Homography based visual servoing is an approach that blends image based feedback with feedback that is reconstructed from the image to control an autonomous system to move along a desired trajectory. Adaptive control methods have been previously developed by compensating for an unknown parameter (i.e., the depth of a feature) in the dynamics, where persistence of excitation assumptions are used for parameter identification. Rather than assume persistent excitation, an augmented adaptive update law that uses recorded data is utilized in this paper to guarantee exponential tracking and parameter identification with only finite excitation. By identifying the depth parameter, the structure of the scene can be reconstructed, enabling simultaneous mapping and control.
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