Regelung flexibler Mehrkörpersysteme mit Umgebungskontakt

Funktionsübersicht des neuen flexiblen Leichtbauroboters Flexor:


Experimentelle Ergebnisse ausgewählter Konzepte angewendet auf den Flexor:


Experimentelle Ergebnisse an der Lambda Kinematik:

Control of Flexible Multibody Systems with Contact to the Environment


Through the growing need for energy efficiency and higher velocities, lightweight machines gain in importance. This relates to classical industrial applications, as well as new applications in the service and medical sector. As a consequence the machines' overall stiffness is significantly reduced. To compensate for the resulting elastic oscillations, the use of modern model-based control and regulation concepts is required. Feedforward approaches like the exact model inversion promise a good tracking behavior without interfering with the stability of the controlled machine. In combination with common control concepts, high-precision trajectory tracking or changes of operating points can be realized.

These model-based concepts require a very accurate model of the machine. Such machines are modeled as flexible multibody systems, due to large operating movements, that are overlaid by small elastic deformations. This extension of the common multibody system allows for the consideration of elastic bodies that can perform large non-linear movements.

Model of a lambda-kinematics machine with a kinematic loop (drives KML).

Simulation environment of the elastic multibody system of a lambda-kinematics machine & Overview poster for Control of Flexible Multibody Systems (click here for PDF in German).

For control it is not meaningful to use finite element models with a large number of degrees of freedom. Therefore, these finite element models are transformed to models with significantly fewer degrees of freedom by means of model reduction methods. The reduced bodies are then integrated into the multibody system by using the method of the floating frame of reference.

Control Concepts
This project focuses on the trajectory tracking control of flexible multibody systems with consideration of endeffector contact. Flexible multibody models allow for the use of model-based feedfoward control concepts such as an exact model inversion to follow desired trajectories. Exact model-inversion means in this context that all dynamic effects of the flexible multibody model are considered in the inverse model. With the help of a non-linear state transformation, the model can be transformed into the so-called input-output normal form, which consists of a set of differentiators, an algebraic part and the internal dynamics. Depending on the stability of the internal dynamics a feedforward control can be computed. As an alternative to the coordinate transformation, servo-constraints can be used to obtain the same results.

The developed concepts are tested experimentally on a flexible lambda-kinematics machine, which has been developed in cooperation with the Institute of Engineering and Computational Mechanics at the University of Stuttgart over the last years.

Lambda-kinematic test rig for the investigation of control concepts for flexible multibody systems.

In this setup significant friction effects, that occur in the movers, need to be compensated. Therefore, model and non-model-based techniques are combined and integrated into the cascade control of these movers. Besides, a curvature controller, which feeds back the curvature velocity of the long and highly elastic arm, has been developed to offer the possibility to rapidly dampen oscillations (see video).

Experimental Results

Student Involvement

The presented project offers a unique combination of mechanics,  control technology and lightweight robotics. Powerful tools, like flexible multibody systems, the finite element method, exact model inversion, etc. are used. Various software-tools are utilized for modelling and simulation (e.g. Ansys/Matlab/Simulink). An objective is also to experimentally validate the models, simulations and designed controllers.

Often, there are interesting opportunities to get involved: analytically, simulatively and experimentally. If you are interested, do not hesitate to contact us (see contact information below).

Selected Publications

  1. Burkhardt, M.; Seifried, R.; Eberhard, P.: Experimental Studies of Control Concepts for a Parallel Manipulator with Flexible Links.  Proceedings Int. Conference on Multibody System Dynamics (IMSD 2014), Busan, South Korea, 2014 (9 pages).
  2. Morlock, M.; Burkhardt, M.; Seifried, R.: Friction Compensation, Gain Scheduling and Curvature Control for a Flexible Parallel Kinematics Robot. Proceedings of the 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2015), Hamburg, Germany, 2015. 10.1109/IROS.2015.7353695
  3. Morlock, M.; Burkhardt, M.; Seifried, R.: Control of vibrations for a parallel manipulator with flexible links - concepts and experimental results. MOVIC & RASD 2016, International Conference, Southampton, England, 2016.
  4. R. Seifried: Dynamics of Underactuated Multibody Systems –Modeling, Control and Optimal Design. Solid Mechanics and Its Applications, vol. 205, Springer, 2014.
  5. Institute of Engineering and Computational Mechanics, Stuttgart:



If you have any questions, or are interested in writing a student thesis in the field of Control of Flexible Multibody Systems, feel free to contact us:

    The Project is funded by Deutscher Forschungsgemeinschaft (DFG / SE1685-3/2).