Reduced Space Sequential Convex Programming for Rapid Trajectory Optimization

Convex optimization is of great interest as an efficient and reliable solver in the field of aerospace engineering. Existing research often focuses on developing proper convexification techniques to handle aerospace problems within the convex optimization framework, with limited attention to further efficiency enhancements in convex optimization solving, such as by reducing the optimization problem size. Motivated by the real-time requirements of onboard aerospac applications, this article presents a unified framework for reduced space sequential convex programming formulations, emphasizing a significant reduction of optimization variables and constraints. The primary idea is to employ an iterative scheme to explicitly approximate the dynamic implicit function and subsequently eliminate the explicitly defined state variables and dynamic equality constraints, thereby constructing a sequence of reduced space optimization subproblems to be solved iteratively. Within the proposed framework, a family of reduced space sequential convex programming methods with different performance–complexity tradeoffs is developed by virtue of the fixed-point iteration, Newton iteration, damped Newton iteration, and simplified Newton iteration. Numerical simulations for a minimum-fuel rocket landing problem inside atmosphere are conducted to demonstrate the performance of the developed methods.