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I am reading about Condition Number which is considered as measure of manipulability of robotic arm, it is defined as

$$ k = \parallel J \parallel \parallel J^{-1} \parallel $$ Where, $$ \parallel J \parallel = \sqrt {tr(JNJ^{T})} $$ How this can be a unique value for given end effector location, as manipulator can reach a point in workspace with different joint variable values, which in turn will change Jacobian value ?

Reference Paper: Comparative study of performance indices for fundamental robot manipulators Serdar Kucuka,1, Zafer Bingulb,

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  • $\begingroup$ Condition number gives a measure of invertibility in general for linear operators. Intuitively it gives the amount of error amplification of errors through the operation. $\endgroup$ – daaxix Oct 19 '17 at 11:19
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Condition number and manipulability are measured at a specific joint configuration, not end-effector location. You already understand it correctly that the values change according to the robot configuration as they are computed from the Jacobian.

You may also want to check out Yoshikawa's original paper on manipulability.

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