Skip to main content
SpringerLink
Log in

The Compass That Steered Robotics

  • Chapter
Book cover Logic and Program Semantics

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7230))

Abstract

Robotics researchers will be aware of Dexter Kozen’s contributions to algebraic algorithms, which have enabled the widespread use of the theory of real closed fields and polynomial arithmetic for motion planning. However, Dexter has also made several important contributions to the theory of information invariants, and produced some of the most profound results in this field. These are first embodied in his 1978 paper On the Power of the Compass, with Manuel Blum. This work has had a wide impact in robotics and nanoscience.

Starting with Dexter’s insights, robotics researchers have explored the problem of determining the information requirements to perform robot tasks, using the concept of information invariants. This represents an attempt to characterize a family of complicated and subtle issues concerned with measuring robot task complexity.

In this vein, several measures have been proposed [14] to measure the information complexity of a task: (a) How much internal state should the robot retain? (b) How many cooperating robots are required, and how much communication between them is necessary? (c) How can the robot change (side-effect) the environment in order to record state or sensory information to perform a task? (d) How much information is provided by sensors? and (e) How much computation is required by the robot? We have considered how one might develop a kind of “calculus” on (a) – (e) in order to compare the power of sensor systems analytically. To this end, information invariants is a theory whereby one sensor can be “reduced” to another (much in the spirit of computation-theoretic reductions), by adding, deleting, and reallocating (a) – (e) among collaborating autonomous robots. As we show below, this work steers using Dexter’s compass.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ben-Or, M., Kozen, D., Reif, J.: The complexity of elementary algebra and geometry. Journal of Computer and System Sciences 32(2), 251–264 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  2. Blum, M., Kozen, D.: On the power of the compass (or, why mazes are easier to search than graphs). In: Proceedings of the 19th Annual Symposium on Foundations of Computer Science, pp. 132–142. IEEE Computer Society (1978)

    Google Scholar 

  3. Blum, M., Sakoda, W.J.: On the capability of finite automata in 2 and 3 dimensional space. In: 18th Annual Symposium on Foundations of Computer Science, pp. 147–161 (1977)

    Google Scholar 

  4. Böhringer, K.-F., Bhatt, V., Donald, B.R., Goldberg, K.: Sensorless manipulation algorithms using a vibrating surface. Algorithmica 26(3/4), 389–429 (2000)

    Article  MathSciNet  Google Scholar 

  5. Böhringer, K.-F., Donald, B.R.: Algorithmic MEMS. In: Proceedings of the 3rd International Workshop on the Algorithmic Foundations of Robotics WAFR, Houston, TX (March 1998)

    Google Scholar 

  6. Böhringer, K.-F., Donald, B.R., Kovacs, G., MacDonald, N., Suh, J.: Computational methods for the design and control of MEMS micromanipulator arrays. IEEE Computational Science and Engineering 4(1), 17–29 (1997); Special Issue on Computational MEMS

    Article  Google Scholar 

  7. Böhringer, K.-F., Donald, B.R., Lamiraux, F., Kavraki, L.: Part orientation with one or two stable equilibria using programmable force fields. IEEE Transactions on Robotics and Automation 16(2), 157–170 (2000)

    Article  Google Scholar 

  8. Böhringer, K.-F., Donald, B.R., MacDonald, N.: Upper and lower bounds for programmable vector fields with applications to MEMS and vibratory plate parts feeders. In: Laumond, J.P., Overmars, M. (eds.) Algorithms for Robotic Motion and Manipulation, pp. 255–276. A. K. Peters, Wellesley (1997)

    Google Scholar 

  9. Böhringer, K.-F., Donald, B.R., MacDonald, N.C.: Programmable Vector Fields for Distributed Manipulation, with Applications to MEMS Actuator Arrays and Vibratory Parts Feeders. International Journal of Robotics Research 18(2) (February 1999)

    Google Scholar 

  10. Böhringer, K.-F., Donald, B.R., MacDonald, N.C., Mihailovich, R.: Sensorless manipulation using massively parallel micro-fabricated actuator arrays. In: Proc. IEEE International Conference on Robotics and Automation, San Diego, CA (May 1994)

    Google Scholar 

  11. Böhringer, K.-F., Donald, B.R., MacDonald, N.C., Mihailovich, R.: A theory of manipulation and control for microfabricated actuator arrays. In: Proc. 7th IEEE Workshop on Micro Electro Mechanical Systems (MEMS 1994), Kanagawa, Japan (January 1994)

    Google Scholar 

  12. Cox, D., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms. Undergraduate Texts in Mathematics. Springer, New York (1991)

