A hybrid Lyapunov based controller for dynamic catch, grasp, and carry tasks of grippers is developed. The Lyapunov controller unifies the trajectory planning and tracking tasks in one, and neither a separate trajectory planning algorithm is needed to run offline nor any type of learning process. The robustness of the controller is demonstrated, through simulations with inertial parametric uncertainties. The concept is presented with the simulations of six degrees-of-freedom (DOF) double revolute (RR) planar manipulator with a 4DOF gripper and a 8DOF triple revolute (RRR) manipulator with a 5DOF gripper.

References

1.
Powell
,
M. J.
,
Zhao
,
H.
, and
Ames
,
A. D.
,
2012
, “
Motion Primitives for Human-Inspired Bipedal Robotic Locomotion: Walking and Stair Climbing
,”
2012 IEEE International Conference on Robotics and Automation (ICRA)
, IEEE,
Piscataway, NJ
, pp.
543
549
.
2.
Kallmann
,
M.
,
Bargmann
,
R.
, and
Mataric
,
M.
,
2004
, “
Planning the Sequencing of Movement Primitives
,”
Proceedings of the International Conference on Simulation of Adaptive Behavior (SAB)
, pp.
193
200
.
3.
Michelman
,
P.
, and
Allen
,
P.
,
1994
, “
Forming Complex Dextrous Manipulations From Task Primitives
,”
1994 IEEE International Conference on Robotics and Automation
, IEEE,
Piscataway, NJ
, pp.
3383
3388
.
4.
Kazemi
,
M.
,
Valois
,
J.-S.
,
Bagnell
,
J. A.
, and
Pollard
,
N.
,
2012
, “
Robust Object Grasping Using Force Compliant Motion Primitives
,”
Proceedings of Robotics: Science and Systems
.
5.
Cohen
,
B. J.
,
Chitta
,
S.
, and
Likhachev
,
M.
,
2010
, “
Search-Based Planning for Manipulation With Motion Primitives
,”
2010 IEEE International Conference on Robotics and Automation (ICRA)
, IEEE,
Piscataway, NJ
, pp.
2902
2908
.
6.
Stulp
,
F.
,
Theodorou
,
E.
,
Kalakrishnan
,
M.
,
Pastor
,
P.
,
Righetti
,
L.
, and
Schaal
,
S.
,
2011
, “
Learning Motion Primitive Goals for Robust Manipulation
,”
2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
, IEEE,
Piscataway, NJ
, pp.
325
331
.
7.
Napier
,
J. R.
, and
Tuttle
,
R.
,
1993
,
Hands
,
Princeton University Press
,
Princeton, NJ
.
8.
Cutkosky
,
M. R.
, and
Howe
,
R. D.
,
1990
, “
Human Grasp Choice and Robotic Grasp Analysis
,”
Dextrous Robot Hands
,
Springer
,
New York
, pp.
5
31
.
9.
Gutman
,
S.
, and
Leitmann
,
G.
,
1976
, “
Stabilizing Control for Linear Systems With Bounded Parameter and Input Uncertainty
,”
Optimization Techniques Modeling and Optimization in the Service of Man Part 2
(Lecture Notes in Computer Science), Vol.
41
,
J.
Cea
, ed.,
Springer
,
Berlin
, pp.
729
755
.
10.
Gutman
,
S.
,
1979
, “
Uncertain Dynamical Systems–A Lyapunov Min-Max Approach
,”
IEEE Trans. Autom. Control
,
24
(
3
), pp.
437
443
.10.1109/TAC.1979.1102073
11.
Khatib
,
O.
,
1986
, “
Real-Time Obstacle Avoidance for Manipulators and Mobile Robots
,”
Int. J. Rob. Res.
,
5
(
1
), pp.
90
98
.10.1177/027836498600500106
12.
Khansari-Zadeh
,
S. M.
, and
Billard
,
A.
,
2012
, “
A Dynamical System Approach to Realtime Obstacle Avoidance
,”
Auton. Rob.
,
32
(
4
), pp.
433
454
.10.1007/s10514-012-9287-y
13.
Branicky
,
M. S.
,
1998
, “
Multiple Lyapunov Functions and Other Analysis Tools for Switched and Hybrid Systems
,”
IEEE Trans. Autom. Control
,
43
(
4
), pp.
475
482
.10.1109/9.664150
14.
Ames
,
A. D.
, and
Powell
,
M.
,
2013
, “
Towards the Unification of Locomotion and Manipulation Through Control Lyapunov Functions and Quadratic Programs
,”
Control of Cyber-Physical Systems
,
Springer
,
Switzerland
, pp.
219
240
.10.1007/978-3-319-01159-2_12
15.
Ames
,
A. D.
,
Galloway
,
K.
,
Sreenath
,
K.
, and
Grizzle
,
J. W.
,
2014
, “
Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics
,”
IEEE Trans. Autom. Control
,
59
(
4
), pp.
876
891
.10.1109/TAC.2014.2299335
16.
Aghili
,
F.
,
2013
, “
Pre- and Post-Grasping Robot Motion Planning to Capture and Stabilize a Tumbling/Drifting Free-Floater With Uncertain Dynamics
,”
2013 IEEE International Conference on Robotics and Automation (ICRA)
, pp.
