Hybrid Method for Constrained and Unconstrained Trajectory Optimization of Space Transportation

In this research, a new method named δ to solve non-linear constrained and un constrained optimal control problems for trajectory optimization was proposed. The main objective of this method was defined as solving optimal control problems by the combination of the orthogonal functions, the heuristic optimization techniques, and the principles of optimal control theory. Three orthogonal functions Fourier, Chebyshev, and Legendre were considered to approximate the control variables. Also, GA-PSO and imperialist competition algorithms were considered as heuristic optimization techniques. Moreover, the motivation of the mentioned method belonged to a novel combination of zero Hamiltonian in the optimal control theory, optimality conditions, and newly proposed criteria. Furthermore, lunar landing, asteroid rendezvous, and low-thrust orbital transfer with respect to minimum-time and minimum-fuel criteria were investigated to show the ability of the proposed method in regard to constrained and un constrained optimal control problems. Results demonstrated that the δ method has high accuracy in the optimal control theory for non-linear problems. Hence, the δ method allows space trajectory and mission designers to solve optimal control problems with a simple and precise method for future works and studies.