Journal of Sensors

Volume 2018, Article ID 2404825, 11 pages

https://doi.org/10.1155/2018/2404825

## A Parallel Ranging-Based Relative Position and Orientation Measurement Method for Large-Volume Components

School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China

Correspondence should be addressed to Fuzhou Du; moc.361@uohzuf_ud

Received 29 April 2018; Accepted 26 July 2018; Published 4 September 2018

Academic Editor: Salvatore Pirozzi

Copyright © 2018 Dian Wu and Fuzhou Du. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In this paper, a novel relative position and orientation (R-P&O) measurement method for large-volume components is proposed. Based on the method, the parallel distances between the cooperative point pairs (CPPs) are collected by multiple pairs of wireless ranging sensors which are installed on respective components and finally turned into the R-P&O. Accordingly, a measurement model is built and an algorithm is designed to solve the model, in which the radial basis function neural network (RBFNN) produces a preliminary solution by offline training and the differential evolution (DE) strategy finds the accurate solution by online heuristic searching. Furthermore, the crucial parameters and the performance of the algorithm are analyzed through simulating a virtual alignment process which proves that the RBFNN-DE algorithm can quickly and accurately find the global optimal solution in the whole effective workspace. Besides the theory study, a ranging device based on ultrasound has been developed along with a calibration method. Depending on the device, an experiment of actual alignment is implemented to verify the algorithm. Experimental results indicate that the error of R-P&O is no more than 4.1 mm and 0.32° when the ranging error is 0.1 mm, compared with the measurement result of indoor GPS (iGPS).

#### 1. Introduction

In aviation, aerospace, and ship manufacturing, the product assembly is characterized by large volume, high accuracy, and complex processes. As the key production procedure, component alignment greatly affects the quality of manufacturing, the priority target of which is measuring R-P&O that means the position and orientation of the moving component coordinate system relative to the immovable component coordinate system. The traditional method is generally to figure out the geometric size of the component by standard gauges with analog transfer, which has been unable to meet the increasing requirements of alignment. Hence, it is of great theoretical and practical value to research for a high-accuracy digital measurement system for the alignment process of a large-volume component [1, 2].

The common digital measuring instrument includes a laser tracker [3, 4], theodolite [5], iGPS [6, 7], industrial camera [8, 9], coordinate measuring machine (CMM) [10, 11], and so on, which depends on transforming the relevant points into the reference coordinate system of a third party to fit the R-P&O of components [12]. Because of the indirect acquisition of R-P&O, this method involves a complex coordinate system transformation and unnecessary error [13]. Considering that the component to be measured has a large volume, it is difficult to cover all the target points with a single instrument. Alternatively combining multiple instruments, the error caused by a transfer station needs to be taken into account [14]. Besides, for all of the above instruments the price is expensive, several of the instruments (theodolite and CMM) are no longer able to work when the R-P&O is changing.

Inspired by the forward kinematics problem (FKP) in the field of robotics, the R-P&O can be calculated based on the distances of CPPs. A pair of corresponding points from two individual components with known coordinates in a local coordinate system is called a CPP. FKP refers to using the kinematic equations of a robot to compute the R-P&O of the end effector through the joint parameters [15]. The difference is that for each measurement task of alignment, the position of CPPs can be different, and they don’t have to be regularly distributed in two planes such as the Stewart platform [16]. In order to solve the complex nonlinear equations contained in the FKP, there are two kinds of methods that are proposed, namely the numerical method [17] and analytical method [18]. The mathematical model of the numerical method is simple, but it is quite dependent on the initial value and cannot deduce all solutions. On the contrary, the elimination process of the analytical method is very complex which may introduce an imaginary root. In addition, a lot of intelligent algorithms were proposed recently, such as particle swarm optimization [19], hybrid immune algorithm [20], and neural network algorithm [21].

The traditional methods for FKP can lead to multisolutions. However, the measurement needs to be synchronized with the alignment process, and there is no condition for judgment manually after each calculation. On the other hand, it is difficult to make a general rule to pick the correct solution for various alignment components, so we turn to intelligent algorithms. Compared with other algorithms, RBFNN has the characteristics of approaching any nonlinear function with arbitrary-precision and having a good global approximation ability. It is also suitable for the solution of multidimensional parameters and can be easily adjusted by changing the number and width of network nodes. Accordingly, it has a natural advantage to solve the FKP. However, this depends on the quality of training, and the result cannot be satisfactory with poor training quality. DE has few controlled parameters and can search for solutions by using individual differences. Its fast convergence capability can solve the real-time problem robustly. It also applies to the solution of multidimensional parameters. Adversely, it easily falls into a local optimal solution and relies on a good initial value. Therefore, considering the complementary advantages of the two algorithms, the preliminary result of RBFNN is used as the initial value of DE, and then a quite accurate result can be solved.

In this paper, a measurement model is built to calculate the R-P&O of large-volume components by parallel ranging, and an intelligent algorithm combining RBFNN [22] and DE [23] is proposed to solve the model in Section 2. For the purpose of analyzing the performance and crucial parameters of the algorithm, a virtual alignment is simulated through a hypothetical trajectory in Section 3. Furthermore, a kind of ranging device is developed based on an ultrasonic signal, and the calibration method of the device is introduced. Finally, the novel method is verified by the actual alignment experiment in Section 4.

#### 2. The Method for R-P&O Measuring

##### 2.1. The Measurement Model Based on Parallel Ranging

In the alignment process, the R-P&O measurement based on parallel ranging involves the immovable and moving component. Meanwhile, a number of wireless sensors are installed on CPPs of the components to measure the distances, which provide support for calculating the R-P&O. The schematic diagram of the measurement model is shown in Figure 1.