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Iterative model

The Jacobian inversion method works in two phases. The partial transformations based on the joint angles are computed in the first phase. After that, the end effector position and the Jacobian are computed. Then the end effector location is changed.

The second phase contains Jacobian matrix inversion and joint angles changes, using equation (7). The next step lies in the repetition of step one and in the change of the end effector position. The obtained differential of the end effector position $dX$ enters in phase two. The mentioned phases repeat until the error (difference between the current and the desired location of the end effector) comes below a defined value $\varepsilon$ or the maximal number of iteration steps is reached: $ \Vert~J(d\theta)~-~dX~\Vert~\leq~\varepsilon \quad \vee \quad iter~\geq~maxiter$ (Figure 3).

Figure 3: The iterative model for the Jacobian inversion method.
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Lukas Barinka 2002-03-21