The influence of coordinates in robotic manipulability analysis

Johannes Lachner*, Vincenzo Schettino, Felix Allmendinger, Mario Daniele Fiore, Fanny Ficuciello, Bruno Siciliano, Stefano Stramigioli

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Scopus)
19 Downloads (Pure)


Coordinates play an essential role in the description of real world objects and physical processes. In robotics, coordinates are used to describe the kinematic structure and the kinematic and dynamic behavior. The description mostly takes place in charts, assigned by the observer of the robotic system. However, it is crucial that the described physical process does not depend on the coordinate choice of the observer. In this work we show the relation between coordinates and manipulability analysis. Manipulability measures are dependent of joint coordinates of the robot and task coordinates in the workspace of the robot. Both relations can be analyzed with tensor geometry. We remove the dependency on joint coordinates through the use of an appropriate metric. With the help of tensor contraction, the resulting induced metric in the workspace can be transformed into a coordinate invariant matrix. After applying eigenvalue decomposition on this matrix, we can visualize the dynamic manipulability of a robot as a coordinate invariant ellipsoid.

Original languageEnglish
Article number103722
Number of pages13
JournalMechanism and machine theory
Early online date17 Dec 2019
Publication statusPublished - Apr 2020


  • UT-Hybrid-D
  • Manipulability ellipsoids
  • Metrics
  • Tensor analysis
  • Coordinate invariance
  • 22/2 OA procedure


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