Regulation of nonholonomic systems: A smooth, time-invariant approach ⁎⁎This paper is supported by the Research Fund from Science and Technology on Underwater Vehicle Technology (6142215180203), NSFC (61473183, U1509211), National Key R&D Program of China (SQ2017YFGH001005), CSC, and by the Government of the Russian Federation (074U01), the Ministry of Education and Science of Russian Federation (14.Z50.31.0031, goszadanie no. 8.8885.2017/8.9).

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 the state to zeroor drive the systems total energyto 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.