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Nonholonomic dynamics and control of a spherical robot with an internal omniwheel platform: Theory and experiments

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Abstract

We present the results of theoretical and experimental investigations of the motion of a spherical robot on a plane. The motion is actuated by a platform with omniwheels placed inside the robot. The control of the spherical robot is based on a dynamic model in the nonholonomic statement expressed as equations of motion in quasivelocities with indeterminate coefficients. A number of experiments have been carried out that confirm the adequacy of the dynamic model proposed.

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References

  1. S.-S. Ahn and Y.-J. Lee, “Novel spherical robot with hybrid pendulum driving mechanism,” Adv. Mech. Eng. 2014, 456727 (2014).

    Google Scholar 

  2. I. A. Bizyaev, A. V. Borisov, and I. S. Mamaev, “The dynamics of nonholonomic systems consisting of a spherical shell with a moving rigid body inside,” Regul. Chaotic Dyn. 19(2), 198–213 (2014) [Nelinein. Din. 9(3), 547–566 (2013)].

    Article  MathSciNet  MATH  Google Scholar 

  3. A. V. Borisov, Yu. L. Karavaev, I. S. Mamaev, N. N. Erdakova, T. B. Ivanova, and V. V. Tarasov, “Experimental investigation of the motion of a body with an axisymmetric base sliding on a rough plane,” Regul. Chaotic Dyn. 20(5), 518–541 (2015) [Nelinein. Din. 11(3), 547–577 (2015)].

    Article  MathSciNet  MATH  Google Scholar 

  4. A. V. Borisov, A. A. Kilin, and I. S. Mamaev, “How to control the Chaplygin ball using rotors. II,” Regul. Chaotic Dyn. 18(1–2), 144–158 (2013) [Nelinein. Din. 9(1), 59–76 (2013)].

    Article  MathSciNet  MATH  Google Scholar 

  5. A. V. Borisov, A. A. Kilin, and I. S. Mamaev, “Dynamics and control of an omniwheel vehicle,” Regul. Chaotic Dyn. 20(2), 153–172 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  6. A. V. Borisov and I. S. Mamaev, “Equations of motion of non-holonomic systems,” Usp. Mat. Nauk 70(6), 203–204 (2015) [Russ. Math. Surv. 70, 1167–1169 (2015)].

    Article  MathSciNet  MATH  Google Scholar 

  7. A. V. Borisov and I. S. Mamaev, “Notes on new friction models and nonholonomic mechanics,” Usp. Fiz. Nauk 185(12), 1339–1341 (2015) [Phys. Usp. 58, 1220–1222 (2015)].

    Article  Google Scholar 

  8. A. V. Borisov, I. S. Mamaev, and I. A. Bizyaev, “The Jacobi integral in nonholonomic mechanics,” Regul. Chaotic Dyn. 20(3), 383–400 (2015) [Nelinein. Din. 11(2), 377–396 (2015)].

    Article  MathSciNet  MATH  Google Scholar 

  9. R. Chase and A. Pandya, “A review of active mechanical driving principles of spherical robots,” Robotics 1(1), 3–23 (2012).

    Article  Google Scholar 

  10. W.-H. Chen, C.-P. Chen, W.-S. Yu, C.-H. Lin, and P.-C. Lin, “Design and implementation of an omnidirectional spherical robot Omnicron,” in Proc. 2012 IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics, Kaohsiung (Taiwan), 2012 (IEEE, Piscataway, NJ, 2012), pp. 719–724.

    Chapter  Google Scholar 

  11. V. A. Crossley, “A literature review on the design of spherical rolling robots,” Preprint (Carnegie Mellon Univ., Pittsburgh, PA, 2006).

    Google Scholar 

  12. F. R. Hogan and J. R. Forbes, “Modeling of spherical robots rolling on generic surfaces,” Multibody Syst. Dyn. 35(1), 91–109 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  13. T. B. Ivanova and E. N. Pivovarova, “Comments on the paper by A.V. Borisov, A.A. Kilin, I.S. Mamaev ‘How to control the Chaplygin ball using rotors. II’,” Regul. Chaotic Dyn. 19(1), 140–143 (2014) [Nelinein. Din. 10(1), 127–132 (2014)].

    Article  MathSciNet  MATH  Google Scholar 

  14. Yu. L. Karavaev and A. A. Kilin, “The dynamics and control of a spherical robot with an internal omniwheel platform,” Regul. Chaotic Dyn. 20(2), 134–152 (2015) [Nelinein. Din. 11(1), 187–204 (2015)].

    Article  MathSciNet  MATH  Google Scholar 

  15. J. Lee and W. Park, “Design and path planning for a spherical rolling robot,” in Proc. ASME 2013 International Mechanical Engineering Congress and Exposition (ASME, 2013, paper no. IMECE2013-64994).

    Google Scholar 

  16. M. Svinin, Y. Bai, and M. Yamamoto, “Dynamic model and motion planning for a pendulum-actuated spherical rolling robot,” in Robotics and Automation: Proc. 2015 IEEE Int. Conf. (ICRA) (IEEE, Piscataway, NJ, 2015), pp. 656–661.

    Chapter  Google Scholar 

  17. T. Ylikorpi, P. Forsman, A. Halme, and J. Saarinen, “Unified representation of decoupled dynamic models for pendulum-driven ball-shaped robots,” in Proc. 28th Eur. Conf. on Modelling and Simulation, Brescia, 2014 (ECMS, 2014), pp. 411–420.

    Google Scholar 

  18. T. Ylikorpi and J. Suomela, “Ball-shaped robots,” in Climbing and Walking Robots: Towards New Applications, Ed. by H. Zhang (I-Tech Educ. Publ., Vienna, 2007), pp. 235–256.

    Google Scholar 

  19. T. Yu, H. Sun, Q. Jia, Y. Zhang, and W. Zhao, “Stabilization and control of a spherical robot on an inclined plane,” Res. J. Appl. Sci. Eng. Technol. 5(6), 2289–2296 (2013).

    Google Scholar 

  20. Q. Zhan, “Motion planning of a spherical mobile robot,” in Motion and Operation Planning of Robotic Systems: Background and Practical Approaches (Springer, Cham, 2015), pp. 361–381.

    Google Scholar 

  21. M. Zheng, Q. Zhan, J. Liu, and Y. Cai, “Control of a spherical robot: Path following based on nonholonomic kinematics and dynamics,” Chin. J. Aeronaut. 24(3), 337–345 (2011).

    Article  Google Scholar 

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Authors and Affiliations

  1. Kalashnikov Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069, Russia

    Yu. L. Karavaev

  2. Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia

    Yu. L. Karavaev & A. A. Kilin

Authors
  1. Yu. L. Karavaev
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  2. A. A. Kilin
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Correspondence to Yu. L. Karavaev.

Additional information

Original Russian Text © Yu.L. Karavaev, A.A. Kilin, 2016, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Vol. 295, pp. 174–183.

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Karavaev, Y.L., Kilin, A.A. Nonholonomic dynamics and control of a spherical robot with an internal omniwheel platform: Theory and experiments. Proc. Steklov Inst. Math. 295, 158–167 (2016). https://doi.org/10.1134/S0081543816080095

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