Laboratory Experiments

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Trajectory planning and tracking control for car parking

The parking of a car with aid of an automatic assistant system is important problem in automotive control. In a previous research project in the area of nonlinear control systems new methods for the collision-free path planning based on a general two step motion planning strategy for mobile robots were developed. Thereby, the algorithm provides the steering angle and the driver still controls the longitudinal motion. The corresponding tracking control system is designed by using the flatness of the car model. The following video

Video: Tracking control for automatic parking.
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shows the implementation of the new method on a laboratory vehicle.

Selected publications

  • Müller, B. and Deutscher, J.: Continuous curvature trajectory design and feedforward control for parking a car. Trans. Control Sys. Technology 15 (2007), pp. 541-553.
  • Müller, B. and Deutscher, J.: Orbital tracking control for car parking via control of the clock using a nonlinear reduced order steering-angle observer. Proc. ECC 2007 in Kos, Greece.
  • Müller, B.: Two-step Trajectory planning for automatic parking. Doctoral thesis, Universität Erlangen-Nürnberg, 2009. Berichte aus der Steuerungs- und Regelungstechnik, Shaker Verlag, Aachen, 2009.

Tracking control of the ball on the plate

In this laboratory experiment the linear step point as well as the tracking control of a ball on a plate is considered. Thereby, a touch pad is used to detect the position of the ball on the plate. By using the flatness of the nonlinear system model a feedforward controller and a nonlinear observer-based tracking controller are designed that assure that the ball moves along specified paths. The following video

Video: Tracking control of a ball on a plate.
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demonstrates the good tracking performance of the control system.

Tracking control of a 2D-crane

The 2D-crane is a laboratory experiment that is a simple model for a gantry crane. In practical applications the main problem is the pendulum motion of the load appearing when changing the position of the load. This experiment shows that the flatness of the 2D-crane can be used to plan a trajectory for the movement of the load without any oscillations. Thereby, the tracking can be stabilized against model uncertainty and external disturbances by using a nonlinear flatness-based tracking controller. The following video

Video: Tracking control of a 2D-crane.
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verifies the excellent tracking performance obtained for the laboratory setup.

Stabilization of the inverted pendulum

The inverted pendulum is a classical laboratory experiment for the demonstration of various control methods. In this experiment the stabilization of the upper equilibrium point using feedback linearization is considered. Since the inverted pendulum is not feedback linearizable a numerical approximate feedback linearization approach was implemented that achieves a larger region of attraction when compared with a linear state feedback. The following video

Video: Stabilization of an inverted pendulum.
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shows the obtained results.

Selected publications

  • Deutscher, J. and Schmid, Ch.: A state space embedding approach to approximate feedback linearization of nonlinear single input control systems. Int. J. Robust and Nonlinear Control 16 (2006), pp. 421-440.
  • Deutscher, J. and Schmid, Ch.: A numerical approach to approximate feedback linearization. Proc. CCA/CACSD/ISIC 2006 in Munich, Germany.