Globally convergent adaptive tracking of angular velocity and inertia identification for a 3-DOF rigid body

This paper addresses the problem of a rigid body, with unknown inertia matrix, tracking a desired angular velocity reference using adaptive feedback control. The control law, which has the form of a sixth-order dynamic compensator, does not require knowledge of the inertia of the rigid body. A Lyapunov argument is used to guarantee that asymptotic tracking is achieved globally. Furthermore, an analytical expression for an upper bound on the magnitude of the required torque is presented for a given reference signal. Next, sufficient conditions on the reference signal are given under which asymptotic identification of the inertia matrix is achieved. Reference signals that satisfy these sufficient conditions are characterized and simulation results that illustrate the control algorithm are presented for a constant spin about a fixed axis and for sinusoidal spins about the body axes. The controller is implemented on an experimental testbed, and experiments are performed for several commanded reference signals. The experimental results demonstrate the tracking performance of the controller, and parameter convergence is observed.