Asymptotic stabilization for the 3-D chained system: the vector field orientation approach

Abstract

The paper presents a proposition of asymptotic stabilization for a 3D chained system with the use of the vector field orientation (VFO) approach first introduced by Michalek and Kozlowski (2004 and 2005), where have been applied to solve a trajectory tracking task for such systems like unicycle cart, nonholonomic manipulator and also for 3D chained system. Proposed approach allows designing a simple control law with an intuitive geometrical interpretation. Stabilization with a VFO controller presented in this work can be treated as some extension of the tracking controller described by Michalek and Kozlowski (2005). Performance of the proposed solution is illustrated by simulation results.