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Mathematical Problems in Engineering
Volume 2015, Article ID 937565, 13 pages
Research Article

Motion Reliability Modeling and Evaluation for Manipulator Path Planning Task

School of Automation, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received 11 October 2014; Accepted 2 March 2015

Academic Editor: Zhan Shu

Copyright © 2015 Tong Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Motion reliability as a criterion can reflect the accuracy of manipulator in completing operations. Since path planning task takes a significant role in operations of manipulator, the motion reliability evaluation of path planning task is discussed in the paper. First, a modeling method for motion reliability is proposed by taking factors related to position accuracy of manipulator into account. In the model, multidimensional integral for PDF is carried out to calculate motion reliability. Considering the complex of multidimensional integral, the approach of equivalent extreme value is introduced, with which multidimensional integral is converted into one dimensional integral for convenient calculation. Then a method based on the maximum entropy principle is proposed for model calculation. With the method, the PDF can be obtained efficiently at the state of maximum entropy. As a result, the evaluation of motion reliability can be achieved by one dimensional integral for PDF. Simulations on a particular path planning task are carried out, with which the feasibility and effectiveness of the proposed methods are verified. In addition, the modeling method which takes the factors related to position accuracy into account can represent the contributions of these factors to motion reliability. And the model calculation method can achieve motion reliability evaluation with high precision and efficiency.