
,
Khosravi
,
A.
, and
Rezaie
,
B.
,
2017
, “
On Position/Force Tracking Control Problem of Cooperative Robot Manipulators Using Adaptive Fuzzy Backstepping Approach
,”
ISA Trans.
,
70
, pp.
432
446
.
25.
Nagata
,
F.
,
Hase
,
T.
,
Haga
,
Z.
,
Omoto
,
M.
, and
Watanabe
,
K.
,
2008
, “
CAD/CAM-Based Position/Force Control for a Ball-End Abrasive Tool and Its Application to an Industrial Robot
,”
J. Adv. Mech. Des. Syst. Manuf.
,
2
(
4
), pp.
742
752
.
26.
Mohy El Dine
,
K.
,
Lequievre
,
L.
,
Corrales Ramon
,
J. A.
,
Mezouar
,
Y.
, and
Fauroux
,
J. C.
,
2018
, “
Hybrid Position/Force Control With Compliant Wrist for Grinding
,” MUGV 2018 (Machines et Usinage Grande Vitesse) and Manufacturing’ 21, Bordeaux, Franc, June 7–8.
27.
Gracia
,
L.
,
Solanes
,
J. E.
,
Muñoz-Benavent
,
P.
,
Miro
,
J. V.
,
Perez-Vidal
,
C.
, and
Tornero
,
J.
,
2018
, “
Adaptive Sliding Mode Control for Robotic Surface Treatment Using Force Feedback
,”
Mechatronics
,
52
, pp.
102
118
.
28.
Zhang
,
T.
,
Yu
,
Y.
, and
Zou
,
Y.
,
2019
, “
An Adaptive Sliding-Mode Iterative Constant-Force Control Method for Robotic Belt Grinding Based on a One-Dimensional Force Sensor
,”
Sensors
,
19
(
7
).
29.
Mahvash
,
M.
, and
Dupont
,
P. E.
,
2011
, “
Stiffness Control of Surgical Continuum Manipulators
,”
IEEE Trans. Rob.
,
27
(
2
), pp.
334
345
.
30.
Aloi
,
V.
,
Black
,
C.
, and
Rucker
,
C.
,
2018
, “
Stiffness Control of Parallel Continuum Robots
,” ASME 2018 Dynamic Systems and Control Conference, Atlanta, GA, Sept. 30–Oct. 03, p.
V001T04A012
.
31.
Du
,
C.
,
Chen
,
G.
,
Zhang
,
Z.
,
Tang
,
L.
, and
Wang
,
H.
,
2019
, “
Design and Experimental Analysis of a Planar Compliant Parallel Manipulator
,” Intelligent Robotics and Applications, Shenyang, China, Aug. 8–11, pp.
637
647
.
32.
Chen
,
G.
,
Zhang
,
Z.
,
Kong
,
L.
, and
Wang
,
H.
,
2019
, “
Analysis and Validation of a Flexible Planar Two Degree-of-Freedom Parallel Manipulator With Structural Passive Compliance
,”
ASME J. Mech Rob.
,
12
(
1
), p.
011011
.
33.
Pan
,
H.
,
Chen
,
G.
,
Kang
,
Y.
, and
Wang
,
H.
,
2020
, “
Design and Kinematic Analysis of a Flexible-Link Parallel Mechanism With a Spatially Quasi-Translational End-Effector
,”
ASME J. Mech Rob.
,
13
(
1
), p.
011022
.
34.
Chen
,
G.
,
Zhang
,
Z.
, and
Wang
,
H.
,
2018
, “
A General Approach to the Large Deflection Problems of Spatial Flexible Rods Using Principal Axes Decomposition of Compliance Matrices
,”
ASME J. Mech Rob.
,
10
(
3
), p.
031012
.
35.
Murray
,
R. M.
,
Sastry
,
S. S.
, and
Li
,
Z. X.
,
1994
,
A Mathematical Introduction to Robotic Manipulation
,
CRC Press
,
Boca Raton, FL
.
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