Abstract
We consider the dynamic interpolation problem for nonlinear control systems modeled by second-order differential equations whose configuration space is a Riemannian manifoldM. In this problem we are given an ordered set of points inM 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 differentiable and the Lagrangian in the optimization problem is given by the norm squared acceleration along the trajectory. The special cases whereM is a connected and compact Lie group or a homogeneous symmetric space are studied in more detail.
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Work supported in part by NSF grant No. 89-14643 and NATO project CRG 910926.
Work supported by ISR, SCIENCE project ERB-SC1*CT90-0433 and NATO project CRG 910926.
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Crouch, P., Leite, F.S. The dynamic interpolation problem: On Riemannian manifolds, Lie groups, and symmetric spaces. Journal of Dynamical and Control Systems 1, 177–202 (1995). https://doi.org/10.1007/BF02254638
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DOI: https://doi.org/10.1007/BF02254638