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Inverse dynamics

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  • Inverse dynamics

    Dear All,

    Happy New Year!

    Chris Kirtley switched the topics of “centrifugal forces” to a more
    important question on how the nervous system perceives and controls
    movements. I reproduce here his question:
    “As far as I know, we have no sensors for segment acceleration - only
    (conceivably) joint angular acceleration, via spindles, joint afferents
    and skin receptors. Would this variable be sufficient, I wonder, for the
    CNS to compute the inverse dynamics?”

    I would like to point out that the term “inverse dynamics hypothesis”
    (in the most explicit form formulated by Hollerbach but the idea is as
    old as Newton’s mechanics) implies that the nervous system pre-plans the
    desired movement kinematics and then, based on some intrinsic
    representation of equations of motion, computes and specifies the
    electromyographic activity, muscle forces and torques, which are
    necessary to actualise the movement plan.

    Chris’s question implies that the nervous system does compute the
    “inverse dynamics”. I suppose that the majority of those who work in the
    field of biomechanics and maybe somewhat smaller % of physiologists
    share this view. I would be pleased to know if this is an exaggeration
    since I belong to those who, following the implicit arguments of Von
    Holst (1969/1973) and very explicit arguments of Bernstein (1967), are
    convinced that the nervous system cannot and does not need to compute
    inverse dynamics to produce perfect movements.

    The inverse computational strategy works well for robotics. I would
    like to point out some simple physical and physiological principles that
    bring us directly to the conclusion that the inverse dynamics control
    strategy cannot be realised in biological systems.
    1. Many human actions consist of movements from one stable posture
    to another. A stable posture is associated not only with the equilibrium
    position at which all forces are balanced but also with the ability of
    the system to generate forces resisting deflections from this position.
    2. According to a general rule of physics (e.g., Glansdorff &
    Prigogine 1971), the spatial coordinates at which the equilibrium is
    established in any physical system are determined not by output
    variables (like EMG, forces, torques) but independently of them, by the
    system’s parameters. For example, in a pendulum, the equilibrium
    (vertical) position is determined not by variable forces but the
    parameters of the pendulum, such as the length of the rope at which the
    pendulum’s mass is suspended, the coordinates of the suspension point,
    and the direction of gravity. Since these parameters are constant, the
    equilibrium position of the pendulum remains the same even when the
    system is put in motion. Thus, the ability of the nervous system to
    change the equilibrium position implies that the nervous system has the
    capacity not only to maintain but also to change appropriate parameters
    or determinants of the equilibrium position and thus produce active
    3. Suppose control levels computed and specified EMG signals and
    forces according to the planned kinematics, as suggested in the
    inverse-dynamic approach. If the system left the parameters that
    determine the equilibrium position unchanged, the programmed forces
    would drive the system from the existing (initial) equilibrium position.
    The inverse dynamic approach does not account for the fact that, like in
    a pendulum, the system will produce additional, resisting forces trying
    to return the system to the initial position and thus destroy the
    programmed action. Even if the inverse-dynamic specifications of the
    computed forces were combined with a shift in the equilibrium position,
    the emerging, additional forces arising due to the difference between
    the initial position and the new equilibrium position would also
    interfere with the computed forces. As a result, the programmed motion
    would again be destroyed. The idea of EMG and force programming thus
    conflicts with the natural physical tendency of the system to generate,
    without programming, muscle activity and forces associated with
    deflections from equilibrium. Briefly, the inverse dynamic approach
    conflicts with the natural dynamics of biological systems.
    4. Experimentally, one parameter (lambda) controlling the
    equilibrium position of the system has been found by Asatryan and
    Feldman (1965).

    I am looking forward to seeing reactions to my comments. In my view,
    the inverse-dynamic approach is just a revival of our old illness - the
    mechanistic tradition of thinking inspired by remarkable successes in
    robotics. The robotics view may, however, be misleading in educating,
    especially, young scientists on how movements are controlled in living

    Best wishes in the New Millenium!

    Dr. Anatol Feldman
    Neurological Science Research Center
    Department of Physiology
    University of Montreal and
    Rehabilitation Institute of Montreal
    6300 Darlington, Montreal, Quebec, Canada H3S 2J4
    Tel (514) 340 2078 ext. 2192
    Fax (514) 340 2154
    Web Site:

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