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Research Papers

Time Optimal Trajectory Tracking of Redundant Planar Cable-Suspended Robots Considering Both Tension and Velocity Constraints

[+] Author and Article Information
Hamid Reza Fahham1

Department of Mechanical Engineering, Islamic Azad University, Marvdasht Branch, Marvdasht 73711-13119, Iranfahham@shirazu.ac.ir

Mehrdad Farid

Department of Mechanical Engineering, Center of Excellence in Computational Mechanics, Shiraz University, Shiraz 71348-51154, Iranfarid@shirazu.ac.ir

Moosa Khooran

Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz 73718-78874, Iranmoosakhooran@yahoo.com

1

Corresponding author.

J. Dyn. Sys., Meas., Control 133(1), 011004 (Nov 24, 2010) (14 pages) doi:10.1115/1.4002712 History: Received May 13, 2009; Revised July 27, 2010; Published November 24, 2010; Online November 24, 2010

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 ṡ2s 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.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Position vectors related to the ith cable

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Figure 2

Force vectors on MP

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Figure 3

Switching points in ṡ2−s plane for solution 1

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Figure 4

Switching points in ṡ2−s plane for solution 2

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Figure 5

Nonredundant and redundant planar cable-suspended robots

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Figure 6

ṡ2−s plane for solution 1 of sample problems

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Figure 7

ṡ2−s plane for solution 2 of sample problems

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Figure 8

Cable tensions versus path parameter in sample problems

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Figure 9

s,ṡ and s̈ versus time in sample problems

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Figure 10

Cable tensions versus time in sample problems

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Figure 11

Cable velocities versus time in sample problems

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Figure 12

Feedback linearization control scheme

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Figure 13

Time optimal trajectory obtained by the proposed algorithm, the feedback linearization, and the forward dynamics

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Figure 14

Cable tensions versus time obtained by the proposed algorithm and the feedback linearization control

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Figure 15

A planar cable-suspended robot with six cables

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Figure 16

y(x) and θ(x) in the interval xi≤x≤xi+1 approximated by cubic splines

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Figure 17

The algorithm of the proposed path planning method

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Figure 18

Minimum motion time of optimal path versus number of interior points

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Figure 19

Time optimal path of planar sample for various numbers of interior positions

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Figure 20

Switching points in ṡ2−s plane of solution 1 for various numbers of interior positions

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Figure 21

Switching points in ṡ2−s plane of solution 2 for various numbers of interior positions

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Figure 22

Cable tensions versus time for various numbers of interior positions

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Figure 23

Cable velocities versus time for various numbers of interior positions

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Figure 24

Time optimal path planning with obstacles for planar sample problem

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