A Lyapunov-Based Approach to Visual Servo Control and Path Planning

Warren Dixon, Ph.D., Assistant Professor, Department of Mechanical and Aerospace Engineering, University of Florida

The Euclidean position and orientation (i.e., pose) of an unmanned vehicle (UV) is typically required for autonomous navigation and control. Often the pose of an UV is determined by a global positioning system (GPS) or an inertial measurement unit (IMU). However, GPS may not be available, and IMUs can drift and accumulate errors over time in a similar manner as dead reckoning. Given recent advances in image extraction/interpretation technology, an interesting approach to overcome the pose measurement, navigation, and control problems is to utilize a vision system. This presentation will describes a series of advances in visual servo control and path planning that are obtained through the use of Lyapunov-based methods. Multi-image photogrammetry will be described as it relates to developing a measurable translation and rotation error system (via a homography decomposition) in both Euclidean and quaternion representations. Lyapunov tools will then be described to adapt for unknown depth information and uncertain camera calibration. Visual servo tracking control results will be described for a camera moving with unconstrained motion and with nonholonomic constraints. The design of a Lyapunov-based path-planning method that ensures targets remain in the camera field of view will be presented. Motivated by field of view issues, discussions will also focus on the use of Lyapunov tools to recover range information from nonaffine catadioptric imaging systems. Concluding remarks will point to future directions in visual servo control.