On the design of synergistic potential functions on SO(3)

This paper deals with the design of synergistic potential functions which are instrumental in hybrid control design on SO(3). We propose a systematic procedure for the construction of central synergistic families of potential functions on SO(3) via angular warping. A new map on SO(3) is introduced allowing for an explicit computation of the critical points of the potential functions as well as the synergistic gap. Some optimization results on the synergistic gap are also provided.