Nonholonomic systems stabilization and tracking control using discontinuous control

In this paper, a new approach to design a controller for nonholonomic systems to follow a pre-specified trajectory and/or stabilize in a fixed point is proposed. Using the nonholonomic chained form and reference model, a nonautonomous system can be obtained and, then, it can be brought to the autonomous form with adequate input signal or feedback controls. Using the Routh-Hurwitz criterion or proper choice of the eigenvalues (of the closed-loop system) it is possible to find conditions that globally stabilize the system. These results are significant to associate linear and geometric control tools with a class of nonlinear systems. It is shown that it is expandable to a n-dimensional two input chained form nonholonomic systems. The simulation of an unicycle control is presented as an application example. Future research include generalization of the method to other forms of nonholonomic systems in Rⁿ with some uncertainties.