Convergence of gradient-type observers for invariant systems on SO(n)

C. Lageman, R. Mahony, J. Trumpf and T. Hamel

Applications in robotic autonomous systems have motivated the recently increasing interest in observers for invariant systems on Lie groups. Here, we consider an observer for left-invariant systems on the special orthogonal group SO(n) with outputs invariant under the left action of SO(n) on the output space Sn-1. We propose an observer construction for these systems based on a gradient law. We give a criterion on the inputs for almost global convergence of this observer.