Distributed Decision Making on Scaling Size for Obstacle Avoidance in Affine Formation Control

Multiple leaders are usually employed in an affine formation control framework. The team formation can be uniquely determined by those pre-selected leaders. However, the affine formation parameters, such as the scaling size, rotation angle, and even transformation matrix, are always given as a priori knowledge in most reported results. In this work, a distributed decision making method on scaling size is proposed for obstacle avoidance in affine formation control. One distinguishing feature of the proposed scale decision method is the maintenance of the collective formation shape, which is especially significant in bearing-sensitive situations. Firstly, the mapping from sensed obstacle information to intuitive local scaling policy is designed. Then, a distributed average tracking control based filter is proposed to integrate those local scaling policies, yielding a formation decision on scaling size in agreement. Consequently, the affine formation obstacle avoidance problem is solved by the proposed control scheme, whose effectiveness is then verified by the simulation results.