This paper presents a new nonlinear adaptive vision-based observer to estimate position and linear velocity information for closed-loop position-based visual servo control of an aerial robot in GPS-denied environments. Specifically, the observer determines the position and linear velocity of the robot for closed-loop control by observing using a low-cost on-board camera at least two feature points fixed in the world frame. The nonlinear adaptive observer takes advantage of the geometry of perspective projection, and is designed to update position and velocity information in real-time. Thus, there are no constraints or assumptions on the depth and initial estimation errors. Furthermore, the proposed parameter estimator addresses the challenge in situations where GPS signals may be weak, unreliable, or nonexistent, such in valleys, canyons, and between tall buildings, or inside of a building and under dense canopy. For closed-loop tracking control using the estimated position and velocity information, a backstepping controller is employed for the underactuated aerial robot system. The Lyapunov method is used to show stability of the closed-loop system. Simulation and experimental results are presented that validate the performance of the observer and control system for hovering and tracking a circular trajectory, where both are defined in the world (lab) frame.

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