This thesis combines optimal control with energy shaping on the Lie group SE(3), which is the configuration space of rigid bodies. Potential shaping on SE(3) has been investigated for quadratic potentials on SE(3). Although passive, such a control law does not take into account any optimality considerations.
This assignment aimed at generalizing such energy shaping controllers on SE(3) beyond the quadratic case, and optimizing them with respect to an arbitrary performance metric. For the control-law definition and the optimization, the Lie group structure of SE(3) was heavily used, and methods from neural ODEs were extended to this scenario.
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