Motion control of nonholonomic system with rolling constraint

In this paper, we propose a control strategy for a class of nonholonomic systems. A system with nonholonomic constraint is called a nonholonomic system, and as Brockett showed, the equilibrium of such systems can not be stabilized with any continuous static state feedbacks even though the system is controllable in the sense of nonlinear. A control strategy we propose is transforming this system into time-state control form by coordinate transformation and input transformation. We will apply this control strategy to the motion control of a rigid ball that is held between two parallel plates.