From Inverse Kinematics to Optimal Control

Numerical optimal control (the approximation of an optimal trajectory using numerical iterative algorithms) is a promising approach to compute the control of complex dynamical systems whose instantaneous linearization is not meaningful. Aside from the problems of computation cost, these methods raise several conceptual problems, like stability, robustness, or simply understanding of the nature of the obtained solution. In this chapter, we propose a rewriting of the Differential Dynamic Programing solver. Our variant is more efficient and numerically more interesting. Furthermore, it draws some interesting comparisons with the classical inverse formulation: in particular, we show that inverse kinematics can be seen as singular case of it, when the preview horizon collapses.

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