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Abstract:
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As a Micro Air Vehicle (MAV) maneuvers through a city, the effect of wind is important to its performance. Concerns include the MAV's size, speed, and turn radius, which cause susceptibility to wind. If an inadequate maneuvering area or strong wind conditions cause turning within the city to be impossible, one solution is to fly through the city while viewing targets and above in expedition to other targets.
We concentrate on flight above the city. Fewer obstacles are present; therefore, the optimal trajectory is the minimum time solution in the presence of wind, considering a minimum turn radius constraint. We prove existence and uniqueness where a wind vector field varies with time but is spatially constant for each time instant. We also prove existence with temporally and spatially varying wind vector fields. After proving existence of one solution, provided certain conditions are satisfied, we conclude existence of the minimum time solution. |