In this paper, time optimal trajectory tracking of redundant planar cable-suspended robots is investigated. The equations of motion of these cable robots are obtained as a system of second order differential equation in terms of path parameter $s$ using the specified path. Besides, the bounds on the cable tensions and cable velocities are transformed into the bounds on the acceleration and velocity along the path. Assuming bang-bang control, the switching points in $ṡ2−s$ plane are obtained. Then the cable tensions are found in terms of path parameter and, subsequently, versus time. The proposed approach is validated and the effect of the number of superfluous cables on the value of minimum time is studied. The next notable challenges include time optimal path planning of cable-suspended robots. By developing a hybrid genetic algorithm and bang-bang control approach, the minimum motion time from initial state to final one and also the corresponding path can be found. The optimum path is the one that minimizes traveling time from initial state to final one, while not exceeding the cable tensions and cable velocities limits, without collision with any obstacles.

1.
Oh
,
S. -R.
, and
Agrawal
,
S. K.
, 2005, “
Cable Suspended Planar Robots With Redundant Cables: Controllers With Positive Tensions
,”
IEEE Transactions on Robotics
,
21
(
3
), pp.
457
465
.
2.
Fattah
,
A.
, and
Agrawal
,
S. K.
, 2005, “
On the Design of Cable-Suspended Planar Parallel Robots
,”
ASME J. Mech. Des.
0161-8458,
127
(
5
), pp.
1021
1028
.
3.
Alp
,
B.
, and
Agrawal
,
S. K.
, 2002, “
Cable Suspended Robots: Design, Planning and Control
,”
Proceedings of International Conference on Robotics and Automation
, Washington, DC, pp.
4275
4280
.
4.
Barrette
,
G.
, and
Gosselin
,
C. M.
, 2005, “
Determination of the Dynamic Workspace of Cable-Driven Planar Parallel Mechanisms
,”
ASME J. Mech. Des.
0161-8458,
127
, pp.
242
248
.
5.
Williams
,
R. L.
, II
, and
Gallina
,
P.
, 2003, “
Translational Planar Cable-Direct-Driven Robots
,”
J. Intell. Robotic Syst.
0921-0296,
37
, pp.
69
96
.
6.
Oh
,
S. R.
, and
Agrawal
,
S. K.
, 2005, “
A Reference Governor Based Controller for a Cable Robot Under Input Constraints
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
13
(
4
), pp.
639
645
.
7.
Oh
,
S. -R.
, and
Agrawal
,
S. K.
, 2006, “
Generation of Feasible Set Points and Control of a Cable Robot
,”
IEEE Transactions on Robotics
,
22
(
3
), pp.
551
558
.
8.
Pontryagin
,
L. S.
,
Boltyanski
,
V. G.
,
Gramkrelidze
,
R. V.
, and
Mishchenko
,
E. F.
, 1962,
The Mathematical Theory of Optimal Processes
,
Wiley
,
New York
.
9.
Niv
,
M.
, and
Auslander
,
D. M.
, 1984, “
Optimal Control of a Robot With Obstacles
,”
Proceedings of the American Control Conference
, pp.
280
287
.
10.
Bobrow
,
J. E.
,
Dubowsky
,
S.
, and
Gibson
,
J. S.
, 1985, “
Time-Optimal Control of Robotics Manipulators Along Specified Paths
,”
Int. J. Robot. Res.
0278-3649,
4
(
3
), pp.
3
17
.
11.
Shin
,
K. G.
, and
McKay
,
N. D.
, 1985, “
Minimum-Time Control of Robotic Manipulators With Geometric Path Constraints
,”
IEEE Trans. Autom. Control
0018-9286,
30
(
6
), pp.
531
541
.
12.
Pfeiffer
,
F.
, and
Johanni
,
R.
, 1987, “
A Concept for Manipulator Trajectory Planning
,”
IEEE J. Robot. Autom.
,
3
(
2
), pp.
115
123
.
13.
,
S.
, and
Khajepour
,
A.
, 2006, “
Time Optimal Trajectory Planning in Cable-Based Manipulator
,”
IEEE Transactions on Robotics
,
22
(
3
), pp.
559
563
.
14.
Fahham
,
H. R.
, and
Farid
,
M.
, 2008, “
Time Optimal Control of Planar Cable-Suspended Robot Along Specified Path
,”
16th Annual International Conference on Mechanical Engineering ISME-2008
, Kerman, Iran.
15.
Sun
,
S. D.
,
Morris
,
A. S.
, and
Zalzala
,
A. M. S.
, 1996, “
Trajectory Planning of Multiple Coordinating Robots Using Genetic Algorithms
,”
Robotica
0263-5747,
14
, pp.
227
234
.
16.
Yue
,
S. G.
,
Henrich
,
D.
,
Xu
,
X. L.
, and
Toss
,
S. K.
, 2002, “
Point-to-Point Trajectory Planning of Flexible Redundant Robot Manipulators Using Genetic Algorithms
,”
Robotica
0263-5747,
20
, pp.
269
280
.
17.
Tian
,
L.
, and
Collis
,
C.
, 2004, “
An Effective Robot Trajectory Planning Method Using a Genetic Algorithm
,”
Mechatronics
0957-4158,
14
, pp.
455
470
.
18.
Zha
,
X. F.
, 2002, “
Optimal Pose Trajectory Planning for Robot Manipulators
,”
Mech. Mach. Theory
0094-114X,
37
, pp.
1063
1086
.
You do not currently have access to this content.