Zusammenfassung
Dieser Beitrag stellt eine modellprädiktive Pfadfolgeregelung für die Kombination mit einer kollisionsfreien Bewegungsplanung für Roboter vor. Zwei Besonderheiten sind mit diesem Anwendungsfall verbunden. Zum einen wird keine hochgenaue Pfadfolge benötigt, solange die Bewegung kollisionsfrei ist. Somit kann die Pfadfolgeregelung vom geplanten Pfad abweichen, um die Zielkonfiguration effizienter zu erreichen. Zum anderen ist eine exakte Bewegung entlang des Pfades prinzipiell möglich, so dass mit Hilfe einer Referenztrajektorie rekursive Lösbarkeit und Stabilität garantiert werden kann. Die Vorteile zeigen sich vor allem bei graphbasierten Planungsverfahren, wo die berechneten Pfade typischerweise stückweise linear sind und eine exakte Pfadfolge sehr aufwändig ist. Die Anwendung der Methodik wird in Simulationen für einen Manipulator und einen mobilen Roboter gezeigt.
Abstract
This article presents a model predictive path-following controller for the combination with collision-free motion planning. Two special characteristics are connected with this combination. Firstly, high accuracy path-following is not required as long as the motion is collision-free. Thus, the controller can deviate from the planned path in order to reach the goal configuration more efficiently. Secondly, an exact motion along the path is possible in principle, so that recursive feasibility and stability can be guaranteed by means of a reference trajectory. The advantages are particularly apparent for graph-based planners, where the resulting paths are typically piecewise linear and exact path-following is very costly. The application of the methodology is shown in simulations for a manipulator and a mobile robot.
Dieser Beitrag ist Herrn Prof. Dr.-Ing. Dr. h.c. Michael Zeitz anlässlich seines 80. Geburtstags gewidmet.
Über die Autoren
Dr.-Ing. Andreas Völz ist akademischer Rat am Lehrstuhl für Regelungstechnik der Friedrich-Alexander-Universität Erlangen-Nürnberg. Hauptarbeitgsgebiete: lokale Optimierungsverfahren für Anwendungen in der Robotik, kollisionsfreie Bewegungsplanung, nichtlineare modellprädiktive Regelung.
Prof. Dr.-Ing. Knut Graichen ist Leiter des Lehrstuhls für Regelungstechnik der Friedrich-Alexander-Universität Erlangen-Nürnberg. Hauptarbeitsgebiete: optimale und modellprädiktive Regelung, nichtlineare Steuerungs- und Regelungsverfahren, eingebettete Umsetzung von optimierungsbasierten Verfahren für mechatronische und vernetzte Systeme.
Literatur
1. Mathias Hauan Arbo, Esten Ingar Grøtli and Jan Tommy Gravdahl. On model predictive path following and trajectory tracking for industrial robots. In Proceedings of the IEEE International Conference on Automation Science and Engineering (CASE), pages 100–105, Xi’an (China), 2017.Search in Google Scholar
2. James E Bobrow, Steven Dubowsky and JS Gibson. Time-optimal control of robotic manipulators along specified paths. The International Journal of Robotics Research, 4(3):3–17, 1985.10.1177/027836498500400301Search in Google Scholar
3. Martin Böck and Andreas Kugi. Real-time nonlinear model predictive path-following control of a laboratory tower crane. IEEE Transactions on Control Systems Technology, 22(4):1461–1473, 2014.10.1109/TCST.2013.2280464Search in Google Scholar
4. John Canny. The Complexity of Robot Motion Planning. MIT press, 1988.10.1109/SFCS.1988.21947Search in Google Scholar
5. Tobias Englert, Andreas Völz, Felix Mesmer, Sönke Rhein and Knut Graichen. A software framework for embedded nonlinear model predictive control using a gradient-based augmented Lagrangian approach (GRAMPC). Optimization and Engineering, 2019. doi.org/10.1007/s11081-018-9417-2.10.1007/s11081-018-9417-2Search in Google Scholar
6. Timm Faulwasser and Rolf Findeisen. Ein prädiktiver Ansatz zur Lösung nichtlinearer Pfadverfolgungsprobleme unter Beschränkungen. at-Automatisierungstechnik, 57(8):386–394, 2009.10.1524/auto.2009.0784Search in Google Scholar
7. Timm Faulwasser and Rolf Findeisen. Nonlinear model predictive control for constrained output path following. IEEE Transactions on Automatic Control, 61(4):1026–1039, 2015.10.1109/TAC.2015.2466911Search in Google Scholar
8. Timm Faulwasser, Tobias Weber, Pablo Zometa and Rolf Findeisen. Implementation of nonlinear model predictive path-following control for an industrial robot. IEEE Transactions on Control Systems Technology, 25(4):1505–1511, 2017.10.1109/TCST.2016.2601624Search in Google Scholar
9. Sertac Karaman and Emilio Frazzoli. Sampling-based algorithms for optimal motion planning. International Journal of Robotics Research, 30(7):846–894, 2011.10.15607/RSS.2010.VI.034Search in Google Scholar
