KoopCast: Trajectory Forecasting via Koopman Operators

We present KoopCast, a lightweight yet efficient model for trajectory forecasting in general dynamic environments. Our approach leverages Koopman operator theory, which enables a linear representation of nonlinear dynamics by lifting trajectories into a higher-dimensional space. The framework follows a two-stage design: first, a probabilistic neural goal estimator predicts plausible long-term targets, specifying where to go; second, a Koopman operator-based refinement module incorporates intention and history into a nonlinear feature space, enabling linear prediction that dictates how to go. This dual structure not only ensures strong predictive accuracy but also inherits the favorable properties of linear operators while faithfully capturing nonlinear dynamics. As a result, our model offers three key advantages: (i) competitive accuracy, (ii) interpretability grounded in Koopman spectral theory, and (iii) low-latency deployment. We validate these benefits on ETH/UCY, the Waymo Open Motion Dataset, and nuScenes, which feature rich multi-agent interactions and map-constrained nonlinear motion. Across benchmarks, KoopCast consistently delivers high predictive accuracy together with mode-level interpretability and practical efficiency.

Egocentric Conformal Prediction for Safe and Efficient Navigation in Dynamic Cluttered Environments

Conformal prediction (CP) has emerged as a powerful tool in robotics and control, thanks to its ability to calibrate complex, data-driven models with formal guarantees. However, in robot navigation tasks, existing CP-based methods often decouple prediction from control, evaluating models without considering whether prediction errors actually compromise safety. Consequently, ego-vehicles may become overly conservative or even immobilized when all potential trajectories appear infeasible. To address this issue, we propose a novel CP-based navigation framework that responds exclusively to safety-critical prediction errors. Our approach introduces egocentric score functions that quantify how much closer obstacles are to a candidate vehicle position than anticipated. These score functions are then integrated into a model predictive control scheme, wherein each candidate state is individually evaluated for safety. Combined with an adaptive CP mechanism, our framework dynamically adjusts to changes in obstacle motion without resorting to unnecessary conservatism. Theoretical analyses indicate that our method outperforms existing CP-based approaches in terms of cost-efficiency while maintaining the desired safety levels, as further validated through experiments on real-world datasets featuring densely populated pedestrian environments.