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Journal of Mechanisms and Robotics | Volume 8 | Issue 4 | research-article
Research Papers

Optimal Design of Cable-Driven Manipulators Using Particle Swarm Optimization

[+] 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 July 11, 2015; final manuscript received November 4, 2015; published online March 7, 2016. Assoc. Editor: Satyandra K. Gupta.

J. Mechanisms Robotics 8(4), 041003 (Mar 07, 2016) (8 pages) Paper No: JMR-15-1197; doi: 10.1115/1.4032103 History: Received July 11, 2015; Revised November 04, 2015
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Citing Articles

The design of cable-driven manipulators is complicated by the unidirectional nature of the cables, which results in extra actuators and limited workspaces. Furthermore, the particular arrangement of the cables and the geometry of the robot pose have a significant effect on the cable tension required to effect a desired joint torque. For a sufficiently complex robot, the identification of a satisfactory cable architecture can be difficult and can result in multiply redundant actuators and performance limitations based on workspace size and cable tensions. This work leverages previous research into the workspace analysis of cable systems combined with stochastic optimization to develop a generalized methodology for designing optimized cable routings for a given robot and desired task. A cable-driven robot leg performing a walking-gait motion is used as a motivating example to illustrate the methodology application. The components of the methodology are described, and the process is applied to the example problem. An optimal cable routing is identified, which provides the necessary controllable workspace to perform the desired task and enables the robot to perform that task with minimal cable tensions. A robot leg is constructed according to this routing and used to validate the theoretical model and to demonstrate the effectiveness of the resulting cable architecture.
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References

Figures

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Fig. 1

Illustration of the PSO velocity calculation

+Illustration of the PSO velocity calculation
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Illustration of the PSO velocity calculation
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Fig. 2

Illustrations of the cable-driven robot leg. (a) Diagram of the 3DoF robot leg with dimensions and locations of the waist, thigh, and shank cuffs used to route the cables. (b) Joint angles and variable cable attachment angles for the robot leg. Hip adduction and flexion are given by +q1 and +q2, respectively, with knee extension given by +q3. At pose (q1, q2, q3) = (0, 0, 0), the leg is fully extended and vertical. (c) Illustration of cable routing with cables 1,2 attached between the base frame and the proximal link and cables 3,4 routed between the base frame and distal link via the proximal link. The attachment angle of cable m on body i is given by θicm.

+Illustrations of the cable-driven robot leg. (a) Diagram of the 3DoF robot leg with dimensions and locations of the waist, thigh, and shank cuffs used to route the cables. (b) Joint angles and variable cable attachment angles for the robot leg. Hip adduction and flexion are given by +q1 and +q2, respectively, with knee extension given by +q3. At pose (q1, q2, q3) = (0, 0, 0), the leg is fully extended and vertical. (c) Illustration of cable routing with cables 1,2 attached between the base frame and the proximal link and cables 3,4 routed between the base frame and distal link via the proximal link. The attachment angle of cable m on body i is given by θicm.
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Illustrations of the cable-driven robot leg. (a) Diagram of the 3DoF robot leg with dimensions and locations of the waist, thigh, and shank cuffs used to route the cables. (b) Joint angles and variable cable attachment angles for the robot leg. Hip adduction and flexion are given by +q1 and +q2, respectively, with knee extension given by +q3. At pose (q1, q2, q3) = (0, 0, 0), the leg is fully extended and vertical. (c) Illustration of cable routing with cables 1,2 attached between the base frame and the proximal link and cables 3,4 routed between the base frame and distal link via the proximal link. The attachment angle of cable m on body i is given by θicm.
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Fig. 3

The walking-gait joint angle trajectory and desired workspace for the robot

+The walking-gait joint angle trajectory and desired workspace for the robot
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The walking-gait joint angle trajectory and desired workspace for the robot
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Fig. 4

Value of the objective function, ψ, versus average cable tension, Tavgmax, for several workspace performance values, Pw

