Abstract:Laser triangulation allows non-contact measurement in the third dimension. Due to the nonlinearities presented in camera and laser sensor, large range distances are quite difficult to measure with high precision. In order to enhance the precision and accuracy of large range measurement based on laser triangulation, we propose a novel scheme composed of four laser emitters, curve fitting subpixel location algorithm for laser center detection, and the linear regression approach based on the Gaussian model for calibration. When an object performs a 100 mm displacement from a closer to a farther point, our system achieved a repeatability up to ±7 µm, an estimated standard deviation of fitting error within 0.0027 mm, an expanded uncertainty of repeatability within 0.13 mm, an average error variation of rotational plane within 0.15 degree and a nonlinearity error within ±0.04% in full scale. Compared to published results, our proposed method shows an enhancement in accuracy. The error is significantly reduced and maintains at the low level for large ranges, which makes this system applicable and suitable for industrial and indoor applications.

The measurement of an object with a short arc is widely encountered in scientific research and industrial production. As the most classic method of arc fitting, the least squares fitting method suffers from low precision when it is used for measurement of arcs with smaller central angles and fewer sampling points. The shorter the arc, the lower is the measurement accuracy. In order to improve the measurement precision of short arcs, a parameter constrained fitting method based on a four-parameter circle equation is proposed in this paper. The generalized Lagrange function was introduced together with the optimization by gradient descent method to reduce the influence from noise. The simulation and experimental results showed that the proposed method has high precision even when the central angle drops below 4° and it has good robustness when the noise standard deviation rises to 0.4 mm. This new fitting method is suitable for the high precision measurement of short arcs with smaller central angles without any prior information.

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Purpose The purpose of this paper is to propose cuckoo optimization algorithm (COA)-based back propagation neural network (BPNN) to reduce the effect of the nonlinearities presented in laser triangulation displacement sensors. The 3D positioning and posture sensor allows access to the third dimension through depth measurement; the performance of the sensor varies according to the level of nonlinearities presented in the system, which leads to inaccuracies in measurement. Design/methodology/approach While applying optimization approach, the mathematical model and the relationship between the key parameters in the laser triangulation ranging and the indexes of the measuring system were analyzed. Findings Based on the performance of the parametric optimization method, the measurement repeatability reached 0.5 µm with an STD value within 0.17 µm, an expanded uncertainty of measurement was within 5 µm, the angle error variation of the object’s rotational plane was within 0.031 degrees and nonlinearity was recorded within 0.006 per cent in a full scale. The proposed approach reduced the effect of the nonlinearity presented in the sensor. Thus, the accuracy and speed of the sensor were greatly increased. The specifications of the optimized sensor meet the requirements for high-accuracy devices and allow wide range of industrial application. Originality/value In this paper, COA-based BPNN is proposed for laser triangulation displacement sensor optimization, on the basis of the mathematical model, clarifying the working space and working angle on the measurement system.

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