Skip to main content
Log in

Kinematic mechanism and path planning of the Essboard

  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

In this paper, we study the kinematic mechanism and path planning for a two-caster nonholonomic vehicle (the Essboard) which is a recent variant of skateboard. Different from the most studied Snakeboard, the Essboard consists of a torsion bar and two platforms, each of which contains a pedal and a caster. We first investigate the relationship between the tilt angles of the pedals and the wheel directions of the casters. This relationship reveals how to control the wheel directions by adjusting the tilt angles. Next, the rotational radius of the Essboard is derived for a given pair of tilt angles of both pedals. The rotational radius of the Essboard is much different than that of the Snakeboard. Then we develop a path-planning algorithm for the Essboard to move from a start position to the goal, using a series of consecutively connected arcs, which are tangent to each other at the connected points. It is shown from a kinematic point of view that the path planning of the Essboard can be solved by a series of pairs of pedals’ tilt angles. Three experiments are conducted to confirm the correctness of the main results. The results in this paper are a foundation for further study of the Essboard.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bloch A M, Antman S S, Marsden J E, et al. Nonholonomic Mechanics and Control. Berlin: Springer, 2003

    Book  MATH  Google Scholar 

  2. Koon W S, Marsden J E. Optimal control for holonomic and nonholonomic mechanical systems with symmetry and lagrangian reduction. SIAM J Control Optim, 1997, 35(3): 901–929

    Article  MathSciNet  MATH  Google Scholar 

  3. Ostrowski J, Lewis A, Murray R, et al. Nonholonomic mechanics and locomotion: The snakeboard example. In: Proc of ICRA 1994, 3: 2391–2397

    Google Scholar 

  4. Kremnev A, Kuleshov A. Nonlinear dynamics and stability of the skateboard. Discrete Cont Dyn-S, 2010, 3(1): 85–103

    Article  MathSciNet  MATH  Google Scholar 

  5. Bullo F, Lewis A. Kinematic controllability and motion planning for the Snakeboard. IEEE Trans Robot Autom, 2003, 19(3): 494–498

    Article  Google Scholar 

  6. Iannitti S, Lynch K. Minimum control-switch motions for the snakeboard: A case study in kinematically controllable underactuated systems. IEEE Trans Robot, 2004, 20(6): 994–1006

    Article  Google Scholar 

  7. Shammas E A, Choset H, Rizzi A A. Towards a unified approach to motion planning for dynamic underactuated mechanical systems with non-holonomic constraints. Int J Robot Res, 2007, 26(10): 1075–1124

    Article  Google Scholar 

  8. Ito S, Takeuchi S, Sasaki M. Motion measurement of a two-wheeled skateboard and its dynamical simulation. Appl Math Modell, 2012, 36(5): 2178–2191

    Article  MathSciNet  MATH  Google Scholar 

  9. Shammas E, de Oliveira M. An analytic motion planning solution for the Snakeboard. In Proc of Robotics: Science and Systems, 2011

    Google Scholar 

  10. Shammas E, de Oliveira M. Motion planning for the Snakeboard. Int J Robot Res, 2012, 31(7): 872–885

    Article  Google Scholar 

  11. Iannitti S, Lynch K. Exact minimum control switch motion planning for the Snakeboard. In Proc of IROS 2003, 2003, 2: 1437–1443

    Google Scholar 

  12. Ispolov Y G, Smolnikov B A. Skateboard dynamics. Comput Meth Appl Mech Eng, 1996, 131(3–4): 327–333

    Article  MATH  Google Scholar 

  13. Ostrowski J, Burdick J. The geometric mechanics of undulatory robotic locomotion. Int J Robot Res, 1998, 17(7): 683–701

    Article  Google Scholar 

  14. Golubev Y F. A method for controlling the motion of a robot snakeboarder. J Appl Math Mech, 2006, 70(3): 319–333

    Article  MathSciNet  Google Scholar 

  15. Ortega L M, Rueda A J, Feito F R. A solution to the path planning problem using angle preprocessing. Robot Auton Syst, 2010, 58(1): 27–36

    Article  Google Scholar 

  16. Liang T, Liu J, Hung G, et al. Practical and flexible path planning for car-like mobile robot using maximal-curvature cubic spiral. Robot Auton Syst, 2005, 52(4): 312–335

    Article  Google Scholar 

  17. Bonfe M, Secchi C. Online smooth trajectory planning for mobile robots by means of nonlinear filters. In Proc of IROS, 2010: 4299–4304

    Google Scholar 

  18. Majumdar A, Tedrake R. Robust online motion planning with regions of finite time invariance. In: Proc of the 10th International Workshop on the Algorithmic Foundations of Robotics, 2012

    Google Scholar 

  19. Muller J, Kohler N, Burgard W. Autonomous miniature blimp navigation with online motion planning and re-planning. In Proc of IROS, 2011: 4941–4946

    Google Scholar 

  20. Hao Y, Agrawal S. Formation planning and control of ugvs with trailers. Auton Robot, 2005, 19: 257–270

    Article  Google Scholar 

  21. Ren D, Zhang J, Zhang J, et al. Trajectory planning and yaw rate tracking control for lane changing of intelligent vehicle on curved road. Sci China Tech Sci, 2011, 54(3): 630–642

    Article  MATH  Google Scholar 

  22. Li Z, Ma S, Li B, et al. Analysis of the constraint relation between ground and self-adaptive mobile mechanism of a transformable wheel-track robot. Sci China Tech Sci, 2011, 54(3): 610–624

    Article  MATH  Google Scholar 

  23. Zhao W, Xu X, Wang C. Multidiscipline collaborative optimization of differential steering system of electric vehicle with motorized wheels. Sci China Tech Sci, 2011, 55(12): 3462–3468

    Article  Google Scholar 

  24. Ostrowski J P, Desai J P, Kumar V. Optimal gait selection for nonholonomic locomotion systems. Int J Robot Res, 2000, 19: 225–237

    Article  Google Scholar 

  25. Kuleshov A S. Various schemes of the skateboard control. Procedia Eng, 2010, 2(2): 3343–3348

    Article  Google Scholar 

  26. Kuleshov A S. Mathematical model of the Snakeboard. Mat Model, 2006, 18(5): 37–48

    MathSciNet  MATH  Google Scholar 

  27. Kuleshov A. Further development of the mathematical model of a Snakeboard. Regul Chaotic Dyn, 2007, 12: 321–334

    Article  MathSciNet  MATH  Google Scholar 

  28. Asnafi A, Mahzoon M. Some new robust pseudo forward and rotation gaits for the Snakeboard. Sci Iran, 2008, 15(5): 644–651

    MathSciNet  Google Scholar 

  29. Asnafi A, Mahzoon M. Some flower-like gaits in the snakeboards locomotion. Nonlinear Dyn, 2007, 48: 77–89

    Article  MathSciNet  MATH  Google Scholar 

  30. Venkataraman P. Applied Optimization with MATLAB Programming. New York: John Wiley & Sons, 2009

    Google Scholar 

  31. Murray R, Sastry S. Nonholonomic motion planning: Steering using sinusoids. IEEE Trans Autom Control, 1993, 38(5): 700–716

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to BaiQuan Su.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Su, B., Wang, T., Wang, J. et al. Kinematic mechanism and path planning of the Essboard. Sci. China Technol. Sci. 56, 1499–1516 (2013). https://doi.org/10.1007/s11431-013-5212-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-013-5212-7

Keywords

Navigation