10. Lydia E Kavraki, Petr Švestka, Jean-Claude Latombe and Mark H Overmars. Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Transactions on Robotics and Automation, 12(4):566–580, 1996.10.1109/70.508439Search in Google Scholar
11. Oussama Khatib. Real-time obstacle avoidance for manipulators and mobile robots. The International Journal of Robotics Research, 5(1):90–98, 1986.10.1109/ROBOT.1985.1087247Search in Google Scholar
12. Denise Lam, Chris Manzie and Malcolm Good. Model predictive contouring control. In Proceedings of the 49th IEEE Conference on Decision and Control (CDC), pages 6137–6142, Atlanta (USA), 2010.10.1109/CDC.2010.5717042Search in Google Scholar
13. Steven M LaValle. Rapidly-exploring random trees a new tool for path planning. Technical report, TR 98-11, Computer Science Department, Iowa State University, 1998.Search in Google Scholar
14. Steven M LaValle. Planning Algorithms. Cambridge University Press, 2006.10.1017/CBO9780511546877Search in Google Scholar
15. Peter Leven and Seth Hutchinson. A framework for real-time path planning in changing environments. International Journal of Robotics Research, 21(12):999–1030, 2002.10.1177/0278364902021012001Search in Google Scholar
16. Mohamed W Mehrez, Karl Worthmann, George KI Mann, Raymond G Gosine and Timm Faulwasser. Predictive path following of mobile robots without terminal stabilizing constraints. In Proceedings of the 20th IFAC World Congress, pages 9852–9857, Toulouse (Frankreich), 2017.10.1016/j.ifacol.2017.08.907Search in Google Scholar
17. Quang-Cuong Pham. A general, fast, and robust implementation of the time-optimal path parameterization algorithm. IEEE Transactions on Robotics, 30(6):1533–1540, 2014.10.1109/TRO.2014.2351113Search in Google Scholar
18. John Schulman, Yan Duan, Jonathan Ho, Alex Lee, Ibrahim Awwal, Henry Bradlow, Jia Pan, Sachin Patil, Ken Goldberg and Pieter Abbeel. Motion planning with sequential convex optimization and convex collision checking. International Journal of Robotics Research, 33(9):1251–1270, 2014.10.1177/0278364914528132Search in Google Scholar
19. Niels van Duijkeren, Robin Verschueren, Goele Pipeleers, Moritz Diehl and Jan Swevers. Path-following NMPC for serial-link robot manipulators using a path-parametric system reformulation. In Proceedings of the European Control Conference (ECC), pages 477–482, Aalborg (Dänemark), 2016.10.1109/ECC.2016.7810330Search in Google Scholar
20. Diederik Verscheure, Bram Demeulenaere, Jan Swevers, Joris De Schutter and Moritz Diehl. Time-optimal path tracking for robots: A convex optimization approach. IEEE Transactions on Automatic Control, 54(10):2318–2327, 2009.10.1109/TAC.2009.2028959Search in Google Scholar
21. Andreas Völz. Collision-free Motion Planning for Dual-Arm Robots in Changing Environments. Dissertation, Univ. Ulm, Shaker Verlag, Düren, 2019.Search in Google Scholar
22. Andreas Völz and Knut Graichen. Computation of collision distance and gradient using an automatic sphere approximation of the robot model with bounded error. In Proceedings of the 50th International Symposium on Robotics (ISR), pages 322–329, München (Deutschland), 2018.Search in Google Scholar
23. Andreas Völz and Knut Graichen. A predictive path-following controller for continuous replanning with dynamic roadmaps. IEEE Robotics and Automation Letters, 4(4):3963–3970, 2019.10.1109/LRA.2019.2929990Search in Google Scholar
24. Anja Wahl and Ernst-Dieter Gilles. Optimale Regelverfahren zur automatischen Bahnführung von Binnenschiffen. at-Automatisierungstechnik, 51(6):255–264, 2003.10.1524/auto.51.6.255.22448Search in Google Scholar
25. Kwangjin Yang, Yeonsik Kang and Salah Sukkarieh. Adaptive nonlinear model predictive path-following control for a fixed-wing unmanned aerial vehicle. International Journal of Control, Automation and Systems, 11(1):65–74, 2013.10.1007/s12555-012-0028-ySearch in Google Scholar
26. Shuyou Yu, Xiang Li, Hong Chen and Frank Allgöwer. Nonlinear model predictive control for path following problems. International Journal of Robust and Nonlinear Control, 25(8):1168–1182, 2015.10.1002/rnc.3133Search in Google Scholar
27. Angelika Zube. Cartesian nonlinear model predictive control of redundant manipulators considering obstacles. In Proceedings of the IEEE International Conference on Industrial Technology (ICIT), pages 137–142, Sevilla (Spanien), 2015.10.1109/ICIT.2015.7125089Search in Google Scholar
28. Matt Zucker, Nathan Ratliff, Anca D Dragan, Mihail Pivtoraiko, Matthew Klingensmith, Christopher M Dellin, J Andrew Bagnell and Siddhartha S Srinivasa. CHOMP: Covariant Hamiltonian optimization for motion planning. International Journal of Robotics Research, 32(9-10):1164–1193, 2013.10.1177/0278364913488805Search in Google Scholar
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