Moving to Make Contact

Abstract

A theory of controlling contact is presented based solely on sensory information about the rho functions of changing gaps and the animal's orientation to gravity. The rho function of a gap is the relative rate of change of size of the gap and is directly available in all sensory modalities, unlike size and rate-of-change of size, which require scaling information. The rhos involved in contacting a moving object are the rho of the distance gap between the animal and the object, the rho of the angular gap between the animal's direction of movement and the direction of the object, and the rho of the vertical gap between the object and the horizontal plane through the animal. Movement to contact is controlled by pair-wise coupling these rhos, i.e., keeping the ratios between rhos constant. The values of the ratios determine whether contact will be gentle or forceful, i.e., achieved with zero or non-zero linear or angular momentum. The theory is applied to explaining sensory guidance of movement to catch a high ball.

Notes

¹ When the movement is very rapid there may be insufficient time to adjust a movement on the basis of information picked up during the movement. Such so-called ballistic movements are probably adjusted on the basis of information picked up during preceding similar movements. An example is trilling on a piano.

² For ease of understanding, but without loss of generality, I here use the mathematical function rho in place of tau. Rho is simply 1/tau.

³ The content of Table 1 is derived from the following equations: Y = CX^λ_Y,X (obtained by integrating Equation (3), where C is a constant) and (obtained by successively differentiating the first equation).