High-Accuracy 3-DoF Hypersonic Reentry Guidance via Sequential Convex Programming

This paper presents a sequential convex programming (SCP) algorithm designed to achieve dynamically feasible solutions for highly nonlinear optimal control problems over sparse time grids. This framework solves a sequence of convex subproblems until convergence to a solution of the original nonconvex problem. The proposed algorithm has the following features to enhance speed and accuracy: (1) a deviation variable model to improve the scaling of each convex subproblem; (2) an exact discretization technique that is inverse-free and permits arbitrarily-precise satisfaction of the dynamics over large time horizons; (3) a virtual buffer approach to eliminate artificial infeasibility that allows each subproblem to be represented as a quadratic program (QP); and (4) a variable time grid that leaves the timesteps between nodes (and thus the time-horizon) as free variables for the optimizer. Discretization is performed via a ``stitching condition'' required for the deviation variable approach. This SCP algorithm demonstrates high-fidelity satisfaction of the dynamics for particularly nonlinear systems, such as hypersonic entry vehicles, while harnessing solution speeds from quadratic programming amenable to real-time implementations. To remove jitter from the resulting control solution, a control rate limit constraint can easily be applied across each timestep due to the continuous first-order-hold parameterization of the control. To demonstrate this performance, a comprehensive study is performed for a 3-degree-of-freedom (DoF) trajectory optimization on multiple hypersonic reentry scenarios formulated as optimal control problems. When compared against state-of-the-art methods, the optimal solutions obtained by this SCP algorithm have reduced residual errors between the solution trajectory and a one-shot integration of the full nonlinear dynamics for hypersonic reentry.