Blue Origin and Space X have shown how rocket launchers can return autonomously to Earth, and now researchers in China have published algorithms for powered descent guidance (PDG) for reusable rockets to accomplish high-precision landing, writes Nick Flaherty.

This is different from the PDG algorithms for autonomous landings on the Moon or Mars, as the powered descent guidance is required to accommodate nonlinear dynamics and more disturbing flight conditions, including engine-thrust fluctuations and aerodynamic uncertainty.

Existing works have considered six-degrees-of-freedom dynamics and the aerodynamic model, but not disturbances in the guidance design. The team of researchers is led by Huifeng Li and Ran Zhang from Beihang University, China.

“We formulated a novel problem called endoatmospheric powered descent guidance with disturbance rejection (Endo-PDG-DR) by dividing and conquering disturbances,” said Huifeng Li, professor at the School of Astronautics at Beihang University, whose research interests focus on the field-of-flight vehicle guidance and control.

“The disturbances are divided into two parts: modelled and unmodelled disturbances. As a result, two different disturbance rejection strategies are accordingly adopted to deal with the two kinds of disturbances.

“The modelled disturbance is proactively exploited by optimising the formulated guidance problem, where the modelled disturbance is augmented as a new state of the dynamics model.

“The unmodelled disturbance is reactively attenuated by adjusting the second-order partial derivative of the Hamiltonian of the optimal guidance problem with a parameterised, time-varying, quadratic performance index.

“The optimal feedback guidance law unifies two functions: the adaptive optimal steering and disturbance attenuation. Adaptive optimal steering accommodates the disturbance, and the disturbance attenuation compensates for the state perturbation effect induced by the remaining unmodelled disturbance.”

All this led to a simple, practical quadratic-weighting parameter to compensate for the unmodelled disturbances.