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A visual servo tracking controller is developed in this paper for a monocular camera system mounted on an underactuated wheeled mobile robot (WMR) subject to nonholonomic motion constraints (i.e., the camera-in-hand problem). A prerecorded image sequence (e.g., a video) of three target points is used to define a desired trajectory for the WMR. By comparing the target points from the prerecorded sequence with the corresponding target points in the live image, projective geometric relationships are exploited to construct a Euclidean homography. The information obtained by decomposing the Euclidean homography is used to develop a kinematic controller. A Lyapunovbased analysis is used to develop an adaptive update law to actively compensate for the lack of depth information required for the translation error system.

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