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 L2-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.

[1]  M. Fujita,et al.  Passivity-based dynamic visual feedback control with uncertainty of camera coordinate frame , 2005, Proceedings of the 2005, American Control Conference, 2005..

[2]  Guoqiang Hu,et al.  Homography-Based Visual Servo Control With Imperfect Camera Calibration , 2009, IEEE Transactions on Automatic Control.

[3]  Masayuki Fujita,et al.  Visual motion observer-based pose synchronization: A passivity approach , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[4]  Hiroyuki Kawai,et al.  Passivity-Based Dynamic Visual Feedback Control for Three-Dimensional Target Tracking: Stability and $L_{2}$-Gain Performance Analysis , 2007, IEEE Transactions on Control Systems Technology.

[5]  A. D. Lewis,et al.  Geometric Control of Mechanical Systems , 2004, IEEE Transactions on Automatic Control.

[6]  François Chaumette,et al.  Potential problems of stability and convergence in image-based and position-based visual servoing , 1997 .

[7]  François Chaumette,et al.  Visual Servoing and Visual Tracking , 2008, Springer Handbook of Robotics.

[8]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[9]  Francois Chaumette,et al.  Potential problems of unstability and divergence in image-based and position-based visual servoing , 1999, 1999 European Control Conference (ECC).

[10]  Vincenzo Lippiello,et al.  Position-Based Visual Servoing in Industrial Multirobot Cells Using a Hybrid Camera Configuration , 2007, IEEE Transactions on Robotics.

[11]  Vijay Kumar,et al.  A Framework for Vision Based Formation Control , 2002 .

[12]  François Chaumette,et al.  Improvements on Visual Servoing From Spherical Targets Using a Spherical Projection Model , 2009, IEEE Transactions on Robotics.

[13]  Philippe Martinet,et al.  2 1/2 D visual servoing with central catadioptric cameras , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[14]  Masayuki Fujita,et al.  Predictive Visual Feedback Control with Eye-In/to-Hand Configuration Via Stabilizing Receding Horizo , 2008 .

[15]  Nicholas R. Gans,et al.  Stable Visual Servoing Through Hybrid Switched-System Control , 2007, IEEE Transactions on Robotics.

[16]  Kostas Daniilidis,et al.  A Unifying Theory for Central Panoramic Systems and Practical Applications , 2000, ECCV.

[17]  Patrick Rives,et al.  Singularities in the determination of the situation of a robot effector from the perspective view of 3 points , 1993 .

[18]  S. Shankar Sastry,et al.  Following the flock [formation control] , 2004, IEEE Robotics & Automation Magazine.

[19]  Domenico Prattichizzo,et al.  EGT for multiple view geometry and visual servoing: robotics vision with pinhole and panoramic cameras , 2005, IEEE Robotics & Automation Magazine.