Non-Collision Conditions in Multi-Agent Virtual Leader-Based Formation Control

Abstract

Formation control is one of the most important issues of group coordination for multi-agent robots systems. Some schemes are based on the leaderfollowers 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.

Method of Coordination of Motion of Swarm Robotic Systems

“…Representation of the robot leader and the robot follower as material points If some robot from the swarm is assigned as the leader, the stability of the swarm is at serious risk: in the case of a leader failure, the whole swarm becomes inoperable. To solve such a problem, we can identify a virtual leader and support a distance related to it [18]. The position of the virtual leader can be simply marked in the center of the swarm.…”

A General Solution to the Formation Control Problem Without Collisions for First-Order Multi-Agent Systems

“…Theorem 2. Consider the system (12) and the control law (22) along with definitions (13), (20) and (21). Suppose at the time instant t 0 there exists an agent, say R r , which is in risk of collision with…”

“…[8][9][10][11] In a first approach, collisions can be predicted, but not avoided, from initial conditions. 12,13 This can be useful if such initial conditions can be selected properly. Another, and the most known approach, consists in the use of Repulsive Potential Functions (RPFs) in combination with Attractive Potential Functions.…”

Decentralized Discrete-Time Formation Control for Multirobot Systems

“…The main contribution is an original formal proof about the convergence of robots to multiple equilibria where the robots are placed in the desired formation. The collision avoidance is not included in the analysis following the practical assumptions of [8,25,26] where reactive routines appear momentarily if the robots detect a shock danger or if the initial postures of robots generated free-collision trajectories, which occur frequently in the nature behaviors.…”