Optimal geometrical path in 3D with curvature constraint

This paper presents a path planning approach for achieving an optimal feasible path satisfying a maximum curvature bound in three dimensional space, given initial and final configurations specified by position and orientation vectors. Based on Dubins strategy two types of solution approaches will be discussed, the first is a numerical technique which is computationally intensive and the second is based on 3D geometry from which we will derive an analytical solution. In the second approach, the computational time is very low and the strategy can be implemented for real-time path planning problems. Unlike the existing iterative methods which yield suboptimal paths and are computationally more intensive, this geometrical method generates an optimal path in lesser time. Due to its simplicity and low computational requirements this approach can be implemented on fixed wing aerial vehicles with constrained turn radius.