Dynamics of a vehicle with omniwheels with massive rollers with account for a roller change contacting with supporting plane

Theoretical mechanics


Аuthors

Gerasimov K. V.*, Zobova A. A.**

Lomonosov Moscow State University, 1, Leninskie Gory, Moscow, 119991, Russia

*e-mail: kiriger@gmail.com
**e-mail: azobova@mech.math.msu.su

Abstract

We study the dynamics of a vehicle with omni-wheels moving along a horizontal plane. In this work, we consider dynamics of the rollers, and suggest the model for contact switching from one roller to another using impact theory. We consider behavior of the simplified model of the omni-wheel as a rigid disk with a non-holonomic sliding constraint (MassLess Rollers Model – MLRM).

Dynamics of a symmetrical vehicle with N omni-wheels, each carrying n rollers, moving along a fixed horizontal absolutely rough plane are considered under the following assumptions: the mass of each roller is nonzero, the plane and rollers are absolutely rigid, so the contact between a supporting roller and the plane occurs in one point. The slippage is allowed only at the instant just after the change of the rollers in contact (a tangent impact).

Between the impacts, the motion dynamics are governed by the equations in pseudovelocities. Compared to MLRM, the additional terms proportional to the rollers’ axial moment of inertia and depending on the angles of wheels’ rotation appear. For free motions (without control), we showed analytically the existence of the energy first integral, cyclic linear integral for the non-supporting rollers, and slow change of the MLRM first integral. It is shown that some MLRM motions disappear. All analytical results were confirmed by simulation. Comparison of the main types of motion for symmetric three-wheeled vehicle for MLRM and the whole model was performed.

For switching between rollers, an impact theory problem is posed and solved, impact forces and energy loss being obtained in assumption of non-elastic impact and ideal constraints. Right before the impact instant only holonomic constraints are imposed on the system. After the impact, a set of differential constraints are applied. The impact problem is then formulated as a system of algebraic equations. The system admits the unique solution. We consider the impact as non-elastic in the sense that it is equivalent to projection of the vector of generalized velocities onto the plane defined by constraints in the space of virtual displacements, orthogonal in the kinetic metric. Thus, the normal part of the generalized velocities vanishes, and the kinetic energy of the system decreases by the value of the kinetic energy of lost generalized velocities, in accordance to Carnot’s theorem. Then the solutions were obtained numerically combining both smooth parts of motion and impacts.

Keywords:

omniwheel, massive rollers, nonholonomic constraint, laconic form of Ya.V. Tatarinov's equations of motion, impact theory, instant instant superposition of differential constraint

References

  1. Campion G., Bastin G., D’Andrea-Novel B. Structural properties and classification of kinematic and dynamic models of wheeled mobile robots, IEEE Transactions on Robotics and Automation, 1996, vol. 12, no. 1, pp. 47 – 62. URL: https://doi.org/10.1109/70.481750

  2. Chung W., Iagnemma K. Wheeled Robots, Springer Handbook of Robotics. Springer International Publishing, 2016, pp. 575 – 594, available at: https://doi.org/10.1007/978-3-319-32552-124

  3. Kanjanawanishkul K. Omnidirectional wheeled mobile robots: wheel types and practical applications, International Journal of Advanced Mechatronic Systems, 2015, vol. 6, no. 6, pp. 289, available at: https://doi.org/10.1504/ijamechs.2015.074788

  4. Zobova A.A., Tatarinov Ya.V. Prikladnaya matematika i mekhanika, 2009, vol. 73, no. 1, pp. 13 – 22.

  5. Martynenko Yu.G., Formal’skii A.M. Izvestiya RAN. Teoriya i sistemy upravleniya, 2007, no. 6, pp. 142 – 149.

  6. Borisov A.V., Kilin A.A., Mamaev I.S. Nelineinaya dinamika, 2011, vol. 7, no. 4 (Mobil’nye roboty), pp. 785 – 801.

  7. Zobova A.A., Tatarinov Ya.V. Vestnik Moskovskogo universiteta. Matematika. Mekhanika, 2008, no. 6, pp. 62 – 65.

  8. Martynenko Yu.G. Prikladnaya matematika i mekhanika, 2010, vol. 74, no. 4, pp. 610 – 619.

  9. Kosenko I.I., Gerasimov K.V. Nelineinaya dinamika, 2016, vol. 12, no. 2, pp. 251 – 262.

  10. Williams R.L., Carter B.E., Gallina P., Rosati G. Dynamic model with slip for wheeled omnidirectional robots, IEEE Transactions on Robotics and Automation, 2002, vol. 18, no. 3, pp. 285 – 293.

