A comparative study of game mechanics and control laws for an adaptive physiological game

Abstract

We present an adaptive biofeedback game that aims to maintain the player’s arousal by modifying game difficulty in response to the player’s physiological state, as measured with wearable sensors. Our approach models the interaction between human physiology and game difficulty during gameplay as a control problem, where game difficulty is the system input and player arousal its output. We validate the approach on a car-racing game with real-time adaptive game mechanics. Specifically, we use (1) car speed, road visibility, and steering jitter as three mechanisms to manipulate game difficulty, (2) electrodermal activity as physiological correlate of arousal, and (3) two types of control law: proportional (P) control, and proportional-integral-derivative (PID) control. We also propose quantitative measures to characterize the effectiveness of these game adaptations and controllers in manipulating the player’s arousal. Experimental trials with 25 subjects in both open-loop (no feedback) and closed-loop (negative feedback) conditions show statistically significant differences in effectiveness among the three game mechanics and also between the two control laws. Specifically, manipulating car speed provides higher control of arousal levels than changing road visibility or vehicle steering. Our results also confirm that PID control leads to lower error and reduced oscillations in the closed-loop response compared to proportional-only control. Finally, we discuss the theoretical and practical implications of our approach.

Appendix

The Zielger Nichols method [37] provides plug-in formulas for the PID gains by considering the unit-step input response of the system. The unit step response generally follows an S-shaped curve characterized by two parameters: the delay time (L) and the time constant (T); see Fig. 9. Both parameters are obtained by drawing a tangent line at the inflection point of the unit-step response and determining the intersection of the tangent with the axes. Once these parameters (L and T), have been obtained, the PID gains can then be computed via the plug-in expressions in Fig. 9. For our experiments, we used the transition from 0 to 100 % difficulty in the open loop phase as a unit step input. This gives rise to the S-shaped NS.SCR response from which L/T and the PID gains are estimated. Calculation according to see Fig. 9 leads to the following PID gains: $k_P =1.115;\,k_I =0.05;k_D =4.861$. These parameter settings were computed on the open-loop experimental data in Sect. 4.2, and used both for the closed-loop simulations and closed-loop experiments.

Fig. 9

Ziegler Nichols method for tuning a PID controller. Here, $c(t)$ is the unit step response and $K$ is its steady state value