Fix the non-robustness issue for a class of minimally rigid undirected formations

Gradient control is a method based on potential functions to locally stabilize undirected rigid formations. However, when there is mismatch between two neighboring agents´ understandings of the desired distance between them, such a potential-based control will almost for certain cause an undirected minimally rigid formation to rotate in the plane. In this paper we propose two methods to fix such a problem: one way is by estimating the distance discrepancy and cancelling it, which proves to work for undirected triangular formations; Another way is to employ a distributed edge orientation algorithm to change a class of minimally rigid undirected formations to be directed ones.