Abstract
In this work we present a novel control design methodology for under-actuated mechanical systems. As part of the design process we use the reachability analysis tool d/dt [ABDM99,D00] to see whether there is a switching sequence which can drive the system to a desired periodic orbit. Much of the work in the design of the control law is done manually using classical control techniques (unlike the fully-automatic approach advocated in [ABD+00]), and d/dt is used to complement these techniques. We hope this work will contribute to the proliferation of reachability-based techniques to the control engineer’s tool box.
This work was partially supported by the European Community Esprit-LTR Project 26270 VHS (Verification of Hybrid systems) and the French-Israeli collaboration project 970maefut5 (Hybrid Models of Industrial Plants).
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References
R. Alur and D.L. Dill, A Theory of Timed Automata, Theoretical Computer Science 126, 183–235, 1994.
R. Alur, C. Courcoubetis, N. Halbwachs, T.A. Henzinger, P.-H. Ho, X. Nicollin, A. Olivero, J. Sifakis and S. Yovine, The Algorithmic Analysis of Hybrid Systems, Theoretical Computer Science 138, 3–34, 1995.
E. Asarin, O. Bournez, T. Dang and O. Maler, Reachability Analysis of Piecewise-Linear Dynamical Systems, in B. Krogh and N. Lynch (Eds.), Hybrid Systems: Computation and Control, 20–31 LNCS 1790, Springer, 2000.
E. Asarin, O. Bournez, T. Dang, O. Maler and A. Pnueli, Effective Synthesis of Switching Controllers for Linear Systems, Proceedings of the IEEE 88, 1011–1025, 2000.
E. Asarin, O. Maler and A. Pnueli, Reachability Analysis of Dynamical Systems having Piecewise-Constant Derivatives, Theoretical Computer Science 138, 35–66, 1995.
B. Espiau, I. Guigues, R. Pissard-Gibollet, Can an Underactuated Leg with a Passive Joint at the Knee Achieve a Ballistic Step?, Proceedings of the International Symposium on Experimental Robotics Sydney, Australia, 26–28 march 1999
T. Dang, Verification and Synthesis of Hybrid Systems, Ph.D. Thesis, INPG Grenoble, 2000, ftp://ftp.imag.fr/pub/Mediatheque.IMAG/theses/2000/Dang.Thi-Xuan-Thao/these.dir
T.A. Henzinger, P.-H. Ho, and H. Wong-Toi, HyTech: A Model Checker for Hybrid Systems, Software Tools for Technology Transfer 1, 110–122, 1997.
C. Tomlin, J. Lygeros and S. Sastry, A Game-Theoretic Approach to Controller Design for Hybrid Systems, in Proceedings of the IEEE 88, 949–970, 2000.
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Asarin, E., Bansal, S., Espiau, B., Thao, D., Maler, O. (2001). On Hybrid Control of Under-Actuated Mechanical Systems. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A. (eds) Hybrid Systems: Computation and Control. HSCC 2001. Lecture Notes in Computer Science, vol 2034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45351-2_10
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DOI: https://doi.org/10.1007/3-540-45351-2_10
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