Skip to main content

Incremental Motion Reshaping of Autonomous Dynamical Systems

  • Conference paper
  • First Online:
Human-Friendly Robotics 2019 (HFR 2019)

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 12))

Included in the following conference series:

  • 373 Accesses

Abstract

This paper presents an approach to incrementally learn a reshaping term that modifies the trajectories of an autonomous dynamical system without affecting its stability properties. The reshaping term is considered as an additive control input and it is incrementally learned from human demonstrations using Gaussian process regression. We propose a novel parametrization of this control input that preserves the time-independence and the stability of the reshaped system, as analytically proved in the performed Lyapunov stability analysis. The effectiveness of the proposed approach is demonstrated with simulations and experiments on a real robot.

M. Saveriano—This work was carried out when the author was at the Human-centered Assistive Robotics, Technical University of Munich.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Saveriano, M., Lee, D.: Point cloud based dynamical system modulation for reactive avoidance of convex and concave obstacles. In: International Conference on Intelligent Robots and Systems, pp. 5380–5387 (2013)

    Google Scholar 

  2. Saveriano, M., Lee, D.: Distance based dynamical system modulation for reactive avoidance of moving obstacles. In: International Conference on Robotics and Automation, pp. 5618–5623 (2014)

    Google Scholar 

  3. Blocher, C., Saveriano, M., Lee, D.: Learning stable dynamical systems using contraction theory. In: Ubiquitous Robots and Ambient Intelligence, pp. 124–129 (2017)

    Google Scholar 

  4. Saveriano, M., Lee, D.: Incremental skill learning of stable dynamical systems. In: International Conference on Intelligent Robots and Systems, pp. 6574–6581 (2018)

    Google Scholar 

  5. Saveriano, M., Hirt, F., Lee, D.: Human-aware motion reshaping using dynamical systems. Pattern Recogn. Lett. 99, 96–104 (2017)

    Article  Google Scholar 

  6. Ijspeert, A., Nakanishi, J., Pastor, P., Hoffmann, H., Schaal, S.: Dynamical movement primitives: learning attractor models for motor behaviors. Neural Comput. 25(2), 328–373 (2013)

    Article  MathSciNet  Google Scholar 

  7. Khansari-Zadeh, S.M., Billard, A.: A dynamical system approach to realtime obstacle avoidance. Auton. Rob. 32(4), 433–454 (2012)

    Article  Google Scholar 

  8. Karlsson, M., Robertsson, A., Johansson, R.: Autonomous interpretation of demonstrations for modification of dynamical movement primitives. In: International Conference on Robotics and Automation, pp. 316–321 (2017)

    Google Scholar 

  9. Talignani Landi, C., Ferraguti, F., Fantuzzi, C., Secchi, C.: A passivity-based strategy for coaching in human–robot interaction. In: International Conference on Robotics and Automation, pp. 3279–3284 (2018)

    Google Scholar 

  10. Kastritsi, T., Dimeas, F., Doulgeri, Z.: Progressive automation with DMP synchronization and variable stiffness control. Robot. Autom. Lett. 3(4), 3279–3284 (2018)

    Article  Google Scholar 

  11. Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice-Hall, Upper Saddle River (1991)

    MATH  Google Scholar 

  12. Kronander, K., Khansari-Zadeh, S.M., Billard, A.: Incremental motion learning with locally modulated dynamical systems. Robot. Auton. Syst. 70, 52–62 (2015)

    Article  Google Scholar 

  13. Rasmussen, C.E., Williams, C.K.I.: Incremental Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006)

    MATH  Google Scholar 

  14. Khansari-Zadeh, S.M., Billard, A.: Learning stable non-linear dynamical systems with gaussian mixture models. Trans. Robot. 27(5), 943–957 (2011)

    Article  Google Scholar 

  15. Gribovskaya, E., Khansari-Zadeh, S.M., Billard, A.: Learning non-linear multivariate dynamics of motion in robotic manipulators. Int. J. Robot. Res. 30(1), 80–117 (2011)

    Article  Google Scholar 

  16. Saveriano, M., An, S., Lee, D.: Incremental kinesthetic teaching of end-effector and null-space motion primitives. In: International Conference on Robotics and Automation, pp. 3570–3575 (2015)

    Google Scholar 

  17. Saveriano, M., Franzel, F., Lee, D.: Merging position and orientation motion primitives. In: International Conference on Robotics and Automation, pp. 7041–7047 (2019)

    Google Scholar 

  18. Saveriano, M., Lee, D.: Learning motion and impedance behaviors from human demonstrations. In: International Conference on Ubiquitous Robots and Ambient Intelligence, pp. 368–373 (2014)

    Google Scholar 

  19. Lee, D., Ott, C.: Incremental kinesthetic teaching of motion primitives using the motion refinement tube. Autonom. Rob. 31(2), 115–131 (2011)

    Article  Google Scholar 

  20. Billard, A., Calinon, S., Dillmann, R., Schaal, S.: Robot Programming by Demonstration. Springer Handbook of Robotics, pp. 1371–1394 (2008)

    Google Scholar 

  21. Calinon, S., Guenter, F., Billard, A.: On learning, representing, and generalizing a task in a humanoid robot. Trans. Syst. Man Cybern. Part B: Cybern. 37(2), 286–298 (2007)

    Article  Google Scholar 

  22. Csató, L.: Gaussian processes - iterative sparse approximations. Ph.D. dissertation, Aston University (2002)

    Google Scholar 

  23. Schreiber, G., Stemmer, A., Bischoff, R.: The fast research interface for the KUKA lightweight robot. In: ICRA Workshop on Innovative Robot Control Architectures for Demanding (Research) Applications - How to Modify and Enhance Commercial Controllers, pp. 15–21 (2010)

    Google Scholar 

  24. Calinon, S., Sardellitti, I., Caldwell, D.: The learning-based control strategy for safe human-robot interaction exploiting task and robot redundancies. In: International Conference on Intelligent Robots and Systems, pp. 249–254 (2010)

    Google Scholar 

  25. Mortari, D.: On the rigid rotation concept in n-dimensional spaces. J. Astronaut. Sci. 49(3), 401–420 (2001)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Matteo Saveriano .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Saveriano, M., Lee, D. (2020). Incremental Motion Reshaping of Autonomous Dynamical Systems. In: Ferraguti, F., Villani, V., Sabattini, L., Bonfè, M. (eds) Human-Friendly Robotics 2019. HFR 2019. Springer Proceedings in Advanced Robotics, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-030-42026-0_4

Download citation

Publish with us

Policies and ethics