---

Discontinuity, Nonlinearity, and Complexity 15(4) (2026) 623--637 | DOI:10.5890/DNC.2026.12.011

Van-Du Nguyen$^{1}$, Ngoc-Hung Chu$^{2}$, Quoc-Huy Ngo$^{1}$

$^{1}$ Department of Mechanical Engineering, Thai Nguyen University of Technology, Thai Nguyen, 250000, Vietnam

$^{2}$ Thai Nguyen University of Economics-Technology, Thai Nguyen, 250000, Vietnam

Download Full Text PDF

 

Abstract

The locomotion efficiency of capsule robots is highly sensitive to environmental resistance forces, especially in fluid-filled conditions. This study investigates a millimeter-scale vibro-impact capsule robot designed for gastrointestinal applications. Building on a validated dry friction model, we incorporate viscous drag and buoyancy to simulate realistic fluidic environments. A comprehensive physical and mathematical framework is developed to characterize the capsule's nonlinear dynamics. Numerical simulations and analytical tools, including time history analysis, phase trajectories, Poincaré maps, and bifurcation diagrams, are used to evaluate displacement efficiency across varying friction thresholds and fluid properties. Results show that high dry friction suppresses mobility, voltage decay reduces propulsion, and moderate fluid viscosity can enhance travel distance. These findings help identify optimal operating conditions for stable bidirectional motion and offer practical guidelines for the design and control of capsule robots in complex environments.

Acknowledgments

This work has been supported by Thai Nguyen University of Technology.

References

1. [1]	Koprowski, R. (2015), Overview of technical solutions and assessment of clinical usefulness of capsule endoscopy, Biomedical Engineering Online, 14, 111.

2. [2]	Alexander, P.B. and Ahalapitiya, J.H. (2020), Analysis of current and future technologies of capsule endoscopy: a mini review, Archives of Preventive Medicine, 5(1), 031-034.

3. [3]	Chen, W., Sui, J., and Wang, C. (2022), Magnetically actuated capsule robots: a review, IEEE Access, 10, 88398-88420.

4. [4]	Glass, P., Cheung, M.S., and Sitti, M. (2008), A legged anchoring mechanism for capsule endoscopes using micropatterned adhesives, IEEE Transactions on Biomedical Engineering, 55(12), 2759-2767.

5. [5]	Kim, H.M., Yang, S., Kim, J., Park, S., Cho, J.H., Park, J.Y., Song, S.Y., Bae, H.I., and Choung, R.S. (2010), Active locomotion of a paddling-based capsule endoscope in an in vitro and in vivo experiment (with videos), Gastrointestinal Endoscopy, 72(2), 381-387.

6. [6]	Yang, S., Kim, J., Park, S., and Kim, H.M. (2021), Autonomous locomotion of capsule endoscope in gastrointestinal tract, IEEE Reviews in Biomedical Engineering, 14, 199-212.

7. [7]	Chi, M., Yan, Y., Guo, B., and Liu, Y. (2021), Coupled steering control of a low torsional torque capsule robot in the intestine, Mechatronics, 77, 102593.

8. [8]	Cao, Q., Chen, W., Sui, J., and Wang, C. (2024), Robotic wireless capsule endoscopy: recent advances and upcoming technologies, Nature Communications, 15(1), 4597.

9. [9]	Geropoulos, G., Psaltis, E., Giannakou, A., Leyba, J., and Sotiropoulos, G.C. (2021), Magnetically controlled capsule endoscopy versus conventional gastroscopy: a systematic review and meta-analysis, Journal of Clinical Gastroenterology, 55(7), 577-589.

10. [10]	Ye, B., Zhang, X., Lu, W., and Wang, X. (2023), Closed-loop active control of the magnetic capsule endoscope with a robotic arm based on image navigation, Journal of Magnetism and Magnetic Materials, 565, 170268.

11. [11]	Zhang, J., Liu, Y., and Paez-Chavez, J. (2024), Vibro-impact dynamics of an experimental rig with two-sided constraint and bidirectional drift, Journal of Sound and Vibration, 571, 118021.

12. [12]	Liu, Y. (2024), The vibro-impact capsule for gut examination: recent advances and new directions, IEEE Transactions on Medical Robotics and Bionics, 6(1), 12-25.

13. [13]	Nguyen, K.T., Yan, Y., and Liu, Y. (2021), The effect of friction on the vibro-impact locomotion system: modeling and dynamic response, Meccanica, 56(8), 2121-2137.

14. [14]	Liu, Y., Yan, Y., and Paez-Chavez, J. (2020), Bifurcation analysis of a vibro-impact experimental rig with two-sided constraint, Meccanica, 55, 2505-2521.

