In the research of multicontact robotic systems, the equilibrium test and contact force distribution are two fundamental problems, which need to determine the existence of feasible contact forces subject to the friction constraint, and their optimal values for counterbalancing the other wrenches applied on the system and maintaining the system in equilibrium. All the wrenches, except those generated by the contact forces, can be treated as a whole, called the external wrench. The external wrench is time-varying in a dynamic system and both problems usually must be solved in real time. This paper presents an efficient procedure for solving the two problems. Using the linearized friction model, the resultant wrenches that can be produced by all contacts constitute a polyhedral convex cone in six-dimensional wrench space. Given an external wrench, the procedure computes the minimum distance between the wrench cone and the required equilibrating wrench, which is equal but opposite to the external wrench. The zero distance implies that the equilibrating wrench lies in the wrench cone, and that the external wrench can be resisted by contacts. Then, a set of linearly independent wrench vectors in the wrench cone are also determined, such that the equilibrating wrench can be written as their positive combination. This procedure always terminates in finite iterations and runs very fast, even in six-dimensional wrench space. Based on it, two contact force distribution methods are provided. One combines the procedure with the linear programming technique, yielding optimal contact forces with linear time complexity. The other directly utilizes the procedure without the aid of any general optimization technique, yielding suboptimal contact forces with nearly constant time complexity. Effective strategies are suggested to ensure the solution continuity.
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e-mail: yuzheng001@gmail.com
e-mail: chewcm@nus.edu.sg
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May 2010
Research Papers
Fast Equilibrium Test and Force Distribution for Multicontact Robotic Systems
Yu Zheng,
Yu Zheng
Control and Mechatronics Laboratory,
e-mail: yuzheng001@gmail.com
National University of Singapore
, Block EA #04-06, 9 Engineering Drive 1, Singapore 117576, Singapore
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Chee-Meng Chew
Chee-Meng Chew
Control and Mechatronics Laboratory,
e-mail: chewcm@nus.edu.sg
National University of Singapore
, Block EA #04-06, 9 Engineering Drive 1, Singapore 117576, Singapore
Search for other works by this author on:
Yu Zheng
Control and Mechatronics Laboratory,
National University of Singapore
, Block EA #04-06, 9 Engineering Drive 1, Singapore 117576, Singaporee-mail: yuzheng001@gmail.com
Chee-Meng Chew
Control and Mechatronics Laboratory,
National University of Singapore
, Block EA #04-06, 9 Engineering Drive 1, Singapore 117576, Singaporee-mail: chewcm@nus.edu.sg
J. Mechanisms Robotics. May 2010, 2(2): 021001 (11 pages)
Published Online: March 24, 2010
Article history
Received:
September 24, 2008
Revised:
October 6, 2009
Online:
March 24, 2010
Published:
March 24, 2010
Citation
Zheng, Y., and Chew, C. (March 24, 2010). "Fast Equilibrium Test and Force Distribution for Multicontact Robotic Systems." ASME. J. Mechanisms Robotics. May 2010; 2(2): 021001. https://doi.org/10.1115/1.4001089
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