Robust Launch Vehicle Trajectory Optimization with Stage Impact and Heat Flux Constraints

Abstract

A fast trajectory optimization/guidance algorithm in the presence of path constraints for a multistage launch vehicle is presented in this work. The optimization problem is to maximize the payload to be injected into a geostationary transfer orbit with constraints on argument of perigee, second-stage impact point longitude, and heat flux constraint on the third stage that flies a low-altitude trajectory. These constraints constitute a unique set of equality and inequality constraints as they are contradictory in nature. Most of the gradient-based trajectory optimization schemes require an initial guess close enough to the optimal value for assured convergence. In addition, the rate of convergence deteriorates in the presence of inequality constraints. These issues are addressed by providing a solution to the optimization problem with low sensitivity to the initial guess profiles. A self-starting optimization scheme that can generate initial guess profiles automatically from boundary conditions is the major contribution of this work. The proposed method presented in this paper also gives a methodology for real-time implementation of the optimization scheme in the onboard computer. The sensitivity to initial guess in a gradient-based optimization procedure, in the presence of inequality constraints, is clearly brought out as part of this work by studying the convergence from random sets of initial guess profiles. The real-time implementation of the algorithm is validated with various initial conditions in deterministic as well as Monte Carlo sense to establish the robustness of the algorithm.