Abstract
Collaborative robots have the potential to simplify the working day of the future. The goal in the development of these robots is to assist human operators by handling all sorts of tasks. A common underlying problem is to move the robot’s tool center point in a desired way. In this work we consider the generation of a feasible trajectory in joint space given a reference in task space. This is done at the example of the Bionic Handling Assistant (BHA), a compliant, redundant and pneumatically driven continuum robot. The trajectory for the BHA is obtained using a model control loop (MCL) which internally realizes a nonlinear model predictive controller (NMPC). We simplify the high dimensional and nonlinear model of the BHA to a computational efficient model which still covers the major effects of the original dynamics. This results not only in a feasible trajectory but also enables the model control loop to be real-time applicable. The proposed method is validated in simulation.
Zusammenfassung
Kollaborative Roboter haben das Potenzial den Arbeitsalltag der Zukunft zu vereinfachen. Das Ziel bei der Entwicklung dieser Roboter ist es, dass sie den Menschen bei der Bewältigung seiner Aufgaben unterstützen. Ein häufiges Grundproblem ist es, das Werkzeug des Roboters auf eine gewünschte Art und Weise zu bewegen. In dieser Arbeit wird die Generierung realisierbarer Trajektorien im Gelenkraum bei einer gegebenen Referenztrajektorie im Aufgabenraum betrachtet. Dies geschieht am Beispiel des Bionischen Handling-Assistenten (BHA), einem nachgiebigen, redundanten und pneumatisch angetriebenen Kontinuum-Roboter. Die Trajektorie für den BHA wird mit Hilfe eines Modellregelkreises (MCL) generiert, der auf einem nichtlinearen modellprädiktiven Regler (NMPC) basiert. Das hochdimensionale und nichtlineare Modell des BHA wird zu einem recheneffizienten Modell vereinfacht, welches jedoch alle wesentlichen Effekte der ursprünglichen Dynamik abbildet. Dies führt nicht nur zu einer realisierbaren Trajektorie, sondern ermöglicht auch die Echtzeitanwendung des Modellregelkreises. Die vorgeschlagene Methodik wird in der Simulation validiert.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: SA 847/20-1
Funding statement: The authors gratefully acknowledge funding of this work by the German Research Foundation (DFG) under grant SA 847/20-1.
About the authors
Annika Mayer received the joint M. Sc. degree in systems, control and mechatronics from the Chalmers University of Technology, Gothenburg, Sweden and in Engineering Cybernetics from the University of Stuttgart, Germany in 2013, where she is also working toward the Ph. D. degree as a Research Assistant with the Institute for System Dynamics. Her current research interests include soft robotics, nonlinear model predictive control and embedded optimal control.
Daniel Müller received his M. Sc. degree in Engineering Cybernetics from the University of Stuttgart, Germany, in 2018. Since spring 2018, he has been a Research Assistant with the Institute for System Dynamics, University of Stuttgart, Germany. His research interests include continuum manipulators, machine learning and optimization.
Adrian Raisch received the M. Sc. degree in Engineering Cybernetics from the University of Stuttgart, Germany, in 2015. Since fall 2015 he has been a Research Assistant at the Institute for System Dynamics, University of Stuttgart, where he is also working towards the Ph. D. degree. His current research interests include modeling and control of pneumatic and electrical drive systems, with a focus on energy efficiency.
Oliver Sawodny received the Dipl.-Ing. degree in electrical engineering from the University of Karlsruhe, Karlsruhe, Germany, in 1991, and the Ph. D. degree from the Ulm University, Ulm, Germany, in 1996. In 2002, he became a Full Professor with the Technical University of Ilmenau, Germany. Since 2005, he has been the director of the Institute for System Dynamics, University of Stuttgart, Stuttgart, Germany. His current research interests include methods of differential geometry, trajectory generation, and applications to mechatronic systems.
