Robust Performance Analysis Using $H_{2}$ -norm for Quadcopter-based Mobility on Small Bodies

This paper presents two major contributions: (1) a novel approach to the robust performance analysis by means of the robust $H_{2}$ -norm metric and (2) the application of this method to a spacecraft lander in an uncertain environment around a Small Solar System Body (SSSB). The objective of the first outcome is to quantify the effect of the uncertainties on the disturbance rejection and noise attenuation of a given control system formulated as a Linear Fractional Transform (LFT) representation. This is accomplished by tracing the robust $H_{2}$ -norm computation back to the structured singular value (SSV). Similar to the robust $H_{\infty}$ -norm computation, the upper and lower bounds on the robust $H_{2}$ -norm are estimated, whose relative gap is improved through a “branch and bound” algorithm. The technique is applied to the position tracking error during the landing scenario of Astrone, a quadcopter-based spacecraft. It utilizes a new mobility concept for enhanced surface mobility by hovering over the SSSB close to the surface. The environmental and system uncertainties of this concept are identified and modeled through an LFT. The results of the analysis are the expansion of nominal to robust performance budgets defined by the robust $H_{2}$ -metric and identifying system drivers in the preliminary controller design. Overall, this methodology assess the impact of estimation uncertainties typical for SSSB missions on the performance of the spacecraft system. Although this approach has been applied to the specific case of Astrone, the methodology allows analyzing any kind of system, whose performance is assessed by the $H_{2}$ -norm.