Kinematic Modeling and Stable Control Law Designing for Four Mecanum Wheeled Mobile Robot Platform Based on Lyapunov Stability Criterion

Tri Dung Nguyen

doi:doi:10.11648/j.eas.20230805.11

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Kinematic Modeling and Stable Control Law Designing for Four Mecanum Wheeled Mobile Robot Platform Based on Lyapunov Stability Criterion

Tri Dung Nguyen

Published in Engineering and Applied Sciences (Volume 8, Issue 5)

Received: 28 July 2023 Accepted: 22 August 2023 Published: 8 September 2023

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Abstract

Transportation in warehouses and production workshops is a matter of urgency today. Most warehouses arrange routes for circulation along the shelves, transportation vehicles will move on this road to perform the task of exporting or importing goods. Routes will be arranged to move in one direction because vehicles do not have enough space to turn around in cramped warehouses. This causes many difficulties in planning the trajectory for transportation vehicles, especially self-propelled vehicles. In order to have an appropriate transportation plan, it is necessary to solve many problems, including: reasonable transport equipment, sufficient number of devices, optimal route layout, algorithm of operation center for Positioning and Navigation of transportation equipment, This study proposes a method for transportation using an omnidirectional automated guided vehicle (AGV). The AGV's omnidirectional mobility is supported by the mecanum wheels, so vehicles can move in multiple directions on the road without turning, even at a junction or an intersection. This study consists of two parts, the first part focuses on kinematic modeling for mecanum wheels and extends to robot’s platform using four mecanum wheels. Part two proposes a diagram to calculate the errors of the robot compared to a reference tracking line, design a control law based on the Lyapunov stability criterion. The stability of the control law is verified and confirmed by simulation on Matlab environment.

Published in	Engineering and Applied Sciences (Volume 8, Issue 5)
DOI	10.11648/j.eas.20230805.11
Page(s)	83-89
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Mecanum Wheels, Omni Directional Mobile Platform, Lyapunov Stability, Line Tracking Robots, AGV

References

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[2]	A. Gfrerrer, Geometry and kinematics of the mecanum wheel, Journal of Computer Aided Geometric Design, Vol. 25, No. 9, pp. 784-791, 2008.
[3]	Y. Li, S. Dai, L. Zhao, X. Yan, and Y. Shi, Topological design methods for mecanum wheel, Journal of Symmetry in Engineering Sciences II, Vol. 11, No. 10, pp. 1-27, 2019.
[4]	I. Doroftei, V. Spinu, and V. Grosu, “Omnidirectional mobile robot – design and implementation”, Journal of Bioinspiration and Robotics: Walking and Climbing Robots, pp. 544, 2007.
[5]	P. Alvito, C. Marques, P. Carriço, and J. Freire, A Robotic Platform for the Social Robot Project, In Proceedings of the 23rd IEEE International Symposium on Robot and Human Interactive Communication (ROMAN 2014) Workshop on Interactive Robots for Aging and/or Impaired People, Edinburgh, UK, 25–29 August 2014.
[6]	J. Qian, B. Zi, D. Wang, Y. Ma, and D. Zhang, the design and development of an omni-directional mobile robot oriented to an intelligent manufacturing system, Journal of Sensors 2017, pp. 17, 2073.
[7]	F. Adăscăli¸tei and I. Doroftei, Practical applications for mobile robots based on mecanum wheels-a systematic survey, In Proceedings of the 3rd International Conference on Innovations, Recent Trends and Challenges in Mechatronics, Mechanical Engineering and New High-Tech Products Development (MECAHITECH’11), Bucharest, Romania, 22–23 September 2011; pp. 112–123.
[8]	P. Hryniewicz, A. Gwiazda, W. Banas, A. S’ekala, and K. Foit, Modelling of a mecanum wheel taking into account the geometry of road rollers, In Proceedings of the IOP Conference Series: Materials Science and Engineering, Sibiu, Romania, 14–17 June 2017; p. 012060.
[9]	C. He, D. Wu, K. Chen, F. Liu, and N. Fan, Analysis of the Mecanum wheel arrangement of an omnidirectional vehicle, Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2019, 233, 5329–5340.
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[12]	K. Hassan Khalil, Lyapunov stability, Journal of Control Systems, Robotics and Automation, Vol. 12, pp. 115-126, 2009.
[13]	J. Wu, C. Ly, L. Zhao, R. Li, and G. Wang, Design and implementation of an omnidirectional mobile robot platform with unified I/O interfaces, In Proceedings of 2017 IEEE International Conference on Mechatronics and Automation (ICMA), Takamatsu, Japan, 06–09 August 2017.
[14]	H. Taheri, B. Qiao, and N. Ghaeminezhad, Kinematic model of a four mecanum wheeled mobile robot, Journal of International Journal of Computer Applications (0975 – 8887), Vol. 113, No. 3, pp. 6-9, 2015.
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APA Style

