Globally Exponentially Stable Velocity Observers on SE(3) Using Pose Measurements

This paper addresses the design of 6-degrees-of freedom (6DOF) velocity observers for rigid bodies when pose measurements are available, in the absence of velocity information. Based on the foundational theory of the gradient-based observers on Lie groups, we construct the velocity observers on SE(3) with the innovation terms derived from the gradient of potential functions. To avoid the unstable critical points of the potential functions on the manifold and achieve global stability, two different hybrid mechanisms are utilized to design the observers, with the former method working by directly changing the state of the observer, while the latter by appropriately selecting the innovation terms determined by the gradient of synergistic potential functions, thus leading to reset-based and synergistic-based hybrid observers, respectively. The resulting observers are shown to be globally exponentially stable. Simulations are conducted to illustrate the performance of the proposed observers.