[go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Trajectory Planning in Robotics

  • Published:
Mathematics in Computer Science Aims and scope Submit manuscript

Abstract

Trajectory planning is a fundamental issue for robotic applications and automation in general. The ability to generate trajectories with given features is a key point to ensure significant results in terms of quality and ease of performing the required motion, especially at the high operating speeds necessary in many applications. The general problem of trajectory planning in Robotics is addressed in the paper, with an overview of the most significant methods, that have been proposed in the robotic literature to generate collision-free paths. The problem of finding an optimal trajectory for a given path is then discussed and some significant solutions are described.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Sciavicco L., Siciliano B., Villani L., Oriolo G.: Robotics. Modelling, Planning and Control. Springer, London (2009)

    Google Scholar 

  2. Latombe J.C.: Robot Motion Planning. Kluwer, Norwell (1991)

    Book  Google Scholar 

  3. Khatib,O.: Real-time obstacle avoidance for manipulators and mobile robots. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 500–505 (1985)

  4. Volpe R.A, Khosla P.K: Manipulator control with superquadric artificial potential functions: theory and experiments. IEEE Trans. Syst. Man Cybern. 20(6), 1423–1436 (1990)

    Article  Google Scholar 

  5. Volpe R.A.: Real and Artificial Forces in the Control of Manipulators: Theory and Experiments. Carnegie Mellon University, The Robotics Institute, Pittsburgh (1990)

    Google Scholar 

  6. Koditschek D.E.: Exact robot navigation using artificial potential functions. IEEE Trans. Robot. Autom. 8(5), 501–518 (1992)

    Article  Google Scholar 

  7. Kim J.O., Khosla P.K.: Real-time obstacle avoidance using harmonic potential functions. IEEE Trans. Robot. Autom. 8(3), 338–349 (1992)

    Article  Google Scholar 

  8. Connoly, C.I., Burns, J.B.: Path planning using Laplace’s equation. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 2102–2106 (1990)

  9. Connoly, C.I., Grupen, RA.: On the application of harmonic functions to robotics. In: Proceedings of the IEEE International Symposium on Intelligent Control, pp. 498–502 (1992)

  10. Guldner J., Utkin V.I.: Sliding mode control for gradient tracking and robot navigation using artificial potential fields. IEEE Trans. Robot. Autom. 11(2), 247–254 (1995)

    Article  Google Scholar 

  11. Ge S.S., Cui Y.J.: New potential functions for mobile robot path planning. IEEE Trans. Robot. Autom. 16(5), 616–620 (2000)

    Article  Google Scholar 

  12. Barraquand J., Latombe J.C.: Robot motion planning: a distributed representation approach. Int. J. Robot. Res. 10(6), 628–649 (1991)

    Article  Google Scholar 

  13. Caselli, S., Reggiani, M., Sbravati, R.: Parallel path planning with multiple evasion strategies. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 260–266 (2002)

  14. Caselli, S., Reggiani M.: ERPP an experience-based randomized path planner. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1002–1008 (2000)

  15. Caselli, S., Reggiani, M., Rocchi R.: Heuristic methods for randomized path planning in potential fields. In: Proceedings of the IEEE International Symposium on Computational Intelligence in Robotics and Automation, pp. 426–431 (2001)

  16. Amato, N.M., Wu, Y.: A randomized roadmap method for path and manipulation planning. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 113–120 (1996)

  17. Hsu D., Kindel R., Latombe J.C., Rock S.: Randomized kinodynamic motion planning with moving obstacles. Int. J. Robot. Res. 21(3), 233–255 (2002)

    Article  Google Scholar 

  18. Nissoux, C., Simon, T., Latombe, J.C.: Visibility based probabilistic roadmaps. In: Proceedings of the IEEE International Conference on Intelligent Robots and Systems, pp. 1316–1321 (1999)

  19. Clark, C.M., Rock S.: Randomized motion planning for groups of nonholomic robots. In: Proceedings of the 6th International Symposium on Artificial Intelligence, Robotics and Automation in Space, pp. 1316–1321 (1999)

  20. Donald, B.R., Xavier, P.G.: Provably good approximation algorithms for optimal kinodynamic planning for Cartesian robots and open chain manipulators. In: Proceedings of the 6th Annual Symposium on Computational Geometry, pp. 290–300 (1990)

  21. Fraichard, T., Laugier, C.: Dynamic trajectory planning, path-velocity decomposition and adjacent paths. In: Proceedings of the 2nd International Joint Conference on Artificial Intelligence, pp. 1592–1597 (1993)

  22. Fiorini, P., Shiller, Z.: Time optimal trajectory planning in dynamic environments. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1553–1558 (1996)

  23. Fraichard T.: Trajectory planning in a dynamic workspace: a state-time space approach. Adv. Robot. 13(1), 74–94 (1999)

    Article  Google Scholar 

  24. Kumar, V., Efran, M., Ostrowski, J.: Motion planning and control of robots. In: Handbook of Industrial Robotics. 2nd edn, Shimon, Y. Nof (ed) (1999)