Tri Dung Nguyen. (2023). Kinematic Modeling and Stable Control Law Designing for Four Mecanum Wheeled Mobile Robot Platform Based on Lyapunov Stability Criterion. Engineering and Applied Sciences, 8(5), 83-89. https://doi.org/10.11648/j.eas.20230805.11

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ACS Style

Tri Dung Nguyen. Kinematic Modeling and Stable Control Law Designing for Four Mecanum Wheeled Mobile Robot Platform Based on Lyapunov Stability Criterion. Eng. Appl. Sci. 2023, 8(5), 83-89. doi: 10.11648/j.eas.20230805.11

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AMA Style

Tri Dung Nguyen. Kinematic Modeling and Stable Control Law Designing for Four Mecanum Wheeled Mobile Robot Platform Based on Lyapunov Stability Criterion. Eng Appl Sci. 2023;8(5):83-89. doi: 10.11648/j.eas.20230805.11

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@article{10.11648/j.eas.20230805.11,
  author = {Tri Dung Nguyen},
  title = {Kinematic Modeling and Stable Control Law Designing for Four Mecanum Wheeled Mobile Robot Platform Based on Lyapunov Stability Criterion},
  journal = {Engineering and Applied Sciences},
  volume = {8},
  number = {5},
  pages = {83-89},
  doi = {10.11648/j.eas.20230805.11},
  url = {https://doi.org/10.11648/j.eas.20230805.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.eas.20230805.11},
  abstract = {Transportation in warehouses and production workshops is a matter of urgency today. Most warehouses arrange routes for circulation along the shelves, transportation vehicles will move on this road to perform the task of exporting or importing goods. Routes will be arranged to move in one direction because vehicles do not have enough space to turn around in cramped warehouses. This causes many difficulties in planning the trajectory for transportation vehicles, especially self-propelled vehicles. In order to have an appropriate transportation plan, it is necessary to solve many problems, including: reasonable transport equipment, sufficient number of devices, optimal route layout, algorithm of operation center for Positioning and Navigation of transportation equipment, This study proposes a method for transportation using an omnidirectional automated guided vehicle (AGV). The AGV's omnidirectional mobility is supported by the mecanum wheels, so vehicles can move in multiple directions on the road without turning, even at a junction or an intersection. This study consists of two parts, the first part focuses on kinematic modeling for mecanum wheels and extends to robot’s platform using four mecanum wheels. Part two proposes a diagram to calculate the errors of the robot compared to a reference tracking line, design a control law based on the Lyapunov stability criterion. The stability of the control law is verified and confirmed by simulation on Matlab environment.},
 year = {2023}
}

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TY  - JOUR
T1  - Kinematic Modeling and Stable Control Law Designing for Four Mecanum Wheeled Mobile Robot Platform Based on Lyapunov Stability Criterion
AU  - Tri Dung Nguyen
Y1  - 2023/09/08
PY  - 2023
N1  - https://doi.org/10.11648/j.eas.20230805.11
DO  - 10.11648/j.eas.20230805.11
T2  - Engineering and Applied Sciences
JF  - Engineering and Applied Sciences
JO  - Engineering and Applied Sciences
SP  - 83
EP  - 89
PB  - Science Publishing Group
SN  - 2575-1468
UR  - https://doi.org/10.11648/j.eas.20230805.11
AB  - Transportation in warehouses and production workshops is a matter of urgency today. Most warehouses arrange routes for circulation along the shelves, transportation vehicles will move on this road to perform the task of exporting or importing goods. Routes will be arranged to move in one direction because vehicles do not have enough space to turn around in cramped warehouses. This causes many difficulties in planning the trajectory for transportation vehicles, especially self-propelled vehicles. In order to have an appropriate transportation plan, it is necessary to solve many problems, including: reasonable transport equipment, sufficient number of devices, optimal route layout, algorithm of operation center for Positioning and Navigation of transportation equipment, This study proposes a method for transportation using an omnidirectional automated guided vehicle (AGV). The AGV's omnidirectional mobility is supported by the mecanum wheels, so vehicles can move in multiple directions on the road without turning, even at a junction or an intersection. This study consists of two parts, the first part focuses on kinematic modeling for mecanum wheels and extends to robot’s platform using four mecanum wheels. Part two proposes a diagram to calculate the errors of the robot compared to a reference tracking line, design a control law based on the Lyapunov stability criterion. The stability of the control law is verified and confirmed by simulation on Matlab environment.
VL  - 8
IS  - 5
ER  -

