Smooth, Time-invariant Regulation of Nonholonomic Systems via Energy Pumping-and-Damping
It provides a novel control design for nonholonomic systems, which are challenging due to Brockett's condition, offering smooth time-invariant feedback that avoids discontinuous or time-varying controllers.
This paper proposes a smooth, time-invariant energy pumping-and-damping controller for regulating nonholonomic systems, achieving almost global asymptotic stability for the nonholonomic integrator and local stability for higher-order chained forms.
In this paper we propose an energy pumping-and-damping technique to regulate nonholonomic systems described by kinematic models. The controller design follows the widely popular interconnection and damping assignment passivity-based methodology, with the free matrices partially structured. Two asymptotic regulation objectives are considered: drive to zero the state or drive the systems total energy to a desired constant value. In both cases, the control laws are smooth, time-invariant, state-feedbacks. For the nonholonomic integrator we give an almost global solution for both problems, with the objectives ensured for all system initial conditions starting outside a set that has zero Lebesgue measure and is nowhere dense. For the general case of higher-order nonholonomic systems in chained form, a local stability result is given. Simulation results comparing the performance of the proposed controller with other existing designs are also provided.