Distributed Attitude Estimation for Multiagent Systems on $SO(3)$

In this article, we consider the problem of distributed attitude estimation of multiagent systems, evolving on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$SO(3)$</tex-math></inline-formula>, relying on individual angular velocity and relative attitude measurements. The interaction graph topology is assumed to be an undirected tree. First, we propose a continuous nonlinear distributed attitude estimation scheme with almost global asymptotic stability guarantees. Thereafter, we propose a hybrid nonlinear distributed attitude estimation scheme enjoying global asymptotic stabilization of the attitude estimation errors to a common constant orientation. Finally, the proposed hybrid attitude estimation scheme is used to solve the pose estimation problem of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula>-vehicles navigating in a 3-D space, with global asymptotic stability guarantees, where the only available measurements are the local relative bearings and the individual linear velocities. Simulation results are provided to illustrate the effectiveness of the proposed estimation schemes.