Trajectory Planning for the 3D Dubins Vehicle

In this thesis, we propose a novel non-linear programming approach to the problem of finding the shortest path in 3D space under the turning radius and pitch angle constraints. The path is divided into a number of segments in 3D space. The proposed formalisation enables to encode straight segments as well as circular arcs using the same equations. Even when initialized by the best-known heuristic method, the optimization is able to reduce the lower bound margin by about 25%, with computational times around one second using 100 segments. The computational time is greatly dependant on the selected segment count. The utilized Ipopt solver converges significantly faster for lower segment counts, at the cost of worse solutions. The proposed formulation is also extended to cover a variant of the problem, in which the path has to visit a number of locations in a given order. This extension achieves similar results as the sampling-based reference solution with much shorter computational times.