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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
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)
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)
Blocher, C., Saveriano, M., Lee, D.: Learning stable dynamical systems using contraction theory. In: Ubiquitous Robots and Ambient Intelligence, pp. 124–129 (2017)
Saveriano, M., Lee, D.: Incremental skill learning of stable dynamical systems. In: International Conference on Intelligent Robots and Systems, pp. 6574–6581 (2018)
Saveriano, M., Hirt, F., Lee, D.: Human-aware motion reshaping using dynamical systems. Pattern Recogn. Lett. 99, 96–104 (2017)
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)
Khansari-Zadeh, S.M., Billard, A.: A dynamical system approach to realtime obstacle avoidance. Auton. Rob. 32(4), 433–454 (2012)
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)
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)
Kastritsi, T., Dimeas, F., Doulgeri, Z.: Progressive automation with DMP synchronization and variable stiffness control. Robot. Autom. Lett. 3(4), 3279–3284 (2018)
Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice-Hall, Upper Saddle River (1991)
Kronander, K., Khansari-Zadeh, S.M., Billard, A.: Incremental motion learning with locally modulated dynamical systems. Robot. Auton. Syst. 70, 52–62 (2015)
Rasmussen, C.E., Williams, C.K.I.: Incremental Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006)
Khansari-Zadeh, S.M., Billard, A.: Learning stable non-linear dynamical systems with gaussian mixture models. Trans. Robot. 27(5), 943–957 (2011)
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)
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)
Saveriano, M., Franzel, F., Lee, D.: Merging position and orientation motion primitives. In: International Conference on Robotics and Automation, pp. 7041–7047 (2019)
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)
Lee, D., Ott, C.: Incremental kinesthetic teaching of motion primitives using the motion refinement tube. Autonom. Rob. 31(2), 115–131 (2011)
Billard, A., Calinon, S., Dillmann, R., Schaal, S.: Robot Programming by Demonstration. Springer Handbook of Robotics, pp. 1371–1394 (2008)
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)
Csató, L.: Gaussian processes - iterative sparse approximations. Ph.D. dissertation, Aston University (2002)
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)
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)
Mortari, D.: On the rigid rotation concept in n-dimensional spaces. J. Astronaut. Sci. 49(3), 401–420 (2001)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
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
DOI: https://doi.org/10.1007/978-3-030-42026-0_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-42025-3
Online ISBN: 978-3-030-42026-0
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)