Sliding-Mode-Control–Based Instantaneously Optimal Guidance for Precision Soft Landing on Asteroid

Abstract

Precision soft landing guidance problem of a spacecraft on asteroid is addressed in this paper. Most of the methods in existing literature require linearized engagement dynamics or accurate time-to-go estimate, which is not easy to obtain in practice. To overcome these drawbacks, a heading error-dependent sliding-mode-control–based guidance approach was recently introduced in literature. However, it too suffered from disadvantages in terms of optimality and constant gravity setup-based formulation. To obviate these limitations, and, moreover, to accommodate the effect of asteroid’s angular rotation on the engagement dynamics, a sliding-mode-control–based instantaneously optimal (SMC-IO) guidance is presented in this paper, under a variable gravity setup, in which a heading-error-based sliding variable and a predefined range-dependent maximum velocity envelope profile are leveraged. A static optimization problem with square of instantaneous guidance command as the performance index and the sliding variable dynamics, velocity profile, equations of engagement, and thrust limit as constraints is solved to obtain the guidance command at every time instant. Simulation studies are presented to demonstrate the effectiveness of the presented SMC-IO guidance. An extensive comparative simulation study suggests superior performance of the SMC-IO guidance over widely referred existing landing guidance in terms of overall control effort and fuel usage.