Modeling spatial navigation in the presence of dynamic obstacles: a differential games approach

Abstract

Obstacle circumvention strategies can be shaped by the dynamic interaction of an individual (evader) and an obstacle (pursuer). We have developed a mathematical model with predictive and emergent components, using experimental data from seven healthy young adults walking toward a target while avoiding collision with a stationary or moving obstacle (approaching head-on, or diagonally 30° left or right) in a virtual environment. Two linear properties from the predictive component enable the evader to predict the minimum distance between itself and the obstacle at all times, including the future intersection of trajectories. The emergent component uses the classical differential games model to solve for an optimal circumvention while reaching the target, wherein the locomotor strategy is influenced by the obstacle, target, and the evader velocity. Both model components were fitted to a different set of experimental data obtained from five poststroke and healthy participants to derive the minimum predicted distance (predictive component) and obstacle influence dimensions (emergent component) during circumvention. Minimum predicted distance between evader and pursuer was kept constant when the evader was closest to the obstacle in all participants. Obstacle influence dimensions varied depending on obstacle approach condition and preferred side of circumvention, reflecting differences in locomotor strategies between poststroke and healthy individuals. Additionally, important associations between model outputs and observed experimental outcomes were found. The model, supported by experimental data, suggests that both predictive and emergent processes can shape obstacle circumvention strategies in healthy and poststroke individuals.NEW & NOTEWORTHY Obstacle circumvention during goal-directed locomotion is modeled with a new mathematical approach comprising both predictive and emergent elements. The major novelty is using differential games solutions to illustrate the dynamic interactions between the individual as an evader and the approaching obstacle as a pursuer. The model is supported by experimental evidence that explains the behavior along the continuum of locomotor adaptation displayed by healthy subjects and individuals with stroke.