Effects of model inaccuracies on reaching movements with intermittent control

Autoři: Igor Gindin aff001;  Miri Benyamini aff001;  Miriam Zacksenhouse aff001
Působiště autorů: Faculty of Mechanical Engineering, Technion Israel’s Institute of Technology, Haifa 32000, Israel aff001
Vyšlo v časopise: PLoS ONE 14(10)
Kategorie: Research Article
doi: https://doi.org/10.1371/journal.pone.0224265


Background and objectives

Human motor control (HMC) has been hypothesized to involve state estimation, prediction and feedback control to overcome noise, delays and disturbances. However, the nature of communication between these processes, and, in particular, whether it is continuous or intermittent, is still an open issue. Depending on the nature of communication, the resulting control is referred to as continuous control (CC) or intermittent control (IC). While standard HMC theories are based on CC, IC has been argued to be more viable since it reduces computational and communication burden and agrees better with some experimental results. However, to be a feasible model for HMC, IC has to cope well with inaccurately modeled plants, which are common in daily life, as when lifting lighter than expected loads. While IC may involve event-driven triggering, it is generally assumed that refractory mechanisms in HMC set a lower limit on the interval between triggers. Hence, we focus on periodic IC, which addresses this lower limit and also facilitates analysis.

Theoretical methods and results

Theoretical stability criteria are derived for CC and IC of inaccurately modeled linear time-invariant systems with and without delays. Considering a simple muscle-actuated hand model with inaccurately modeled load, both CC and IC remain stable over most of the investigated range, and may become unstable only when the actual load is much smaller than expected, usually smaller than the minimum set by the actual mass of the forearm and hand. Neither CC nor IC is consistently superior to the other in terms of the range of loads over which the system remains stable.

Numerical methods and results

Numerical simulations of time-delayed reaching movements are presented and analyzed to evaluate the effects of model inaccuracies when the control and observer gains are time-dependent, as is assumed to occur in HMC. Both IC and CC agree qualitatively with previously published experimental results with inaccurately modeled plants. Thus, our study suggests that IC copes well with inaccurately modeled plants and is indeed a viable model for HMC.

Klíčová slova:

Control theory – Covariance – Eigenvalues – Noise reduction – Simulation and modeling – Gaussian noise


1. Todorov E, Jordan MI, Optimal feedback control as a theory of motor coordination, Nature neuroscience, 5(11), 1226–1235 (2002). doi: 10.1038/nn963 12404008

2. Todorov E, Optimality principles in sensorimotor control, Nature neuroscience, 7(9), 907–915 (2004). doi: 10.1038/nn1309 15332089

3. Todorov E, Stochastic optimal control and estimation methods adapted to the noise characteristics of the sensorimotor system, Neural computation, 17(5), 1084–1108, (2005). doi: 10.1162/0899766053491887 15829101

4. Shadmehr R, Krakauer JW, A computational neuroanatomy for motor control, Experimental Brain Research, 185(3), 359–381 (2008). doi: 10.1007/s00221-008-1280-5 18251019

5. Gawthrop P, Loram I, Lakie M, Gollee H, Intermittent control: a computational theory of human control, Biological cybernetics, 104(1), 31–51 (2011). doi: 10.1007/s00422-010-0416-4 21327829

6. Stengel RF, Optimal Control and Estimation. Courier Corporation (1994).

7. Ronco E, Arsan T, & Gawthrop P J., Open-loop intermittent feedback control: practical continuous-time GPC. IEE Proceedings-Control Theory and Applications, 146(5), 426–434, (1999). doi: 10.1049/ip-cta:19990504

8. Meyer DE, Abrams RA, Kornblum S, Wright CE, & Keith Smith JE, Optimality in human motor performance: ideal control of rapid aimed movements. Psychological review, 95(3), 340 (1988). doi: 10.1037/0033-295x.95.3.340 3406245

9. Neilson P. D., Neilson M. D., & O’dwyer N. J., Internal models and intermittency: A theoretical account of human tracking behavior. Biological Cybernetics, 58(2), 101–112, (1988). doi: 10.1007/bf00364156 3349110

10. Karniel A, Open questions in computational motor control, Journal of integrative neuroscience, 10(3), 385–411 (2011). doi: 10.1142/S0219635211002749 21960308

11. Garcia E, Antsaklis PJ, Montestruque LA, Model-based control of networked systems. Birkhuser (2014).

12. Montestruque LA, Antsaklis PJ, On the model-based control of networked systems, Automatica, 39(10), 1837–1843, (2003). doi: 10.1016/S0005-1098(03)00186-9

13. Vince MA, The Intermittency of control movements and the psychological refractory period, British Journal of Psychology. General Section, 38(3), 149–157, (1948). doi: 10.1111/j.2044-8295.1948.tb01150.x

14. Navas F, Stark L, Sampling or intermittency in hand control system dynamics, Biophysical Journal, 8(2), 252–302 (1968). doi: 10.1016/S0006-3495(68)86488-4 5639937

15. Gawthrop P J, Wang L. Event-driven intermittent control. International Journal of Control, 82(12), 2235–2248 (2009). doi: 10.1080/00207170902978115

