View Full Version : Inverse dynamics

Anatol Feldman
01-08-2001, 04:49 AM
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: http://www.crosswinds.net/~afeldman/

To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl
For information and archives: http://isb.ri.ccf.org/biomch-l