Stable navigation in formation for a multi-robot system based on a constrained virtual structure

•Constrained virtual structure approach for multi-robot navigation in formation.•Stable multi-controller architecture (Obstacle avoidance and Attraction to Dynamical target) based on Lyapunov synthesis.•Attainability demonstration of dynamic targets set-points while respecting the kinematic constraints of the group of mobile robots.

This paper deals with the navigation in formation of a group of mobile robots. A set of virtual targets (points) forms a virtual structure of the same shape as the desired formation. Hence, to join and to remain in this formation, each robot has only to track one of these targets. In order to track the chosen target, it has to be attainable by the robot despite its kinematic constraints. This paper studies then the maximum allowed dynamic of the virtual structure according to the kinematic constraints of the robots. Both linear and angular velocities of the targets are constrained. Moreover, depending on these velocities, some relative positions (targets) in the formation become unattainable. These positions are also defined. A stable control law allows us to attain the generated set-points. Simulation and experimental results validate the proposed contributions.