Fractional-Order Information in the Visual Control of Lateral Locomotor Interception

Previous work on locomotor interception of a target moving in the transverse plane has suggested that interception is achieved by maintaining the target's bearing angle (often inadvertently confused and/or confounded with the target heading angle) at a constant value. However, dynamics-based model simulations testing the veracity of the underlying control strategy of nulling the rate of change in the bearing angle have been restricted to limited conditions of target motion, and only a few alternatives have been considered. Exploring a wide range of target motion characteristics with straight and curving ball trajectories in a virtual reality setting, we examined how soccer goalkeepers moved along the goal line to intercept long-range shots on goal, a situation in which interception is naturally constrained to movement along a single dimension. Analyses of the movement patterns suggested reliance on combinations of optical position and velocity for straight trajectories and optical velocity and acceleration for curving trajectories. As an alternative to combining such standard integer-order derivatives, we demonstrate with a simple dynamical model that nulling a single informational variable of a self-tuned fractional (rather than integer) order efficiently captures the timing and patterning of the observed interception behaviors. This new perspective could fundamentally change the conception of what perceptual systems may actually provide, both in humans and in other animals.