The learning of visually guided action: an information-space analysis of pole balancing

In cart-pole balancing, one moves a cart in 1 dimension so as to balance an attached inverted pendulum. We approached perception-action and learning in this task from an ecological perspective. This entailed identifying a space of informational variables that balancers use as they perform the task and demonstrating that they improve by traversing the space to the loci of more useful variables. We presented a novel information space-including fractional derivatives of pendulum angle (e.g., halfway between angle and angular velocity)-as possible information for balancing. Fourteen college students tried to meet a criterion of balancing the pole for 30 s on 3 of 5 successive trials, up to a maximum of 150 attempts. Loci in the fractional derivative space predicted the time series of force production well. Systematic differences were seen in loci as a function of success, and systematic changes in locus were seen with learning. The fractional derivatives were shown to predict pole angles a short time interval into the future, allowing balancers to prospectively control the action and thereby nullify visuomotor delay. In addition to loci in the information space, we analyzed loci in a calibration space, reflecting the gain relating force to information.