Collision-free leader-following formation navigation with consideration of initial movements of followers

In this paper, we discuss the leader-following formation navigation (LFFN), which is one of the most important issues in formation control. In this formation, one leader is controlled by a human operator, while multiple followers pass along the leader´s trajectory in the same motion to the leader. The collision avoidance problem in the LFFN has been discussed in a previous work. However, the problem of initial movements of followers still remains. The followers move along the leader´s path behind the leader at some intervals. Thus, around the initial time, the followers cannot determine routes to track because there is no leader´s path before the initial time. This paper discusses how the followers should move around the initial time in order to start up naturally and to achieve the LFFN afterwards. The effectiveness of the proposed method is demonstrated by a simulation with three mobile robots.