Abstract
We have developed a formalism for describing and analyzing a very simple representative of a class of robotic tasks which involve repeated robot-environment interactions, among them the task of juggling. We review our empirical success to date with a new class of control algorithms for this task domain that we call “mirror algorithms.” These new nonlinear feedback algorithms were motivated strongly by experimental insights after the failure of local controllers based upon a linearized analysis. We offer here a proof that a suitable mirror algorithm is correct with respect to the local version of a specified task — the “vertical one-juggle” — but observe that the resulting ability to place poles of the local linearized system does not achieve noticeably superior transient performance in experiments. We discuss the further analysis and experimentation that should provide a theoretical basis for improving performance.
This work has been supported in part by PMI Motion Technologies, INMOS Corporation and the the National Science Foundation under a Presidential Young Investigator Award held by the second author.
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E. Aboaf, S. Drucker, and C. Atkeson. Task-level robot learning: juggling a tennis ball more accurately. In Proc. IEEE International Conference on Robotics and Automation, pages 1290–1295, Scottsdale, AZ, May 1989.
R. Bellman. Introduction to Matrix Analysis. McGraw Hill, New York, 1965.
M. Bühler and D. E. Koditschek. Analysis of a simplified hopping robot. In IEEE International Conference on Robotics and Automation, pages 817–819, Philadelphia, PA, Apr 1988.
M. Bühler and D. E. Koditschek. A prelude to juggling. In 26th IEEE Conference on Decision and Control, pages (paper available from authors — not in proceedings), Los Angeles, CA, Dec 1987.
M. Bühler, D. E. Koditschek, and P. J. Kindlmann. A family of robot control strategies for intermittent dynamical environments. In IEEE International Conference on Robotics and Automation, pages 1296–1301, Scottsdale, AZ, May 1989.
M. Bühler, D. E. Koditschek, and P. J. Kindlmann. A one degree of freedom juggler in a two degree of freedom environment. In Proc. IEEE Conference on Intelligent Systems and Robots, pages 91–97, Tokyo, Japan, Oct 1988.
M. Bühler, D. E. Koditschek, and P. J. Kindlmann. Planning and Control of Robotic Juggling Tasks. In H. Miura, editor, Fifth International Symposium on Robotics Research, page (to appear), MIT Press, Tokyo, Japan, 1989.
P. Collet and J. P. Eckmann. Iterated Maps on the Interval as Dynamical Systems. Birkhäuser, Boston, 1980.
D. E. Koditschek and M. Bühler. Analysis of a simplified hopping robot. The International Journal of Robotics Research, (to appear).
F. Levin, M. Bühler, and D. E. Koditschek. The Yale Real-Time Distributed Control Node. In Second Annual Workshop on Parallel Computing, Oregon State University, Portland, OR, Apr 1988.
T. McGeer. Passive Bipedal Running. Technical Report IS-TR-89-02, Simon Fraser University, Centre for Systems Science, Apr 1989.
T. McGeer. Powered flight, child's play, silly wheels and walking machines. In Proc. IEEE International Conference on Robotics and Automation, pages 1592–1597, May 1989.
T. McGeer. Stability and Control of Two-Dimensional Biped Walking. Technical Report IS-TR-88-01, Simon Fraser University, Centre for Systems Science, Sep 1988.
Marc H. Raibert. Legged Robots That Balance. MIT Press, Cambridge, MA, 1986.
J. F. Schaefer and R. H. Cannon Jr. On the control of unstable mechanical systems. In IFAC, pages 6c.1–6c.13, London, Jun 1966.
I. M. Singer and J. A. Thorpe. Lecture Notes on Elementary Topology and Geometry. Springer-Verlag, NY, 1967.
J. L. Synge and B. A. Griffith. Principles of Mechanics. McGraw Hill, London, 1959.
Yu Wang. Dynamic Analysis and Simulation of Mechanical Systems with Intermittent Constraints. PhD thesis, Carnegie-Mellon University, 1989.
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Bühler, M., Koditschek, D.E., Kindlmann, P.J. (1990). A simple juggling robot: Theory and experimentation. In: Hayward, V., Khatib, O. (eds) Experimental Robotics I. Lecture Notes in Control and Information Sciences, vol 139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042512
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DOI: https://doi.org/10.1007/BFb0042512
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