Application of UKFs in under-actuated mechanical systems

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Dr. Kiss Bálint
Department of Control Engineering and Information Technology


The equations describing the behavior of a simplified gantry crane, moving its load in the horizontal plane only, are nonlinear. To stabilize the load position or to track a reference trajectory, the state variables must be provided to the feedback law. Since not all of these variables are measured an Unscented Kalman Filter must be used.

The state equations of the model are derived using the Langrange function. The configuration variables are the rope length, the horizontal position of the suspension point and the rope angle w.r.t. the vertical. The measured variables are the rope length and the position of the suspension point. Two laser slot sensors can detect fixed rope angles. The sensor fusion achieved by UKF can estimate correctly the rope angle where they are not detected by the laser slot sensors. The correctness of the estimates provided by the UKF was tested in closed-loop control for anti-sway stabilization and by a trajectory tracking control based on exact linearization. The test results show that the UKF with the laser slot sensors provide reliable estimation for rope angle. As a result, the estimates may be used in a closed-loop control application.


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