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Fault-Tolerant Force in Human and Robot Cooperation

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Abstract

Fault-tolerant solutions greatly benefit the dependability of robotic systems. This advantage is critical for robotic systems that perform in collaboration with humans. This work addresses the fault tolerance of robotic manipulators for cooperatively manipulating an object together with a human. Cooperation occurs for slow lifting or pushing of the object. Reconfiguration of the manipulator is performed to maintain the cooperative force level despite the occurrence of robot joint failures. We present several strategies that are investigated for optimally maintaining the required force level for human-robot task cooperation. For each strategy, a reconfiguration control law is introduced that optimises the fault tolerance of the maintained force level. Three case studies are introduced to validate the proposed reconfiguration laws,demonstrating that this approach results in an optimal fault-tolerant force in human-robot cooperation.

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Acknowledgements

This research was supported by Centre for Intelligent Systems Research—Deakin University in part with U.S. National Science Foundation under contract IIS-0812437.

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Authors and Affiliations

  1. Center for Intelligent Systems Research, Deakin University, Geelong Waurn Ponds Campus, Victoria, 3217, Australia

    Hamid Abdi, Saeid Nahavandi & Zoran Najdovski

  2. Electrical and Computer Engineering Department, Colorado State University, Fort Collins, CO, 80523, USA

    Hamid Abdi & Anthony A. Maciejewski

Authors
  1. Hamid Abdi
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  2. Saeid Nahavandi
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  3. Zoran Najdovski
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  4. Anthony A. Maciejewski
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Correspondence to Hamid Abdi.

Appendices

Appendix A

The pseudo inverse of full rank square matrices is obtained by regular inverse or

$$\mathbf{B}^{\dag} = \mathbf{B}^{ - 1} $$

when B is a skinny full rank matrix, then the pseudo inverse is defined by left inverse or

$$\mathbf{B}^{\dag} = \bigl( \mathbf{B}^{T}\mathbf{B} \bigr)^{ - 1}\mathbf{B}^{T} $$

when B is a fat and full rank matrix, then the pseudo inverse is defined by right inverse or

$$\mathbf{B}^{\dag} = \mathbf{B}^{T} \bigl( \mathbf{BB}^{T} \bigr)^{ - 1} $$

Appendix B

Reduced matrices are defined by eliminating columns of the matrices. For example, by eliminating the kth column of A, the kth reduced matrix is obtained as

$${}^{k}\mathbf{A} = \left [ \begin{array}{c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c} \mathbf{a}_{1} & \cdots & \mathbf{a}_{k - 1} & \mathbf{a}_{k + 1} & \cdots & \mathbf{a}_{n} \\\end{array} \right ] $$

Reduced vectors are defined similar to reduced vertices eliminating the rows. The kth reduced vector of τ is

For single locked joint failures, there are n reduced matrices of A which are shown by 1 A,2 A,…,n A.

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Abdi, H., Nahavandi, S., Najdovski, Z. et al. Fault-Tolerant Force in Human and Robot Cooperation. Int J of Soc Robotics 5, 103–116 (2013). https://doi.org/10.1007/s12369-012-0151-1

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