A novel disturbance rejection optimal guidance method for enhancing precision landing performance of reusable rockets

Powered descent guidance (PDG) is a key technology for reusable rockets to accomplish high-precision landing on Earth. Different from the well-established PDG for lunar landing and planetary landing, endoatmospheric powered descent guidance is required to accommodate nonlinear dynamics and more disturbing flight conditions, including engine thrust fluctuation, aerodynamic uncertainty, and winds. For example, the winds can produce a persistent aerodynamic force disturbance on the rocket, resulting in the decrease of landing accuracy, the increase of propellant usage, and even the divergence of guidance commands. Existing works have considered six-degree-of-freedom dynamics and aerodynamic model, but do not systematically deal with disturbances in the guidance design. Therefore, addressing the disturbance rejection issue for endoatmospheric nonlinear optimal guidance is imperative, and the objective is the determination of guidance commands to steer the rocket to fly a trajectory that satisfies the terminal landing conditions and optimizes the performance index of propellant usage in the presence of disturbances.

Recently, a team of researchers led by Huifeng Li and Ran Zhang from Beihang University, China proposed an optimal feedback guidance method with disturbance rejection objective. This work represents an advanced engineering design methodology that is capable of unifying optimal guidance performance and disturbance rejection level.

The team published their work in 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 School of Astronautics at Beihang University (China), a senior expert whose research interests focus on the field of flight vehicle guidance and control.

“A new Pseudospectral Differential Dynamic Programming (PDDP) method is developed to solve the Hamilton-Jacobi-Bellman equation of the Endo-PDG-DR problem, and correspondingly a robust neighboring optimal state feedback law is obtained with a simple affine form that is favorable for real-time implementation. More importantly, 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.” said Huifeng Li.

“Using the derived optimal feedback guidance law, a disturbance rejection level is quantitatively measured by rigorously characterizing an input-output property from the unmodeled disturbance to the predicted guidance error. Based on the quantified disturbance rejection level, a simple and practical quadratic weighting parameter tuning law is proposed to attenuate the adverse effect of unmodeled disturbance.” said Huifeng Li.

However, more delicate research works are still needed to explore guidance robustness. In this regard, Li also put forward three major development directions may be pursued in future works including online model identification, highly constrained optimal trajectory generation, and guidance parameter learning.

Other contributors include Ran Zhang and Xinglun Chen from School of Astronautics at Beihang University (China).

This work was supported by the National Natural Science Foundation of China (No. 62103014).

About Chinese Journal of Aeronautics 

Chinese Journal of Aeronautics (CJA) is an open access, peer-reviewed international journal covering all aspects of aerospace engineering, monthly published by Elsevier. The Journal reports the scientific and technological achievements and frontiers in aeronautic engineering and astronautic engineering, in both theory and practice. CJA is indexed in SCI (IF = 5.3, top 4/52, Q1), EI, IAA, AJ, CSA, Scopus.