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Research Papers: Mechanisms and Robotics

# On the Joint Velocity Jump for Redundant Robots in the Presence of Locked-Joint Failures

[+] Author and Article Information
Zhao Jing

The College of Mechanical Engineering & Applied Electronics Technology, Beijing Polytechnic University, Beijing 100022, P.R.C.zhaojing@bjut.edu.cn

Li Qian

The College of Mechanical Engineering & Applied Electronics Technology, Beijing Polytechnic University, Beijing 100022, P.R.C.leeqian020112@yahoo.com

J. Mech. Des 130(10), 102305 (Sep 09, 2008) (7 pages) doi:10.1115/1.2943302 History: Received June 28, 2007; Revised January 30, 2008; Published September 09, 2008

## Abstract

The joint velocity jump for redundant robots in the presence of locked-joint failures is discussed in this paper. First, the analytical formula of the optimal joint velocity with minimum jump is derived, and its specific expressions for both all joint failure and certain single joint failure are presented. Then, the jump difference between the minimum jump solution and the least-norm velocity solution is mathematically analyzed, and the influence factors on this difference are also discussed. Based on this formula, a new fault tolerant algorithm with the minimum jump is proposed. Finally, simulation examples are implemented with a planar $3R$ robot and a $4R$ spatial robot, and an experimental study is also done. Study results indicate that the new algorithm proposed in this paper is well suited for real time implementation, and can further reduce the joint velocity jump thereby improving the motion stability of redundant robots in fault tolerant operations. Also, the fewer the possible failed joints are, the more obvious the effect of this new algorithm becomes.

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## Figures

Figure 12

Power-cube planar 3R robot

Figure 13

The path of the robot’s end effector

Figure 14

The path errors of the robot’s end effector

Figure 1

A planar 3R robot

Figure 2

Fault tolerant indexes when X=[0.35,0]Tm

Figure 3

Joint configurations

Figure 4

Fault tolerant indices when X=[0.4,0]Tm

Figure 5

Fault tolerant indices when X=[0.35,0]Tm

Figure 6

Joint configurations

Figure 7

Fault tolerant indices when X=[0.35,0]Tm

Figure 8

Joint configurations

Figure 9

A PUMA spatial 4R robot

Figure 10

Fault tolerant indexes when X=[0.09,0.21,0.27]Tm

Figure 11

Fault tolerant indices when X=[−0.21,0.2,0.35]Tm

## Errata

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