Carnegie Mellon University
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Variation-Based Linearization of Nonlinear Systems Evolving on SO(3) and S2

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posted on 2015-08-01, 00:00 authored by Guofan Wu, Koushil SreenathKoushil Sreenath

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.


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