  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.
