Micro Air Vehicle Trajectory Planning in Winds

Abstract

M ICRO aerial vehicles (MAVs) are small aerial vehicles, generallywith dimensions on the order of 1 ft (or 0.3m). Their small sizes often imply that their flight speeds are also small, roughly on the order of 20–60 km=h. MAVs come in a wide variety of forms, such as fixed wing, flapping wing, and rotary wing [1]. They are finding increasingly more applications in such areas as military missions, reconnaissance of hazardous or remote areas, and monitoring of indoor areas. Because of their small sizes and light weights, MAV flight trajectories are significantly susceptible to winds in general. For example, it is possible for the wind to be so strong that the MAV is unable to advance in certain directions. (This problem can be formulated in terms of the controllability of a point and its associated reachable set, see [2].) It is therefore necessary to develop a systematic approach toMAV trajectory generation that addresses the characteristic issues of MAV flights in winds. Specifically, the following three points must be considered: 1) Target points may not always be feasible due to winds. 2) Wind profiles may have significant effects on fuel costs (both desirable and undesirable). 3) Trajectory generation must always yield a feasible solution due to the absence of human operators. The main goal of this note is to study meaningful trajectory generation problem formulations for MAV trajectories in winds, to address all three of the issues discussed above that characterize MAV flights. Specifically, MAV flights in winds are formulated as nonlinear optimal control problems, with proper constraints on states and controls. In particular, the reaching of a target point is enforced via a penalty term in the performance index. Thus, while a target point is not necessarily reached, a flyable trajectory that is optimal under prevailing conditions is obtained. Both constant and position dependent wind is considered.