New guidance scheme for the aerodynamical ascent path

The optimal steering for the vehicles like spaceplane shows the different behavior from that of conventional rockets. This is because both thrust and lift force depend on the atmospheric dynamic pressure. This indicates that it is required the new guidance strategy for these kind of vehicles. The authors have proposed the trigonometrical functional form as the guidance strategy to approximate the numerical optimal steering directly. This method showed good performance, but the parameters have to be determined by solving the two-boundary value problem. And its computational load is too heavy to perform the task on the onboard computer. In this paper, we propose another new guidance strategy. This method is derived from some analytical assumptions and approximates the steering in simple linear and logarithmic function. Substituting this relation into the equation of motion, we can get the approximate description as for the vertical acceleration. Carrying out the numerical integration of this, the parameters are determined to satisfy the terminal boundary conditions. This procedure doesn't include the optimization process, but by sweeping the flight time to search parameters that the terminal horizontal speed is maximized, we can get the quasi-optimal solution. And its computational load is relatively light because only numerical integration has to be done to obtain the parameter. The simulation results show almost equivalent to that of the optimization method.