A Path-level Smooth Transition Method with Curvature Bound between Non-smoothly Connected Paths

매끄럽지 않게 연결된 두 곡선에 대해 제한된 곡률로 부드럽게 연결할 수 있는 천이 궤적 생성 방법

  • Published : 2008.07.25

Abstract

For a smooth transition between consecutive paths, conventional robot controllers usually generate a transition trajectory by blending consecutive paths in a time coordinate. However, this has two inherent drawbacks: the shape of a transition path cannot be designed coherently and the speed during transition is uncontrollable. To overcome these problems, this paper provides a path-level, rather than trajectory-level, smooth transition method with the curvature bound between non-smoothly connected paths. The experiment results show that the resultant transition trajectory is more smoothly connected than the conventional methods and the curvature is closely limited to the desired bound within the guaranteed level ($0.02{\sim}1$).

연속적인 경로 사이를 부드러운 곡선으로 잇기 위해서 기존의 로봇 제어기들은 일반적으로 연속적인 경로를 시간 축에서 합성하는 방법을 사용해 왔다. 하지만 이런 방법은 다음과 같은 두 가지 단점을 내재하고 있다. 천이 경로의 형태가 연접하게 생성될 수 없다는 점과 천이하는 동안 속력을 제어할 수 없다는 점이 그것이다. 이러한 문제점들을 극복하기 위해서 본 논문은 매끄럽지 않게 연결된 두 경로들을 부드럽게 잇기 위해 곡률이 제한된 새로운 천이 궤적 생성 방법을 제시하고자 한다. 실험 결과는 기존의 방법들보다 천이 궤적이 더 부드럽게 생성되는 것을 보여주며, 또한 보장된 곡률의 제한 수준은 $0.02{\sim}1$임을 보여준다.

Keywords

References

  1. R. P. Paul, Robot Manipulators: Mathematics, Programming, and Control, MIT Press, Massachusets, 1981
  2. R.H. Taylor, "Planning and execution of straight line manipulator trajectories", IBM J. Res. Develop., Vol. 23, no. 4, pp.454-436, July 1979
  3. R. Volpe, "Task space velocity blending for real-time trajectory generation", Proc. of IEEE Conf. on Robo. Automa., Vol. 2, pp. 680-687, May 1993
  4. J. Lloyd, and V. Hayward, "Trajectory generation for sensor-driven and time-varying tasks", Int. J. Robo. Res., Vol. 12, no. 4, pp. 380-393, 1993 https://doi.org/10.1177/027836499301200405
  5. C. Guarino Lo Bianco, and A. Piazzi, "Optimal trajectory planning with quintic $G^2$-splines", Proc. IEEE Intelli. Vehi. Sym., pp.620-625, Oct. 2000
  6. A. Piazzi, C. Guarino Lo Bianco, M. Bertozzi, A. Fascioli, and A. Broggi, "Quintic G2-splines for the iterative steering of vision based autonomous vehicles", IEEE Trans. on Intelli. Trans. Sys., Vol. 3, no. 1, pp.27-36, March 2002 https://doi.org/10.1109/6979.994793
  7. K. Erkorkmaz, and Y. Altintas, "High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation", Int. J. Mach. Tools Manuf., Vol. 44, no. 9, pp. 1323-1345, July 2001
  8. S. Macfarlane, and E.A. Croft. "Jerk-bounded manipulator trajectory planning: Design for real-time applications", IEEE Trans. on Robot. Automa., Vol. 19, no. 1, pp. 42-52, Feb. 2003 https://doi.org/10.1109/TRA.2002.807548
  9. S.H. Nam, and M.Y. Yang. "A study on a generalized parametric interpolator with real-time jerk-limited acceleration", Computer-Aided Design, Vol. 36, no. 1, pp. 27-36, Jan. 2004 https://doi.org/10.1016/S0010-4485(03)00066-6
  10. S.Y. Jeong, Y.J. Choi, P. Park, and S.G. Choi. "Jerk limited velocity profile generation for high speed industrial robot trajectories", IFAC World Cong., Prague, Czech Rep., July 2005
  11. M. Shpitalni, Y. Koren, and C.C. Lo, "Realtime curve interpolators", Computer-Aided Design, Vol. 26, no. 11, pp. 832-838, Nov. 1994 https://doi.org/10.1016/0010-4485(94)90097-3
  12. D.C.H. Yang, and T. Kong, "Parametric interpolator versus linear interpolator for precision CNC machining", Computer-Aided Design, Vol. 26, no. 3, pp. 225-234, March 1994 https://doi.org/10.1016/0010-4485(94)90045-0
  13. X. Zhiming, C. Jincheng, and F. Zhengjin. "Performance evaluation of a real-time interpolation algorithm for NURBS curves", Int. J. Adv. Manuf. Tech., Vol. 20, no. 4, pp. 270-276, Aug. 2002 https://doi.org/10.1007/s001700200152
  14. L. Sciavicco L, and B. Siciliano, Modeling and Control of Robot Manipulators, Springer, London, 2000
  15. R.T. Farouki, and Y.F. Tsai, "Exact taylor series coefficients for variable-feedrate CNC curve interpolators", Computer-Aided Design, Vol. 33, no. 2, pp. 155-165, Feb. 2001 https://doi.org/10.1016/S0010-4485(00)00085-3
  16. D.T. Greenwood. Principles of Dynamics, Prentice-Hall, New Jersey, 1980
  17. S.Y. Jeong, Y.J. Choi, and P. Park, "Parametric interpolation using sampled data", Computer- Aided Design, Vol. 38, no. 1, pp. 39-47, Jan. 2006 https://doi.org/10.1016/j.cad.2005.06.002