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In this paper we propose an energy pumping-and-damping technique to regulatenonholonomic systems described by kinematic models. The controller designfollows the widely popular interconnection and damping assignmentpassivity-based methodology, with the free matrices partially structured. Twoasymptotic regulation objectives are considered: drive to zero the state ordrive the systems total energy to a desired constant value. In both cases, thecontrol laws are smooth, time-invariant, state-feedbacks. For the nonholonomicintegrator we give an almost global solution for both problems, with theobjectives ensured for all system initial conditions starting outside a setthat has zero Lebesgue measure and is nowhere dense. For the general case ofhigher-order nonholonomic systems in chained form, a local stability result isgiven. Simulation results comparing the performance of the proposed controllerwith other existing designs are also provided.

Smooth, Time-invariant Regulation of Nonholonomic Systems via Energy Pumping-and-Damping