Motion of a Four-Wheeled Omnidirectional Mobile Robot without Slipping and Detachment from the Surface

The article is devoted to the motion analysis of a highly maneuverable mobile robot with four omniwheels, taking into account the conditions for the appearance of wheel detachment from the surface, and the occurrence of wheel slipping. Within the motion analysis the task of determination support reactions for a mobile robot is considered. To solve this task, the design of a mobile robot is presented in the form of the frame with rods. To disclosure the static indeterminacy of the considered system the forces method is used. Dependences of support reactions from the position of the center mass are obtained. The feature of the considered system is that the obtained dependencies of the support reactions are nonlinear. Based on the obtained dependences of the support reactions, the influence of the position of the center of mass of a mobile robot with four wheels on the occurrence of detachment and slipping of wheels of a mobile robot was considered. Investigation was carried out within the framework of the dry friction model, according to which module of the friction force proportionally depends on the support reaction acting on the wheel from the side of the motion surface. Simulation was carried out, as a result of which the conditions for the position of the center of mass of a mobile robot were determined, in which wheels of a mobile robot do not detach from the motion surface, and there is no wheel slipping.

1. Martynenko Yu. G., Formalsky A. M. On the movement of a mobile robot with omniwheels, Izv. RAS. Theory and Control Systems, 2007, no. 6, pp. 142—149 (in Russian).

2. Martynenko Yu. G. Stability of stationary movements of a mobile robot with roller-bearing wheels and a displaced center of mass, PMM, 2010, vol. 74, no. 4, pp. 610—619 (in Russian).

3. Kolesnichenko E. Y., Pavlovsky V. E., Orlov I. A., Aliseychik A. P., Gribkov D. A., Podoprosvetov A. V. Mathematical Model of a Robot with Omni-Wheels Located at the Vertices of the Right Triangle, Mekhatronika, Avtomatizatsiya, Upravlenie, 2018, vol. 19, no. 5, pp. 327—330 (in Russian).

4. Malyshenko A. M. Input-Output Force-Torque Mappings for the Chassis of Robocars with Three Ilon’s Wheels, Mekhatronika, Avtomatizatsiya, Upravlenie, 2022, vol. 23, no. 9, pp. 486—495 (in Russian).

5. Mamaev I. S., Kilin A. A., Karavaev Y. L., Shestakov V. A. Criteria of Motion Without Slipping for an Omnidirectional Mobile Robot, Rus. J. Nonlin. Dyn., 2021, vol. 17, no. 4, pp. 527—546.

6. Labakhua L., Martins I., Merkuryev I. Control of a mobile robot with Swedish wheels, Proc. of the 2017 IEEE International Conference on Power, Control, Signals and Instrumentation Engineering (ICPCSI), Chennai, India, 21—22 September 2017, pp. 267—272.

7. Stonier D., Cho Sl., Choi S., Kuppuswamy N., Kim J. Nonlinear slip dynamics for an omniwheel mobile robot platform, Proc. of the IEEE International Conference on Robotics and Automation, Roma, Italy, 10—14 April 2007, pp. 2367—2372.

8. Williams R., Carter B., Gallina P., Rosati G. Dynamic Model with Slip for Wheeled Omni-Directional Robots, IEEE Transactions on Robotics and Automation, 2002, vol. 18, pp. 285—293.

9. Balakrishna R., Ghosal A. Modeling of Slip for Wheeled Mobile Robots, IEEE Transactions on robotics and automation, 1995, vol. 11, pp. 126—131.

10. Vlakhova A.V, Novoderova A. P. The skidding modelling of an apparatus with turned front wheels, Mechanics of Solids, 2019, vol. 54, no. 1, pp. 19—38.

11. Adamov B. I., Saypulaev G. R. Research on the Dynamics of an Omnidirectional Platform Taking into Account Real Design of Mecanum Wheels (as Exemplified by KUKA youBot), Rus. J. Nonlin. Dyn., 2020, vol. 16, no. 2, pp. 291—307.

12. Blundell M., Harty D. The Multibody Systems Approach to Vehicle Dynamics (Second Edition), Butterworth-Heinemann, 2015.

13. Milliken W. F., Milliken D. L. Race Car Vehicle Dynamics, Great Britain, Society of Automotive Engineers Inc., 1996.

14. Dugoff H., Segel L., Fancher P. An analysis of tire traction properties and their influence on vehicle dynamic performance, SAE Transactions, 1970, vol. 79, pp. 1219—1243.

15. Chang C., Lee T. Stability analysis of three- and four-wheel vehicles, JSME international journal, 1990, vol. 33, no. 4, pp. 567—574.

16. Pennestri E., Rossi V., Salvini P., Valentini P. Review and comparison of dry friction force models, Nonlinear Dynamics, 2016, vol. 83, pp. 1785—1801.

17. Shirobokov B. N., Algin V. B., Ivanov V. G. Models of interaction of a wheel with a support surface in a longitudinal plane, Theoretical and applied Mechanics: international scientific and Technical collection, 2007, vol. 22, pp. 38—47 (in Russian).

18. Adamov B. I., Saypulaev G. R. A study of the dynamics of an omnidirectional platform, taking into account the design of Mecanum wheels and multicomponent contact friction, Proc. of the 2020 International Conference Nonlinearity, Information and Robotics (NIR), Innopolis, Russia, 03—06 December 2020, pp. 1—6.

19. Olson B., Shaw S., Stepan G. Nonlinear dynamics of vehicle traction, Vehicle System Dynamics, 2003, vol. 40, no. 6, pp. 377—399. 20. Pacejka H. B. Tire and Vehicle Dynamics, UK, Elsevier, 2006.