The dynamics and control of a spherical robot with an internal omniwheel platform

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• 作者：Yury L. Karavaev (1)
  Alexander A. Kilin (2)
  
  1. M. T. Kalashnikov Izhevsk State Technical University ; ul. Studencheskaya 7 ; Izhevsk ; 426069 ; Russia
  2. Udmurt State University ; ul. Universitetskaya 1 ; Izhevsk ; 426034 ; Russia
  
• 关键词：93B18 ; 93B52 ; spherical robot ; kinematic model ; dynamic model ; nonholonomic constraint ; omniwheel
• 刊名：Regular and Chaotic Dynamics
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：20
• 期：2
• 页码：134-152
• 全文大小：879 KB
• 参考文献：1. Kilin, AA (2001) The Dynamics of Chaplygin Ball: The Qualitative and Computer Analysis. Regul. Chaotic Dyn. 6: pp. 291-306 CrossRef
  2. Borisov, A V, Mamaev, I S, Kilin, AA (2002) The Rolling Motion of a Ball on a Surface: New Integrals and Hierarchy of Dynamics. Regul. Chaotic Dyn. 7: pp. 201-219 CrossRef
  3. Chase, R, Pandya, A (2012) A Review of Active Mechanical Driving Principles of Spherical Robots. Robotics 1: pp. 3-23 CrossRef
  4. Crossley, VA (2006) A Literature Review on the Design of Spherical Rolling Robots.
  5. Ylikorpi, T, Suomela, J Ball-Shaped Robots. In: Zhang, H eds. (2007) Climbing and Walking Robots: Towards New Applications. InTech, Vienna
  Borisov, A V, Mamaev, I S, Karavaev, Yu L eds. (2013) Mobile Robots: Ball-Shaped Robot and Wheel Robot. R&C Dynamics, Institute of Computer Science, Izhevsk
  6. Borisov, A V, Kilin, AA, Mamaev, I S (2011) An Omni-Wheel Vehicle on a Plane and a Sphere. Rus. J. Nonlin. Dyn. 7: pp. 785-801
  7. Chen, W-H, Chen, Ch-P, Yu, W-Sh, Lin, Ch-H, Lin, P-Ch (2012) Design and Implementation of an Omnidirectional Spherical Robot Omnicron. IEEE/ASME Internat. Conf. on Advanced Intelligent Mechatronics. pp. 719-724
  8. Borisov, A V, Kilin, AA, Mamaev, I S (2012) How To Control Chaplygin鈥檚 Sphere Using Rotors. Regul. Chaotic Dyn. 17: pp. 258-272 CrossRef
  9. Borisov, A V, Kilin, AA, Mamaev, I S (2013) How To Control Chaplygin鈥檚 Sphere Using Rotors: 2. Regul. Chaotic Dyn. 18: pp. 144-158 CrossRef
  10. Svinin, M, Morinaga, A, Yamamoto, M (2013) On the Dynamic Model and Motion Planning for a Spherical Rolling Robot Actuated by Orthogonal Internal Rotors. Regul. Chaotic Dyn. 18: pp. 126-143 CrossRef
  11. Morinaga, A, Svinin, M, Yamamoto, M (2014) A Motion Planning Strategy for a Spherical Rolling Robot Driven by Two Internal Rotors. IEEE Trans. on Robotics 30: pp. 993-1002 CrossRef
  12. Svinin, M., Morinaga, A., and Yamamoto, M., On the Dynamic Model and Motion Planning for a Class of Spherical Rolling Robots, in / Proc. of the IEEE Internat. Conf. on Robotics and Automation (ICRA, 14鈥?8 May, 2012), pp. 3226鈥?231.
  13. Kazakov, A O (2013) Strange Attractors and Mixed Dynamics in the Problem of an Unbalanced Rubber Ball Rolling on a Plane. Regul. Chaotic Dyn. 18: pp. 508-520 CrossRef
  14. Ivanova, T B, Pivovarova, E N (2013) Dynamics and Control of a Spherical Robot with an Axisymmetric Pendulum Actuator. Rus. J. Nonlin. Dyn. 9: pp. 507-520
  15. Koshiyama, A, Yamafuji, K (1993) Design and Control of an All-Direction Steering Type Mobile Robot. Int. J. Robot. Res. 12: pp. 411-419 CrossRef
  16. Balandin, D V, Komarov, MA, Osipov, G V (2013) A Motion Control for a Spherical Robot with Pendulum Drive. J. Comput. Sys. Sc. Int. 52: pp. 650-663 CrossRef
  17. Kayacan, E, Bayraktaroglu, Z Y, Saeys, W (2012) Modeling and Control of a Spherical Rolling Robot: A Decoupled Dynamics Approach. Robotica 30: pp. 671-680 CrossRef
  18. Yoon, J.-C., Ahn, S.-S., and Lee, Y.-J., Spherical Robot with New Type of Two-Pendulum Driving Mechanism, in / Proc. 15th IEEE Internat. Conf. on Intelligent Engineering Systems (INES) (Poprad, High Tatras, Slovakia, 2011), pp. 275鈥?79.
