  A novel coupled path planning and energy management problem for a hybrid
unmanned air vehicle is considered, where the hybrid vehicle is powered by a
dual gas/electric system. Such an aerial robot is envisioned for use in an
urban setting where noise restrictions are in place in certain zones
necessitating battery only operation. We consider the discrete version of this
problem, where a graph is constructed by sampling the boundaries of the
restricted zones, and develop a path planning algorithm. The planner
simultaneously solves the path planing along with the energy mode switching
control, under battery constraints and noise restrictions. This is a coupled
problem involving discrete decision making to find the path to travel, and
determining the state of charge of the battery along the path, which is a
continuous variable. A sampling based algorithm to find near optimal solution
to this problem is presented. To quantify the efficacy of the solution, an
algorithm that computes tight lower bounds is also presented. The algorithms
presented are verified using numerical simulations, and the average gap between
the feasible solutions (upper bounds) and the lower bounds are, empirically,
shown to be within 15% of each other.
