Metamorphic Testing of Multimodal Human Trajectory Prediction

Context: Predicting human trajectories is crucial for the safety and reliability of autonomous systems, such as automated vehicles and mobile robots. However, rigorously testing the underlying multimodal Human Trajectory Prediction (HTP) models, which typically use multiple input sources (e.g., trajectory history and environment maps) and produce stochastic outputs (multiple possible future paths), presents significant challenges. The primary difficulty lies in the absence of a definitive test oracle, as numerous future trajectories might be plausible for any given scenario. Objectives: This research presents the application of Metamorphic Testing (MT) as a systematic methodology for testing multimodal HTP systems. We address the oracle problem through metamorphic relations (MRs) adapted for the complexities and stochastic nature of HTP. Methods: We present five MRs, targeting transformations of both historical trajectory data and semantic segmentation maps used as an environmental context. These MRs encompass: 1) label-preserving geometric transformations (mirroring, rotation, rescaling) applied to both trajectory and map inputs, where outputs are expected to transform correspondingly. 2) Map-altering transformations (changing semantic class labels, introducing obstacles) with predictable changes in trajectory distributions. We propose probabilistic violation criteria based on distance metrics between probability distributions, such as the Wasserstein or Hellinger distance. Conclusion: This study introduces tool, a MT framework for the oracle-less testing of multimodal, stochastic HTP systems. It allows for assessment of model robustness against input transformations and contextual changes without reliance on ground-truth trajectories.