TrajRS: Towards Certified Robustness in Pedestrian Trajectory Prediction
Authors: Liang Zhang, Gaojie Jin, Yao Shi, Quanzhi Li, Cheng-Chao Huang, David N. Jansen, Lijun Zhang
Abstract
The robustness of trajectory prediction models is crucial for developing safe autonomous driving systems. Adversarial attacks on trajectory prediction can significantly impair the accuracy of predicted trajectories, leading to hazardous driving behaviors. While heuristic defense strategies have been implemented to enhance the robustness of trajectory prediction models, these measures often fail against more sophisticated, targeted adversarial attacks. Hence, there is a pressing need to establish verifiable safety assurances for trajectory prediction models. In this paper, we extend the traditional Randomized Smoothing framework to "TrajRS", which provides a certified robust radius for smoothed trajectory predictors. We clarify and expand the formal definitions of robustness in trajectory prediction and tailor the practical TrajRS scheme specifically to "robustness for the optimal prediction" and "robustness for all possible predictions". An extensive set of experiments demonstrates that TrajRS effectively achieves robustness certification for all smoothed pedestrian trajectory predictors in this work.
Accurate and reliable vehicle trajectory prediction is essential for safe autonomous driving. Recent studies have incorporated safety risk into trajectory prediction to quantify dangers posed by surrounding agents. However, most risk-aware approaches use past risk information as a secondary signal to help guide decisions, overlooking its future evolution and uncertainty. In this paper, we propose a risk horizon profiling (RHP) module that incorporates a continuous, learnable potential field model for risk-aware trajectory prediction. The RHP module calculates the spatial-temporal proximity of surrounding objects to profile risk distributions across future horizons, which supports better trajectory prediction by adaptively identifying what human drivers perceive as critical moments. We evaluate our method on two datasets from different driving settings, highD for highway corridors and SHRP2 for urban streets, which cover diverse risk scenarios including safe, near-crash, and crash events. Compared to the baseline methods, our framework achieves a 25.0% reduction in 5s RMSE on the highD dataset and a 29.1% reduction in 5s minFDE on SHRP2. These results indicate strong performance for both short and long horizon prediction and robust generalization across highway and urban scenarios. The proposed method enables more realistic AV path planning and strategic selection, thereby supporting safer autonomous driving and more advanced driver-assistance systems. The source code for this work is available at: https://github.com/bilab-nyu/RHP
Accurate trajectory prediction is critical for safe autonomous navigation in crowded environments. While many trajectory predictors output Gaussian distributions to represent the multi-modal distribution over future pedestrian positions, the reliability of their confidence levels often remains unaddressed. This limitation can lead to unsafe or overly conservative motion planning when the predictor is integrated with an uncertainty-aware planner. Existing Gaussian trajectory predictors primarily rely on the Negative Log-Likelihood loss, which is prone to predict over- or under-confident distributions, and may compromise downstream planner safety. This paper introduces a novel loss function for calibrating prediction uncertainty which leverages Kernel Density Estimation to estimate the empirical distribution of confidence levels. The proposed formulation enforces consistency with the properties of a Gaussian assumption by explicitly matching the estimated empirical distribution to the Chi-squared distribution. To ensure accurate mean prediction, a Mean Squared Error term is also incorporated in the final loss formulation. Experimental results on real-world trajectory datasets show that our method significantly improves the reliability of confidence levels predicted by different State-Of-The-Art Gaussian trajectory predictors. We also demonstrate the importance of providing planners with reliable probabilistic insights (i.e. calibrated confidence levels) for collision-free navigation in complex scenarios. For this purpose, we integrate Gaussian trajectory predictors trained with our loss function with an uncertainty-aware Model Predictive Control on scenarios extracted from real-world datasets, achieving improved planning performance through calibrated confidence levels.
Most evaluations of autonomous driving policies under adversarial conditions are conducted in simulation, due to cost efficiency and the absence of physical risk. However, purely virtual testing fails to capture structural inconsistencies, supervision constraints, and state-representation effects that arise in real-world data and fundamentally shape policy robustness. This work presents an offline trajectory-learning and adversarial robustness evaluation framework grounded in real-world intersection driving data. Within a controlled data contract, we train and compare three trajectory-learning paradigms: Multi-Layer Perceptron (MLP)-based Behavior Cloning (BC), Transformer-based object-tokenized BC, and inverse reinforcement learning (IRL) formulated within a Generative Adversarial Imitation Learning (GAIL) framework. Models are evaluated using Average Displacement Error (ADE) and Final Displacement Error (FDE). Inference-time robustness is assessed by subjecting trained policies to gradient-based adversarial perturbations across multiple intersection scenarios, yielding a structured robustness evaluation matrix. Results show that state-structure design and architectural inductive biases critically influence adversarial stability, leading to markedly different robustness profiles despite comparable nominal prediction accuracy (ADE < 0.08). Inference-time Projected Gradient Descent (PGD) attacks induce final displacement errors of up to approximately 8 meters. The proposed framework establishes a scalable benchmark for studying offline trajectory learning and adversarial robustness in real-world autonomous driving settings.