Optimal static soaring of UAVs using vehicle routing with time windows

Abstract

Soaring, a biologically inspired technique recognized as a sport worldwide, has recently been investigated for Unmanned Aerial Vehicle (UAV) applications. Satisfactory experimental results have been obtained in terms of significant endurance, range and crosscountry speed improvements. Substantial human intervention, however, is required to define the flight trajectory reducing the autonomy level of the UAV. Variations in the climb rate of atmospheric air currents and the limited duration periods for which these currents are available for soaring flight pose extra constraints on static soaring. If these constraints are not properly addressed, the resultant performance of the vehicle can be quite far from optimal. We propose that the optimal static soaring problem can be efficiently adapted to a Vehicle Routing Problem (VRP), a generic combinatorial optimization problem well-known in academic literature. This problem formulation proves capable of being conveniently extended to the VRP with Time Windows (VRPTW) to consider duration constraints such as limited thermal lifespan whereas the variations in the air currents can possibly be modeled as a Dynamic Vehicle Routing Problem (DVRP). Based on our VRPTW formulation of static soaring problem, we develop an exact solution method including preprocessing, route optimization and route validation. The optimal flight route along with the optimal set of horizontal flight velocities for corresponding inter-thermal flight arcs are determined, and the total flight time minimization is achieved while certain temporal criteria are essentially satisfied. As a result, the ability to effectively plan the flight path is improved, and considerable increase in the level of autonomy of a soaring UAV is attained. Simulation results demonstrate that the VRP approach motivates further research in the discussion of optimal soaring performance of UAVs.