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Biological Cybernetics

, Volume 56, Issue 5–6, pp 279–292 | Cite as

Deducing planning variables from experimental arm trajectories: Pitfalls and possibilities

  • J. M. Hollerbach
  • C. G. Atkeson
Article

Abstract

This paper investigates whether endpoint Cartesian variables or joint variables better describe the planning of human arm movements. For each of the two sets of planning variables, a coordination strategy of linear interpolation is chosen to generate possible trajectories, which are to be compared against experimental trajectories for best match. Joint interpolation generates curved endpoint trajectories calledN-leaved roses. Endpoint Cartesian interpolation generates curved joint trajectories, which however can be qualitatively characterized by joint reversal points.

Though these two sets of planning variables ordinarily lead to distinct predictions under linear interpolation, three situations are pointed out where the two strategies may be confused. One is a straight line through the shoulder, where the joint trajectories are also straight. Another is any trajectory approaching the outer boundary of reach, where the joint rate ratio always appears to be approaching a constant. A third is a generalization to staggered joint interpolation, where endpoint trajectories virtually identical to straight lines can sometimes be produced. In examining two different sets of experiments, it is proposed that staggered joint interpolation is the underlying planning strategy.

Keywords

Endpoint Linear Interpolation Reversal Point Coordination Strategy Joint Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Abend W, Bizzi E, Morasso P (1982) Human arm trajectory formation. Brain 105:331–348Google Scholar
  2. Atkeson CG, Hollerbach JM (1985) Kinematic features of unrestrained vertical arm movements. J Neurosci 5:2318–2330Google Scholar
  3. Bernstein N (1967) The coordination and regulation of movements. Pergamon Press, OxfordGoogle Scholar
  4. Bishop A, Harrison A (1977) Kots and Syrovegin, (1966) — a demonstration of modular units in motor programming? J Human Movement Stud 3:99–109Google Scholar
  5. Bizzi E, Chapple W, Hogan N (1982) Mechanical properties of muscles: implications for motor control. Trends Neurosci 5 (11):395–398Google Scholar
  6. Bizzi E, Accornero N, Chapple W, Hogan N (1984) Posture control and trajectory formation during arm movement. J Neurosci 4:2738–2745Google Scholar
  7. Brady JM (1982) Trajectory planning. In: Brady JM, Hollerbach JM, Johnson TL, Lozano-Perez T, Mason MT (ed) Robot motion: planning and control. MIT Press Cambridge, MA, pp 221–243Google Scholar
  8. Burlington RS (1942) Handbook of mathematical tables and formulas. Handbook Publ Inc, Sandusky, OhioGoogle Scholar
  9. Flash T, Hogan N (1985) The coordination of arm movements: an experimentally confirmed mathematical model J Neurosci 5:1688–1703Google Scholar
  10. Hildreth EC, Hollerbach JM (1986) Artificial Intelligence: a computational approach to vision and motor control. In: Plum F (ed) Handbook of physiology. American Physiological Society (in press)Google Scholar
  11. Hogan N (1984) An organizing principle for a class of voluntary movements. J Neurosci 4:2745–2754Google Scholar
  12. Hollerbach JM (1981) An oscillation theory of handwriting. Biol Cybern 39:139–156Google Scholar
  13. Hollerbach JM (1985) Computers, brains, and the control of movement. In: Evarts EV, Wise SP, Bousfield D (ed) The motor system in neurobiology. Elsevier Biomedical Press, Amsterdam, pp 140–146Google Scholar
  14. Hollerbach JM (1985) Optimum kinematic design for a seven degree of freedom manipulator. In: Hanafusa H, Inoue H (ed) Robotics research: the second international symposium. MIT Press Cambridge, MA, pp 215–222Google Scholar
  15. Hollerbach JM, Atkeson CG (1986) Characterization of joint-interpolated arm movements. In: Heuer H, Fromm C (ed) Generation and modulation of action patterns. Springer New York (in press)Google Scholar
  16. Hollerbach JM, Flash T (1982) Dynamic interactions between limb segments during planar arm movement. Biol Cybern 44:67–77Google Scholar
  17. Kots YM, Syrovegin AV (1966) Fixed set of variants of interaction of the muscles of two joints used in the execution of simple voluntary movements. Biofizika 11:1061–1066Google Scholar
  18. Lacquaniti F, Terzuolo CA, Viviani P (1983) The law relating the kinematic and figural aspects of drawing movements. Acta Psycologica 54:115–130Google Scholar
  19. Morasso P (1981) Spatial control of arm movements. Exp Brain Res 42:223–227Google Scholar
  20. Morasso P, Mussa Ivaldi FA (1982) Trajectory formation and handwriting: a computational model. Biol Cybern 45:131–142Google Scholar
  21. Nashner LM, McCollum G (1985) The organization of human postural movements: a formal basis and experimental synthesis. Behav Brain Sci 8:135–172Google Scholar
  22. Polit A, Bizzi E (1979) Characteristics of motor programs underlying arm movements in monkeys. J Neurophysiol 42:183–194Google Scholar
  23. Sahar G, Hollerbach JM (1986) Planning of minimum-time trajectories for robot arms. Int J Robotics Res 5 (3):90–100Google Scholar
  24. Soechting JF, Lacquaniti F (1981) Invariant characteristics of a pointing movement in man. J Neurosci 1:710–720Google Scholar
  25. Soechting JF, Lacquaniti F, Terzuolo CA (1986) Coordination of arm movements in three-dimensional space. Sensorimotor mapping during drawing movement. Neuroscience 17:295–311Google Scholar
  26. Soechting JF, Ross B (1984) Psychophysical determination of coordinate representation of human arm orientation. Neuroscience 13:595–604Google Scholar
  27. Viviani P, Terzuolo C (1982) Trajectory determines movement dynamics. Neuroscience 7:431–437Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • J. M. Hollerbach
    • 1
    • 2
  • C. G. Atkeson
    • 1
    • 2
  1. 1.Center for Biological Information ProcessingMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Artificial Intelligence LaboratoryCambridgeUSA

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