Autonomous Robots

, Volume 40, Issue 1, pp 159–173 | Cite as

Spatial adaption of robot trajectories based on laplacian trajectory editing

  • Thomas NierhoffEmail author
  • Sandra Hirche
  • Yoshihiko Nakamura


Assuming that a robot trajectory is given from a high-level planning or learning mechanism, it needs to be adapted to react to dynamic environment changes. In this article we propose a novel approach to deform trajectories while keeping their local shape similar, which is based on the discrete Laplace–Beltrami operator. The approach can be readily extended and covers multiple deformation techniques including fixed waypoints that must be passed, positional constraints for collision avoidance or a cooperative manipulation scheme for the coordination of multiple robots. Due to its low computational complexity it allows for real-time trajectory deformation both on local and global scale and online adaptation to changed environmental constraints. Simulations illustrate the straightforward combination of the proposed approach with other established trajectory-related methods like artificial potential fields or prioritized inverse kinematics. Experiments with the HRP-4 humanoid successfully demonstrate the applicability in complex daily-life tasks.


Robotics Trajectory adaption Trajectory retargeting Trajectory similarity Local trajectory properties Multiresolution approach Obstacle avoidance 



This work was partially supported by the EU Horizon2020 project RAMCIP, under Grant Agreement No. 643433 and by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (S), 2008-2012, 20220001, “Establishing Human-Machine Communication through Kinesiology and Linguistics Integration” (PI: Y. Nakamura).

Supplementary material

Supplementary material 1 (mp4 106809 KB)


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Chair of Information-oriented ControlTechnische Universität MünchenMunichGermany
  2. 2.Department of Mechano InformaticsUniversity of TokyoTokyoJapan

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