In this work, a new approach for motion planning of kinematically redundant parallel manipulators is proposed and compared with a method previously proposed by the authors called point-to-point motion planning (PPMP). Overall motion planning (OMP) consists of determining actuation schemes that optimize the manipulator’s performance while considering the entire given trajectory of the end-effector at once. The results of OMP are compared with those of PPMP of a kinematically redundant manipulator. It is shown that the proposed OMP strategy can generate actuation schemes for given trajectories such that the manipulator avoids singular configurations better than the PPMP strategy.

References

1.
Merlet
,
J.-P.
, 2007, “
A Local Motion Planner for Closed-Loop Robots
,”
Proceedings of the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems
, San Diego, CA, pp.
3088
3093
.
2.
LaValle
,
S. M.
, 2006,
Planning Algorithms
,
Cambridge University Press
,
Cambridge, MA
.
3.
Han
,
L.
, and
Amato
,
N. M.
, 2000, “
A Kinematics-Based Probabilistic Roadmap Method for Closed Chain Systems
,” Workshop on the Algorithmic Foundations of Robotics, Hanover, NH.
4.
Dasgupta
,
B.
, and
Mruthyunjaya
,
T. S.
, 1998, “
Singularity-Free Path Planning for the Stewart Platform Manipulator
,”
Mech. Mach. Theory
,
33
(
6
), pp.
711
725
.
5.
Abdellatif
,
H.
, and
Heimann
,
B.
, 2008, “
A Novel Multiple-Heuristic for Singularity-Free Motion Planning of Spatial Parallel Manipulators
,”
Robotica
,
26
(
5
), pp.
679
689
.
6.
Lee
,
S.
, and
Kim
,
S.
, 1993, “
Kinematic Analysis of Generalized Parallel Manipulator Systems
,”
Proceedings of the IEEE Conference on Decision and Control
, San Antonio, TX, Vol.
2
, pp.
1097
1102
.
7.
Zanganeh
,
K. E.
, and
Angeles
,
J.
, 1994, “
Instantaneous Kinematics and Design of a Novel Redundant Parallel Manipulator
,”
Proceedings of IEEE Conference on Robotics and Automation
, San Diego, CA, pp.
3043
3048
.
8.
Merlet
,
J.-P.
, 1996, “
Redundant Parallel Manipulators
,”
Lab. Rob. Autom.
,
8
(
1
), pp.
17
24
.
9.
Wang
,
J.
, and
Gosselin
,
C. M.
, 2004, “
Kinematic Analysis and Design of Kinematically Redundant Parallel Mechanisms
,”
ASME J. Mech. Des.
,
126
(
1
), pp.
109
118
.
10.
Garg
,
V.
,
Nokleby
,
S. B.
, and
Carretero
,
J. A.
, 2009, “
Wrench Capability Analysis of Redundantly Actuated Spatial Parallel Manipulators
,”
Mech. Mach. Theory
,
44
(
5
), pp.
1070
1081
.
11.
Ebrahimi
,
I.
,
Carretero
,
J. A.
, and
Boudreau
,
R.
, 2008, “
A Family of Kinematically Redundant Planar Parallel Manipulators
,”
ASME J. Mech. Des.
,
130
(
6
),
0623061
.
12.
Cha
,
S.
,
Lasky
,
T. A.
, and
Velinsky
,
S. A.
, 2007, “
Kinematically-Redundant Variations of the 3-RRR Mechanism and Local Optimization-Based Singularity Avoidance
,”
Mech. Based Des. Struct. Mach.
,
35
(
1
), pp.
15
38
.
13.
Weihmann
,
L.
,
Martins
,
D.
, and
Coelho
,
L. S.
, 2011, “
Force Capabilities of Kinematically Redundant Planar Parallel Manipulators
,”
Proceedings of the 2011 IFToMM World Congress
, Guanajuato, Mexico, June 19–25.
14.
Kotlarski
,
J.
,
Thanh
,
T. D.
,
Heimann
,
B.
, and
Ortmaier
,
T.
, 2010, “
Optimization Strategies for Additional Actuators of Kinematically Redundant Parallel Kinematic Machines
,”
Proceedings of IEEE Conference on Robotics and Automation
, Anchorage, AK, pp.
656
661
.
15.
Zarkandi
,
S.
,
Vafadar
,
A.
, and
Esmaili
,
M. R.
, 2011, “
PRRRRRP Redundant Planar Parallel Manipulator: Kinematics, Workspace and Singularity Analysis
,”
Proceedings of IEEE Conference on Robotics, Automation and Mechatronics (RAM)
, Qingdao, China, pp.
61
66
.
16.
Cha
,
S.
,
Lasky
,
T. A.
, and
Velinsky
,
S. A.
, 2007, “
Determination of the Kinematically Redundant Active Prismatic Joint Variable Ranges of a Planar Parallel Mechanism for Singularity-Free Trajectories
,”
Mech. Mach. Theory
,
44
(
5
), pp.
1032
1044
.
17.
Ebrahimi
,
I.
,
Carretero
,
J. A.
, and
Boudreau
,
R.
, 2007, “
Path Planning for the 3-PRRR Redundant Planar Parallel Manipulator
,”
Proceedings of the 2007 IFToMM World Congress
, Besançon, France, June.
18.
Ebrahimi
,
I.
,
Carretero
,
J. A.
, and
Boudreau
,
R.
, 2008, “
Kinematic Analysis and Path Planning of a New Kinematically Redundant Planar Parallel Manipulator
,”
Robotica
,
26
(
3
), pp.
405
413
.
19.
Byrd
,
R. H.
,
Gilbert
,
J. C.
, and
Nocedal
,
J.
, 2000, “
A Trust Region Method Based on Interior Point Techniques for Nonlinear Programming
,”
Math. Program.
,
89
(
1
), pp.
149
185
.
20.
Price
,
K.
, and
Storn
,
R.
, 1997, “
Differential Evolution
,”
Dr. Dobb’s J. Softw. Tools Prof. Program.
,
22
(
4
), pp.
18
24
.
You do not currently have access to this content.