  11. Ashmore M., Barnes N. Omni-drive robot motion on curved paths: the fastest path between two points is not a straight-line, 15th Australian Joint Conference on Articial Intelligence, 2002, pp. 225 – 236.

  12. Gerasimov K.V., Zobova A.A. Prikladnaya matematika i mekhanika, 2018, vol. 82, no. 4, pp. 427-440

  13. Bramanta A., Virgono A., Saputra R. Control system implementation and analysis for omniwheel vehicle, 2017 International Conference on Control, Electronics, Renewable Energy and Communications (ICCREC), IEEE, Sep. 2017, available at: https://doi.org/10.1109/iccerec.2017.8226711

  14. Field J., Salman M. Kinematic motion studies of an Omni Directional mobile robot, 2017 IEEE International Symposium on Robotics and Intelligent Sensors (IRIS), IEEE, Oct. 2017, available at: https://doi.org/10.1109/iris.2017.8250141

  15. Huang J., Hung T.V., Tseng M. Smooth Switching Robust Adaptive Control for Omnidirectional Mobile Robots, IEEE Transactions on Control Systems Technology, 2015, vol. 23, no. 5, pp. 1986 – 1993, available at: https://doi.org/10.1109/tcst.2015.2388734

  16. Kalmar-Nagy T. Real-time trajectory generation for omni-directional vehicles by constrained dynamic inversion, Mechatronics, 2016, vol. 35, pp. 44 – 53. available at: https://doi.org/10.1016/j.mechatronics.2015.12.004.

  17. Szayer G., Kovacs B., Tajti F., Korondi P. Feasible utilization of the inherent characteristics of holonomic mobile robots, Robotics and Autonomous Systems, 2017, vol. 94, pp. 12 – 24, available at: https://doi.org/10.1016/j.robot.2017.04.002

  18. Ivanov A. On the control of a robot ball using two omniwheels, Regular and Chaotic Dynamics, 2015, vol. 20, no. 4, pp. 441 – 448, available at: https://doi.org/10.1134/s1560354715040036

  19. Karavaev Yu., Kilin A. The dynamics and control of a spherical robot with an internal omniwheel platform, Regular and Chaotic Dynamics, 2015. vol. 20, no. 2. pp. 134 – 152, available at: https://doi.org/10.1134/s1560354715020033

  20. Weiss A., Langlois R., Hayes M. Dynamics and vibration analysis of the interface between a non-rigid sphere and omnidirectional wheel actuators, Robotica, 2014, vol. 33, no. 09, pp. 1850 – 1868, available at: https://doi.org/10.1017/s0263574714001088

  21. Zhan Q., Cai Y., Yan C. Design, analysis and experiments of an omni-directional spherical robot, 2011 IEEE International Conference on Robotics and Automation, IEEE, 2011, available at: https://doi.org/10.1109/icra.2011.5980491

  22. Nguen N.M. Trudy MAI, 2012, no. 58, available at: http://trudymai.ru/eng/published.php?ID=33459

  23. Taha B.M., Norsehah A.K., Norazlin I., Fazliza S., Murniwati A., Muhammad A.R., Mohamad I.I. Development of mobile robot drive system using mecanum wheels. 2016 International Conference on Advances in Electrical, Electronic and Systems Engineering (ICAEES), IEEE, 2016, available at: https://doi.org/10.1109/icaees.2016.7888113

  24. Tatarinov Ya.V. Vestnik Moskovskogo universiteta. Matematika. Mekhanika, 2003, no. 3, pp. 67 – 76.

  25. Zobova A.A. Nelineinaya dinamika, 2011, vol. 7, no. 4. pp. 771 – 783.

  26. Vilke V.G. Teoreticheskaya mekhanika (Theoretical Mechanics), Saint-Petersburg, Lan’, 2003, 304 p.

  27. Bolotin S.V., Karapetyan A.V., Kugushev E.I., Treshhev D.V. Teoreticheskaya mekhanika (Theoretical Mechanics), Moscow, Academia, 2010, 432 p.


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