Spatial Robotic Isotropy

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Abstract
Previous work on posture optimization for robots has examined the condition number as a measure of kinematic dexterity. When the condition number equals an optimal value of one, the robot is described as isotropic. Isotropic configurations have a number of advantages, including good servo accuracy, noise rejection, and singularity avoidance. This article introduces a definition for spatial isotropy of a robot, which is comhined isotropy for both positioning and orienting the end effector. Generally iso tropy may be used either as a robotic design criterion or as a posture optimization function for redundant manipu lators. This work demonstrates design techniques using positional, orientational, or spatial isotropy and presents some algorithms for locating isotropic designs without explicit evaluation of singular values. Several representa tive robot designs illustrate these concepts for both nonre dundant and redundant manipulators.

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