zbMATH — the first resource for mathematics

How humans control arm movements. (English) Zbl 1236.93012
Proc. Steklov Inst. Math. 261, 44-58 (2008) and Tr. Mat. Inst. Steklova 261 (2008).
Summary: This paper is devoted to the behavior of human arms during pointing movements. Several assumptions have already been made about the planning of such motions. None of these assumptions is able, up to now, to explain certain non-intuitive dynamic phenomena, in particular certain asymmetries in the motion and certain time intervals of inactivity of the muscles. In this paper, we propose an assumption explaining all these phenomena. Two strong points in this work are the following. First, our assumption is that human beings minimize a certain criterion that physically makes sense, namely, a compromise between the absolute work of external forces and a comfort term. Second, our conclusions do not rely on any numerical experiment and are completely justified mathematically (i.e., without any argument from simulation or “experimental mathematics,” such arguments being usually considered as acceptable in neurobiology). Also, the conclusion that total inactivity holds during some time subintervals of the movement is shown to be a stable property (in our model).

93A30 Mathematical modelling of systems (MSC2010)
93C10 Nonlinear systems in control theory
70E55 Dynamics of multibody systems
92C10 Biomechanics
93C15 Control/observation systems governed by ordinary differential equations
Full Text: DOI
[1] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Fizmatgiz, Moscow, 1961; Pergamon Press, Oxford, 1964).
[2] E. B. Lee and L. Markus, Foundations of Optimal Control Theory (J. Wiley and Sons, New York, 1967).
[3] J.-P. Gauthier and I. Kupka, Deterministic Observation Theory and Applications (Cambridge Univ. Press, Cambridge, 2001). · Zbl 0990.93001
[4] E. Todorov, ”Optimality Principles in Sensorimotor Control,” Nat. Neurosci. 7(9), 907–915 (2004). · doi:10.1038/nn1309
[5] C. Papaxanthis, T. Pozzo, and M. Schieppati, ”Trajectories of Arm Pointing Movements on the Sagittal Plane Vary with Both Direction and Speed,” Exp. Brain Res. 148(4), 498–503 (2003). · doi:10.1007/s00221-002-1327-y
[6] R. Gentili, V. Cahouet, and C. Papaxanthis, ”Motor Planning of Arm Movements Is Direction-Dependent in the Gravity Field,” Neuroscience 145(1), 20–32 (2007). · doi:10.1016/j.neuroscience.2006.11.035
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.