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Author Information

Tri Dung Nguyen

Industrial Maintenance Training Center, Ho Chi Minh City University of Technology, Hochiminh City, Vietnam

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Plain Text BibTeX RIS

APA Style

Tri Dung Nguyen. (2023). Kinematic Modeling and Stable Control Law Designing for Four Mecanum Wheeled Mobile Robot Platform Based on Lyapunov Stability Criterion. Engineering and Applied Sciences, 8(5), 83-89. https://doi.org/10.11648/j.eas.20230805.11

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ACS Style

Tri Dung Nguyen. Kinematic Modeling and Stable Control Law Designing for Four Mecanum Wheeled Mobile Robot Platform Based on Lyapunov Stability Criterion. Eng. Appl. Sci. 2023, 8(5), 83-89. doi: 10.11648/j.eas.20230805.11

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AMA Style

Tri Dung Nguyen. Kinematic Modeling and Stable Control Law Designing for Four Mecanum Wheeled Mobile Robot Platform Based on Lyapunov Stability Criterion. Eng Appl Sci. 2023;8(5):83-89. doi: 10.11648/j.eas.20230805.11

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@article{10.11648/j.eas.20230805.11,
  author = {Tri Dung Nguyen},
  title = {Kinematic Modeling and Stable Control Law Designing for Four Mecanum Wheeled Mobile Robot Platform Based on Lyapunov Stability Criterion},
  journal = {Engineering and Applied Sciences},
  volume = {8},
  number = {5},
  pages = {83-89},
  doi = {10.11648/j.eas.20230805.11},
  url = {https://doi.org/10.11648/j.eas.20230805.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.eas.20230805.11},
  abstract = {Transportation in warehouses and production workshops is a matter of urgency today. Most warehouses arrange routes for circulation along the shelves, transportation vehicles will move on this road to perform the task of exporting or importing goods. Routes will be arranged to move in one direction because vehicles do not have enough space to turn around in cramped warehouses. This causes many difficulties in planning the trajectory for transportation vehicles, especially self-propelled vehicles. In order to have an appropriate transportation plan, it is necessary to solve many problems, including: reasonable transport equipment, sufficient number of devices, optimal route layout, algorithm of operation center for Positioning and Navigation of transportation equipment, This study proposes a method for transportation using an omnidirectional automated guided vehicle (AGV). The AGV's omnidirectional mobility is supported by the mecanum wheels, so vehicles can move in multiple directions on the road without turning, even at a junction or an intersection. This study consists of two parts, the first part focuses on kinematic modeling for mecanum wheels and extends to robot’s platform using four mecanum wheels. Part two proposes a diagram to calculate the errors of the robot compared to a reference tracking line, design a control law based on the Lyapunov stability criterion. The stability of the control law is verified and confirmed by simulation on Matlab environment.},
 year = {2023}
}

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TY  - JOUR
T1  - Kinematic Modeling and Stable Control Law Designing for Four Mecanum Wheeled Mobile Robot Platform Based on Lyapunov Stability Criterion
AU  - Tri Dung Nguyen
Y1  - 2023/09/08
PY  - 2023
N1  - https://doi.org/10.11648/j.eas.20230805.11
DO  - 10.11648/j.eas.20230805.11
T2  - Engineering and Applied Sciences
JF  - Engineering and Applied Sciences
JO  - Engineering and Applied Sciences
SP  - 83
EP  - 89
PB  - Science Publishing Group
SN  - 2575-1468
UR  - https://doi.org/10.11648/j.eas.20230805.11
AB  - Transportation in warehouses and production workshops is a matter of urgency today. Most warehouses arrange routes for circulation along the shelves, transportation vehicles will move on this road to perform the task of exporting or importing goods. Routes will be arranged to move in one direction because vehicles do not have enough space to turn around in cramped warehouses. This causes many difficulties in planning the trajectory for transportation vehicles, especially self-propelled vehicles. In order to have an appropriate transportation plan, it is necessary to solve many problems, including: reasonable transport equipment, sufficient number of devices, optimal route layout, algorithm of operation center for Positioning and Navigation of transportation equipment, This study proposes a method for transportation using an omnidirectional automated guided vehicle (AGV). The AGV's omnidirectional mobility is supported by the mecanum wheels, so vehicles can move in multiple directions on the road without turning, even at a junction or an intersection. This study consists of two parts, the first part focuses on kinematic modeling for mecanum wheels and extends to robot’s platform using four mecanum wheels. Part two proposes a diagram to calculate the errors of the robot compared to a reference tracking line, design a control law based on the Lyapunov stability criterion. The stability of the control law is verified and confirmed by simulation on Matlab environment.
VL  - 8
IS  - 5
ER  -

Copy | Download