Passivity-Based Dynamic Visual Feedback Control for Three-Dimensional Target Tracking: Stability and $L_{2}$-Gain Performance Analysis

Abstract

This paper investigates vision-based robot control based on passivity for three-dimensional (3-D) target tracking. First, using standard body-attached coordinate frames (the world frame, camera frame, and object frame), we represent the relative position and orientation between a moving target and a camera as an element of SE(3). Using this representation we derive a nonlinear observer to estimate the relative rigid body motion from the measured camera data. We then establish the relationship between the estimation error in a 3-D workspace and in the image plane. We show passivity of the dynamic visual feedback system by combining the passivity of both the visual feedback system and the manipulator dynamics which allows us to prove stability in the sense of Lyapunov for the full 3-D dynamic visual feedback system. The L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2 </sub> -gain performance analysis, which deals with the disturbance attenuation problem, is then considered via dissipative systems theory. Finally, experimental results are presented to verify the stability and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -gain performance of the dynamic visual feedback system