Abstract
Trajectory generation is a fundamental part of planning for an autonomous aerial vehicle. For the purpose of flight path generation, it is usually sufficient to treat only the translational motion. One component of the weather that greatly affects an aircraft trajectory is the wind. Study of the accessibility of this nonlinear affine system with drift makes use of the Lie algebra rank condition. The second part of this paper presents 3D time optimal translational trajectories characterization for an aircraft in steady wind. If unaccounted for, winds can substantially degrade the performance of an autonomous aircraft guidance system. We consider finding a time optimal trajectory for an airplane from some starting point and orientation to some final point and orientation, assuming that the system has independent bounded control over the acceleration as well as the turning rates for the flight path and heading angles. Through the use of the Pontryagin maximum principle, we characterize the time optimal trajectories for the system.
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