5461
5468
.
17.
Kim
,
S.
,
Shukla
,
A.
, and
Billard
,
A.
,
2014
, “
Catching Objects in Flight
,”
IEEE Trans. Rob.
,
30
(
5
), pp.
1049
1065
.10.1109/TRO.2014.2316022
18.
Lampariello
,
R.
,
Nguyen-Tuong
,
D.
,
Castellini
,
C.
,
Hirzinger
,
G.
, and
Peters
,
J.
,
2011
, “
Trajectory Planning for Optimal Robot Catching in Real-Time
,”
2011 IEEE International Conference on Robotics and Automation (ICRA)
, IEEE,
Piscataway, NJ
, pp.
3719
3726
.
19.
Horowitz
,
M. B.
, and
Burdick
,
J. W.
,
2012
, “
Combined Grasp and Manipulation Planning as a Trajectory Optimization Problem
,”
2012 IEEE International Conference on Robotics and Automation (ICRA)
, IEEE,
Piscataway, NJ
, pp.
584
591
.
20.
Berenson
,
D.
,
Kuffner
,
J.
, and
Choset
,
H.
,
2008
, “
An Optimization Approach to Planning for Mobile Manipulation
,”
IEEE International Conference on Robotics and Automation (ICRA 2008)
, IEEE,
Piscataway, NJ
, pp.
1187
1192
.
21.
Ko
,
C.-H.
,
Lin
,
S.-H.
, and
Chen
,
J.-K.
,
2013
, “
Motion Planning of Multifingered Hand-Arm System With Optimal Grasping Force
,”
2013 IEEE International Symposium on Next-Generation Electronics (ISNE)
, IEEE,
Piscataway, NJ
, pp.
262
265
.
22.
Bauml
,
B.
,
Wimbock
,
T.
, and
Hirzinger
,
G.
,
2010
, “
Kinematically Optimal Catching a Flying Ball With a Hand-Arm-System
,”
2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
, pp.
2592
2599
.
23.
Moreau
,
J. J.
,
1988
, “
Bounded Variation in Time
,”
Topics in Nonsmooth Mechanics
,
J. J.
Moreau
,
P. D.
Panagiotopoulos
, and
G.
Strang
, eds.,
Birkhäuser
,
Basel, Switzerland
, pp.
1
74
.
24.
Moreau
,
J. J.
,
1988
, “
Unilateral Contact and Dry Friction in Finite Freedom Dynamics
,”
Nonsmooth Mechanics and Applications
(CISM Courses and Lectures), Vol.
302
,
J. J.
Moreau
, and
P. D.
Panagiotopoulos
, eds.,
Springer
,
New York
, pp.
1
82
.
25.
Yunt
,
K.
,
2014
, “
On the Relation of the Principle of Maximum Dissipation to the Principles of Jourdain and Gauss for Rigid Body Systems
,”
ASME J. Comput. Nonlinear Dyn.
,
9
(
3
), p.
031017
.10.1115/1.4026122
26.
Glocker
,
C.
,
2001
,
Set-Valued Force Laws—Dynamics of Non-Smooth Systems
(Lecture Notes in Applied Mechanics), Vol.
1
,
Springer
,
Berlin
.
27.
Yunt
,
K.
,
2011
, “
An Augmented Lagrangian Based Shooting Method for the Optimal Trajectory Generation of Switching Lagrangian Systems
,”
Dyn. Contin. Discrete Impulsive Syst., Ser. B
,
18
(
5
), pp.
615
645
.
28.
Utkin
,
V. I.
,
Guldner
,
J.
, and
Shi
,
J.
,
1999
,
Sliding Mode Control in Electromechanical Systems
, Vol.
9
,
CRC Press
,
Boca Raton
.
29.
Edwards
,
C.
, and
Spurgeon
,
S. K.
,
1998
,
Sliding Mode Control: Theory and Applications
, Vol.
7
,
CRC Press
,
Boca Raton
.
30.
Sabanovic
,
A.
,
Fridman
,
L.
, and
Spurgeon
,
S. K.
,
2004
,
Variable Structure Systems: From Principles to Implementation
, Vol.
66
,
IET
,
Stevenage, UK
.
31.
Venkataraman
,
S.
, and
Gulati
,
S.
,
1993
, “
Control of Nonlinear Systems Using Terminal Sliding Modes
,”
ASME J. Dyn. Syst., Meas., Control
,
115
(
3
), pp.
554
560
.10.1115/1.2899138
32.
Itkis
,
U.
,
1976
,
Control Systems of Variable Structure
,
Wiley
,
New York
.
33.
Draženović
,
B.
,
1969
, “
The Invariance Conditions in Variable Structure Systems
,”
Automatica
,
5
(
3
), pp.
287
295
.10.1016/0005-1098(69)90071-5
34.
Paden
,
B.
, and
Sastry
,
S.
,
1987
, “
A Calculus for Computing Filippov's Differential Inclusion With Application to the Variable Structure Control of Robot Manipulators
,”
IEEE Trans. Circuits Syst.
,
34
(
1
), pp.
73
82
.10.1109/TCS.1987.1086038
You do not currently have access to this content.