Testing models of path integration in a triangle completion task

Abstract

Path integration—the constant updating of position and orientation in an environment— is commonly tested using a triangle completion task. To complete the task successfully, the participant must integrate the distance traveled on the first two legs with the turn angle to produce an accurate homebound trajectory. Large, systematic errors are observed in triangle completion, which could be due to (i) error in perceiving and remembering (—encoding—) distances and angles traveled, and (ii) error in integrating these estimates to determine the homebound path. The aim of this study is to test different models of path integration, such as a geometric coordinate frame (Mittelstadt & Mittelstadt, 1973), an egocentric framework (Benhamou et al., 1990), or continuous updating (Gallistel, 1990). One model (Fujita et al., 1993) focuses solely on encoding as a potential source of error. The present study independently measures participants' encoding errors in distance and angle reproduction tasks, and uses them to predict errors in a triangle completion task. Participants completed the tasks in a virtual hedge maze, which provides both visual and idiothetic information. This approach dissociates angle from distance, which are confounded in triangle completion. By using Monte Carlo methods to sample the observed distribution of encoding errors, different models of integration were tested by using them to predict the homebound path, and comparing the predictions to observed triangle completion behavior. Errors in the homebound trajectory are not due solely to encoding error, but also due to integration error, including potential non-linear combinations of error.