15. [15]	Yan, Y., Liu, Y., and Paez-Chavez, J. (2019), Modelling of a vibro-impact self-propelled capsule in the small intestine, Nonlinear Dynamics, 96(1), 123-144.

16. [16]	Liu, P., Yu, H., and Cang, S. (2019), Modelling and analysis of dynamic frictional interactions of vibro-driven capsule systems with viscoelastic property, European Journal of Mechanics - A/Solids, 74, 16-25.

17. [17]	Liao, M., Liu, Y., Zhang, J., and Paez-Chavez, J. (2022), Speed optimisation and reliability analysis of a self-propelled capsule robot moving in an uncertain frictional environment, International Journal of Mechanical Sciences, 221, 107156.

18. [18]	Nguyen, V.D., Yan, Y., and Liu, Y. (2017), The effect of inertial mass and excitation frequency on a Duffing vibro-impact drifting system, International Journal of Mechanical Sciences, 124-125, 9-21.

19. [19]	Nguyen, K.T., Yan, Y., and Liu, Y. (2021), The effect of friction on the vibro-impact locomotion system: modeling and dynamic response, Meccanica, 56, 2121-2137.

20. [20]	Guo, B., Yan, Y., and Liu, Y. (2020), Self-propelled capsule endoscopy for small-bowel examination: proof-of-concept and model verification, International Journal of Mechanical Sciences, 174, 105506.

21. [21]	Yin, S., Yan, Y., and Liu, Y. (2023), Dynamics of a self-propelled capsule robot in contact with different folds in the small intestine, Communications in Nonlinear Science and Numerical Simulation, 126, 107445.

22. [22]	Tian, J., Yan, Y., and Liu, Y. (2023), Dynamic analysis of a soft capsule robot self-propelling in the small intestine via finite element method, Nonlinear Dynamics, 111(11), 9777-9798.

23. [23]	Yan, Y., Yin, S., and Liu, Y. (2022), Dynamics of a vibro-impact self-propelled capsule encountering a circular fold in the small intestine, Meccanica, 58(2-3), 451-472.

24. [24]	Yan, Y., Yin, S., and Liu, Y. (2022), Evaluating the resistant force of an endoscopic capsule self-propelling in the small intestine, Archive of Applied Mechanics, 92(12), 3861-3875.

25. [25]	Tian, J., Liu, Y., and Yan, Y. (2021), Finite element analysis of a self-propelled capsule robot moving in the small intestine, International Journal of Mechanical Sciences, 206, 106621.

26. [26]	Guo, B., Liu, Y., and Prasad, S. (2019), Modelling of capsule–intestine contact for a self-propelled capsule robot via experimental and numerical investigation, Nonlinear Dynamics, 98(4), 3155-3167.

27. [27]	Gao, J., Zhang, Z., and Yan, G. (2019), Development of a capsule robot for exploring the colon, Micromachines, 10(7), 438.

28. [28]	Wang, J., Guo, B., Yan, Y., and Liu, Y. (2018), Influence of different lubricating fluids on friction trauma of small intestine during enteroscopy, Tribology International, 126, 29-38.

29. [29]	Zhang, C. and Liu, H. (2016), Analytical friction model of the capsule robot in the small intestine, Tribology Letters, 64(3), 44.

30. [30]	Sliker, L.J., Ciuti, G., Menciassi, A., and Rentschler, M.E. (2016), Frictional resistance model for tissue-capsule endoscope sliding contact in the gastrointestinal tract, Tribology International, 102, 472-484.

31. [31]	Fracczak, L., Yan, Y., and Liu, Y. (2020), The influence of lubricants on friction coefficient between the intestines and a silicone, International Journal of Mechanical Engineering and Robotics Research, 925-930.

32. [32]	Monsia, M.D. and Kpomahou, Y.J.F. (2014), Simulating nonlinear oscillations of viscoelastically damped mechanical systems, Engineering, Technology & Applied Science Research, 4(6), 714-723.

33. [33]	La, N.T., Ngo, Q.H., Yan, Y., and Liu, Y. (2025), A vibro-impact capsule in millimeter scale: size reduction and nonlinear dynamics, Nonlinear Dynamics, 113, 1-15.

34. [34]	Ngo, Q.H., La, N.T., Yan, Y., and Liu, Y. (2025), A vibro-impact remote-controlled capsule in millimeter scale: design, modeling, experimental validation and dynamic response, Journal of Sound and Vibration, 596, 118746.

35. [35]	Feng, Z. and Michaelides, E.E. (2023), A general and accurate correlation for the drag on spherocylinders, International Journal of Multiphase Flow, 168, 104579.

36. [36]	Mapara, S.S. and Patravale, V.B. (2017), Medical capsule robots: a renaissance for diagnostics, drug delivery and surgical treatment, Journal of Controlled Release, 261, 337-351.