Passive configuration decomposition and practical stabilization of nonholonomic mechanical systems with symmetry

We consider a certain class of nonholonomic mechanical systems with symmetry. First, we introduce the notion of passive configuration decomposition, which enables us to decompose the system´s Lagrange-D´Alembert dynamics into two decoupled systems, evolving on their respective configuration spaces according to the symmetry and individually possessing Lagrangian-like structure and passivity. We then propose passivity-based time-varying and switching control laws, which achieve practical stabilization by controlling the two decoupled systems on their own configuration spaces individually. Multiple wheeled mobile robots formation stabilization simulation is also performed to support the theory.