Optimal Control for Autonomous Task Execution

The research described in this paper addresses the problem of automatic execution of a robotic task. The objective is to develop a control methodology that can be used to give autonomy to a robotic device during the execution of a specific task. In particular we focus on the application domain of robotic surgery and we want to explore the possibility of adding autonomous capability to the robotic device performing the surgery, to be of help to the surgeon. In this context, by "task" we mean a small sequence of coded surgical gestures, that is well described in the medical literature and that can, potentially, be described in algorithmic form. We first model the task with a suitable Hybrid System, then we compute the nominal controls by minimizing various performance indices, and finally we define a quality measure to provide feedback during real time execution. We model a complex task with a hybrid automaton, whose elementary states represent distinct actions in the task, and we account for uncertainty with appropriate state transitions. The desired behavior is represented by the optimal trajectory computed off-line, whereas the on-line compensation aims at zeroing trajectory errors and the cost of the jumps between states. We conclude the paper with some simulation and experimental results proving the feasibility of this approach.