An affine connection control system is defined on a configuration space Q with an affine connection is governed by the forced geodesic equations. This system class includes a large number of applications, and also possesses an extremely rich geometric structure.

We shall explore the relationship between low-order controllability and motion planning for such systems. That there is an explicit link between these two topics has only recently been made clear. Remarkably, the idea the ties together low-order controllability and motion planning is a vector-valued quadratic form that one can associate with the system.

One of the interesting developments of this work has been the identification of a large number of examples whose controllability can be determined at low-order, and which are, as a consequence, amenable to certain easily understood, explicit motion planning strategies. Such examples include models for a hovercraft and an underwater vehicle, and the snakeboard. We shall also consider some examples that fail to satisfy the controllability conditions.

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Last Updated: Tue Jun 18 09:12:22 2024