WITHDRAWN: A Robust Framework for Aerodynamic Trajectory Generation

Dynamic Soaring is a technique of maintaining flight by utilizing wind shear. It is observed among birds like albatrosses and offers promise for unmanned aerial vehicle missions. Earlier works on dynamic soaring have focused on trajectory generation, using direct optimal control and differential flatness. In this paper, an improvement to the existing six-degree-of-freedom (6-DOF) trajectory generation formulation using differential flatness, to include sideslip and all stability and control derivatives, has been proposed. The old and new formulations have been compared from the standpoint of the Floquet exponents and control inputs. Dynamic soaring trajectories with the non-zero Floquet exponents having a negative real-part have been generated by assuming constant derivatives. A Vortex Lattice Method (VLM) solver has been used to compute steady forces and moments. These have been compared with the constant derivative trajectory. The steady forces and moments from the VLM solver have been used to check for convergence in the simulation of a 6-DOF unmanned aerial vehicle in a dynamic soaring orbit, with stability augmented by a Linear Quadratic Regulator. The divergence of this simulation brings out the insufficiency of the constant derivative formulation. Hence trajectory generation has been carried out by considering the variation of the stability and control derivatives, with flight conditions, taken from a lookup table. The method is shown to be effective through a simulation of dynamic soaring orbit.