Learning Dynamics under Environmental Constraints via Measurement-Induced Bundle Structures

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.