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<p>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&#xa0;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&#xa0;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: <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(+4.7\%\)</EquationSource> </InlineEquation> (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(x\)</EquationSource> </InlineEquation>), <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(+8.1\%\)</EquationSource> </InlineEquation> (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(z\)</EquationSource> </InlineEquation>), and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(-2.7\%\)</EquationSource> </InlineEquation> (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(y\)</EquationSource> </InlineEquation>). 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月5日

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  • Ihtisham Ul Haq,
  • Luigi D’ Alfonso,
  • Luigi Longo,
  • Giuseppe Fedele,
  • Francesco Lamonaca

摘要

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.