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Languages, Behaviors, Hybrid Architectures, and Motion Control

  • Chapter
Mathematical Control Theory

Abstract

In this paper we put forward a framework that integrates features of reactive planning models with modern control-theory-based approaches to motion control of robots. We introduce a motion description language, MDLe, inspired by Roger Brockett’s MDL, that provides a formal basis for robot programming using behaviors, and at the same time permits incorporation of kinematic and dynamic models of robots given in the form of differential equations. In particular, behaviors for robots are formalized in terms of kinetic state machines, a motion description language, and the interaction of the kinetic state machine with realtime information from (limited range) sensors. This formalization allows us to create a mathematical basis for the study of such systems, including techniques for integrating sets of behaviors. In addition we suggest cost functions for comparing both atomic and compound behaviors in various environments. We demonstrate the use of MDLe in the area of motion planning for nonholonomic robots. Such models impose limitations on stabilizability via smooth feedback; piecing together open-loop and closed-loop trajectories becomes essential in these circumstances, and MDLe enables one to describe such piecing together in a systematic manner. A reactive planner using the formalism of this discussion is described. We demonstrate obstacle avoidance with limited range sensors as a test of this planner.

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References

  1. M.A. Arbib. Schema theory. In Encyclopedia of Artificial Intelligence, pages 1427–1443. Wiley-Interscience, New York, 1992.

    Google Scholar 

  2. M.A. Arbib. Schema-theoretic models of arm, hand, and eye movements. In P. Rudomin, M.A. Arbib, F. Cervantes-Perez, and R. Romo, editors, Neuroscience: From Neural Networks to Artificial Intelligence, pages 43–60. Springer-Verlag, New York, 1993.

    Google Scholar 

  3. C.R. Arkin. Motor schema-based mobile robot navigation. The Int. Journal of Robotics Research, 8(4):92–112, 1988.

    Article  Google Scholar 

  4. C.R. Arkin. Behaviour-based robot navigation for extended domains. Adaptive Behaviour, 1(2):201–225, 1992.

    Article  Google Scholar 

  5. N. Bernstein. The Coordination and Regulation of Movement. Pergamon Press, Oxford, 1967.

    Google Scholar 

  6. E. Bienestock and S. Geman. Compositionality in neural systems. In M.A. Arbib, editor, The Handbook of Brain Theory and Neural Networks, pages 223–226. MIT Press, Cambridge, MA, 1995.

    Google Scholar 

  7. B. Blumberg and T. Galyean. Multi-level direction of autonomous creatures for realtime virtual envorinments. In Computer Graphics Proceedings, SIGGRAPH-95, pages 47–54, 1995.

    Google Scholar 

  8. J. Barraquand and J.C. Latombe. Robot motion planning: A distributed representation approach. Technical Report STAN-CS-89–1257, Stanford University, May 1989.

    Google Scholar 

  9. R. W. Brockett. Asymptotic stability and feedback stabilization. In R.W. Brockett, R.S. Millman, and HJ. Sussmann, editors, Differential Geometric Control Theory, pages 181–191. Birkhauser, Boston, 1983.

    Google Scholar 

  10. R.W. Brockett. Robotic manipulators and the product of exponential formula. In P.A. Fuhrmann, editor, Mathematical Theory of Networks and Systems, pages 120–129. Springer-Verlag, New York, 1984.

    Chapter  Google Scholar 

  11. R.A. Brooks. A robust layered control system for a mobile robot. IEEE Journal of Robotics and Automation, 2(1):14–23, 1986.

    Article  Google Scholar 

  12. R.W. Brockett. On the computer control of movement. In Proc. of the 1988 IEEE Conference on Robotics and Automation, pages 534–540. IEEE, New York, 1988.

    Chapter  Google Scholar 

  13. R.W. Brockett. Formal languages for motion description and map making. In Robotics, pages 181–193. American Mathematical Society, Providence, RI, 1990.

    Google Scholar 

  14. R. W. Brockett. Hybrid models for motion control. In H. Trentelman and J.C. Willems, editors, Perspectives in Control, pages 29–51. Birkhauser, Boston, 1993.

    Google Scholar 

  15. J.-M. Coron. Global asymptotic stabilization for controllable systems. Mathematics of Control, Signals and Systems, 5(3), 1992.

    Google Scholar 

  16. C. Canudas de Wit and O.J. Sordalen. Exponential stabilization of mobile robots with nonholonomic constraints. IEEE Transactions on Automatic Control, 37(11): 1791–1797, November 1992.

    Article  MathSciNet  MATH  Google Scholar 

  17. C. Fernandes, L. Gurvits, and Z.X. Li. Foundations of nonholonomic motion planning. In Z. X. Li and J. F. Canny, editors, Nonholonomic Motion Planning. Kluwer, 1993.

    Google Scholar 

  18. H. Hu and M. Brady. A Bayesian approach to real-time obstacle avoidance for a mobile robot. Autonomous Robots, 1(1):69–92, 1995.