16. McVea DA, & Pearson KG, Stepping of the forelegs over obstacles establishes long-lasting memories in cats. Current Biology 17, no. 16: R621–R623 (2007). doi: 10.1016/j.cub.2007.06.026 17714644

17. Hiebert GW, Whelan PJ, Prochazka A & Pearson KG, Contribution of hindlimb flexor muscle afferents to the timing of phase transitions in the cat step cycle, J. Neurophysiol. 75, 1126–1137 (1996). doi: 10.1152/jn.1996.75.3.1126 8867123

18. Doeringer JA, Hogan N, Intermittency in preplanned elbow movements persists in the absence of visual feedback, Journal of Neurophysiology, 80(4), 1787–1799 (1998). doi: 10.1152/jn.1998.80.4.1787 9772239

19. van de Kamp C, Gawthrop PJ, Gollee H, & Loram ID, Refractoriness in sustained visuo-manual control: is the refractory duration intrinsic or does it depend on external system properties?. PLoS computational biology, 9(1), e1002843 (2013). doi: 10.1371/journal.pcbi.1002843 23300430

20. Fishbach A, Roy SA, Bastianen C, Miller LE, & Houk JC, Deciding when and how to correct a movement: discrete submovements as a decision making process. Experimental brain research, 177(1), 45–63 (2007). doi: 10.1007/s00221-006-0652-y 16944111

21. Groß J, Timmermann L, Kujala J, Dirks M, Schmitz F, Salmelin R, Schnitzler A, The neural basis of intermittent motor control in humans, Proceedings of the National Academy of Sciences, 99(4), 2299–2302 (2002). doi: 10.1073/pnas.032682099

22. Gollee H, Gawthrop P J, Lakie M, Loram ID. Visuo-manual tracking: does intermittent control with aperiodic sampling explain linear power and non-linear remnant without sensorimotor noise? The Journal of physiology, 595(21), 6751–6770 (2017). doi: 10.1113/JP274288 28833126

23. Bhanpuri NH, Okamura AM, Bastian AJ, Predicting and correcting ataxia using a model of cerebellar function. Brain, 137(7), 1931–1944 (2014). doi: 10.1093/brain/awu115 24812203

24. Benyamini M, Zacksenhouse M, Optimal feedback control successfully explains changes in neural modulations during experiments with brain-machine interfaces, Frontiers in systems neuroscience, 9 (2015). doi: 10.3389/fnsys.2015.00071 26042002

25. Winter D A, Biomechanics and motor control of human movement. John Wiley & Sons, (2009). doi: 10.1002/9780470549148

26. Saunders J. A., & Knill D. C., Visual feedback control of hand movements, Journal of Neuroscience, 24(13): 3223–3234, (2004). doi: 10.1523/JNEUROSCI.4319-03.2004 15056701

27. Kleinman D, Optimal control of linear systems with time-delay and observation noise. IEEE Transactions on Automatic Control, 14(5), 524–527 (1969). doi: 10.1109/TAC.1969.1099242

28. Kleinman DL, Baron S, Levison WH, An optimal control model of human response part I: Theory and validation, Automatica, 6(3), 357–369 (1970). doi: 10.1016/0005-1098(70)90051-8

29. Kwakernaak H, Sivan R, Linear optimal control systems, Vol. 1. New York: Wiley-interscience (1972).

30. NASA Handbook, NASA Human Integration Design Handbook (HIDH)-NASA (Vol. 3407). SP-2010 (2010).

31. Popescu F., Hidler J.M., & Rymer W.Z., Elbow impedance during goal-directed movements. Experimental brain research, 152(1):17–28, (2003). doi: 10.1007/s00221-003-1507-4 12879184

32. Shadmehr R, & Wise SP, The computational neurobiology of reaching and pointing: a foundation for motor learning. MIT press (2005).

33. Asai Y, Tasaka Y, Nomura K, Nomura T, Casadio M, Morasso P, A model of postural control in quiet standing: robust compensation of delay-induced instability using intermittent activation of feedback control. PLoS One, 4(7), e6169 (2009). doi: 10.1371/journal.pone.0006169 19584944

34. Tanabe H, Fujii K, Suzuki Y, & Kouzaki M, Effect of intermittent feedback control on robustness of human-like postural control system. Scientific reports, 6, 22446 (2016). doi: 10.1038/srep22446 26931281

35. Flash T, Hogan N, The coordination of arm movements: an experimentally confirmed mathematical model, Journal of neuroscience, 5(7), 1688–1703 (1985). doi: 10.1523/JNEUROSCI.05-07-01688.1985 4020415

36. Yang Y, Pei L, Li H, An H∞, control model of human postural control in quiet upright standing, Control and Decision Conference (CCDC) IEEE.Chicago, 2483-2486 (2011).

37. Zacksenhouse M, Bogacz R, and Holmes P, Robust versus optimal strategies for two-alternative forced choice tasks, J Math. Psychology, 54:230–246 (2010). doi: 10.1016/j.jmp.2009.12.004

Článek vyšel v časopise


2019 Číslo 10
Nejčtenější tento týden