Nonlinear Trajectory Control of Cable Robots


Cable robots are widely applicable for industrial tasks such as load transport, camera positioning in stadiums and driving simulators. As an advantage, they can cover large working areas while transporting heavy loads. In order for the crane to perform actions at specific locations, it is necessary to position it accurately and to prevent it from swinging. The load swinging of such a system is only weakly damped and poses safety risks in limited work spaces. In the current research project, model based controllers are designed to move the load platform on prescribed trajectories.

The crane system is modeled as a nonlinear rigid multibody system. Linearizing the dynamics neglects important nonlinear dynamics. Therefore, nonlinear control theory is used for controller design.

  • Two-dimensional crane model.


Trajectory control is achieved by using a feedforward control based on an inverse model of the system. This inverse model can be obtained by numerical as well as analytical methods. At the moment, the method of servo-constraints is applied for model inversion. For this method, a system of nonlinear high-index differential-algebraic equations (DAE) is solved in real-time. The solution of the DAE system poses the feedforward control inputs. Since the inverse model is just a feedforward control, it cannot react to disturbances or model uncertainties. By designing a feedback control, the system can be stabilized around the prescribed trajectory. Linear as well as nonlinear control theory methods are applicable for the design of a feedback part.

The designed controllers can be implemented and tested on the laboratory crane of our institute. The test bench consists of a trolley and a load platform attached to the trolley by four individual ropes. The trolley has a motion range of approximately 13 m. The rope length can be changed within 9 m by winches attached to the trolley. Therefore it’s possible to follow large trajectories. The test bench is controlled by a LabVIEW program running on a real-time computer.

  • Laboratory crane of the Institute of Mechanics and Ocean Engineering.


With the applied methods, the feedforward control is calculated in real-time. Later on, it is desirable to generate and modify nonlinear trajectories during crane motion. All this should be done on-line based on user input.

The two videos show the controlled crane test bench. The first video demonstrated trajectory control of a semicircle with a sliding mode controller. This can be used for collision avoidance. The designed sliding mode controller is also applicable for damping of the swing motion. This is demonstrated in the second video. The uncontrolled weakly damped system is shown in transparent.




Moreover, the setup of the test bench allows to actuate all four ropes separately. This property is used not only to control the position of the load but also its orientation. For example, a condition can be applied to enforce that a (virtual) object lying on top of the container experiences zero acceleration. This is shown in the video below.



Im letzten Video wird ein Regler verwendet, um die Lastplattform auf einen Winkel von 5 Grad zu kippen. Anschließend wird die Plattform wieder zurück auf 0 Grad geregelt. Dafür wird ein DAE basierter LQR Regler verwendet, da dieses System aufgrund der kinematischen Schleife als DAE modelliert wird. Das Video zeigt den Versuch in vierfacher Geschwindigkeit.



The last video shows an experiment for tilting the container platform from 0 degrees to 5 degrees and then back to horizontal position. This is done with a DAE based LQR controller because the model equations are DAEs due to the kinematic loop of the cables. The video is sped up 4 times.



This research project is a combination of mechanics and control systems. Often there are options for student research projects in modelling and control. Do not hesitate to contact us if you are interested in writing your thesis in this area.