Formulation of the Necessary Conditions for Optimality for a Parameter Dependent Optimal Control Problem Evolving on a Principal Fibre Bundle

The main objective of this research is the presentation of a maximisation of payload haulage by use of UAV for payload spraying purposes of a pesticide in a regular field. Optimal control from principles of calculus of variations is applied to formulate the maximisation problem. The variable payload models the parameter dependant UAV. The system evolves on a principle fibre bundle on a SE(3) x S² manifold necessitating a from principles calculus of variations optimal formulation which is the key contribution of this paper. An illustrative spraying example is used to demonstrate a maximal pesticide spraying problem. Future work will include the formulation of optimal control problems on the semi-direct function Manifold