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

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

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.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Bowling, A. P. , 2007, “ Mass Distribution Effects on Dynamic Performance of a Cable-Drived Hexapod,” ASME J. Mech. Des., 129(8), pp. 887–890. [CrossRef]
Kljuno, E. , Zhu, J. J. , Williams, R. L., II , and Reily, S. M. , 2011, “ A Biomimetic Elastic Cable Driven Quadruped Robot: The Robocat,” ASME Paper No. IMECE2011-63534.
Kawamura, S. , Kino, H. , and Won, C. , 2000, “ High-Speed Manipulation by Using Parallel Wire-Driven Robots,” Robotica, 18(1), pp. 13–21. [CrossRef]
Mao, Y. , and Agrawal, S. , 2012, “ Design of a Cable-Driven ARm EXoskeleton (CAREX) for Neural Rehabilitation,” IEEE Trans. Rob., 28(4), pp. 922–931. [CrossRef]
Jin, X. , Cui, X. , and Agrawal, S. K. , 2015, “ Design of a Cable-Driven Active Leg Exoskeleton (C-ALEX) and Gait Training Experiments With Human Subjects,” IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, May 26–30, pp. 5578–5583.
Mao, Y. , Jin, X. , Dutta, G. , Scholz, J. , and Agrawal, S. , 2015, “ Human Movement Training With a Cable Driven Arm Exoskeleton (Carex),” IEEE Trans. Neural Syst. Rehabil. Eng., 23(1), pp. 84–92. [CrossRef] [PubMed]
Ming, A. , and Higuchi, T. , 1994, “ Study on Multiple Degree-of-Freedom Positioning Mechanism Using Wires (Part 1): Concept, Design and Control,” Int. J. Jpn. Soc. Precis. Eng., 28(2), pp. 131–138.
Mustafa, S. , and Agrawal, S. , 2012, “ On the Force-Closure Analysis of n-DOF Cable-Driven Open Chains Based on Reciprocal Screw Theory,” IEEE Trans. Rob., 28(1), pp. 22–31. [CrossRef]
Rezazadeh, S. , and Behzadipour, S. , 2011, “ Workspace Analysis of Multibody Cable-Driven Mechanisms,” ASME J. Mech. Rob., 3(2), pp. 1–10. [CrossRef]
Goldberg, D. E. , 1989, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, MA.
Haupt, R. L. , and Haupt, S. E. , 2004, Practical Genetic Algorithms, 2nd ed., Wiley, Hoboken, NJ.
Fouskakis, D. , and Draper, D. , 2002, “ Stochastic Optimization: A Review,” Int. Stat. Rev., 70(3), pp. 315–349. [CrossRef]
Bahrami, A. , Aghbali, B. , and Bahrami, M. N. , 2012, “ Design Optimization of a 3-D Three Cable Driven Manipulator,” ASME Paper No. DETC2012-70195.
Jamwal, P. K. , Xie, S. , and Aw, K. C. , 2009, “ Kinematic Design Optimization of a Parallel Ankle Rehabilitation Robot Using Modified Genetic Algorithm,” Rob. Auton. Syst., 57(10), pp. 1018–1027. [CrossRef]
Kennedy, J. , and Eberhart, R. , 1995, “ Particle Swarm Optimization,” IEEE International Conference on Neural Networks (ICNN), Perth, WA, Nov. 27–Dec. 1, Vol. 4, pp. 1942–1948.
Perez, R. E. , and Behdinan, K. , 2007, “ Particle Swarm Optimization in Structural Design,” Swarm Intelligence, Focus on Ant and Particle Swarm Optimization, F. T. S. Chan and M. K. Tiwari , eds., Itech Education and Publishing, Vienna, Austria.
Hassan, R. , Cohanim, B. E. , and de Weck, O. L. , 2005, “ A Comparison of Particle Swarm Optimization and the Genetic Algorithm,” 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, American Institute of Aeronautics and Astronautics, Austin, TX, Apr. 18–21, AIAA Paper No. 2005-1897.
Ma, M. , and Wang, J. , 2011, “ Hydraulic-Actuated Quadruped Robot Mechanism Design Optimization Based on Particle Swarm Optimization Algorithm,” 2nd International Conference on Artificial Intelligence, Management Science and Electronic Commerce (AIMSEC), Deng Feng, China, Aug. 8–12, pp. 4026–4029.
Gouttefarde, M. , and Gosselin, C. M. , 2006, “ Analysis of the Wrench-Closure Workspace of Planar Parallel Cable-Driven Mechanisms,” IEEE Trans. Rob., 22(3), pp. 434–445. [CrossRef]
Bosscher, P. , Riechel, A. T. , and Ebert-Uphoff, I. , 2006, “ Wrench-Feasible Workspace Generation for Cable-Driven Robots,” IEEE Trans. Rob., 22(5), pp. 890–902. [CrossRef]
Fattah, A. , and Agrawal, S. K. , 2005, “ On the Design of Cable-Suspended Planar Parallel Robots,” ASME J. Mech. Des., 127(5), pp. 1021–1028. [CrossRef]
Diao, X. , and Ma, O. , 2009, “ Force-Closure Analysis of 6-DOF Cable Manipulators With Seven or More Cables,” Robotica, 27(3), pp. 209–215. [CrossRef]


Grahic Jump Location
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.

Grahic Jump Location
Fig. 1

Illustration of the PSO velocity calculation

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
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

Grahic Jump Location
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.

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In