Safe Navigation in Dynamic Environments Using Data-Driven Koopman Operators and Conformal Prediction

2025-04-01

AI Summary

To address safety-critical navigation of autonomous systems in dynamic environments, this paper proposes a novel model predictive control (MPC) framework integrating data-driven Koopman operator modeling with conformal prediction (CP). Methodologically, we are the first to embed CP within the Koopman framework, enabling verifiable error bounds for nonlinear dynamics estimation; these statistical error bounds are explicitly incorporated as constraint tightening terms in the MPC formulation to ensure closed-loop safety. Our key contributions are: (1) the first Koopman–CP joint modeling scheme with rigorous theoretical error guarantees; and (2) an error-driven constraint tightening strategy that strictly enforces collision avoidance at a user-specified confidence level. Extensive simulations demonstrate that the proposed approach significantly enhances robustness and safety in scenarios with uncertain dynamic obstacles, while maintaining real-time computational efficiency.

Technology Category

• Intelligent Robots: State Estimation
• Natural Language Processing: Safety and Robustness
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

We propose a novel framework for safe navigation in dynamic environments by integrating Koopman operator theory with conformal prediction. Our approach leverages data-driven Koopman approximation to learn nonlinear dynamics and employs conformal prediction to quantify uncertainty, providing statistical guarantees on approximation errors. This uncertainty is effectively incorporated into a Model Predictive Controller (MPC) formulation through constraint tightening, ensuring robust safety guarantees. We implement a layered control architecture with a reference generator providing waypoints for safe navigation. The effectiveness of our methods is validated in simulation.

Problem

• Safe navigation in dynamic environments using data-driven methods
• Quantifying uncertainty with conformal prediction for robust safety
• Integrating Koopman operators and MPC for nonlinear dynamics control

Innovation

• Data-driven Koopman operators learn nonlinear dynamics
• Conformal prediction quantifies uncertainty statistically
• MPC with tightened constraints ensures robust safety