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Self-Balancing Controlled Lagrangian and Geometric Control of Unmanned Mobile Robots

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Abstract

This work presents a novel geometric framework for self-balancing as well as planar motion control of wheeled vehicles with two fewer control inputs than the configuration variables. For self-balancing control, we shape the kinetic energy in such a way that the upright direction of the robot’s body becomes a nonlinearly stable equilibrium for the corresponding controlled Lagrangian which is inherently a saddle point. Then for planar motion control of the robot, we set its position and attitude as an element of the special Euclidean group SE(2) and apply a logarithmic feedback control taking advantage of the Lie group exponential coordinates. For simulation and evaluating the controllers, the unified dynamic model of the self-balancing mobile robot (SMR) is developed using the constrained Euler-Lagrange equations.

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Acknowledgements

This work is supported by National Natural Science Foundation (NNSF) of China under Grant 61374033. The authors would also like to thank the reviewers for the valuable comments.

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Authors and Affiliations

  1. The State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering Science, Peking University, Beijing, 100871, China

    Morteza Tayefi & Zhiyong Geng

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  1. Morteza Tayefi
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  2. Zhiyong Geng
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Correspondence to Zhiyong Geng.

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Tayefi, M., Geng, Z. Self-Balancing Controlled Lagrangian and Geometric Control of Unmanned Mobile Robots. J Intell Robot Syst 90, 253–265 (2018). https://doi.org/10.1007/s10846-017-0666-7

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  • DOI: https://doi.org/10.1007/s10846-017-0666-7

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