This article proposes a decentralized navigation controller for a group of differential mobile robots that yields autonomous navigation, which allows reaching a certain desired position with a specific desired orientation, while avoiding collisions with dynamic and static obstacles. The navigation controller is constituted by two control loops, the so-called \emph{external control} loop is based on crowd dynamics, it brings autonomous navigation properties to the system, the \emph{internal control loop} transforms the acceleration and velocity references, given by the external loop, into the driving translational and rotational control actions to command the robots. The controller physical application could be based on several onboard sensors information, in such a way that the control strategy can be programmed individually into a group of mobile robots, this allows a decentralized performance, rendering the crowd dynamics behavior. Each mobile robot is considered as an agent to which it is associated a \emph{comfort zone} with a certain radius, that produces a repulsive force when it is trespassed by its environment or by another agent, this yields the necessary response to avoid collisions. Meanwhile, attractive forces drive the agents from their instantaneous position to the desired one. For collision-free navigation, Lyapunov stability method allows obtaining the stability conditions of the proposed controller and guarantees asymptotic convergence to the desired position and orientation. The navigation controller is tested by simulations, which supports the stability and convergence theoretical results.
crowd dynamics, mobile robot, autonomous navigation
68T40, 68T42, 93C85