  19. Zhao, B., Li, M., Yu, H., Hu, H., and Sun, L., Dynamics and Motion Control of a Two Pendulums Driven Spherical Robot, in / Proc. of the 2010 IEEE/RSJ Internat. Conf. on Intelligent Robots and Systems (IROS) (Taipei, Taiwan, October 2010), pp. 147鈥?53.
  20. Bolsinov, AV, Borisov, A V, Mamaev, I S (2012) Rolling of a Ball without Spinning on a Plane: The Absence of an Invariant Measure in a System with a Complete Set of Integrals. Regul. Chaotic Dyn. 17: pp. 571-579 CrossRef
  21. Borisov, A V, Fedorov, Yu N, Mamaev, I S (2008) Chaplygin Ball over a Fixed Sphere: An Explicit Integration. Regul. Chaotic Dyn. 13: pp. 557-571 CrossRef
  22. Borisov, A V, Mamaev, I S (2007) Rolling of a Non-Homogeneous Ball over a Sphere without Slipping and Twisting. Regul. Chaotic Dyn. 12: pp. 153-159 CrossRef
  23. Borisov, AV, Mamaev, I S (2007) Isomorphism and Hamilton Representation of Some Nonholonomic Systems. Siberian Math. J. 48: pp. 26-36 CrossRef
  24. Ahn, S-S, Lee, Y-J (2014) Novel Spherical Robot with Hybrid Pendulum Driving Mechanism. Adv. Mech. Eng. 2014: pp. 456727
  25. Forbes, JR, Barfoot, T D, Damaren, Ch J (2010) Dynamic Modeling and Stability Analysis of a Power-Generating Tumbleweed Rover. Multibody Syst. Dyn. 24: pp. 413-439 CrossRef
  26. Hartl, AE, Mazzoleni, AP (2010) Dynamic Modeling of a Wind-Driven Tumbleweed Rover Including Atmospheric Effects. J. of Spacecraft and Rockets 47: pp. 493-502 CrossRef
  27. Hartl, A E, Mazzoleni, AP (2008) Parametric Study of Spherical Rovers Crossing a Valley. J. Guid. Control Dynam. 31: pp. 775-779 CrossRef
  28. Hogan, FR, Forbes, JR (2014) Modeling of Spherical Robots Rolling on Generic Surfaces. Multibody Syst. Dyn..
  29. Hogan, FR, Forbes, JR, Barfoot, TD (2014) Rolling Stability of a Power-Generating Tumbleweed Rover. J. of Spacecraft and Rockets 51: pp. 1895-1906 CrossRef
  30. Lee, J. and Park, W., Design and Path Planning for a Spherical Rolling Robot, in / ASME Internat. Mechanical Engineering Congress and Exposition (San Diego, Calif., Nov. 15鈥?1, 2013): Vol. 4A. Dynamics, Vibration and Control, IMECE2013-64994, 8 pp.
  31. Yu, T, Sun, H, Jia, Q, Zhang, Y, Zhao, W (2013) Stabilization and Control of a Spherical Robot on an Inclined Plane. Res. J. Appl. Sci. Eng. Technology 5: pp. 2289-2296
  32. Kilin, AA, Karavaev, Yu L (2014) The Kinematic Control Model for a Spherical Robot with an Unbalanced Internal Omniwheel Platform. Rus. J. Nonlin. Dyn. 10: pp. 497-511
  33. Borisov, A V, Kilin, AA, Mamaev, I S (2012) Generalized Chaplygin鈥檚 Transformation and Explicit Integration of a System with a Spherical Support. Regul. Chaotic Dyn. 17: pp. 170-190 CrossRef
  34. Borisov, A V, Kilin, AA, Mamaev, I S (2011) Rolling of a Homogeneous Ball over a Dynamically Asymmetric Sphere. Regul. Chaotic Dyn. 16: pp. 465-483 CrossRef
  35. Borisov, AV, Mamaev, I S (2005) Rigid Body Dynamics: Hamiltonian Methods, Integrability, Chaos. R&C Dynamics, Institute of Computer Science, Izhevsk
  36. Kilin, AA, Karavaev, Yu L, Klekovkin, A V (2014) Kinematic Control of a High Manoeuvrable Mobile Spherical Robot with Internal Omni-Wheeled Platform. Rus. J. Nonlin. Dyn. 10: pp. 113-126
  37. Borisov, A V, Mamaev, I S (2007) Rolling of a Non-Homogeneous Ball over a Sphere without Slipping and Twisting. Regul. Chaotic Dyn. 12: pp. 153-159 CrossRef
  38. Borisov, A V, Mamaev, I S, Bizyaev, I A (2013) The Hierarchy of Dynamics of a Rigid Body Rolling without Slipping and Spinning on a Plane and a Sphere. Regul. Chaotic Dyn. 8: pp. 277-328 CrossRef
  39. Bolsinov, AV, Borisov, A V, Mamaev, I S (2012) Rolling of a Ball without Spinning on a Plane: The Absence of an Invariant Measure in a System with a Complete Set of Integrals. Regul. Chaotic Dyn. 17: pp. 571-579 CrossRef
