"An ideal metric for path planning in SE(3) would correspond to a measure of the minimum sweptvolume in the workspace while moving a rigid object from one configuration to another. The most simple and commonly used metrics consider the Cspace as a Cartesian space and define aEuclidean metric. For example, if X and R represent the translation and rotation components of the configuration q = (X;R) respectively, then:
. . . . .\(\displaystyle \large{\rho(q_0,\, q_1)\, =\, w_t \X_0\, \, X_1\\, +\, w_r\, f(R_0,\, R_1)}\)
is a weighted metric with the translation component using a standard Euclidean norm, and the positive scalar function f(R0;R1) returning an approximate measure of the distance between the rotations R0;R1 . The rotation distance is scaled relative to the translation distance via the weights wt and wr. One of the difficulties with this method is deciding proper weight values."
I've read this somewhere, and my question is, what is idea for calculating these weight values?
. . . . .\(\displaystyle \large{\rho(q_0,\, q_1)\, =\, w_t \X_0\, \, X_1\\, +\, w_r\, f(R_0,\, R_1)}\)
is a weighted metric with the translation component using a standard Euclidean norm, and the positive scalar function f(R0;R1) returning an approximate measure of the distance between the rotations R0;R1 . The rotation distance is scaled relative to the translation distance via the weights wt and wr. One of the difficulties with this method is deciding proper weight values."
I've read this somewhere, and my question is, what is idea for calculating these weight values?
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