On the Geometry of Virtual Nonlinear Nonholonomic Constraints

Virtual constraints are relations imposed on a control system that become invariant via feedback control, as opposed to physical constraints acting on the system. Nonholonomic systems are mechanical systems with nonintegrable constraints on the velocities. In this work, we introduce the notion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">virtual nonlinear nonholonomic constraints</i> in a geometric framework which is a controlled invariant submanifold and we show the existence and uniqueness of a control law preserving this submanifold.