Coordinate transformations in the control of cat posture

1. Global geometric variables represent high-order parameters in the control of cat posture. In particular, limb length and orientation are accurately controlled in response to tilts of the support platform. There is now electrophysiological evidence, obtained in anesthetized cats, that spinal sensory neurons projecting to the cerebellum are broadly tuned to limb length and orientation. Limb length and orientation specify the position of the limb end-points in body-centered polar coordinates. They define an intended posture in a global manner, leaving the detailed geometric configuration of the limbs undetermined. The planar covariation of limb joint angles described in the accompanying paper suggests the existence of an intermediate processing stage that transforms endpoint coordinates into the angular coordinates of the joints (inverse mapping). In this paper we address the question of the nature of this coordinate transformation. Because the number of degrees of freedom of angular motion in each limb exceeds that of endpoint motion in world space, several different angular configurations are compatible with any given endpoint position in world space. Thus the problem of coordinate transformation is a priori indeterminate. We have tested a number of different hypotheses. 2. Coordinate transformation could be accomplished implicitly by means of discrete kinematic synergies. Any given geometric configuration of the limb would result from a weighed combination of only two distinct patterns of angular covariations, the first pattern affecting selectively limb length and the second pattern affecting limb orientation. This decomposition, however, was found in only a few sporadic cases. 3. We also tested the possibility that the coordinate transformation involves the Moore-Penrose generalized inverse. We found that this algorithm produces a planar covariation of the joint angles, but with an orientation orthogonal to the experimental plane. By contrast, a linear transformation with constant, position-independent terms can fit the experimental plane of angular covariations but predicts large errors in endpoint position. 4. The particular orientation in joint space of the experimental plane, coupled with the scatter of data points around the plane, bears a specific implication for the problem of inverse mapping. The experimental plane crosses the constant position lines (the loci of all possible changes of the joint angles that correspond with an invariant position of the endpoint) at an acute angle. Consequently the specification of limb orientation is little sensitive to joint configurations: relatively small changes in orientation can be produced by large changes in joint configurations.(ABSTRACT TRUNCATED AT 400 WORDS)