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Research Papers

Configuration Robustness Analysis of the Optimal Design of Cable-Driven Manipulators

[+] Author and Article Information
Joshua T. Bryson

Department of Mechanical Engineering,
University of Delaware,
Newark, DE 19716
e-mail: jtbryson@udel.edu

Xin Jin

Department of Mechanical Engineering,
Columbia University,
New York, NY 10027
e-mail: x.jin@columbia.edu

Sunil K. Agrawal

Professor
Department of Mechanical Engineering,
Columbia University,
New York, NY 10027
e-mail: sunil.agrawal@columbia.edu

Manuscript received November 16, 2015; final manuscript received May 18, 2016; published online September 6, 2016. Assoc. Editor: Satyandra K. Gupta.

J. Mechanisms Robotics 8(6), 061006 (Sep 06, 2016) (9 pages) Paper No: JMR-15-1321; doi: 10.1115/1.4033695 History: Received November 16, 2015; Revised May 18, 2016

Designing an effective cable architecture for a cable-driven robot becomes challenging as the number of cables and degrees of freedom of the robot increase. A methodology has been previously developed to identify the optimal design of a cable-driven robot for a given task using stochastic optimization. This approach is effective in providing an optimal solution for robots with high-dimension design spaces, but does not provide insights into the robustness of the optimal solution to errors in the configuration parameters that arise in the implementation of a design. In this work, a methodology is developed to analyze the robustness of the performance of an optimal design to changes in the configuration parameters. This robustness analysis can be used to inform the implementation of the optimal design into a robot while taking into account the precision and tolerances of the implementation. An optimized cable-driven robot leg is used as a motivating example to illustrate the application of the configuration robustness analysis. Following the methodology, the effect on robot performance due to design variations is analyzed, and a modified design is developed which minimizes the potential performance degradations due to implementation errors in the design parameters. A robot leg is constructed and is used to validate the robustness analysis by demonstrating the predicted effects of variations in the design parameters on the performance of the robot.

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Figures

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Fig. 1

Example 2D objective function surface, ψ(x1, x2), with the optimal point  ox=(ox1,ox2)

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Fig. 2

Example objective function performance along x1

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Fig. 3

Example objective function performance along x2

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Fig. 4

Illustrations of the cable-driven robot leg. The waist, thigh, and shank cuffs are used to route the cables, with cables 1, 2 attached between the waist cuff and the thigh cuff, while cables 3, 4 are routed between the waist cuff and shank cuff via the thigh cuff. The attachment angle of cable m on cuff i is given by  iθcm, and at pose (q1, q2, q3) = (0, 0, 0) the leg is fully extended and vertical.

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Fig. 5

The walking gait joint angle trajectory for the robot

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Fig. 6

Objective function slices surrounding the optimal point

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Fig. 7

Objective function slice along x6 showing the −4.5 deg adjustment to the optimal value

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Fig. 8

Objective function slice along x7 showing the −4.5 deg adjustment to the optimal value

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Fig. 9

Objective function slice along x10 showing the −2.5 deg adjustment to the optimal value

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Fig. 10

The cable-driven robot leg with the cables in the optimal configuration,  ox

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Fig. 11

Controller cable tensions and robot response for the 50%, 80%, and full-scale trajectories

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Fig. 12

Comparison of modeled configuration robustness to experimental robot performance for varying cable 1 attachment angles, (x1 and x2)

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Fig. 13

Comparison of modeled configuration robustness to experimental robot performance for varying cable 3 attachment angles, (x6 and x7)

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