Matrix Array
A mathematical array of algebraic expressions used to model and compensate for multi-variable non-linearities and cross-sensitivities in multi-axis sensor arrays provides the theoretical framework for advanced calibration. Implementing a polynomial matrix allows engineers to represent complex relationships where each element of the matrix is a polynomial function of the sensor inputs. This approach is common in robotic multi-axis force sensors that experience coupled deformation.
By applying the matrix, the raw output signals are converted into decoupled physical measurements.
Calibration Correction
Solving for the coefficients within the array requires gathering a dense set of known reference loads and matching output voltages. The polynomial matrix is populated during the factory calibration process by applying least-squares regression to the calibration dataset. This step establishes the mathematical relationship that maps sensor outputs to real-world force vectors.
Once these coefficients are determined, they are stored in the sensor’s non-volatile memory for real-time computation.
Cross Sensitivity
Multi-axis transducers often suffer from mechanical coupling where a load in one direction produces a false signal in another. In a multi-axis sensing system, the polynomial matrix corrects for this behavior by subtracting the computed cross-talk from each axis’s output.
Numerical Stability
Raising input variables to higher powers can lead to calculation instability if the polynomial degree is too high. Designers must balance the accuracy gained from a high-order polynomial matrix against the computational resources and round-off errors of the embedded processor. If the polynomial degree is excessive, the sensor’s output can oscillate wildly between the calibration points, a phenomenon known as Runge’s phenomenon.
Keeping the matrix elements to second or third-order polynomials avoids this instability while providing sufficient correction for most industrial transducers.