    Google Scholar 

  13. Donald, B.R.: Error Detection and Recovery in Robotics. LNCS, vol. 336. Springer, Heidelberg (1989)

    MATH  Google Scholar 

  14. Donald, B.R.: Information invariants in robotics. Artificial Intelligence 72, 217–304 (1995)

    Article  Google Scholar 

  15. Donald, B.R., et al.: MEMS Videos. Department of Computer Science, Duke University (July 2008), http://www.cs.duke.edu/donaldlab/research_movies_mems.php

  16. Donald, B.R., et al.: Robotics Videos. Department of Computer Science, Duke University (July 2008), http://www.cs.duke.edu/donaldlab/research_movies_robots.php

  17. Donald, B.R., Jennings, J., Rus, D.: Towards a theory of information invariants for cooperating autonomous mobile robots. In: Proceedings of the International Symposium of Robotics Research ISRR, Hidden Valley, PA (October 1993)

    Google Scholar 

  18. Donald, B.R., Kapur, D., Mundy, J.: Symbolic and Numerical Computation for Artificial Intelligence. Academic Press, Harcourt Jovanovich (1992)

    MATH  Google Scholar 

  19. Donald, B.R., Levey, C., McGray, C., Paprotny, I., Rus, D.: An untethered, electrostatic, globally-controllable MEMS micro-robot. Journal of Microelectromechanical Systems 15(1), 1–15 (2006)

    Article  Google Scholar 

  20. Donald, B.R., Levey, C., Paprotny, I.: Planar microassembly by parallel actuation of MEMS microrobots. Journal of Microelectromechanical Systems 17(4), 789–808 (2008)

    Article  Google Scholar 

  21. Donald, B.R., Xavier, P.: Provably good approximation algorithms for optimal kinodynamic planning for cartesian robots and open chain manipulators. Algorithmica 14(6), 443–479 (1995)

    Article  MathSciNet  Google Scholar 

  22. Donald, B.R., Xavier, P.: Provably good approximation algorithms for optimal kinodynamic planning: Robots with decoupled dynamics bounds. Algorithmica 14(6), 480–530 (1995)

    Article  MathSciNet  Google Scholar 

  23. Donald, B.R., Jennings, J., Rus, D.: Information invariants for distributed manipulation. International Journal of Robotics Research 16(5), 673–702 (1997)

    Article  Google Scholar 

  24. Donald, B.R., Xavier, P., Canny, J., Reif, J.: Kinodynamic motion planning. Journal of the ACM 40(5), 1048–1066 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  25. Erdmann, M.: Using backprojections for fine motion planning with uncertainty. Int. J. Rob. Res. 5, 19–45 (1986)

    Article  Google Scholar 

  26. Erdmann, M.: On Probabilistic Strategies for Robot Tasks. PhD thesis, MIT Department of EECS, MIT Department of EECS, MIT A.I. Lab, Cambridge MIT-AI-TR 1155 (1989)

    Google Scholar 

  27. Erdmann, M.: Towards task-level planning: Action-based sensor design. Technical report, Carnegie-Mellon, Carnegie-Mellon School of Computer Science, Tech. report, CMU-CS-92-116 (February 1991)

    Google Scholar 

  28. Erdmann, M., Mason, M.: An exploration of sensorless manipulation. In: Proceedings of the 1986 IEEE International Conference on Robotics and Automation, vol. 3, pp. 1569–1574 (April 1986)

    Google Scholar 

  29. Fischer, M.J., Lynch, N.A., Merritt, M.: Easy impossibility proofs for distributed consensus problems. J. Distrib. Comput. 1, 26–39 (1986)

    Article  MATH  Google Scholar 

  30. Fisher, P.C.: Turing machines with restricted memory access. Information and Control 9(4), 364–379 (1966)

    Article  MathSciNet  Google Scholar 

  31. Yu Grigor’ev, D.: Complexity of deciding Tarski algebra. Journal of Symbolic Computation 5(1-2), 65–108 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  32. Hopcroft, J.E., Schwartz, J.T., Sharir, M.: On the complexity of motion planning for multiple independent objects; PSPACE-hardness of the “Warehouseman’s problem”. The International Journal of Robotics Research 3(3), 76–88 (1984)

    Article  Google Scholar 

  33. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley (1979)

    Google Scholar 

  34. Jennings, J., Donald, B.R.: Sensor interpretation and task-directed planning using perceptual equivalence classes. In: Proc. IEEE International Conference on Robotics and Automation, Sacramento, CA, pp. 190–197 (April 1991)

