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Controlling an uncertain mobile robot with prescribed performance

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Abstract

Uncertain mobile robot (UMR) has been playing an increasingly important role in modern industry. Implementing motion control of UMR is a critical and challenging problem due to the uncertainty. This study investigates the tracking control problem of UMR with prescribed transient and steady-state performance, in which uncertainty is (possibly fast) time-varying, bounded but with unknown bounds, and includes mismatched portions, i.e., not all the uncertainties are within the range space of the input matrix. The control is designed via constraint-following, i.e., formulating the tracking goals as servo constraints. Therefore, the system performance is indexed by the constraint-following error and the desired transient and steady state performance specifications are imposed on the constraint-following error. By a state transformation technique incorporating the prescribed performance, we are able to design a class of adaptive robust controls rendering the system motion to approximately follow the servo constraints with the prescribed performance satisfied, in which an adaptive law is constructed to emulate the unknown uncertainty bounds. The control is approximation-free and does not assume mismatched uncertainties to be sufficiently small, thus can tolerate large mismatched uncertainties. The effectiveness of the proposed approach is illustrated by rigorous proof and the simulation results.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

The paper is supported by the Open Funds of State Key Laboratory of Advanced Design, Manufacturing for Vehicle Body, Hunan University (No.31915002) and the National Natural Science Foundation of China (Grant No. 52105096), the GuangDong Basic and Applied Basic Research Foundations, China (Grant Nos. 2021A1515011752 and 2020A1515110769), China-Japan Science and Technology Joint Committee of the Ministry of Science and Technology of the People’s Republic of China (Grant No. 2017YFE0128400).

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, Hunan, People’s Republic of China

    Duo Fu & Hui Yin

  2. School of Vehicle and Mobility, Tsinghua University, Beijing, 100084, People’s Republic of China

    Jin Huang

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  1. Duo Fu
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  2. Jin Huang
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  3. Hui Yin
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Correspondence to Hui Yin.

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Fu, D., Huang, J. & Yin, H. Controlling an uncertain mobile robot with prescribed performance. Nonlinear Dyn 106, 2347–2362 (2021). https://doi.org/10.1007/s11071-021-06899-x

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