Virtual nonholonomic constraints: A geometric approach

Virtual constraints are relations imposed in a control system that become invariant via feedback instead of real physical acting on the system. Nonholonomic systems mechanical with non-integrable velocities. In this work, we introduce notion virtual nonholonomic geometric framework. More precisely, it is controlled distribution associated an affine connection We show existence and uniqueness law defining constraint characterize trajectories closed-loop as solutions induced constrained connection. Moreover, dynamics for terms constraints, i.e., when can obtain from constraints.