Force ellipsoid in a robot (1): definition and basic examples

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 11:53

Summary:

This video defines the force ellipsoid of a robotic manipulator. Said ellipsoid is the ellipsoid of end-effector forces that could be compensated to keep the manipulator immobile if the joint torques lie on the unit sphere.

The basic theoretical formulas are justified in the video [elipf1EN], which you should watch before this one. Indeed, the fundamental idea is that the torque vector $\tau$ that compensates a force $f$ in the end effector is $\tau =J^{T}f$, so ${\tau }^T\tau =f^T\cdot (J\cdot J^T)\cdot f\le 1$ defines an ellipsoid (said “force ellipsoid’ ’ ). The video introduces the possible scaling and draws the ellipsoid in different poses.

Theoretical SVD analysis continues in video [elipf3EN], and the relationship between manipulability ellipsoids (velocities) and forces is discussed in video [elipf4EN].

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