Static output feedback control for the rotation of a 2-DOF differential-algebraic quaternion camera

Maurício S. Richter; Aurélio T. Salton

doi:10.20906/sbai.v1i1.2839

Maurício S. Richter School of Engineering, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS
Aurélio T. Salton School of Engineering, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS

DOI: https://doi.org/10.20906/sbai.v1i1.2839

Keywords: Nonlinear Systems, Visual-Based Rotation Control, Differential Algebraic Representation, Linear Matrix Inequalities, Static Output Feedback

Abstract

This work proposes a static output feedback (SOF) image-based control design for a 2 Degree-of-Freedom (2-DOF) camera rotation with the objective of positioning an external feature at a desired projected display coordinate. Using a Differential-Algebraic Representation (DAR) of the nonlinear system to model the rigid-body dynamic equations in terms of quaternions, the Lyapunov stability analysis results in bilinear matrix inequalities (BMI) which are turned into an optimization problem subject to constraints. An algorithm that searches iteratively for the gain and the Lyapunov function coefficients by solving individual linear matrix inequalities (LMI) is used. Numerical examples are provided to evaluate the stabilization and performance results obtained with the proposed method.