Trajectory Optimization of Launch Vehicles Using Steepest Descent Method – A Novel Approach

摘要

Trajectory optimization o f a generic launch vehicle is considered in this paper. The direct application of a nonlinear programming method is used in recent literature, which transforms the original problem into a nonlinear optimization problem.To study the rocket motion under the influence of gravitational field, 2-D simulator is developed. The rocket motion is analyzed for a gravity turn trajectory. The objective is to ensure desired terminal conditions as well as minimum control effort in the low dynamic pressure region. Design of optimal trajectory for a single stage rocket is a two point boundary problem. Trajectory is designed for a single stage liquid rocket.Trajectory is computed for a given initial and final condition using equations of motion of rocket in 2-D plane. Hamiltonian is formulated for the given constraints. The non-linear equations are solved using steepest descent method.It is assumed that the launch vehicle is not experiencing any perturbations. Results are compared for Runge-kutta and Euler.s integration methods,which clearly brings out the potential advantages of the proposed approach