Improving design of reentry vehicle trajectory optimization using direct collocation method

Indirect optimization method, used for a long time for reentry vehicle trajectory optimization, suffers shortcomings such as large amount of computation, unsatisfactory real-time performance and high sensitivity to choice of initial values. We now propose direct collocation method to reduce greatly such shortcomings. The description of the problem of reentry vehicle trajectory optimization) is firstly put forward. Then, the establishment of equations of motion, selection of performance index and constraint conditions are proposed. The angle-of-attack and bank angle are selected to be control variables. The terminal velocity is selected to be maximized. We explain that, during the flight, reentry vehicle is subjected to heat rate, overload and dynamic pressure constraints and terminal state variable constraints are path inclination angle and altitude. How to use direct collocation method is presented thereafter. The third order Simpson method and description of the nonlinear programming (NLP) problem are proposed. The optimal control problem is transformed into NLP problem using direct collocation method or, in other words, dynamic optimization problem is transformed into static parameter optimization problem. Finally we give a numerical simulation example, in which the state and control variables are selected as optimal parameters at all nodes and collocation nodes. Parameter optimization problem was solved using the SNOPT software package which we found to have high convergence for NLP problem. The simulation results demonstrate that the direct collocation method is not sensitive to reentry initial conditions; they also show that the optimal solutions of trajectory optimization problem are fairly good in real-time. Therefore, the direct collocation method is a viable approach to the reentry vehicle trajectory optimization problem.