G1 and some known relationship between the zeros of f and the solution sets of Eq. (6.1). For example, another choice of f may be
f(E1) = qL.qL q.q
(6.29)
or any difference between corresponding quantities from the left and right side of Eq. (6.2). The function choice is important in terms of minimal computation complexity and filtering of extraneous solutions which are discussed next. In all practical experiments the function defined in Eq. (6.8) has given good results.
Extraneous solutions. An extraneous solution set is one that the iterative method converges to, i.e. it satisfies the reduced system of equations (6.15)-(6.18!)- and f(91) = 0 but yet it is not a solution for Eq. (6.1). The iterative method just described may converge to such a, set. This problem was also reported by Tsai and Morgan (1984) who developed a different inverse kinematic method that makes use of a similar reduced system of equations.
In deriving the reduced system of equations (5.13)(5.16) in chapter 5, vectors u and q,and the inner-products u.q and q.q are the only pose related quantities that were involved. This means that -a solution set obtained by convergence of the method just described does not necessarily satisfy-other pose requirements from Eq.- (6.1). Extraneous solutions can be filtered out by- a choice of
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