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Motion Description Languages for Multi-Modal Control in Robotics

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Control Problems in Robotics

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 4))

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Abstract

In this paper we outline how motion description languages provide useful tools when designing multi-modal control laws in robotics. Of particular importance is the introduction of the description length as a measure of how complicated a given control procedure is. This measure corresponds to the number of bits needed for coding the input string. Description length arguments can furthermore be invoked for selecting sensors and actuators in a given robotics application, thus providing a unified framework in which a number of major areas of robotics research can coexist.

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References

  1. R. Alur, J. Esposito, M. Kim, V. Kumar, and I. Lee. Formal Modeling and Analysis of Hybrid Systems: A Case Study in Multirobot Coordination. Proceedings of the World Congress on Formal Methods, LNCS 1708, pp. 212–232, Springer, 1999.

    Google Scholar 

  2. R.C. Arkin. Behavior Based Robotics. The MIT Press, Cambridge, MA, 1998.

    Google Scholar 

  3. A. Bicci, A. Margio, and B. Piccoli. On the Reachability of Quantized Control Systems. IEEE Transactions on Automatic Control, Vol. 47, No. 4, April 2002.

    Google Scholar 

  4. M.S. Branicky. Multiple Lyapunov Functions and Other Analysis Tools for Switched and Hybrid Systems. IEEE Transactions on Automatic Control, Vol. 43, No. 4, pp. 475–482, April 1998.

    Article  MATH  MathSciNet  Google Scholar 

  5. R.W. Brockett. On the Computer Control of Movement. In the Proceedings of the 1988 IEEE Conference on Robotics and Automation, pp. 534–540, New York, April 1988.

    Google Scholar 

  6. R.W. Brockett. Hybrid Models for Motion Control Systems. In Perspectives in Control, Eds. H. Trentelman and J.C. Willems, pp. 29–54, Birkhäuser, Boston, 1993.

    Google Scholar 

  7. R. Brooks. A Robust Layered Control System for Mobile Robots. IEEE Journal of Robotics and Automation, Vol. RA-2, No. 1, pp. 14–23, 1986.

    Google Scholar 

  8. F. Buckley and F. Harary. Distance in Graphs. Addison-Wesley Publishing Company, New York, 1990.

    MATH  Google Scholar 

  9. J. Canny. The Complexity of Robot Motion Planning. The MIT Press, Cambridge, MA, 1987.

    Google Scholar 

  10. T.M. Cover and J.A. Thomas. Elements of Information Theory, John Wiley & Sons, Inc., New York, 1991.

    MATH  Google Scholar 

  11. D.F. Delchamps. The Stabilization of Linear Systems with Quantized Feedback. Proceedings of the IEEE Conference on Decision and Control, Austin, TX, Dec. 1988.

    Google Scholar 

  12. M. Egerstedt. Linguistic Control of Mobile Robots. IEEE/RSJ International Conference on Intelligent Robots and Systems, Maui, Hawaii, Oct. 2001.

    Google Scholar 

  13. M. Egerstedt. Some Complexity Aspects of the Control of Mobile Robots. American Control Conference, Anchorage, Alaska, May, 2002.

    Google Scholar 

  14. M. Egerstedt and R.W. Brockett. Feedback Can Reduce the Specification Complexity of Motor Programs. To appear in IEEE Transactions on Automatic Control, 2002.

    Google Scholar 

  15. N. Elia and S.K. Mitter. Stabilization of Linear Systems With Limited Information. IEEE Transactions on Automatic Control, Vol. 46, No. 9, Sept. 2001.

    Google Scholar 

  16. A. Ginzburg. Algebraic Theory of Automata. ACM Monograph Series, Academic Press, New York, 1968.

    MATH  Google Scholar 

  17. J.E. Hopcroft and G. Wilfong. Motion of Objects in Contact. The International Journal of Robotics Research, Vol. 4, No. 4, pp. 32–46, 1986.

    Article  Google Scholar 

  18. D. Hristu and S. Andersson. Directed Graphs and Motion Description Languages for Robot Navigation and Control. IEEE Conference on Robotics and Automation, May 2002.

    Google Scholar 

  19. D.A. Huffman. A Method for the Construction of Minimum Redundancy Codes. Proceedings of IRE, Vol. 40, pp. 1098–1101, 1952.

    Article  Google Scholar 

  20. M. Johansson and A. Rantzer. Computation of Piecewise Quadratic Lyapunov Functions for Hybrid Systems. IEEE Transactions on Automatic Control, Vol. 43, No. 4, pp. 555–559, April 1998.

    Article  MATH  MathSciNet  Google Scholar 

  21. V. Manikonda, P.S. Krishnaprasad, and J. Hendler. Languages, Behaviors, Hybrid Architectures and Motion Control. In Mathematical Control Theory, Eds. Willems and Baillieul, pp. 199–226, Springer-Verlag, 1998.

    Google Scholar 

  22. J. Rissanen. Stochastic Complexity in Statistical Inquiry. World Scientific Publishing Company, River Edge, NJ, 1989.

    MATH  Google Scholar 

  23. C.E. Shannon. A Mathematical Theory of Communication. Bell Systems Technical Journal, Vol. 27, pp. 379–423, 1948.

    MathSciNet  Google Scholar 

  24. C. Tomlin, G.J. Pappas, and S. Sastry. Conflict Resolution for Air Traffic Management: A Study in Multi-Agent Hybrid Systems. IEEE Transactions on Automatic Control, Vol. 43, No. 4, April 1998.

    Google Scholar 

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Egerstedt, M. (2003). Motion Description Languages for Multi-Modal Control in Robotics. In: Bicchi, A., Prattichizzo, D., Christensen, H.I. (eds) Control Problems in Robotics. Springer Tracts in Advanced Robotics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36224-X_5

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  • DOI: https://doi.org/10.1007/3-540-36224-X_5

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  • Print ISBN: 978-3-540-00251-2

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