Manipulabilifty ellipsoid of robot arm (2): theory, example, polyhedron approach

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 17:52

Summary:

This video continues the manipulability discussion started in video [elipm1EN], which is summarized here in the first two and a half minutes.

In this video emphasis is placed on defining what is called the manipulability ellipsoid: the locus of end-effector velocities when joint velocities are on the unit sphere (after some scaling/normalizing).

After a theoretical review, said ellipsoid is represented graphically and the relationship of the principal maneuvers of the SVD of the scaled Jacobian with said ellipsoid is illustrated.

The final part of the video superimposes the manipulability ellipsoid with the locus of end-effector velocities when joint velocities are in the cube of vertices $\pm 1$. The ellipsoid approximates it reasonably, and allows the SVD principal maneuvre interpretation that the polyhedron approach does not easily allow. By contrast, the polyhedron is an exact representation of practical achievable speeds. Everything has its advantages and disadvantages.

Examples in other poses and animations will be illustrated in the video [elipm3EN], a continuation of this one.

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