Rapid ascent trajectory optimization for guided rockets via sequential convex programming

Abstract

A sequential convex programming algorithm is proposed to solve the complex ascent trajectory optimization problems for guided rockets in this paper. Due to the nonlinear dynamics and constraints, especially, the nonlinear thrust terms and aerodynamic drag, ascent trajectory optimization problems for guided rockets are always difficult to be solved rapidly. In this paper, first, the complex thrust terms in the dynamic equation are approximately transformed into linear (convex) functions of the angle of attack. Secondly, the nonlinear drag coefficient is transformed into a linear (convex) function of design variables by introducing two new control variables. The relaxation technique is used to relax the constraints between the control variables to avoid non- convexity, and the accuracy of the relaxation is proved using the optimal control theory. Then, nonconvex objective functions and dynamical equations are convexified by first-order Taylor expansions. At last, a sequential convex programming iterative algorithm is proposed to solve the ascent trajectory planning problem accurately and rapidly. The ascent trajectory optimization problem for the terminal velocity maximum is simulated comparing with the general pseudospectral optimal control software method, which demonstrates the effectiveness and rapidity of the proposed method.