    Google Scholar 

  35. Jennings, J., Donald, B.R.: Constructive recognizability for task-directed robot programming. In: Proc. IEEE International Conference on Robotics and Automation, Nice, France, pp. 2446–2452 (May 1992)

    Google Scholar 

  36. Jennings, J., Donald, B.R.: Constructive recognizability for task-directed robot programming. Jour. Robotics and Autonomous Systems 9(1), 41–74 (1992) (invited)

    Article  Google Scholar 

  37. Jennings, J., Rus, D.: Active model acquisition for near-sensorless manipulation with mobile robots. In: International Association of Science and Technology for Development (IASTED) International Conference on Robotics and Manufacturing, Oxford, England (1993)

    Google Scholar 

  38. Kozen, D.: Automata and planar graphs. In: Proceedings of the 2nd Symposium on Fundamentals of Computing Theory, FCT 1979, Berlin, pp. 243–254 (1979)

    Google Scholar 

  39. Lozano-Perez, T.: Spatial planning: A configuration space approach. IEEE Transactions on Computers C-32(2), 108–120 (1983)

    Article  MathSciNet  Google Scholar 

  40. Lozano-Pérez, T., Mason, M.T., Taylor, R.H.: Automatic synthesis of fine-motion strategies for robots. Int. J. of Robotics Research 3, 3–24 (1984)

    Article  Google Scholar 

  41. Lumelsky, V.J., Stepanov, A.A.: Path-planning strategies for a point mobile automaton moving amidst unknown obstacles of arbitrary shape. Algorithmica, 403–430 (1987)

    Google Scholar 

  42. Mason, M.T.: Mechanics and planning of manipulator pushing operations. The International Journal of Robotics Research 5(3), 53–71 (1986)

    Article  Google Scholar 

  43. Minsky, M.L.: Recursive unsolvability of Post’s problem of “Tag” and other topics in theory of Turing machines. The Annals of Mathematics 74(3), 437–455 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  44. Natarajan, B.K.: On planning assemblies. In: Proceedings of the fourth Annual Symposium on Computational Geometry, pp. 299–308. ACM (1988)

    Google Scholar 

  45. Rees, J., Donald, B.R.: Program mobile robots in scheme. In: Proc. IEEE International Conference on Robotics and Automation, Nice, France, pp. 2681–2688 (May 1992)

    Google Scholar 

  46. Reif, J.H.: Complexity of the mover’s problem and generalizations. In: Proceedings of the 20th Annual Symposium on Foundations of Computer Science, Washington, DC, USA, pp. 421–427 (1979); Schwartz, J., Hopcroft, J., Sharir, M.: Planning, Geometry and Complexity of Robot Motion, ch. 11, pp. 267–281. Ablex publishing corp., New Jersey (1987)

    Google Scholar 

  47. Rosenschein, S.J.: Synthesizing information-tracking automata from environment descriptions. Technical report, Teleos Research TR No. 2 (1989)

    Google Scholar 

  48. Rus, D., Donald, B.R., Jennings, J.: Moving furniture with teams of autonomous mobile robots. In: Proc. IEEE/Robotics Society of Japan International Workshop on Intelligent Robots and Systems, Pittsburgh, PA, pp. 235–242 (1995)

    Google Scholar 

  49. Suh, J., Darling, R.B., Böhringer, K.-F., Donald, B.R., Baltes, H., Kovacs, G.: CMOS integrated organic ciliary actuator arrays for general-purpose micromanipulation tasks. Journal of Microelectromechanical Systems 8(4), 483–496 (1999)

    Article  Google Scholar 

  50. Tarski, A.: A decision method for elementary algebra and geometry. Rand report. Rand Corp. (1948)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Duke University, USA

    Bruce R. Donald

  2. Department of Biochemistry, Duke University Medical Center, USA

    Bruce R. Donald

Authors
  1. Bruce R. Donald
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Computer Science Department, Cornell University, 4149 Upson Hall, 14853, Ithaca, NY, USA

    Robert L. Constable

  2. Intelligent Systems Faculty of Science, Institute for Computing and Information Sciences, Radboud University Nijmegen, Postbus 9010, 6500 GL, Nijmegen, The Netherlands

    Alexandra Silva

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Donald, B.R. (2012). The Compass That Steered Robotics. In: Constable, R.L., Silva, A. (eds) Logic and Program Semantics. Lecture Notes in Computer Science, vol 7230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29485-3_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29485-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29484-6

  • Online ISBN: 978-3-642-29485-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation