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.

Articulated object manipulation remains a critical challenge in robotics due to the complex kinematic constraints and the limited physical reasoning of existing methods. In this work, we introduce ArtGS, a novel framework that extends 3D Gaussian Splatting (3DGS) by integrating visual-physical modeling for articulated object understanding and interaction. ArtGS begins with multi-view RGB-D reconstruction, followed by reasoning with a vision-language model (VLM) to extract semantic and structural information, particularly the articulated bones. Through dynamic, differentiable 3DGS-based rendering, ArtGS optimizes the parameters of the articulated bones, ensuring physically consistent motion constraints and enhancing the manipulation policy. By leveraging dynamic Gaussian splatting, cross-embodiment adaptability, and closed-loop optimization, ArtGS establishes a new framework for efficient, scalable, and generalizable articulated object modeling and manipulation. Experiments conducted in both simulation and real-world environments demonstrate that ArtGS significantly outperforms previous methods in joint estimation accuracy and manipulation success rates across a variety of articulated objects. Additional images and videos are available on the project website: sites.google.com/view/artgs.

Stochastic optimal control methods often struggle in complex non-convex landscapes, frequently becoming trapped in local optima due to their inability to learn from historical trajectory data. This paper introduces Memory-Augmented Potential Field Theory, a unified mathematical framework that integrates historical experience into stochastic optimal control. Our approach dynamically constructs memory-based potential fields that identify and encode key topological features of the state space, enabling controllers to automatically learn from past experiences and adapt their optimization strategy. We provide a theoretical analysis showing that memory-augmented potential fields possess non-convex escape properties, asymptotic convergence characteristics, and computational efficiency. We implement this theoretical framework in a Memory-Augmented Model Predictive Path Integral (MPPI) controller that demonstrates significantly improved performance in challenging non-convex environments. The framework represents a generalizable approach to experience-based learning within control systems (especially robotic dynamics), enhancing their ability to navigate complex state spaces without requiring specialized domain knowledge or extensive offline training.

Fluid interactions are crucial in daily tasks, with properties like density and viscosity being key parameters. The property states can be used as control signals for robot operation. While density estimation is simple, assessing viscosity, especially for different fluid types, is complex. This study introduces a novel differentiable fitting framework, DiffStir, tailored to identify key physics parameters through stirring. Then, given the estimated physics parameters, we can generate commands to guide the robotic stirring. Comprehensive experiments were conducted to validate the efficacy of DiffStir, showcasing its precision in parameter estimation when benchmarked against reported values in the literature. More experiments and videos can be found in the supplementary materials and on the website: https://diffstir.robotflow.ai.

Neural ODEs (NODEs) are continuous-time neural networks (NNs) that can process data without the limitation of time intervals. They have advantages in learning and understanding the evolution of complex real dynamics. Many previous works have focused on NODEs in concise forms, while numerous physical systems taking straightforward forms in fact belong to their more complex quasi-classes, thus appealing to a class of general NODEs with high scalability and flexibility to model those systems. This however may result in intricate nonlinear properties. In this paper, we introduce ControlSynth Neural ODEs (CSODEs). We show that despite their highly nonlinear nature, convergence can be guaranteed via tractable linear inequalities. In the composition of CSODEs, we introduce an extra control term for learning the potential simultaneous capture of dynamics at different scales, which could be particularly useful for partial differential equation-formulated systems. Finally, we compare several representative NNs with CSODEs on important physical dynamics under the inductive biases of CSODEs, and illustrate that CSODEs have better learning and predictive abilities in these settings.