Construction of Synergistic Potential Functions on SO(3) with Application to Velocity-Free Hybrid Attitude Stabilization

TL;DR

This paper introduces a systematic method for constructing synergistic potential functions on SO(3), enabling global hybrid attitude stabilization using only inertial vector measurements, with demonstrated advantages over smooth control schemes.

Contribution

It presents a new angular warping map for explicit potential function construction and optimization of the synergistic gap, advancing hybrid control design on SO(3).

Findings

Successful global attitude stabilization with velocity-free hybrid control.

Explicit construction of potential functions with critical point analysis.

Simulation shows improved performance over smooth control schemes.

Abstract

We propose a systematic and comprehensive procedure for the construction of synergistic potential functions, which are instrumental in hybrid control design on SO(3). A new map via angular warping on SO(3) is introduced for the construction of such a family of potential functions allowing an explicit determination of the critical points and the synergistic gap. Some optimization results on the synergistic gap are also provided. The proposed synergistic potential functions are used for the design of a global velocity-free hybrid attitude stabilization scheme relying solely on inertial vector measurements. Comparative simulation results between the proposed global hybrid control scheme and the almost global smooth control scheme have been carried out.