A shape-constrained arc-length reformulation for sequential convex programming in hypersonic reentry trajectory optimization

Hypersonic reentry trajectory optimization must satisfy stringent terminal conditions and path constraints involving heat flux, dynamic pressure, load factor, and no-fly-zone (NFZ) avoidance under strongly nonlinear dynamics. This paper proposes SHARP-SCP (Shape-constrained Hierarchical Arc-length Reformulated Projection), a Bezier-based sequential convex programming framework that uses arc length as the independent variable and parameterizes states and controls with piecewise control points. The Bezier convex-hull property transfers linear state/control bounds from dense collocation nodes to sparse control points, ensuring continuous segment-wise satisfaction and reducing inter-node leakage. In the arc-length/log-velocity domain, the limits on heat flux and dynamic pressure are exactly reconstructed as linear inequalities under an exponential-atmosphere model, while only the aerodynamic term in the load factor constraint requires sequential approximation. Arc-length Gauss collocation induces velocity-adaptive time spacing, concentrating nodes in high-speed segments without mesh refinement. With virtual control, projection updates, and hierarchical refinement, SHARP-SCP converges from simple initial guesses and reduces total constraints by 42.9% relative to pointwise enforcement. Compared with hp-ARSCP and hp-ARPM on maximum-terminal-velocity and minimum-total-heat-load tasks, it achieves near-benchmark terminal performance, consistent NFZ avoidance, smoother controls, and runtimes below 47.9% of those of hp-ARSCP and below 3.04% of those of hp-ARPM. Local nonlinear integration confirms dynamic feasibility. A 200-case Monte Carlo study with initial-state, aerodynamic, and density perturbations demonstrates robustness under hard terminal-time and terminal-speed constraints.