Date of Original Version




Rights Management

© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Abstract or Description

In this paper, we propose a variation-based method to linearize the nonlinear dynamics of robotic systems, whose configuration spaces contain the manifolds S 2 and SO(3), along dynamically-feasible reference trajectories. The proposed variation-based linearization results in an implicitly time-varying linear system, representing the error dynamics, that is globally valid. We illustrate this method through three different systems, a 3D pendulum, a spherical pendulum, and a quadrotor with a suspended load, whose dynamics evolve on SO(3), S 2 , and SE(3) × S 2 respectively. We show that for these systems, the resulting time-varying linear system obtained as the linearization about a reference trajectory is controllable for all possible reference trajectories. Finally, a Linear Quadratic Regulator (LQR)-based controller is designed to attenuate the error so as to locally exponentially stabilize tracking of a reference trajectory for the nonlinear system. Several simulations results are provided to validate the effectiveness of this method.




Published In

IEEE Access, 3, 1592-1604.