Geometric Attractor Monitoring: A Robust and Frugal Framework for Multi-modal Industrial Robotic Cycles

Monitoring the health of heterogeneous industrial robot fleets is severely challenged by the multi-modal nature of their operational cycles and a persistent scarcity of run-to-failure data. Standard data-driven approaches, particularly deep learning architectures relying on sequential reconstruction, often struggle in this specific setting; they tend to over-smooth complex dynamics, masking early signs of degradation. To address these industrial constraints, we reframe the monitoring problem through a framework based on Phase Space Reconstruction (PSR). Instead of predicting temporal sequences, this framework transforms univariate sensor data into a geometric attractor, explicitly unfolding the mechanical states independently of their temporal occurrence. By evaluating various anomaly scoring techniques within this space, we demonstrate that discrete support estimation provides an effective and computationally frugal Health Indicator (HI). Validated on a real-world dataset of 21 heterogeneous robots over three years and a synthetic Langevin system, our approach outperforms standard deep learning baselines. We show that aligning the algorithmic bias with the geometric properties of the target system yields a pragmatic, traceable and easily deployable approach perfectly tailored to the realities of industrial constraints.