Optimal path planning for an aerial vehicle in 3D space

We address optimal path planning in three-dimensional space for an aerial vehicle with bounded turn radius. The objective is to calculate a feasible path of minimum length when the initial and final positions and orientations of the vehicle are given. The proposed method is based on 3D geometry. Unlike the existing iterative methods, which yield suboptimal path and are computationally more intensive, this geometrical method generates an optimal path in much lesser time. Due to its simplicity and low computational requirements this approach can be implemented on an aerial vehicle with constrained turn radius to reach a final point with a prescribed orientation. But, if the path demands very high pitch angle (as in the case of steep climbs), then the generated path may not be flyable for an aerial vehicle with limited range of flight path angle and we need to use a numerical method such as multiple shooting to obtain the optimal solution.