Almost global attitude stabilization of a rigid body for both internal and external actuation schemes

One of the recent developments in attitude control is the notion of almost-global asymptotic stabilization (AGAS) using coordinate-free control laws. In this paper, we examine two aspects related to this line of research. The first is the problem of AGAS with internal actuation. Since all of the results concerning AGAS so far focus on external actuation, we address the internal actuation case and show that there exists a class of control laws that can almost globally stabilize the desired equilibria either by external or internal actuation. The second aspect we analyze is the construction of potential functions leading to AGAS. We show that it is possible to construct such potential functions in such a way that the resulting control torque depends only on two vector observations, thus avoiding the need for explicitly computing the attitude matrix for the purpose of feedback. We also show that these potentials are nothing but the commonly used error functions, namely the modified trace functions.