Step 6. Complete the solution set by uniquely
computing G6 from
C6 nx
R6x X 6 R5_ 14_ 13_ 12_ 1Rin y (7.41)
0 n
Step 7. Check the solution set for consistency with Eq. (7.1).
Choice of functions f and g. The functions f and g
defined by Eqs. (7.12) and (7.13) are computationally economical since they do not require computation of the forward kinematics or the inverse jacobian of ,the manipulator. In fact, even the value of e6 is not required to compute f and g since Eq. (7.41) is considered only after convergence. Unfortunately, a pair (01, 82) for which both f and g are zero is not guaranteed to correspond to a solution set of Eq. (7.1). Extraneous solution sets can be
converged to as well. These are joint values that will*
yield an end-effector pose that is not exactly the desired one.
Other functions that fully constraint the end-effector pose can be defined at the cost of greater computational complexity. Wu and Paul (1982) have shown that the
difference between actual and desired end-effector poses can be expressed as a 6 x 1 vector xe given by
..