## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 976-999 |

Number of pages | 24 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 76 |

Issue number | 3 |

DOIs | |

State | Published - 2016 |

## Keywords

- Conjugate points
- Optimal control
- Path-connectedness
- Scale invariance

## ASJC Scopus subject areas

- Applied Mathematics