References
1. Alin Albu-Schäffer, Christian Ott and Gerd Hirzinger. “A unified passivity-based control framework for position, torque and impedance control of flexible joint robots.” The International Journal of Robotics Research 26.1 (Jan. 2007), pp. 23–39. doi: 10.1177/0278364907073776.Search in Google Scholar
2. John Baillieul, John Hollerbach and Roger Brockett. “Programming and control of kinematically redundant manipulators.” In: IEEE Conference on Decision and Control. Vol. 23. 1984, pp. 768–774.10.1109/CDC.1984.272110Search in Google Scholar
3. David J. Braun et al.“Robots driven by compliant actuators: Optimal control under actuation constraints.” IEEE Transactions on Robotics 29.5 (2013), pp. 1085–1101.10.1109/TRO.2013.2271099Search in Google Scholar
4. Stefano Chiaverini. “Singularity-robust task-priority redundancy resolution for real-time kinematic control of robot manipulators.” IEEE Transactions on Robotics and Automation 13.3 (1997), pp. 398–410.10.1109/70.585902Search in Google Scholar
5. Howie M. Choset et al.Principles of Robot Motion: Theory, Algorithms, and Implementation. MIT Press, 2005.Search in Google Scholar
6. Moritz Diehl, Hans Joachim Ferreau and Niels Haverbeke. “Efficient numerical methods for nonlinear MPC and moving horizon estimation.” In: Nonlinear Model Predictive Control. Springer, 2009, pp. 391–417.10.1007/978-3-642-01094-1_32Search in Google Scholar
7. Moritz Diehl et al.“Fast direct multiple shooting algorithms for optimal robot control.” In: Fast Motions in Biomechanics and Robotics. Springer, 2006, pp. 65–93.10.1007/978-3-540-36119-0_4Search in Google Scholar
8. Ying Ding et al.“Model predictive control and its application in agriculture: A review.” Computers and Electronics in Agriculture 151 (2018), pp. 104–117.10.1016/j.compag.2018.06.004Search in Google Scholar
9. Adrien Escande, Nicolas Mansard and Pierre-Brice Wieber. “Hierarchical quadratic programming: Fast online humanoid-robot motion generation.” The International Journal of Robotics Research 33.7 (2014).10.1177/0278364914521306Search in Google Scholar
10. Valentin Falkenhahn. “Modellierung und modellbasierte Regelung von Kontinuum-Manipulatoren.” Dissertation. Universität Stuttgart, 2017.Search in Google Scholar
11. Valentin Falkenhahn et al.“Dynamic control of the bionic handling assistant.” IEEE/ASME Transactions on Mechatronics 22.1 (Feb. 2016), pp. 6–17. doi: 10.1109/TMECH.2016.2605820.Search in Google Scholar
12. Valentin Falkenhahn et al.“Dynamic modeling of bellows-actuated continuum robots using the Euler–Lagrange formalism.” IEEE Transactions on Robotics 31.6 (Dec. 2015), pp. 1483–1496. doi: 10.1109/TRO.2015.2496826.Search in Google Scholar
13. Lars Grüne and Jürgen Pannek. “Nonlinear model predictive control.” In: Nonlinear Model Predictive Control: Theory and Algorithms. Springer London, 2017. isbn: 978-0-85729-501-9. doi: 10.1007/978-0-85729-501-9_3.Search in Google Scholar
14. Alexander Hildebrandt, Rüdiger Neumann and Oliver Sawodny. “Optimal system and design of SISO-servopneumatic and positioning drives.” IEEE Transactions on Control Systems Technology 18.1 (Jan. 2010), pp. 35–44. doi: 10.1109/TCST.2008.2009879.Search in Google Scholar
15. Yanjun Huang et al.“Model predictive control power management strategies for HEVs: A review.” Journal of Power Sources 341 (2017), pp. 91–106.10.1016/j.jpowsour.2016.11.106Search in Google Scholar
16. Robert J. Webster III and Bryan A. Jones. “Design and kinematic modeling of constant curvature continuum robots: a review.” The International Journal of Robotics Research 29.13 (2010), pp. 1661–1683. doi: 10.1177/0278364910368147.Search in Google Scholar
17. Christian Kirches. Fast Numerical Methods for Mixedinteger Nonlinear Model-Predictive Control. Springer, 2011.10.1007/978-3-8348-8202-8Search in Google Scholar
18. Danica Kragic et al.“Interactive, collaborative robots: challenges and opportunities.” In: International Joint Conferences on Artificial Intelligence. 2018.10.24963/ijcai.2018/3Search in Google Scholar
19. Fabian Krank et al.“Ip2go: An interior point source code generator for solving linear-quadratic optimal control problems.” In: 20th IFAC World Congress. 2017.10.1016/j.ifacol.2017.08.1753Search in Google Scholar
20. H.-B. Kuntze et al.“On the predictive functional control of an elastic industrial robot.” In: IEEE Conference on Decision and Control. 1986, pp. 1877–1881.10.1109/CDC.1986.267314Search in Google Scholar
21. S.M. LaValle. Planning Algorithms. Cambridge University Press, 2006.10.1017/CBO9780511546877Search in Google Scholar
