Abstract
Saccadic eye movement is highly stereotyped and commonly believed to be governed by an open-loop control mechanism. We propose a principle combining time-optimal and minimum control energy criteria to account for the saccade main sequence as observed from empirical data. The model prediction revealed that the weighting factor of the energy conservation becomes more dominant than the time-optimal when the saccade amplitude is large. We demonstrate that the proposed model is a general form synthesizing the time-optimum, minimum torque change, and minimum control effort models. In addition, we show the connection between our model and the stochastic minimum variance models from the aspect of optimization.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Athans M, Falb P (1966) Optimal control: an introduction to the theory and its applications. McGraw-Hill, New York
Bahill AT, Adler D et al (1975) Most naturally occurring human saccades have magnitudes of 15 degrees or less. Investig Ophthalmol 14(6): 468–469
Clark M, Stark L (1974) Control of human eye movements: I. Modelling of extraocular muscle. Math Biosci 20(3–4): 191–211
Collewijn H, Erkelens CJ et al (1988) Binocular co-ordination of human horizontal saccadic eye movements. J Physiol 404(1): 157–182
Dean P (1996) Motor unit recruitment in a distributed model of extraocular muscle. J Neurophysiol 76(2): 727
Enderle J, Wolfe J (1987) Time-optimal control of saccadic eye movements. IEEE Trans Biomed Eng 34: 43–55
Fuchs A, Binder M (1983) Fatigue resistance of human extraocular muscles. J Neurophysiol 49(1): 28–34
Harris CM, Wolpert DM (1998) Signal-dependent noise determines motor planning. Nature 394(6695): 780–784
Harris C, Wolpert D (2006) The main sequence of saccades optimizes speed-accuracy trade-off. Biol Cybern 95(1): 21–29
Harwood M, Mezey L et al (1999) The spectral main sequence of human saccades. J Neurosci 19(20): 9098
Hatze H (1977) A myocybernetic control model of skeletal muscle. Biol Cybern 25(2): 103–119
Hogan N (1984) An organizing principle for a class of voluntary movements. J Neurosci 4(11): 2745
Kardamakis AA, Moschovakis AK (2009) Optimal Control of Gaze Shifts. J Neurosci 29(24): 7723–7730
Kirk D (2004) Optimal control theory: an introduction. Dover Publications, New York
Koene AR, Erkelens CJ (2004) Properties of 3D rotations and their relation to eye movement control. Biol Cybern 90(6): 410–417
Nelson W (1983) Physical principles for economies of skilled movements. Biol Cybern 46(2): 135–147
Rao AV, Benson DA, et al. (2010) Algorithm 902: GPOPS, A MATLAB software for solving multiple-phase optimal control problems using the gauss pseudospectral method. Acm Trans Math Software 37(2)
Robinson DA (1973) Models of saccadic eye-movement control-system. Kybernetik 14(2): 71–83
Robinson DA (1981) Models of the mechanics of eye movements. In: Zuber B (eds) Models of oculomotor behavior and control. CRC Press, Inc., Chicago, pp 21–42
Robinson D, Gordon J et al (1986) A model of the smooth pursuit eye movement system. Biol Cybern 55(1): 43–57
Tanaka H, Krakauer JW et al (2006) An optimization principle for determining movement duration. J Neurophysiol 95(6): 3875–3886
Tanaka H, Tai MH et al (2004) Different predictions by the minimum variance and minimum torque-change models on the skewness of movement velocity profiles. Neural Comput 16(10): 2021–2040
Uno Y, Kawato M et al (1989) Formation and control of optimal trajectory in human multijoint arm movement. Biol Cybern 61(2): 89–101
van Beers RJ (2008) Saccadic eye movements minimize the consequences of motor noise. PLos One 3(4): e2070
van Gisbergen JAM, Robinson DA et al (1981) A quantitative-analysis of generation of saccadic eye-movements by burst neurons. J Neurophysiol 45(3): 417–442
Van Opstal A, Van Gisbergen J et al (1985) Reconstruction of neural control signals for saccades based on an inverse method. Vis Res 25(6): 789
Winters J, Stark L (1985) Analysis of fundamental human movement patterns through the use of in-depth antagonistic muscle models. IEEE Trans Biomed Eng 32: 826–839
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, X., Hsiang, S.M. Modeling trade-off between time-optimal and minimum energy in saccade main sequence. Biol Cybern 104, 65–73 (2011). https://doi.org/10.1007/s00422-011-0420-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00422-011-0420-3