  25. Gupta K., del Pobil A.P.: Practical Motion Planning in Robotics: Current Approaches and Future Directions. Wiley, West Sussex (1998)

    MATH  Google Scholar 

  26. Bobrow J.E, Dubowsky S., Gibson J.S.: Time-optimal control of robotic manipulators along specified paths. Int. J. Robot. Res. 4(3), 554–561 (1985)

    Article  Google Scholar 

  27. Shin K.G., McKay N.D.: Minimum-time control of robotic manipulators with geometric path constraints. IEEE Trans. Autom. Control 30(6), 531–541 (1985)

    Article  MATH  Google Scholar 

  28. Shin K.G., McKay N.D.: A dynamic programming approach to trajectory planning of robotic manipulators. IEEE Trans. Autom. Control 31(6), 491–500 (1986)

    Article  MATH  Google Scholar 

  29. Balkan T.: A dynamic programming approach to optimal control of robotic manipulators. Mech. Res. Commun. 25(2), 225–230 (1998)

    Article  MATH  Google Scholar 

  30. Croft E.A., Benhabib B., Fenton R.G.: Near time-optimal robot motion planning for on-line applications. J. Robot. Syst. 12(8), 553–567 (1995)

    Article  MATH  Google Scholar 

  31. Pardo-Castellote, G., Cannon, R.H. Jr.: Proximate time-optimal algorithm for on-line path parameterization and modification. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1539–1546 (1996)

  32. Costantinescu, D.: Smooth Time Optimal Trajectory Planning for Industrial Manipulators. PhD Thesis, The University of British Columbia (1998)

  33. Constantinescu D., Croft E.A.: Smooth and time-optimal trajectory planning for industrial manipulators along specified paths. J. Robot. Syst. 17(5), 233–249 (2000)

    Article  MATH  Google Scholar 

  34. Shiller Z.: Time-energy optimal control of articulated systems with geometric path constraints. J. Dyn. Syst. Meas. Control 11(8), 139–143 (1996)

    Article  Google Scholar 

  35. Lin C.S., Chang P.R., Luh J.Y.S: Formulation and optimization of cubic polynomial joint trajectories for industrial robots. IEEE Trans. Autom. Control 28(12), 1066–1073 (1983)

    Article  MATH  Google Scholar 

  36. Wang C.H., Horng J.G.: Constrained minimum-time path planning for robot manipulators via virtual knots of the cubic B-Spline functions. IEEE Trans. Autom. Control 35(5), 573–577 (1990)

    Article  MATH  Google Scholar 

  37. Piazzi A., Visioli A.: Global minimum-time trajectory planning of mechanical manipulators using interval analysis. Int. J. Control 71(4), 631–652 (1988)

    Article  MathSciNet  Google Scholar 

  38. Piazzi, A., Visioli, A.: A global optimization approach to trajectory planning for industrial robots. In: Proceedings of the IEEE-RSJ International Conference on Intelligent Robots and Systems, pp. 1553–1559 (1997)

  39. Piazzi, A.,Visioli, A.: A cutting-plane algorithm for minimum-time trajectory planning of industrial robots. In: Proceedings of the 36th Conference on Decision and Control, pp. 1216–1218 (1997)

  40. Horst, R., Pardalos, P.M. (eds): Handbook of Global Optimization. Kluwer, Dordrecht (1995)

    MATH  Google Scholar 

  41. Guarino Lo Bianco, C., Piazzi, A.: A semi-infinite optimization approach to optimal spline trajectory planning of mechanical manipulators. In: Goberna e, M.A., Lopez, M.A. (eds.) Semi-infinite Programming: Recent Advances (2001)

  42. GuarinoLo Bianco C., Piazzi A.: A hybrid algorithm for infinitely constrained optimization. Int. J. Syst. Sci. 32(1), 271–297 (2001)

    MathSciNet  Google Scholar 

  43. Cao, B., Dodds, G.I.: Time-optimal and smooth constrained path planning for robot manipulators. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1853–1858 (1994)

  44. Dong J., Ferreira P.M., Stori J.A.: Feed-rate optimization with jerk constraints for generating minimum-time trajectories. Int. J. Mach. Tools Manuf. 47(12), 1941–1955 (2007)

    Article  Google Scholar 

  45. van Dijk, N.J.M., van de Wouw, N., Nijmeijer, H., Pancras, W.C.M.: Path-constrained motion planning for robotics based on kinematic constraints. In: Proceedings of the ASME IDETC/CIE Conference, pp. 1–10 (2007)

  46. Dongmei, X., Daokui, Q., Fang, X.: Path constrained time-optimal robot control. In: Proceedings of the International Conference on Robotics and Biomimetics, pp. 1095–1100 (2006)

  47. Tangpattanakul, P., Artrit, P.: Minimum-Time Trajectory of Robot Manipulator Using Harmony Search Algorithm. In: Proceedings of the IEEE 6th International Conference on ECTI-CON, pp. 354–357 (2009)

  48. Joonyoung K., Sung-Rak K., Soo-Jong K., Dong-Hyeok K.: A practical approach for minimum-time trajectory planning for industrial robots. Ind. Robots Int. J. 37(1), 51–61 (2010)

