Matteo Lancini, Ileana Bodini, Simone Pasinetti, David Vetturi Ration, David Vetturi
MIMO NON-LINEAR SENSORS CALIBRATION BASED ON GENETIC ALGORITHMS
The increasing integration between electronics and mechanical engineering brings to the industrial market very hi-tech sensors, often non-linear, capable of more than a single input and single output. A problem more and more relevant for sensors like these is calibration. Classic linear calibration procedures, when applied to this extremely engineered sensors, lead to poor accuracy and are generally not satisfactory.
The case study is the calibration of a bi-dimensional laser based position sensor, in particular a positive sensitive detector, that is an optical position transducer based on series of photodiodes commonly used as multidimensional sensor. To perform the calibration a micrometric positioning table was used to test the whole photodiode active area in both directions. The sensor studied showed a very linear behaviour in the central region of the working range, and a limited nonlinearity closer to the range limits and was to be used to verify robot movement capabilities; to reduce uncertainty associated with nonlinearities, a set of non- standard, non-linear, calibrations were performed, pointing out residual values in order to compare different algorithms. In a previous work, authors have already tested a linear model against an algorithm based on radial basis functions (RBF) and Nelder-Mead simplex method. Object of this paper is the definition of a procedure based on RBF and genetic algorithms for multi-dimensional interpolation of data cloud and a comparison between this updated procedure results and the ones of the previous studied algorithms.
The reference model for calibration was a black box with two inputs, X and Y position of the laser spot, and two outputs, voltages Vx and Vy, while the calibration procedure was split in two separate layers, one for each output depending on both inputs. Given N data points in a M-dimensional environment and N values that represent the non linearity residual, purpose of the algorithm is to approximate a data cloud with a real function, that is represented as a sum of a polynomial (linear) part and L radial basis functions, each associated with a different center (node) and weighted by an appropriate coefficient, that the procedure also allow to assess.
When no starting guess for nodes are given in input, nodes coordinates are the output of a non-linear optimizer based on a genetic algorithm, whose goal is to locally minimize the objective function. The algorithm stops itself whenever it reaches a certain tolerance level, a user specified number of nodes or when the previous iteration has a better value of the objective function. This study has been performed for various RBF classes, and shows an increased accuracy, thus a better metrological behaviour, with respect to the standard linear (planar) calibration model traditionally used.
