Consider a fixed-endpoint, fixed time optimal control problem with state and input taking values in Euclidean space. We show that if the Hamiltonian function associated with this problem satisfies a scale invariance property, then the set of all local solutions to this problem---over all possible terminal state constraints---is path-connected. We also show that this result extends to problems with additional constraints such as a bound on total cost. Finally, we use this result to show that the set of all curves that can be realized by a planar elastica is path-connected, and we describe how this result can be applied to the problem of robotic manipulation for nonrigid objects.
['Andy Borum', 'Timothy Bretl']
Sufficient conditions for a path-connected set of local solutions to an optimal control problem