TF/TA optimal Flight trajectory planning using a novel regenerative flattener mapping method

In this paper, a new methodology has been proposed to enhance the conformal mapping applications in the process of optimum trajectory planning in Terrain Following (TF) and Terrain Avoidance (TA) Flights. The new approach uses the conformal mapping concept as a flattener tool to transform the constrained trajectory-planning problem with flight altitude restrictions due to the presence of obstacles into a regenerated problem with no obstacle and minimal height constraints. In this regard, the Schwarz–Christoffel theorem has been utilized to incorporate the height constraints into the aircraft dynamic equations of motion. The regenerated optimal control problem then is solved employing a numerical method namely the direct Legendre-Gauss-Radau pseudospectral algorithm. A composite performance index of flight time, terrain masking, and aerodynamic control effort is optimized. Furthermore, to obtain realistic trajectories, the aircraft maximum climb and descent rates are imposed as inequality constraints in the solution algorithm. Several case studies for two-dimensional flight scenarios show the applicability of this approach in TF/TA trajectory-planning. Extensive simulations confirm the efficiency of the proposed approach and verify the feasibility of solutions satisfying all of the constraints underlying the problem