Daisy Chaining Based Visual Servo Control Part I: Adaptive Quaternion-Based Tracking Control

A quaternion-based visual servo tracking controller for a moving six degrees of freedom object is developed based on image feedback from a moving camera. The control objective is for the object to track a desired trajectory determined by a sequence of prerecorded images from a stationary camera. To achieve this result, several technical issues were resolved including: discriminating the relative velocity between the moving camera and the moving object, compensating for the unknown time-varying distance measurement from the camera to the object, relating the unknown attitude of the control object to some measurable signals, and using unit quaternion to formulate the rotation motion and rotation error system. By utilizing multi-view image geometry to develop homography relationships between the moving camera frame and the moving planar patch coordinate systems, the relative velocity issue is resolved. By using the depth ratios obtained from the homography decomposition, the unknown depth information is related to an unknown constant that can be compensated for by a Lyapunov-based adaptive update law. Lyapunov-based methods are provided to prove the adaptive asymptotic tracking result.