A solution to simultaneous arrival of multiple UAVs using Pythagorean hodograph curves

Abstract

This paper presents a solution to the problem of simultaneous arrival of a swarm of UAVs by safe and continuously flyable paths. Continuously flyable-paths are generated by satisfying the curvature constraint throughout the path-length. The flyable paths ensure the safety of the UAVs by changing the shape of the flyable-paths by adjusting curvature of the paths. The main idea used in this paper is that a specific type of path is used in the first place for path planning and the shape of the path is varied to meet the multiple constraints. Pythagorean hodograph curves are used for the path planning algorithm. The principle of differential geometry that a planar curve is completely determined by its curvature is used for changing the shape of the path. The multiple constraints are: (i) curvature constraints (ii) minimum-separation-distance and (iii) non-intersection of paths at equal length.