A Unified Stabilization Control of Nonholonomic Systems With or Without State Constraints

In this paper, we present a control scheme for nonholonomic systems with or without state constraints in a unified manner. A tan-type barrier Lyapunov function is considered to address time-varying constrains for the x0-subsystem. By introducing a new nonlinear state-dependent function that purely depends on constrained states to deal with asymmetric time-varying state constraints for the x-subsystem. A coordinate transformation are constructed to convert the original state-constrained space into a free space. We design a dynamic surface control based backstepping design, removing the demanding feasibility conditions on virtual controllers. As a result, cumbersome off-line calculations are not required for feasibility verification, enabling designers to choose design parameters more freely and leading to the system to handle a wider range of initial conditions.