Stabilization and optimality results for the attitude control problem

Abstract

In this paper we present some recent results on the description and control of the attitude motion of rotating rigid bodies We derive a new class of globally asymptotically stabilizing feedback control laws for the complete i e dynamics and kinematics attitude motion We show that the use of a Lyapunov function which involves the sum of a quadratic term in the angular velocities and a logarithmic term in the kinematic parameters leads to the design of linear controllers We also show that the feedback control laws for the kinematics minimize a quadratic cost in the state and control variables for all initial conditions For the complete system we construct a family of exponentially stabilizing control laws and we investigate their optimality characteristics The proposed control laws are given in terms of the classical Cayley Rodrigues parameters and the Modi ed Rodrigues parameters