Abstract
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.
Explore similar work
Aug 31, 2026cs.CV
Most trajectory forecasting models are trained on clean annotated histories, and are often evaluated under the same idealized assumption, although practical deployments rely on trajectories produced by imperfect multi-object trackers. The real-world observations exhibit localization jitter, missed or unstable detections, and data-association ambiguity, which are usually either ignored or removed through denoising. This paper instead treats tracking-derived reliability cues as an informative signal to be propagated to the predictor. We propose a plug-in uncertainty-aware formulation in which each observed state is encoded as an uncertain state representation, modeled by a Gaussian distribution whose covariance combines detection-level localization uncertainty and association-level ambiguity through the law of total variance. Existing backbones are adapted with minimal architectural changes: input trajectories are represented as Gaussian observations, and predicted trajectories are produced as Gaussian forecasts rather than deterministic coordinates. To train predictors that remain robust under structured observation noise, we combine temporally correlated Ornstein-Uhlenbeck perturbations with response-based knowledge distillation from a teacher trained on clean trajectories. Experiments on Oxford Town Centre and VIRAT using real tracker outputs, together with a complementary ETH/UCY pseudo-detection protocol, show that the proposed formulation improves displacement accuracy and the reliability-sharpness trade-off of probabilistic forecasts.
Stephane Da Silva Martins, Victor Petrovic, Emanuel Aldea +1
Jun 27, 2026cs.AI
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.
Liang Zhang, Gaojie Jin, Yao Shi +4
Aug 8, 2026cs.RO
Safe robot navigation in crowded spaces requires planning that accounts for where people will be, not only where they are now. Model Predictive Path Integral (MPPI) control is an effective sampling-based planner, but many implementations encode humans as static point obstacles at their current positions, underestimating risk in dynamic scenes. We propose Predictive Gaussian Interaction Fields (PGIF), a spatiotemporal cost formulation that propagates pedestrian predictions forward over the full planning horizon and encodes them as anisotropic Gaussian repulsive fields aligned with each pedestrian's direction of motion. The forward spread of each field grows with the pedestrian's speed, creating a motion cone danger zone that penalises robot trajectories entering the pedestrian's path of travel more strongly than those approaching from behind. The formulation is closed-form and fully parallelisable across rollouts, adding no measurable computational overhead. Evaluated over 300 randomised crowd scenarios at three density levels, PGIF-MPPI achieves a 0% collision rate at every density level, compared with up to 82% for vanilla MPPI, while maintaining real-time planning performance.
Chinmay Mundane