Adaptive Backstepping Control for a Fully-Actuated Rigid-Body in a Dual-Quaternion Framework

Abstract

We address the trajectory tracking problem for a fully actuated rigid-body with unknown mass and inertia parameters and unknown disturbance forces, using an adaptive backstepping controller based on dual-quaternions. We show that the proposed controller, in closed loop with a nonlinear model of the system, renders the equilibrium points uniformly asymptotically stable. The proposed controller is proved to be uniformely asymptotically stable. Numerical simulations are provided to demonstrate the performance of the controller. In addition it is shown through a numeric example that the parameter update law for the mass and inertia parameters can converge to the true mass and inertia parameters with a proper choice of desired trajectory