Learning Dynamics under Environmental Constraints via Measurement-Induced Bundle Structures

TL;DR

This paper introduces a geometric framework using fiber bundle structures to improve learning of system dynamics under environmental constraints, especially with limited local measurements, by integrating neural ODEs and measurement-aware control methods.

Contribution

It proposes a novel geometric approach that unifies measurements, constraints, and dynamics learning, enabling adaptive control and efficient learning under uncertain local sensing conditions.

Findings

Enhanced learning efficiency in simulations

Improved constraint satisfaction with limited sensing

Theoretical guarantees of convergence and constraint adherence

Abstract

Learning unknown dynamics under environmental (or external) constraints is fundamental to many fields (e.g., modern robotics), particularly challenging when constraint information is only locally available and uncertain. Existing approaches requiring global constraints or using probabilistic filtering fail to fully exploit the geometric structure inherent in local measurements (by using, e.g., sensors) and constraints. This paper presents a geometric framework unifying measurements, constraints, and dynamics learning through a fiber bundle structure over the state space. This naturally induced geometric structure enables measurement-aware Control Barrier Functions that adapt to local sensing (or measurement) conditions. By integrating Neural ODEs, our framework learns continuous-time dynamics while preserving geometric constraints, with theoretical guarantees of learning convergence and constraint satisfaction dependent on sensing quality. The geometric framework not only enables efficient dynamics learning but also suggests promising directions for integration with reinforcement learning approaches. Extensive simulations demonstrate significant improvements in both learning efficiency and constraint satisfaction over traditional methods, especially under limited and uncertain sensing conditions.