Dynamic scaling-based immersion and invariance adaptive pose tracking control using dual quaternions

Abstract

This paper investigates the position and attitude (pose) tracking control of a rigid body with uncertain mass and inertia. By virtue of the dual quaternion description, a six-degree-of-freedom (6-DOF) relative motion model is established in an integrated and compact way. Then an adaptive pose tracking controller is proposed based on the immersion and invariance (I&I) theory, where the key integrability obstacle is overcome by the dynamic scaling technique. Compared with the existing filter system-based method that constructs a filter system to circumvent the integrability obstacle, the dynamic scaling-based method is directly designed based on the original system, which is capable of retaining all benefits of the I&I design with much lower dimension dynamic extensions. Comparisons with the filter system-based I&I method and the classical certainty equivalent method are first carried out from the theoretical analyses, which elucidate benefits of the proposed method in lower control demands. Then the comparative simulations are conducted to verify the features and effectiveness of the proposed dynamic scaling-based I&I adaptive control scheme.