Optimal Motion Planning and Energy-Based Control of a Single Mast Stacker Crane

Authors

Hubert Rams, Markus Schoberl, Kurt Schlacher

Abstract

This brief presents a flatness-based optimal trajectory planning methodology combined with an energy-based feedback for a single mast stacker crane in, for instance, automated warehouses. By means of a laboratory model, we address the classical problems modeling, flatness analysis, optimal trajectory planning, and feedback design. The main focus is on the efficient formulation of the trajectory planning problem as well as on a novel energy-based feedback methodology exploiting structural invariants (Casimir functionals). To solve the arising optimization problem, state-of-the-art software packages are utilized. Moreover, experimental results obtained from the laboratory model demonstrate the capability of the proposed feedforward and feedback methodology.

Citation

• Journal: IEEE Transactions on Control Systems Technology
• Year: 2018
• Volume: 26
• Issue: 4
• Pages: 1449–1457
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/tcst.2017.2710953

BibTeX

@article{Rams_2018,
  title={{Optimal Motion Planning and Energy-Based Control of a Single Mast Stacker Crane}},
  volume={26},
  ISSN={1558-0865},
  DOI={10.1109/tcst.2017.2710953},
  number={4},
  journal={IEEE Transactions on Control Systems Technology},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Rams, Hubert and Schoberl, Markus and Schlacher, Kurt},
  year={2018},
  pages={1449--1457}
}

Download the bib file

References

• Rudolph, J. Flatness-based control by quasi-static feedback illustrated on a cascade of two chemical reactors. International Journal of Control vol. 73 115–131 (2000) – 10.1080/002071700219821
• Ilchmann, A. & Mueller, M. Time-Varying Linear Systems: Relative Degree and Normal Form. IEEE Transactions on Automatic Control vol. 52 840–851 (2007) – 10.1109/tac.2007.895843
• Freund, E. Zeitvariable Mehrgrößensysteme. (Springer Berlin Heidelberg, 1971). doi:10.1007/978-3-642-48185-7 – 10.1007/978-3-642-48185-7
• martin, Flat systems. Proc Plenary Lectures Mini-Courses Eur Control Conf (1997)
• Guay, M. & Peters, N. Real-time dynamic optimization of nonlinear systems: A flatness-based approach. Computers & Chemical Engineering vol. 30 709–721 (2006) – 10.1016/j.compchemeng.2005.11.009
• Kolar, B., Rams, H. & Schlacher, K. Time-optimal flatness based control of a gantry crane. Control Engineering Practice vol. 60 18–27 (2017) – 10.1016/j.conengprac.2016.11.008
• luo, Stability and Stabilization of Infinite Dimensional Systems with Applications (1998)
• Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
• Macchelli, A. & Melchiorri, C. Modeling and Control of the Timoshenko Beam. The Distributed Port Hamiltonian Approach. SIAM Journal on Control and Optimization vol. 43 743–767 (2004) – 10.1137/s0363012903429530
• Schoberl, M. & Siuka, A. On Casimir Functionals for Infinite-Dimensional Port-Hamiltonian Control Systems. IEEE Transactions on Automatic Control vol. 58 1823–1828 (2013) – 10.1109/tac.2012.2235739
• Schindele, D. & Aschemann, H. Adaptive LQR-Control Design and Friction Compensation for Flexible High-Speed Rack Feeders. Journal of Computational and Nonlinear Dynamics vol. 9 (2013) – 10.1115/1.4025351
• staudecker, Passivity based control and time optimal trajectory planning of a single mast stacker crane. Proc 17th IFAC World Congr (2008)
• Walther, A. & Griewank, A. Getting Started with ADOL-C. Chapman & Hall/CRC Computational Science 181–202 (2012) doi:10.1201/b11644-8 – 10.1201/b11644-8
• Wächter, A. & Biegler, L. T. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical Programming vol. 106 25–57 (2005) – 10.1007/s10107-004-0559-y
• Slaughter, W. S. The Linearized Theory of Elasticity. (Birkhäuser Boston, 2002). doi:10.1007/978-1-4612-0093-2 – 10.1007/978-1-4612-0093-2
• meirovitch, Principles and Techniques of Vibrations (1997)
• Kostin, G., Aschemann, H., Rauh, A. & Saurin, V. Optimal Real-Time Control of Flexible Rack Feeders Using the Method of Integrodifferential Relations. IFAC Proceedings Volumes vol. 45 1147–1152 (2012) – 10.3182/20120215-3-at-3016.00203
• Bachmayer, M., Ulbrich, H. & Rudolph, J. Flatness-based control of a horizontally moving erected beam with a point mass. Mathematical and Computer Modelling of Dynamical Systems vol. 17 49–69 (2011) – 10.1080/13873954.2010.537517
• Rathinam, M. & Murray, R. M. Configuration Flatness of Lagrangian Systems Underactuated by One Control. SIAM Journal on Control and Optimization vol. 36 164–179 (1998) – 10.1137/s0363012996300987
• Schöberl, M. & Siuka, A. Jet bundle formulation of infinite-dimensional port-Hamiltonian systems using differential operators. Automatica vol. 50 607–613 (2014) – 10.1016/j.automatica.2013.11.035
• Schöberl, M. & Schlacher, K. On an intrinsic formulation of time-variant Port Hamiltonian systems. Automatica vol. 48 2194–2200 (2012) – 10.1016/j.automatica.2012.06.014