    Article  Google Scholar 

  19. Robert Hermann. Accessibility problems for path systems. In Differential Geometry and the Calculus of Variations, Chapter 18, pages 241–257. Math Sci Press, Brookline, MA, 1968. 2nd Edition.

    Google Scholar 

  20. I. Horswill, Polly: A vision-based artificial agent. Proc. of the Eleventh Conference on Artificial Intelligence, MIT Press, Cambridge, MA, 1993.

    Google Scholar 

  21. O. Khatib. Real-time obstacle avoidance for manipulators and mobile robots. The Int. Journal of Robotics Research, 5(1):90–99, Spring 1986.

    Article  MathSciNet  Google Scholar 

  22. D.E. Koditschek. Exact robot navigation by means of potential functions: Some topological considerations. In Proc. of the IEEE Int. Conference on Robotics and Automation, pages 1–6. IEEE, New York, 1987.

    Google Scholar 

  23. D.M. Lyons and M.A. Arbib. A formal model of computation for sensory-based robotics. IEEE Tran. on Robotics and Automation, 5(3):280–293, June 1989.

    Article  Google Scholar 

  24. J.P. Laumond. Nonholonomic motion planning versus controllability via the multibody car system example. Technical Report STAN-CS-90–1345, Stanford University, December 1990.

    Google Scholar 

  25. N.E. Leonard and P.S. Krishnaprasad. Averaging for attitude control and motion planning. In Proc. of the 32nd IEEE Conference on Decision and Control, pages 3098–3104. IEEE, New York, 1993.

    Google Scholar 

  26. T. Lozano-Perez. Spatial planning: A configuration space approach. AI memo 605, MIT Artificial Intelligence Laboratory, Cambridge, MA, 1980.

    Google Scholar 

  27. V.J. Lumelsky. Algorithmic and complexity issues of robot motion in an uncertain environment. Journal of Complexity, 3: 146–182, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  28. Vikram Manikonda. A hybrid control strategy for path planning and obstacle avoidance with nonholonomic robots. Master’s thesis, University of Maryland, College Park, MD, 1994.

    Google Scholar 

  29. B. Mirtich and J.F. Canny. Using skeletons for nonholonomic path planniing among obstacles. In Proc. of the Int. Conference on Robotics and Automation, pages 2533–2540. IEEE, New York, 1992.

    Chapter  Google Scholar 

  30. V. Manikonda, J. Hendler, and P.S. Krishnaprasad. Formalizing behavior-based planning for nonholonomic robots. In Proc. of the 14th Int. Joint Conference on Artificial Intelligence, pages 142–149, Morgan Kaufmann, San Mateo, CA, 1995.

    Google Scholar 

  31. V. Manikonda, P.S. Krishnaprasad, and J. Hendler. A motion description language and hybrid architecure for motion planning with nonholonomic robots. In Proc. of the IEEE Int. Conference on Robotics and Automation. IEEE, New York, 1995.

    Google Scholar 

  32. R.M. Murray, Z. Li, and S.S. Sastry. A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton, FL, 1994.

    MATH  Google Scholar 

  33. R.M. Murray and S.S. Sastry. Steering nonholonomic systems using sinusoids. In Proc. of the 29th IEEE Conference on ecision and Control, pages 2097–2101. IEEE, New York, 1990.

    Chapter  Google Scholar 

  34. J.B. Pomet. Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift. Systems and Control letters, 18: 147–158, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  35. R. Shahidi, M.A. Shayman, and P.S. Krishnaprasad. Mobile robot navigation using potential functions. In Proc. of the IEEE Int. Conference on Robotics and Automation, pages 2047–2053. IEEE, New York, 1991.

    Chapter  Google Scholar 

  36. H.J. Sussmann. Local controllability and motion planning for some classes of systems without drift. In Proc. of the 30th Conference on Decision and Control, pages 1110–1114. IEEE, New York, 1991.

    Chapter  Google Scholar 

  37. J.C. Willems. Paradigms and puzzles in the theory of dynamical systems. IEEE Transactions on Automatic Control, 36: 259–294, 1991.

    Article  MathSciNet  MATH  Google Scholar 

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Authors
  1. Vikram Manikonda
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  2. P. S. Krishnaprasad
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  3. James Hendler
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Editor information

Editors and Affiliations

  1. College of Engineering, Boston University, Boston, MA, 02215-2407, USA

    J. Baillieul

  2. Mathematics Institute, University of Groningen, 9700 AV, Groningen, The Netherlands

    J. C. Willems

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© 1999 Springer Science+Business Media New York

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Manikonda, V., Krishnaprasad, P.S., Hendler, J. (1999). Languages, Behaviors, Hybrid Architectures, and Motion Control. In: Baillieul, J., Willems, J.C. (eds) Mathematical Control Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1416-8_6

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  • DOI: https://doi.org/10.1007/978-1-4612-1416-8_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7136-9

  • Online ISBN: 978-1-4612-1416-8

  • eBook Packages: Springer Book Archive

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