Non-uniqueness in time-optimal control of robotic manipulators

For serially-actuated open-chain robotic manipulators, the existence of non-unique extremals for the state-to-state time-optimal control problem is established. Non-uniqueness is shown to arise through infinite order singular extremals, the properties of which depend on the coupling that is present in the manipulator. Furthermore, it is demonstrated using counter-examples, that infinite order singularity does not necessarily occur, when the actuation is not serial or when the manipulator has a closed chain structure.