Uncertainty-aware Cartesian error compensation in industrial robots via point interval prediction and residual calibration

Accurate Cartesian positioning in industrial robots remains challenging under drift, friction, and regime changes. This paper presents an uncertainty-aware, two-stage compensation pipeline for a four-degree-of-freedom (4-DOF) serial robot using only joint telemetry. Stage I combines a long short-term memory (LSTM) point predictor with an auxiliary network that learns per-axis prediction intervals (PIs) via a loss balancing prediction-interval coverage probability (PICP) and mean prediction-interval width (MPIW). Stage II performs residual calibration from three features: point value, PI width, and point midpoint skew, using compact models (ridge, two-regime linear, and adaptive neuro-fuzzy inference system, ANFIS) with safety gates. Evaluation on a synthetic dataset containing slow drifts, a large step change, and strong periodic content shows calibrated or near-calibrated uncertainty on two axes and under-coverage on the stepped axis, consistent with probability integral transform (PIT) diagnostics. Translating PIs into residuals yields axis-dependent root-mean-square error (RMSE) changes: $$+4.7\%$$ ( $$x$$ ), $$+8.1\%$$ ( $$z$$ ), and $$-2.7\%$$ ( $$y$$ ). The results indicate that coupling point predictions with calibrated uncertainty enables conservative compensation near regime shifts and tighter corrections in smooth or periodic regimes, offering a transparent and deployable baseline for uncertainty-aware robot error compensation.