Spacecraft Trajectory Optimization by Improved Sequential Convex Programming for a Starship-Like Vehicle, Executing Atmospheric Hypersonic Entry Glide to Precision-Land on Mars

Abstract

Mars entry guidance faces a critical challenge: navigating hypersonic velocities within the thin atmospheric layers (120 – 45 𝑘𝑚 altitude) while balancing conflicting objectives of precision targeting, thermal survival, and structural integrity. This study addresses a core research question on a successive convexification algorithm that enables precise trajectory optimization for Starship’s hypersonic glide through the upper atmosphere of Mars while enforcing hard physical constraints such as heat flux, g-load, equilibrium glide and dynamic pressure. By formulating such successive convexification - based framework, the inherently non-convex entry problem is decomposed into iteratively refined convex sub-problems, enabling computational tractability under Mars’ variable CO₂-rich atmosphere. The guidance architecture integrates bank angle modulation for lift vectoring and angle-of-attack adjustments for thermal management, optimizing energy dissipation while mitigating heating spikes and aerodynamic stress.

Simulations demonstrate that the collocation discretization strategy used ensures trajectory adherence within the entry corridor, achieving terminal positioning errors below 3 𝑘𝑚 at 45 𝑘𝑚 altitude. The algorithm’s robustness is validated under ±10% dispersions in initial velocity (4.3 𝑘𝑚/𝑠) and flight-path angle (−15°) from a parking orbit around the planet, with heat flux, dynamic pressure, and g-load profiles remaining within mission-critical limits. Sensitivity analyses reveal that atmospheric density uncertainties induce predictable deviations compensated by rapid convex optimizations. These results align and improve on previous NASA mission data.

The study bridges theoretical convex optimization with operational reality, demonstrating that modern computational guidance outperforms legacy predictor-corrector methods in handling nonlinear dynamics and path constraints. By extending the convex framework with adaptive trust regions and sequential convex programming, the proposed method reduces terminal errors by 40% compared to state-of-the-art approaches (Mars 2020). This advancement not only enhances Starship’s capability to deliver crewed and cargo payloads to predefined Martian coordinates but also establishes a foundation for integrating the hypersonic glide phase with the subsequent powered descent phases. As humanity strides toward sustained Mars exploration, this work underscores the viability of successive convexification as a paradigm for achieving precise atmospheric glide through the Martian atmosphere.