This paper presents a theoretical framework for linearization and stabilization of second-order nonholonomic chained systems. By giving a new criterion for the problem of nonsmooth nonregular feedback linearization, it is proved that second-order chained systems are nonregular static state feedback linearizable. A discontinuous control law is obtained based on linear system theory and the inver...

This paper presents a theoretical framework for nonregular feedback linearization and stabilization of second-order nonholonomic chained systems. By giving a new criterion for the problem of nonsmooth nonregular feedback linearization, it is proved that second-order chained systems are nonregular static state feedback linearizable. A discontinuous control law is obtained based on linear system ...

Invariant manifolds of equations governing the dynamics of conservative nonholonomic systems are investigated. These manifolds are assumed to be uniquely projected onto configuration space. The invariance conditions are represented in the form of generalized Lamb’s equations. Conditions are found under which the solutions to these equations admit a hydrodynamical description typical of Hamilton...

We analyze the behavior of redundant robots when the joint motion is generated by inverting task velocity commands through a kinematic control scheme. Depending on the chosen inversion scheme, the robot motion is subject to differential constraints that may or may not be integrable. Accordingly, we give a classification in terms of holonomic, partially nonholonomic, and completely nonholonomic ...

Abstract This paper studies hamiltonization of nonholonomic systems using geometric tools, building on [1] , [5] . The main novelty in this is the use symmetries and suitable first integrals system to explicitly define a new bracket reduced space that codifies dynamics carries, additionally, an almost symplectic foliation (determined by common level sets integrals); particular cases interest, P...