Centralized feedback stabilization of multiple nonholonomic agents under input constraints

In this paper we use the centralized multirobot navigation function methodology established by the authors, augmented with an enhanced dipolar navigation field suitable for non-holonomic vehicles. A properly designed discontinuous feedback control law is applied to steer the nonholonomic vehicles. The resulting high frequency switching behavior, known as chattering, which is inherent in discontinuous controllers, is tackled with an appropriately designed discontinuous backstepping controller, which effectively reduces chattering. The vehicles are assumed to have limitations on their maximum achievable velocities. Those issues are taken into account in the control law design. The resulting closed form control scheme provides robust navigation with guaranteed collision avoidance and global convergence properties, as well as fast feedback, rendering the methodology particularly suitable for real time implementation, on systems with limited actuation capabilities. Collision avoidance and global convergence properties are verified through non - trivial computer simulations.