The Dynamic Interpolation Problem : on R I E M a N N I a N Manifolds , Lie Groups , a N D Symmetric Spaces
نویسنده
چکیده
We consider the dynamic interpolation problem for nonlinear control systems modeled by second-order differential equations whose configuration space is a Riem~nnlan manifold M. In this problem we are given an ordered set of points in M and would like to generate a trajectory of the system through the application of suitable control functions, so that the resulting trajectory in configuration space interpolates the given set of points. We also impose smoothness constraints on the trajectory and typically ask that the trajectory be also optimal with respect to some physically interesting cost function. Here we are interested in the situation where the trajectory is twice continuously differentlable and the Lagrangian in the optimization problem is given by the norm squared acceleration along the trajectory. The special cases where M is a connected and compact Lie group or a homogeneous symmetric space are studied in more detail.
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