Estimation of an Admissible Domain of Uncontrolled Disturbances during Reorientation of an Asymmetric Rigid Body

Abstract

A nonlinear game problem of the reorientation of an asymmetric rigid body is considered for the case of uncontrolled disturbances, only their estimates being known. The domain of admissible controls is limited by an ellipsoid or a sphere. In the case of a sphere, the limitation corresponds to a pair of swiveling (vernier) engines. A method [1–4] of solving this problem is developed based on “equivalent linearization” of nonlinear conflict-controlled systems. Direct estimates are found of the admissible (with respect to executing a reorientation) domain of uncontrolled disturbances, as a function of both the given constraints on the controls and the initial location of the body. These estimates are convenient at the first stage of a solution process, when the possibility is determined of using the controls proposed in [1–4] in order to support the necessary reorientation. If the aforementioned estimates are satisfied with a safety margin, then (at the second stage of the solution) a particular value of the guaranteed time of reorientation can be found by iteration algorithms [1–4]. The results of calculations are presented.