Christian Schenk

I am a PhD student working in the group at the Max Planck Institute for Biological Cybernetics.

Goal of my phd is the development of a framework that includes control, modelling and estimation techniques for a redundant Cable-driven Robot with 6 Degrees of freedom.

My research adresses the implementation of a robust control algorithm, different kinematic and dynamic models and an Unscented Kalman Filter for state estimation on a real system.

Title

Modeling and control of a 6 degrees of freedom (DoF) cable driven parallel robot with 8 cables

Introduction

Motion simulators are devices used to arouse in a person the feeling of being in a moving vehicle, for instance to train pilots or to study human perception. Suitable sensorial cues are necessary to create this illusion of motion and, in this sense, vestibular cues have been proven to be fundamental [2]. However, the realization of realistic vestibular cues is challenging because motion platforms have a limited (small) workspace in comparison to the space where a vehicle would move. For this reason, developing novel simulators based on improved motion platforms is an active topic of research.

Goals

The goal of our research is to design a novel motion simulation framework based on the use of a fully constrained 6 DoF cable driven parallel robot (CDPR) that combines the advantages of classic Stewart platforms and of serial platforms, i.e. high stiffness, a high workload total weight ratio, high accelerations and a large workspace. To the best of our knowledge there are no existing setups of this kind and we expect it to allow for a better reproduction of vestibular cues.

Methods

A CDPR is a multi-body object comprising several mechanical and electrical parts (moving platform, winches, pulleys, cables). The kinematic and dynamic model of the system can be derived using geometrico-static relations (loop closure of a kinematic chain) and Newton-Euler equations of motion [1] or Euler-Lagrange methods. The model depends on many kinematic and dynamic parameters that will have to be calibrated using linear regression methods [5] or by minimizing a cost function which depends on a set of predefined parameters. Based on this  model, we plan to design a control strategy [4, 3] to let the robot follow a desired acceleration profile that is unknown a priori (it depends one the inputs from the pilot). The quality of reproduction of vestibular cues depends mainly on the kinematic and dynamic accuracy and robustness, the simulation framework can provide. Thus we have to take unmodelled dynamics and uncertain parameters into account which may downgrade the quality of the motion cue. Cable vibrations as the result of unmodelled dynamics and the total mass which may change from trial to trial are good examples for an uncertain parameter. Thus the construction of a model which reflects all relevant dynamics is an important subtask of the framework construction. The second part of the framework belongs to the goal of finding a control strategy to run the goal of an experiment smoothly. Our plan is to use an adaptive formulation of the controller in order to adapt to unmodelled dynamics and the natural changes in the parameters that are encountered in the intended application. Finally, the redundancy of the system can be exploited to optimize the tension distribution on the cables.

Initial Results

Since the CDPR is still under construction our results are of simulative nature. In practical preliminary tests with the cables, it was shown that the eigen-modes of the cables strongly influence in the dynamics of the CDPR and therefore also the quality of a motion with respect to accuracy. Thus the current status of the simulation model includes the end-effector dynamics as well as the dynamics of the cables. In order to deal with unmodelled dynamics and uncertain parameters we implemented an adaptive super-twisting controller [6] with variable gains [7]. Keeping the gains variable has the advantage to reduce longitudinal cable vibration which is called chattering. These vibrations may result from unnecessary high controller gains. Preliminary tests in Matlab/Simulink with our super-twisting controller in comparison with a control scheme with constant high gains show that chattering effects can be strongly reduced by keeping the controller gains as low as possible but as high as necessary.

In my second study [8] I was evaluating the goodness of two commonly used linear cable models, based on Finite-Elements and on Partial differential equations. In two experiments I showed that these models can predict eigenfrequencies of a cable with fixed length as long as the pretension is high enough and the shape of the cable is similar to a straight line. If the cable becomes slack, nonlinearities such as hysteresis effects and internal couplings become more evident and the accuracy of a linear model drops very fast. Furthermore it turned out, that vibrations are not limited to longitudinal directions which is a commonly used assumption in literature.

Current work

At the moment I am focusing on the implementation of the Adaptive Sliding-Mode Controller and an Unscented Kalman Filter for state and parameter estimation.

References

1. R. Chellal, E. Laroche, L. Cuvillon, and J. Ganglo
   . An identication methodology for 6-DoFcable-driven parallel robots parameters application to the INCA 6D robot. In T. Bruckmann and A. Pott, editors, Cable-Driven Parallel Robots, volume 12 of Mechanisms and Machine Science, pages 301{317. Springer Berlin Heidelberg, 2013.
2. E. L. Groen and W. Bles. How to use body tilt for the simulation of linear self motion. Journal of Vestibular Research, 14(5):375{385, 2004.
3. A. Isidori. Nonlinear Control Systems, 3rd edition. Springer, 1995.
4. J. Lamaury, M. Gouttefarde, A. Chemori, and P.-E. Herve. Dual-space adaptive control of redundantly actuated cable-driven parallel robots. In 2013 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pages 4879{4886, Nov 2013.
5. P. Miermeister, W. Kraus, and A. Pott. Di
   erential kinematics for calibration, system investigation, and force based forward kinematics of cable-driven parallel robots. In T. Bruckmann and A. Pott, editors, Cable-Driven Parallel Robots, volume 12 of Mechanisms and Machine Science,
   pages 319{333. Springer Berlin Heidelberg, 2013.
6. Y. Shtessel, C. Edwards, L. Fridman, and A. Levant, Sliding Mode Control and Observation. Springer, 2014.
7. Y. B. Shtessel, J. A. Moreno, F. Plestan, L. Fridman, and A. S. Poznyak, “Super-twisting adaptive sliding mode control: A Lyapunov design,” in 2010 IEEE Conf. on Decision and Control, Dec 2010, pp. 5109–5113.
8. Christian Schenk, Carlo Masone, Philip Miermeister and Heinrich H. Bülthof, "Modeling and Analysis of Cable Vibrations for a Cable-Driven Parallel Robot", in 2016 IEEE International Conference on Information and Automation, August 2016