22. Tobias Mahl. Strukturmechanische Optimierung, Modellierung und Regelung pneumatisch aktuierter kontinuierlicher Roboter. Shaker, 2015.Search in Google Scholar
23. Andrew D. Marchese, Russ Tedrake and Daniela Rus. “Dynamics and trajectory optimization for a soft spatial fluidic elastomer manipulator.” The International Journal of Robotics Research 35.8 (2016).10.1109/ICRA.2015.7139538Search in Google Scholar
24. Jacob Mattingley and Stephen Boyd. “CVXGEN: A code generator for embedded convex optimization.” Optimization and Engineering 13.1 (2012), pp. 1–27.10.1007/s11081-011-9176-9Search in Google Scholar
25. Pauline Maurice et al.“Human-oriented design of collaborative robots.” International Journal of Industrial Ergonomics 57 (2017), pp. 88–102.10.1016/j.ergon.2016.11.011Search in Google Scholar
26. Annika Mayer et al. Operational-Space Reference Tracking. YouTube. 2019. url: https://youtu.be/S5d8r1bnAGM.Search in Google Scholar
27. David Q. Mayne. “Model predictive control: Recent developments and future promise.” Automatica 50.12 (2014), pp. 2967–2986. issn: 0005-1098. doi: 10.1016/j.automatica.2014.10.128.10.1016/j.automatica.2014.10.128Search in Google Scholar
28. Jun Nakanishi et al.“Operational space control: A theoretical and empirical comparison.” The International Journal of Robotics Research 27.6 (2008), pp. 737–757. doi: 10.1177/0278364908091463.Search in Google Scholar
29. Marcus Nolte et al.“Model predictive control based trajectory generation for autonomous vehicles – An architectural approach.” In: 2017 IEEE Intelligent Vehicles Symposium (IV). IEEE. 2017, pp. 798–805.10.1109/IVS.2017.7995814Search in Google Scholar
30. Toshiyuki Ohtsuka. “A continuation/GMRES method for fast computation of nonlinear receding horizon control.” Automatica 40.4 (2004), pp. 563–574.10.1016/j.automatica.2003.11.005Search in Google Scholar
31. Christian Ott, Alexander Dietrich and Alin Albu-Schäffer. “Prioritized multi-task compliance control of redundant manipulators.” Automatica 53 (2015), pp. 416–423.10.1016/j.automatica.2015.01.015Search in Google Scholar
32. Günter Roppenecker. “State feedback control of linear systems – A renewed approach.” at – Automatisierungstechnik 57.10 (2009).10.1524/auto.2009.0796Search in Google Scholar
33. Behzad Sadrfaridpour and Yue Wang. “Collaborative assembly in hybrid manufacturing cells: An integrated framework for human–robot interaction.” IEEE Transactions on Automation Science and Engineering 15.3 (2018), pp. 1178–1192.10.1109/TASE.2017.2748386Search in Google Scholar
34. Ulf Schaper et al.“Constrained real-time model-predictive reference trajectory planning for rotary cranes.” In: 2013 IEEE/ASME International Conference on Advanced Intelligent Mechatronics. IEEE. 2013, pp. 680–685.10.1109/AIM.2013.6584171Search in Google Scholar
35. Bruno Siciliano and Oussama Khatib, eds. Handbook of Robotics. 2nd ed. Heidelberg, Deutschland: Springer, 2016. isbn: 978-3-540-23957-4. doi: 10.1007/978-3-319-32552-1.Search in Google Scholar
36. Mikael Svenstrup, Thomas Bak and Hans Jørgen Andersen. “Trajectory planning for robots in dynamic human environments.” In: IEEE/RSJ International Conference on Intelligent Robots and Systems. 2010, pp. 4293–4298.10.1109/IROS.2010.5651531Search in Google Scholar
37. Deepak Trivedi et al.“Soft robotics: Biological inspiration, state of the art, and future research.” Applied Bionics and Biomechanics 5.3 (Dec. 2008), pp. 99–117. doi: 10.1080/11762320802557865.Search in Google Scholar
38. Robin Verschueren et al.“Towards a modular software package for embedded optimization.” IFAC-PapersOnLine 51.20 (2018), pp. 374–380. IFAC Conference on Nonlinear Model Predictive Control, issn: 2405-8963.10.1016/j.ifacol.2018.11.062Search in Google Scholar
39. Luca Zaccarian. “Dynamic allocation for input redundant control systems.” Automatica 45.6 (2009), pp. 1431–1438.10.1109/CDC.2007.4434679Search in Google Scholar
40. Andrea Maria Zanchettin et al.“Safety in human-robot collaborative manufacturing environments: Metrics and control.” IEEE Transactions on Automation Science and Engineering 13.2 (2016), pp. 882–893.10.1109/TASE.2015.2412256Search in Google Scholar
41. Andrea Zanelli et al.“FORCES NLP: an efficient implementation of interior-point methods for multistage nonlinear nonconvex programs.” International Journal of Control (2017), pp. 1–17.10.1080/00207179.2017.1316017Search in Google Scholar
42. Melanie N. Zeilinger et al.“On real-time robust model predictive control.” Automatica 50.3 (2014), pp. 683–694. doi: 10.1016/j.automatica.2013.11.019.Search in Google Scholar
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