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Peer-reviewedCC BY 4.0Mathematics

Mode-Dependent Differential-Algebraic Kinematic Modeling of a Four-Wheel Wall-Climbing Robot on Cylindrical Inner Surfaces

  • Dapeng Zhang1,2
  • Yongchang Zhang1,2,3
  • Shasha Wang1,2
  • Weihao Mao2
  • Junlong Guo2
  • Jianwen Zhao1,2
  • Zhiguang Xing1,2,4
4 affiliations
  1. 1State Key Laboratory of Robotics and Systems, Harbin Institute of Technology, Harbin 150001, China
  2. 2Institute of Robotics and Intelligent Equipment, Harbin Institute of Technology, Weihai 264200, China
  3. 3Department of Control Science and Engineering, Harbin Institute of Technology, Harbin 150001, China
  4. 4Qingdao Innovation and Development Base, Harbin Institute of Technology (Weihai), Qingdao 266000, China
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Abstract

Multi-wheel wall-climbing robots operating on cylindrical inner surfaces are subject to configuration-dependent wheel-surface contacts and nonholonomic rolling constraints, making planar differential-drive or fixed-contact kinematic models insufficient when the active contact topology changes. This study develops a mode-dependent differential-algebraic kinematic model for a four-wheel wall-climbing robot on cylindrical inner surfaces. Given the instantaneous active contact set, the wheel-surface geometry is reconstructed from nonlinear point-on-surface and tangency constraints using an adaptive Levenberg–Marquardt method. The reconstructed contact geometry is then used to assemble normal-velocity compatibility and rolling constraints, yielding an analytical mapping from a nominal body-twist reference to active-wheel speed commands. The model is integrated into trajectory-based motion generation and assessed through multibody co-simulation incorporating contact and friction effects. For unidirectional and S-shaped motions, the axial root-mean-square errors (RMSEs) are 5.6 mm and 11.5 mm, with normalized axial errors of 0.112% and 0.096%, respectively; the circumferential-angle RMSEs are 1.25° and 1.32°, with normalized angular errors of 1.39% and 0.73%. These results demonstrate the applicability of the model to contact-dependent geometric reconstruction and wheel-speed command generation under varying multi-wheel contact topologies on cylindrical inner surfaces, and offer an extensible approach to the kinematic modeling of multi-wheel locomotion in cylindrical environments.

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Cite

BibTeXRIS
BibTeX
@article{zhang2026modedependent,
  title = {{Mode-Dependent Differential-Algebraic Kinematic Modeling of a Four-Wheel Wall-Climbing Robot on Cylindrical Inner Surfaces}},
  author = {Dapeng Zhang and Yongchang Zhang and Shasha Wang and Weihao Mao and Junlong Guo and Jianwen Zhao and Zhiguang Xing},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203645},
  url = {https://www.mdpi.com/2227-7390/14/20/3645},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Mode-Dependent Differential-Algebraic Kinematic Modeling of a Four-Wheel Wall-Climbing Robot on Cylindrical Inner Surfaces
AU  - Dapeng Zhang
AU  - Yongchang Zhang
AU  - Shasha Wang
AU  - Weihao Mao
AU  - Junlong Guo
AU  - Jianwen Zhao
AU  - Zhiguang Xing
PY  - 2026
DA  - 2026/10/09
JO  - Mathematics
DO  - 10.3390/math14203645
UR  - https://www.mdpi.com/2227-7390/14/20/3645
AB  - Multi-wheel wall-climbing robots operating on cylindrical inner surfaces are subject to configuration-dependent wheel-surface contacts and nonholonomic rolling constraints, making planar differential-drive or fixed-contact kinematic models insufficient when the active contact topology changes. This study develops a mode-dependent differential-algebraic kinematic model for a four-wheel wall-climbing robot on cylindrical inner surfaces. Given the instantaneous active contact set, the wheel-surface geometry is reconstructed from nonlinear point-on-surface and tangency constraints using an adaptive Levenberg–Marquardt method. The reconstructed contact geometry is then used to assemble normal-velocity compatibility and rolling constraints, yielding an analytical mapping from a nominal body-twist reference to active-wheel speed commands. The model is integrated into trajectory-based motion generation and assessed through multibody co-simulation incorporating contact and friction effects. For unidirectional and S-shaped motions, the axial root-mean-square errors (RMSEs) are 5.6 mm and 11.5 mm, with normalized axial errors of 0.112% and 0.096%, respectively; the circumferential-angle RMSEs are 1.25° and 1.32°, with normalized angular errors of 1.39% and 0.73%. These results demonstrate the applicability of the model to contact-dependent geometric reconstruction and wheel-speed command generation under varying multi-wheel contact topologies on cylindrical inner surfaces, and offer an extensible approach to the kinematic modeling of multi-wheel locomotion in cylindrical environments.
SN  - 2227-7390
ER  -