It is well-known that affine differential geometry is useful in classical mechanics as a means for organising the description of certain systems, e.g., the geodesics of the Levi-Civita connection are the solutions of the Euler-Lagrange equations for kinetic energy Lagrangians. In this talk an overview will be given of how affine differential geometry is useful in the control theory for mechanical systems. As control systems, the problems considered are challenging as they are not amenable to well-established methods in control. The emphasis will be on optimal control, controllability, and motion planning for these systems.

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