Approximate Analytical Solution for Attitude Motion of a Free-flying Space Robot and Analysis of Its Nonholonomic Properties

Abstract

In recent years, many advanced space missions, such as on-orbit construction and on-orbit repair, have been proposed, and it is expected that free-flying space robots will need to be more intelligent, versatile, and dexterous in the future. One of the technologies required for such advanced missions is attitude control that actively uses the nonholonomic properties of attitude motion. Although some control methods have been proposed in previous studies, their applicability is limited. Therefore, it is necessary to develop an analytical tool that can be applied to advanced space robots. In the present study, analytical investigations of attitude motion are conducted for future free-flying space robots that actively use nonholonomic properties. In order to derive the solution in a general form, we use a rotational matrix kinematics equation and solve this equation using Magnus expansion. Owing to this analysis, the derived solution preserves the structure of the Lie group of three-dimensional attitude motion. As a practical solution, we derive the solution for "rectilinear actuation," which contributes to concise formulation. We also apply the derived solution to the analysis of the nonholonomy of attitude motion and confirm that the analytical solution can be useful to comprehensively understand the nonholonomic system.