Passivity-based visual motion observer with panoramic camera for pose control

This paper considers the vision-based estimation and pose control with a panoramic camera via passivity approach. First, a hyperbolic projection of a panoramic camera is presented. Next, using standard body-attached coordinate frames (the world frame, mirror frame, camera frame and object frame), we represent the body velocity of the relative rigid body motion (position and orientation). After that, we propose a visual motion observer to estimate the relative rigid body motion from the measured camera data. We show that the estimation error system with a panoramic camera has the passivity which allows us to prove stability in the sense of Lyapunov. The visual motion error system which consists of the estimation error system and the pose control error system preserves the passivity. After that, stability and L ₂-gain performance analysis for the closed-loop system are discussed via Lyapunov method and dissipative systems theory, respectively. Finally, simulation and experimental results are shown in order to confirm the proposed method.