+Value of the objective function, ψ, versus average cable tension, Tavgmax, for several workspace performance values, Pw
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Value of the objective function, ψ, versus average cable tension, Tavgmax, for several workspace performance values, Pw
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Fig. 5

Illustrations of the cable-driven robot leg configured according to the (a) optimized configuration (config 1) and the (b) comparison configuration (config 2) listed in Table 2

+Illustrations of the cable-driven robot leg configured according to the (a) optimized configuration (config 1) and the (b) comparison configuration (config 2) listed in Table 2
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Illustrations of the cable-driven robot leg configured according to the (a) optimized configuration (config 1) and the (b) comparison configuration (config 2) listed in Table 2
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Fig. 6

Picture of the cable-driven robot leg used to validate modeling and demonstrate optimization results. The robot shown is configured according to config 1.

+Picture of the cable-driven robot leg used to validate modeling and demonstrate optimization results. The robot shown is configured according to config 1.
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Picture of the cable-driven robot leg used to validate modeling and demonstrate optimization results. The robot shown is configured according to config 1.
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Fig. 7

Results of the experimental static pose testing of the robot configured according to config 1 and config 2

+Results of the experimental static pose testing of the robot configured according to config 1 and config 2
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Results of the experimental static pose testing of the robot configured according to config 1 and config 2
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Fig. 8

Simulated tensions for config 1 for the 50% scale and full-scale trajectories. The Tavgmax values of 18.3 N for the 50% scale and 22 N for the full-scale trajectories are also shown.

+Simulated tensions for config 1 for the 50% scale and full-scale trajectories. The Tavgmax values of 18.3 N for the 50% scale and 22 N for the full-scale trajectories are also shown.
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Simulated tensions for config 1 for the 50% scale and full-scale trajectories. The Tavgmax values of 18.3 N for the 50% scale and 22 N for the full-scale trajectories are also shown.
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Fig. 9

Simulated tensions for config 2 for the 50% scale and full-scale trajectories. The Tavgmax values of 36 N for the 50% scale and 42.6 N for the full-scale trajectories are also shown.

+Simulated tensions for config 2 for the 50% scale and full-scale trajectories. The Tavgmax values of 36 N for the 50% scale and 42.6 N for the full-scale trajectories are also shown.
View Large  |  Save Figure  |  Download Slide (.ppt)
Simulated tensions for config 2 for the 50% scale and full-scale trajectories. The Tavgmax values of 36 N for the 50% scale and 42.6 N for the full-scale trajectories are also shown.
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Fig. 10

Controller cable tensions and robot response for the 50% scale walking-gait trajectory for the optimal config 1. The Tavgmax value of 18.7 N is also shown.

+Controller cable tensions and robot response for the 50% scale walking-gait trajectory for the optimal config 1. The Tavgmax value of 18.7 N is also shown.
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Controller cable tensions and robot response for the 50% scale walking-gait trajectory for the optimal config 1. The Tavgmax value of 18.7 N is also shown.
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Fig. 11

Controller cable tensions and robot response for the 50% scale walking-gait trajectory for config 2. The Tavgmax value of 38.7 N is also shown.

+Controller cable tensions and robot response for the 50% scale walking-gait trajectory for config 2. The Tavgmax value of 38.7 N is also shown.
View Large  |  Save Figure  |  Download Slide (.ppt)
Controller cable tensions and robot response for the 50% scale walking-gait trajectory for config 2. The Tavgmax value of 38.7 N is also shown.
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Fig. 12

Controller cable tensions and robot response for the full-scale walking-gait trajectory for the optimal config 1. The Tavgmax value of 26 N is also shown.

+Controller cable tensions and robot response for the full-scale walking-gait trajectory for the optimal config 1. The Tavgmax value of 26 N is also shown.
View Large  |  Save Figure  |  Download Slide (.ppt)
Controller cable tensions and robot response for the full-scale walking-gait trajectory for the optimal config 1. The Tavgmax value of 26 N is also shown.

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