Controller Gains of an Inverted Pendulum are Influenced by the Visual Feedback Position

In this study we experimentally test and model the control behavior of human participants when controlling inverted pendulums of different dynamic lengths, and with visual feedback of varying congruence to these dynamic lengths. Participants were asked to stabilize the inverted pendulum of L = 1 m and L = 4 m, with visual feedback shown at various distances along the pendulum. We fit a family of linear models to the control input (cart velocity) applied by participants. We further tested the models by predicting this control input for a pendulum with dynamic length L = 2 m and comparing the prediction to the experimental data. We show that the sum of proportional error correction and a term inversely proportional to visual feedback gain can well describe the control in human participants.