Finding 3D Dubins Paths with Pitch Angle Constraint Using Non-linear Optimization

Abstract

This paper presents a novel non-linear programming formulation to find the shortest 3D Dubins path with a limited pitch angle. Such a path is suitable for fix-wing aircraft because it satisfies both the minimum turning radius and pitch angle constraints, and thus it is a feasible and smooth path in the 3D space. The proposed method utilizes the existing decoupled approach as an initial solution and improves its quality by dividing the path into small segments with constant curvature. The proposed formulation encodes the path using the direction vectors that significantly reduce the needed optimization variables. Therefore, a path with 100 segments can be optimized in about one second using conventional computational resources. Although the decoupled paths are usually within 2 % from the lower bound, the proposed approach further reduces the gap by about 30 %.