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 S^n-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.