Kinematic design of optimally fault tolerant robots for different joint failure probabilities

Biyun Xie; Anthony A. Maciejewski

doi:10.1109/LRA.2018.2792691

Kinematic design of optimally fault tolerant robots for different joint failure probabilities

Biyun Xie, Anthony A. Maciejewski

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

A measure of fault tolerance for different joint failure probabilities is defined based on the properties of the singular values of the Jacobian after failures. Using this measure, methods to design optimally fault tolerant robots for an arbitrary set of joint failure probabilities and multiple cases of joint failure probabilities are introduced separately. Given an arbitrary set of joint failure probabilities, the optimal null space that optimizes the fault tolerant measure is derived, and the associated isotropic Jacobians are constructed. The kinematic parameters of the optimally fault tolerant robots are then generated from these Jacobians. One special case, i.e., how to construct the optimal Jacobian of spatial 7R robots for both positioning and orienting is further discussed. For multiple cases of joint failure probabilities, the optimal robot is designed through optimizing the sum of the fault tolerant measures for all the possible joint failure probabilities. This technique is illustrated on planar 3R robots, and it is shown that there exists a family of optimal robots.

Original language	English
Pages (from-to)	827-834
Number of pages	8
Journal	IEEE Robotics and Automation Letters
Volume	3
Issue number	2
DOIs	https://doi.org/10.1109/LRA.2018.2792691
State	Published - Apr 2018

Bibliographical note

Funding Information:
Manuscript received September 10, 2017; accepted December 31, 2017. Date of publication January 12, 2018; date of current version January 25, 2018. This letter was recommended for publication by Associate Editor A. Dietrich and Editor P. Rocco upon evaluation of the reviewers’ comments. This work was supported in part by the National Science Foundation under Contract IIS-0812437. (Corresponding author: Biyun Xie.) The author are with the Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523 USA (e-mail: biyunxie@ rams.colostate.edu; aam@colostate.edu). Digital Object Identifier 10.1109/LRA.2018.2792691

Publisher Copyright:
© 2017 IEEE.

Keywords

Fault tolerant robots
Kinematics
Redundant robots

ASJC Scopus subject areas

Control and Systems Engineering
Biomedical Engineering
Human-Computer Interaction
Mechanical Engineering
Computer Vision and Pattern Recognition
Computer Science Applications
Control and Optimization
Artificial Intelligence

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10.1109/LRA.2018.2792691

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abstract = "A measure of fault tolerance for different joint failure probabilities is defined based on the properties of the singular values of the Jacobian after failures. Using this measure, methods to design optimally fault tolerant robots for an arbitrary set of joint failure probabilities and multiple cases of joint failure probabilities are introduced separately. Given an arbitrary set of joint failure probabilities, the optimal null space that optimizes the fault tolerant measure is derived, and the associated isotropic Jacobians are constructed. The kinematic parameters of the optimally fault tolerant robots are then generated from these Jacobians. One special case, i.e., how to construct the optimal Jacobian of spatial 7R robots for both positioning and orienting is further discussed. For multiple cases of joint failure probabilities, the optimal robot is designed through optimizing the sum of the fault tolerant measures for all the possible joint failure probabilities. This technique is illustrated on planar 3R robots, and it is shown that there exists a family of optimal robots.",

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Kinematic design of optimally fault tolerant robots for different joint failure probabilities

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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