Скачать или смотреть [2/7] Robot manipulability ellipsoid, theory, example + polyhedron approach

This video continues the robot manipulability discussion started in video    • [1/7] manipulability (robotics): jacobian,...   , summarized here in the first two and a half minutes (please watch    • [3/7] SVD manipulability ellipsoid animati...   for animations and examples).

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 +/-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 2D animations will be illustrated in the video    • [3/7] SVD manipulability ellipsoid animati...   , a continuation of this one. You are strongly advised to watch it for a much clearer understanding of the key ideas here: an animation is worth a thousand words!
PLAYLIST:    • Robot arm manipulability/force ellipsoids:...  
________________
PDF/code/notes at: http://personales.upv.es/asala/YT/V/e...
#robotics #svd #ellipsoid
_________________
Antonio Sala, UPV, Valencia, Spain
Full collection of videos at: http://personales.upv.es/asala/YT/ind...