Math & Kinematics

Manipulability Ellipsoid

The manipulability ellipsoid is a geometric representation of a manipulator's instantaneous capacity to generate end-effector velocities in different directions, derived from the singular value decomposition of the Jacobian at a given configuration. Introduced by Yoshikawa, whose scalar manipulability measure is proportional to the ellipsoid's volume, it shrinks to lower dimension near singularities. A dual force ellipsoid characterizes achievable end-effector forces.

Why it matters for physical AI

Configuration-dependent dexterity determines where in the workspace a robot can move and exert force effectively; manipulability metrics guide redundancy resolution, workcell layout, and grasp approach selection.