Geometric PID-type attitude tracking control on SO(3)

TL;DR

This paper introduces a geometric nonlinear PID-type control scheme for rigid body attitude tracking on SO(3), demonstrating stability, robustness, and improved integrator performance through Lyapunov analysis and simulations.

Contribution

It presents a novel geometric PID-type control method on SO(3) with proven stability and enhanced robustness over existing PD schemes.

Findings

Almost global asymptotic stability demonstrated

Robustness to disturbance torque confirmed

Numerical comparison shows improved integrator effectiveness

Abstract

This article develops and proposes a geometric nonlinear proportional-integral-derivative (PID) type tracking control scheme on the Lie group of rigid body rotations, SO(3). Like PD-type attitude tracking control schemes that have been proposed in the past, this PID-type control scheme exhibits almost global asymptotic stability in tracking a desired attitude profile. The stability of this PID-type tracking control scheme is shown using a Lyapunov analysis. A numerical simulation study demonstrates the stability of this tracking control scheme, as well as its robustness to a disturbance torque. In addition, a numerical comparison study shows the effectiveness of the proposed integrator term.