טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentErdos David
SubjectMinimum Fuel UAV Trajecttories
DepartmentDepartment of Electrical Engineering
Supervisor Professor Nahum Shimkin
Full Thesis textFull thesis text - English Version


Abstract

The problem of finding the optimal path for an airplane from point A to point B
has been thoroughly studied in literature. The question then arises of how optimality is defined. Some common definitions of optimality for airplane trajectories, or more specifically UAV (Unmanned Aerial Vehicle) trajectories, include minimum-time, minimum exposure to threats, maximum sensor coverage, etc. However, the issue of minimizing the fuel consumption for UAV trajectories has not received as much attention.


A common approach for modeling the flight path of airplanes, in particular UAV trajectories is what is known as a Dubins path. A Dubins path is a trajectory in a plane which is a concatenation of circular segments and straight lines, and for a fixed speed vehicle, was shown to be optimal (i.e., minimum-time) by Dubins in 1957. Although this is a good model for fixed speed vehicles, most aircraft have a range of speeds at which they can operate. It turns out that exploiting the capability of an aircraft to vary its speed over a range can be used to generate more efficient trajectories than a Dubins path, both in terms of travel time and also fuel consumption.


We will focus our attention on minimum fuel consumption trajectories for UAVs. It turns out that the common approach of modeling a UAV as a fixed speed vehicle with a minimum turn radius (i.e., a Dubins vehicle) is not necessarily the best approach if we are interested in minimizing fuel consumption.


The optimal control problem for minimum-fuel trajectories is formulated and solved numerically; results are presented for both a fixed-altitude and a variable-altitude airplane model. Affects of various parameters on minimum-fuel trajectories are examined including initial speed, maximum power available, wind, and the distance between waypoints. The minimum-fuel trajectories are compared to Dubins paths of various speeds in order to evaluate the fuel savings obtained relative to the ubiquitous Dubins path. We will show that significant fuel savings can be obtained by flying minimum-fuel trajectories if the waypoints are moderately close together. Additionally, further fuel savings can be achieved by the variable-altitude minimum-fuel trajectories relative to the fixed-altitude case.