Parameter Optimization with Chebyshev Polynomials for Trajectory Design of A RLV

Abstract

A trajectory optimal control problem is converted to a parameter optimization problem by approximating the states and control using piecewise Chebyshev polynomials. The Chebyshev points which control the polynomial fit is used to match the dynamics at the nodal points. Midpoint strategy significantly reduced the number of parameters to be optimized without having to sacrifice on accuracy. The resultant non- linear programming problem is solved using sequential quadratic programming method. Ascent phase trajectory optimization of a reusable launch vehicle having typical path and terminal constraints is taken as a test case.