Manipulability of robotic arm (1): modelling, jacobian, singular value decomposition

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 16:33

Summary:

This video introduces the concept of manipulability analysis, the discussion of which will continue in the video [elipm2EN] (manipulability ellipsoid) and [elipm3EN] (more examples and animations).

Specifically, the basic idea of the analysis is based on the robot Jacobian (the matrix that relates joint velocities to end-effector velocities) and its singular value decomposition $J=US{V}^T$, which gives rise to the “principal manoeuvres”. A theoretical analysis discussing the relationship between singular value decomposition (SVD) and ellipsoid geometry is further discussed in video [ellip7EN].

This video makes a brief theoretical review of the Jacobian concept, models a robot with three articulated elements (planar one, no gravity), obtains said Jacobian, and analyzes its SVD. The case study continues in the videos referred to at the beginning of the description.

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.