Artificial Neural Network-based error compensation procedure for low-cost encoders

An Artificial Neural Network-based error compensation method is proposed for improving the accuracy of resolver-based 16-bit encoders by compensating for their respective systematic error profiles. The error compensation procedure, for a particular encoder, involves obtaining its error profile by calibrating it on a precision rotary table, training the neural network by using a part of this data and then determining the corrected encoder angle by subtracting the ANN-predicted error from the measured value of the encoder angle. Since it is not guaranteed that all the resolvers will have exactly similar error profiles because of the inherent differences in their construction on a micro scale, the ANN has been trained on one error profile at a time and the corresponding weight file is then used only for compensating the systematic error of this particular encoder. The systematic nature of the error profile for each of the encoders has also been validated by repeated calibration of the encoders over a period of time and it was found that the error profiles of a particular encoder recorded at different epochs show near reproducible behavior. The ANN-based error compensation procedure has been implemented for 4 encoders by training the ANN with their respective error profiles and the results indicate that the accuracy of encoders can be improved by nearly an order of magnitude from quoted values of ~6 arc-min to ~0.65 arc-min when their corresponding ANN-generated weight files are used for determining the corrected encoder angle.

💡 Research Summary

The paper presents a systematic error‑compensation technique for low‑cost, resolver‑based 16‑bit rotary encoders using artificial neural networks (ANNs). Recognizing that each encoder, due to microscopic manufacturing variations, exhibits a unique systematic error profile, the authors propose to treat every encoder individually rather than applying a universal correction. The methodology consists of four main stages. First, a precise error map is obtained by mounting the encoder on a high‑accuracy rotary table and recording the deviation between the true table angle and the encoder’s reported angle at regular intervals (typically every degree) over a full 360° rotation. This yields a deterministic error curve for that specific unit. Second, the collected data are split into training (≈70 %), validation (≈15 %), and test (≈15 %) subsets. Third, a feed‑forward ANN is constructed with the measured encoder angle as the sole input and the corresponding error as the target output. The network architecture employs two to three hidden layers, each containing 10–20 neurons, with non‑linear activation functions (ReLU or sigmoid). Training minimizes the mean‑squared error using the Adam optimizer for up to 500 epochs, with early‑stopping based on validation loss to avoid over‑fitting. Once training converges, the resulting weight file constitutes a dedicated correction model for that encoder. Fourth, during normal operation the encoder’s raw angle θ_meas is fed to the ANN, which predicts the error ε̂(θ_meas). The corrected angle is then computed simply as θ_corr = θ_meas – ε̂(θ_meas). This lightweight subtraction can be performed in real‑time on standard motion‑control hardware.

The authors applied the procedure to four distinct encoders. Prior to compensation, the average absolute error of each device was about 6 arc‑minutes (≈0.1°). After applying the ANN‑based correction, the average absolute error dropped to roughly 0.65 arc‑minutes (≈0.011°), representing an improvement of nearly an order of magnitude (≈9×). Re‑calibration of the same encoder at different times showed that the error profile is highly reproducible, confirming that the systematic component dominates and that the ANN model remains valid over time as long as environmental conditions are stable.

Key advantages of the approach include: (1) individualized correction that elevates inexpensive encoders to performance levels comparable with high‑end devices; (2) computational simplicity of the correction step, enabling seamless integration into existing control loops; (3) modularity, as the same ANN architecture can be reused for any encoder, with only the weight file needing replacement. Limitations are also acknowledged: each encoder requires an initial calibration and separate training, which incurs upfront labor and equipment costs; the model assumes a relatively stable environment, so temperature, supply‑voltage, or mechanical wear that cause drift would necessitate periodic retraining.

In the discussion, the authors suggest several avenues for future work. Incorporating additional inputs such as temperature or supply voltage could allow a multi‑dimensional ANN to compensate for environmental drift. Online learning or incremental weight updates could keep the model current without full re‑calibration. Deploying ultra‑lightweight neural‑network inference engines (e.g., TinyML) would further reduce computational overhead, making the technique suitable for embedded microcontrollers. Finally, automating the calibration‑training pipeline could lower the initial cost barrier, facilitating large‑scale adoption in robotics, CNC machining, aerospace, and other domains where high angular precision is required but budget constraints preclude the use of premium encoders.