This paper addresses the problem of identifying parsimonious explicit piece-wise polynomial relationships that might involve a relatively large number of raw features. The algorithm leverages a recently proposed identification algorithm that yields parsimonious implicit relationships enabling to derive normality characterization in the context of anomaly detection and localization. The algorithm proposed in this paper goes a step further by deriving explicit piece-wise representations that are built using the set of polynomials involved in the implicit representations. The framework is illustrated on the problem of identifying parsimonious explicit representations of the inverse model of a 6-axis manipulator robot. Moreover, further experiments on a 4-axis robot are also shown which are designed to investigate the generalization capability of parsimonious models compared to state-of-the-art DNNs structures, when models face unseen contexts of use.
Robot policies are typically MLPs mapping observations to actions. Yet robot observations are physical variables, and many action-relevant cues arise not from individual variables but from their interactions; power, inertial effects, contact, slip, and compliance depend on products among observable signals. We introduce PRISM, a policy representation that makes polynomial interactions among observable physical variables explicit, learnable, and compact. Rather than listing all polynomial terms, PRISM uses a factorized polynomial module to expose higher-order interaction features efficiently. In reinforcement learning, it keeps the standard MLP backbone but applies a gradually activated element-wise polynomial function after it. In imitation learning, it replaces linear proprioceptive conditioning in Diffusion Policy with a polynomial layer trained end-to-end. Across humanoid locomotion and contact-rich manipulation, PRISM improves performance over standard MLP policies and larger MLPs with matched capacity, showing that interaction structure cannot be replaced by capacity alone. It also yields sensorless compliant behavior without force, wrench, tactile input, contact labels, or admittance control. These results suggest that polynomial representations should become a standard architectural choice for embodied motor control. The project page is available at https://lsh3163.github.io/prism/
We introduce the first universal pretraining corpus for industrial time-series data: FactoryNet. 51M datapoints across 23k end-to-end task executions (13.3k real, 9.8k synthetic) on six embodiments, unified by a shared schema that enables robust zero-shot cross-embodiment transfer and highly parameter-efficient anomaly detection. We introduce a novel schema: Setpoint, Effort, Feedback, Context (S-E-F-C) underlying the whole pipeline that maps any actuated system into a common representational frame. The corpus spans 27 annotated anomaly types alongside healthy baselines and counterfactual pairs across robotic manipulation and machining domains. Cross-embodiment transfer experiments yield positive results: under bias-aware metrics our model demonstrates fair cross-embodiment transfer capabilities on the evaluated source-target pair, while 24 schema-aligned signals achieves competitive anomaly detection performance compared to high-dimensional baselines. We release FactoryNet as a growing, multi-embodiment dataset to drive progress toward industrial foundation models.
Karim Othman, Jonas Petersen, Matei Ignuta-Ciuncanu +5
Many stages of the robotic lifecycle, from morphology synthesis to operation, rely fundamentally on the reachable workspace. However, current methods for approximating workspaces are slow, imprecise, or tied to a single morphology. We introduce Reachability Across Morphologies (RAM): a morphology-conditioned, implicit neural representation that acts as a fast, differentiable surrogate for pose reachability, generalising to unseen morphologies while inherently accounting for self-collisions. To train RAM, we publish a large-scale dataset of 3⋅1010 samples generated solely from forward kinematics. Experiments show that our model achieves an F1-score of 86% at nanosecond inference, outperforming the baseline by 14% while reducing inference time by three orders of magnitude. We further demonstrate speed-ups of one and two orders of magnitude for gradient-based morphology and trajectory optimisation, respectively. Website: https://timwalter.github.io/ram.