Improving precision landing of reusable rockets

Improving precision landing of reusable rockets
by Simon Mansfield
Sydney, Australia (SPX) Dec 27, 2024

Powered descent guidance (PDG) plays a critical role in enabling reusable rockets to achieve precise landings on Earth. Unlike lunar or planetary landings, endoatmospheric PDG must contend with complex nonlinear dynamics and challenging conditions such as engine thrust fluctuations, aerodynamic uncertainties, and wind disturbances. These factors can significantly affect landing accuracy, increase propellant consumption, and lead to erratic guidance commands. Although six-degree-of-freedom dynamics and aerodynamic models are considered in existing studies, they often lack robust disturbance management in guidance design. Addressing this limitation is essential to optimize propellant usage and ensure accuracy under adverse conditions.

A research team led by Huifeng Li and Ran Zhang from Beihang University, China, has introduced an innovative optimal feedback guidance method aimed at mitigating disturbances. Their study presents a framework combining optimal guidance performance with advanced disturbance rejection strategies. This research was published in the Chinese Journal of Aeronautics on December 14, 2024.

"In this work, we formulated a novel problem called Endoatmospheric Powered Descent Guidance with Disturbance Rejection (Endo-PDG-DR) by dividing and conquering disturbances. The disturbances are divided into two parts, modeled and unmodeled disturbances; as a result, two different disturbance rejection strategies are accordingly adopted to deal with the two kinds of disturbances: the modeled disturbance is proactively exploited by optimizing the formulated guidance problem where the modeled disturbance is augmented as a new state of the dynamics model; the unmodeled disturbance is reactively attenuated by adjusting the second-order partial derivative of the Hamiltonian of the optimal guidance problem with a parameterized time-varying quadratic performance index," said Huifeng Li, professor at the School of Astronautics, Beihang University.

The team employed a newly developed Pseudospectral Differential Dynamic Programming (PDDP) method to solve the Hamilton-Jacobi-Bellman equation. This approach produced a robust state feedback law with an affine form suitable for real-time use. Li noted, "The obtained optimal feedback guidance law unifies two synergistic functionalities, i.e., adaptive optimal steering and disturbance attenuation. The adaptive optimal steering accommodates the modeled disturbance, and the disturbance attenuation compensates for the state perturbation effect induced by the remaining unmodeled disturbance."

The team also devised a quantitative metric to measure disturbance rejection levels by analyzing the relationship between unmodeled disturbances and guidance error. Based on this metric, a practical quadratic weighting parameter tuning law was introduced to minimize the impact of unmodeled disturbances.

Despite these advancements, Li emphasized the need for further research to enhance guidance robustness. "Future studies should explore online model identification, highly constrained optimal trajectory generation, and guidance parameter learning," he said.

Research Report:Optimal feedback guidance with disturbance rejection for endoatmospheric powered descent