Non-Collision Conditions in Multi-Agent Virtual Leader-Based Formation Control
Eduardo Gamaliel Hernández-Martínez, Eduardo Aranda-Bricaire · International Journal of Advanced Robotic Systems · 2012
Formation control is one of the most important issues of group coordination for multi-agent robots systems. Some schemes are based on the leader-followers approach where some robots are considered as group leaders which influence the group behaviour. In this work, we address a formation strategy using a virtual leader which has communication with the rest of the follower robots, considered as omnidirectional robots. The virtual leader approach presents advantages such as analysis simplification and fewer sensing requirements in the control law implementation. The formation control is based on attractive potential functions only. The control law guarantees the convergence to the desired formation but, in principle, does not avoid inter-agent collisions. A set of necessary and sufficient non-collision conditions based on the explicit solution of the closed-loop system is derived. The conditions allow concluding from the initial conditions whether or not the agents will collide. The results are extended to the case of unicycle-type robots.