Robust stabilization of uncertain kinematic systems in nonholonomic mobile robots with one trailer

Based on visual servoing feedback, this paper provides a novel uncertain model of the kinematic systems in nonholonomic mobile robots with one trailer with uncalibrated visual servoing parameters. The strongly nonlinear disturbances and drift terms in its uncertain chained form of this model fails to meet the so called triangularity condition. The methods available in the literatures are not suitable to be used to investigate its stabilizing problem of the system. In order to deal with this difficulty, the special structure of the systems is exploited to design the stabilizing controller, which is divided into three phases. In the first phase, a newly state transformation is exploited to propose a stabilizing controller to make most of the states of the system tends to zero only excepts one state. In the second phase, the left state is stabilized and the other states remain little change by designing another controller. In the final phase, the control inputs can be set zero. The states remain constant. Finally, the simulation is presented to illustrate the stabilizing performance of the developed control algorithm.