  40. Koiller, J, Ehlers, K M (2007) Rubber Rolling over a Sphere. Regul. Chaotic Dyn. 12: pp. 127-152 CrossRef
  41. Borisov, AV, Kazakov, AO, Sataev, IR (2014) The Reversal and Chaotic Attractor in the Nonholonomic Model of Chaplygin鈥檚 Top. Regul. Chaotic Dyn. 19: pp. 718-733 CrossRef
  42. Borisov, AV, Kazakov, AO, Kuznetsov, SP (2014) Nonlinear Dynamics of the Rattleback: A Nonholonomic Model. Physics-Uspekhi 57: pp. 453-460 CrossRef
  43. Borisov, AV, Mamaev, I S (2003) Strange Attractors in Rattleback Dynamics. Physics-Uspekhi 46: pp. 393-403 CrossRef
  44. Borisov, A V, Kilin, AA, Mamaev, I S (2006) New Effects in Dynamics of Rattlebacks. Dokl. Phys. 51: pp. 272-275 CrossRef
  45. Vetchanin, E V, Mamaev, I S, Tenenev, V A (2013) The Self-Propulsion of a Body with Moving Internal Masses in a Viscous Fluid. Regul. Chaotic Dyn. 18: pp. 100-117 CrossRef
  46. Bolotin, S V, Popova, T V (2013) On the Motion of a Mechanical System inside a Rolling Ball. Regul. Chaotic Dyn. 18: pp. 159-165 CrossRef
  47. Rutstam, N (2013) High Frequency Behavior of a Rolling Ball and Simplification of the Separation Equation. Regul. Chaotic Dyn. 18: pp. 226-236 CrossRef
  48. Borisov, A V, Mamaev, I S (2013) Topological Analysis of an Integrable System Related to the Rolling of a Ball on a Sphere. Regul. Chaotic Dyn. 18: pp. 356-371 CrossRef
  49. Borisov, A V, Mamaev, I S (2013) The Dynamics of the Chaplygin Ball with a Fluid-Filled Cavity. Regul. Chaotic Dyn. 18: pp. 490-496 CrossRef
  50. Gonchenko, A S, Gonchenko, SV, Kazakov, AO (2013) Richness of Chaotic Dynamics in Nonholonomic Models of a Celtic Stone. Regul. Chaotic Dyn. 18: pp. 521-538 CrossRef
  51. Borisov, A V, Kilin, AA, Mamaev, I S (2013) The Problem of Drift and Recurrence for the Rolling Chaplygin Ball. Regul. Chaotic Dyn. 18: pp. 832-859 CrossRef
  52. Takano, H (2014) Spin Reversal of a Rattleback with Viscous Friction. Regul. Chaotic Dyn. 19: pp. 81-99 CrossRef
  53. Mamaev, I S, Ivanova, T B (2014) The Dynamics of a Rigid Body with a Sharp Edge in Contact with an Inclined Surface in the Presence of Dry Friction. Regul. Chaotic Dyn. 19: pp. 116-139 CrossRef
  54. Ivanova, T B, Pivovarova, E N (2014) Comments on the Paper by A. V. Borisov, A. A. Kilin, I. S. Mamaev 鈥淗ow To Control the Chaplygin Ball Using Rotors: 2鈥? Regul. Chaotic Dyn. 19: pp. 140-143 CrossRef
  55. Bizyaev, IA, Borisov, AV, Mamaev, I S (2014) The Dynamics of Nonholonomic Systems Consisting of a Spherical Shell with a Moving Rigid Body Inside. Regul. Chaotic Dyn. 19: pp. 198-213 CrossRef
  56. Burlakov, D, Treschev, D (2014) A Rigid Body on a Surface with Random Roughness. Regul. Chaotic Dyn. 18: pp. 296-309 CrossRef
  57. Borisov, AV, Erdakova, NN, Ivanova, TB, Mamaev, I S (2014) The Dynamics of a Body with an Axisymmetric Base Sliding on a Rough Plane. Regul. Chaotic Dyn. 19: pp. 607-634 CrossRef
  58. Borisov, A V, Mamaev, I S, Kilin, AA (2008) Stability of Steady Rotations in the Nonholonomic Routh Problem. Regul. Chaotic Dyn. 13: pp. 239-249 CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Dynamical Systems and Ergodic Theory
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1468-4845

文摘

This paper deals with the problem of a spherical robot propelled by an internal omniwheel platform and rolling without slipping on a plane. The problem of control of spherical robot motion along an arbitrary trajectory is solved within the framework of a kinematic model and a dynamic model. A number of particular cases of motion are identified, and their stability is investigated. An algorithm for constructing elementary maneuvers (gaits) providing the transition from one steady-state motion to another is presented for the dynamic model. A number of experiments have been carried out confirming the adequacy of the proposed kinematic model.