For simple angles you can use an element of SO(2) as your state. But if the algorithm calls for a difference of two states, the result would have to be an element of a real vector space (in this case a single number between -pi and pi). Analogue to this an addition of a state manifold and a vector also results in a state manifold. You can switch between those representations using the exp and log functions. In the papers these „new“ operators are described as boxplus and boxminus. And the elegant thing of this approach is that in most cases you just would replace plus with boxplus and minus with boxminus and it just works(tm)