Predicting Pedestrian Confidence Regions by Distributional Robust Optimization: Incorporating Parameter and Distributional Uncertainty in the Social Force Model

Pedestrian confidence region prediction is crucial for ensuring safety in autonomous driving, particularly in urban scenarios. Recent work models pedestrian dynamics via the Social Force Model (SFM), providing deterministic trajectory predictions. However, these approaches often fail to account for the inherent uncertainty in pedestrian behavior and biases across datasets. We formulate a Distributionally Robust Optimization (DRO) problem that integrates parameter and distributional uncertainty into the SFM to estimate pedestrian confidence regions at a future time. To solve this, we apply a sample-based approximation that transforms probabilistic constraints into a tractable deterministic form, with uniform convergence guarantees. A case study on pedestrian-vehicle interaction demonstrates improved prediction accuracy and robustness under uncertainty.