    Article  Google Scholar 

  49. Saramago S.F.P, Steffen V. Jr: Optimization of the trajectory planning of robot manipulators tacking into account the dynamics of the system. Mech. Mach. Theory 33(7), 883–894 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  50. Saramago S.F.P, Steffen V. Jr: Optimal trajectory planning of robot manipulators in the presence of moving obstacles. Mech. Mach. Theory 35(7), 1079–1094 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  51. Saravan R., Ramabalan S., Balamurugan C.: Evolutionary multi-criteria trajectory modeling of industrial robots in the presence of obstacles. Eng. Appl. Artif. Intell. 22, 329–342 (2009)

    Article  Google Scholar 

  52. Verscheure, D., Demeulenaere, B., Swevers, J., De Schutter, J., Diehl, M.: Time-energy optimal path tracking for robots: a numerically efficient optimization approach. In: Proceedings of the 10th International Workshop on Advanced Motion Control, pp. 727–732 (2008)

  53. Xu, H., Zhuang, J., Wang, S., Zhu, Z.: Global Time-Energy Optimal Planning of Robot Trajectories. In: Proceedings of the International Conference on Mechatronics and Automation, pp. 4034–4039 (2009)

  54. Martin B.J., Bobrow J.E.: Minimum effort motions for open chain manipulators with task-dependent end-effector constraints. Int. J. Robot. Res. 18(2), 213–224 (1999)

    Google Scholar 

  55. Simon D.: The application of neural networks to optimal robot trajectory planning. Robot. Autonom. Syst. 11, 23–34 (1993)

    Article  Google Scholar 

  56. Bobrow J.E., Martin B., Sohl G., Wang E.C., Park F.C., Kim J.: Optimal robot motion for physical criteria. J. Robot. Syst. 18(12), 785–795 (2001)

    Article  MATH  Google Scholar 

  57. Kyriakopoulos, K.J., Saridis, G.N.: Minimum jerk path generation. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 364–369 (1998)

  58. Simon D., Isik C.: A trigonometric trajectory generator for robotic arms. Int. J. Control 57(3), 505–517 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  59. Piazzi, A., Visioli, A.: An interval algorithm for minimum-jerk trajectory planning of robot manipulators. In: Proceedings of the 36th Conference on Decision and Control, pp. 1924–1927 (1997)

  60. Piazzi A., Visioli A.: Global minimum-jerk trajectory planning of robot manipulators. IEEE Trans. Ind. Electron. 47(1), 140–149 (2000)

    Article  Google Scholar 

  61. Corke, P.I.: Robotics toolbox for Matlab. Available on http://petercorke.com/RoboticsToolbox.html, 2010

  62. Huang P., Xu Y., Liang B.: Global minimum-jerk trajectory planning of space manipulator. Int. J. Control Autom. Syst. 4(4), 405–413 (2006)

    Google Scholar 

  63. Petrinec, K., Kovacic, Z.: Trajectory planning algorithm based on the continuity of jerk. In: Proceedings of the Mediterranean Conference on Control and Automation, pp. 1–5 (2007)

  64. Gasparetto A., Zanotto V.: A new method for smooth trajectory planning of robot manipulators. Mech. Mach. Theory 42(4), 455–471 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  65. Gasparetto A., Zanotto V.: A technique for time-jerk optimal planning of robot trajectories. Robot. Comput. Integr. Manuf. 24(3), 415–426 (2008)

    Article  Google Scholar 

  66. Gasparetto, A., Lanzutti, A., Vidoni, R., Zanotto, V.: Trajectory planning for manufacturing robots: algorithm definition and experimental results. In: Proceedings of the ASME 10th Biennial Conference on Engineering Systems Design and Analysis, pp. 609–618 (2010)

  67. Lombai, F., Szederkenyi, G.: Trajectory tracking control of a 6-degree-of-freedom robot arm using nonlinear optimization. In: Proceedings of the IEEE International Workshop on Advanced Motion Control, pp. 655–660 (2008)

  68. Lombai, F., Szederkenyi, G.: Throwing motion generation using nonlinear optimization on a 6-degree-of-freedom robot manipulator. In: Proceedings of the IEEE IInternational Conference on Mechatronics, pp. 1–6 (2009)

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Elettrica, Gestionale e Meccanica, Universita’ di Udine, Via delle Scienze 208, 33100, Udine, Italy

    Alessandro Gasparetto, Paolo Boscariol & Albano Lanzutti

  2. Faculty of Science and Technology, Free University of Bolzano-Bozen, Piazza Universita’ 5, 39100, Bolzano, Italy

    Renato Vidoni

Authors
  1. Alessandro Gasparetto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paolo Boscariol
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Albano Lanzutti
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Renato Vidoni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alessandro Gasparetto.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gasparetto, A., Boscariol, P., Lanzutti, A. et al. Trajectory Planning in Robotics. Math.Comput.Sci. 6, 269–279 (2012). https://doi.org/10.1007/s11786-012-0123-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11786-012-0123-8

Keywords

Mathematics Subject Classification (2000)

Search

Navigation