Adaptive quaternion feedback regulation for eigenaxis rotations

Abstract

A controller to rotate a rigid body between two successive orientations is designed. Particular features are the fact that it is based on the quaternion approach, known to provide singularity-free attitude description, and it is adaptive in the sense that it does not need specific knowledge of the inertia matrix. Global stability of the overall controller is proved analytically and tested in computer simulations. In this paper, we design a nonlinear adaptive controller that per- forms vehicle orientation in the presence of large uncertainties of the inertia matrix. The concept of adaptive control for linear time- invariant systems dates back to the 1950s although reliable designs of proven stability did not appear before the late 1970s.14'15 Both di- rect and indirect adaptive control schemes are presented. The direct adaptive controller has the advantage of simplicity in the imple- mentation, since it is based on a simple gradient-type adaptation law. However, the indirect approach we present, although of more complex implementation, is based on a recursive least-squares iden- tification algorithm that has the advantage of converging faster. In general, adaptive controllers of nonlinear systems are based on a linearized model of the plant, and stability can be shown only locally. In a few cases the particular structure of a nonlinear system lends itself to a globally stable adaptive control algorithm, such as the case of robotic manipulators.16 The adaptive controller presented below falls in this category, for which we can show global stability of the overall system composed of the plant and the controller with recursive estimates of the inertia matrix. Eigenaxis rotation is presented in Sec. II. Three control tech- niques are given next: a sliding-mode technique in Sec. Ill, direct adaptive control in Sec. IV followed by an indirect approach in Sec. V, whereas examples and conclusions are given in Sec. VI and VII, respectively.