Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 369747, 11 pages

http://dx.doi.org/10.1155/2015/369747

## Research on Construction Method of Operational Reliability Control Model for Space Manipulator Based on Particle Filter

^{1}School of Automation, Beijing University of Posts and Telecommunications, No. 10, Xitucheng Road, Haidian District, Beijing 100876, China^{2}School of Automation, Beihang University, No. 37, Xueyuan Road, Haidian District, Beijing 100191, China

Received 28 August 2015; Accepted 18 October 2015

Academic Editor: Panos Liatsis

Copyright © 2015 Xin Gao et al. 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

The operational reliability of the space manipulator is closely related to the control method. However the existing control methods seldom consider the operational reliability from the system level. A method to construct the operational reliability system control model based on particle filter for the space manipulator is presented in this paper. Firstly, the definition of operational reliability and the degree of operational reliability are given and the state space equations of the control system are established as well. Secondly, based on the particle filter algorithm, a method to estimate the distribution of the end position error and calculate the degree of operational reliability with any form of noise distribution in real time is established. Furthermore, a performance model based on quality loss theory is built and a performance function is obtained to evaluate the quality of the control process. The adjustment value of the end position of the space manipulator can be calculated by using the performance function. Finally, a large number of simulation results show that the control method proposed in this paper can improve the task success rate effectively compared to the simulation results using traditional control methods and control methods based on Bayesian estimation.

#### 1. Introduction

Space manipulators can assist or replace astronauts to finish complex and dangerous space tasks [1, 2]. With the development of space technologies, space application tasks are becoming increasingly diverse, and the structure of space manipulators is also becoming more and more complicated [3–5]. Meanwhile, due to its harsh working environment and difficulty to repair and maintain, how to maintain a high reliability of space manipulator is a research hotspot and difficult point of space technology [6, 7].

The reliability of space manipulator includes the inherent reliability and the operational reliability [8], and the inherent reliability is given during its process of design and manufacture, relevant to various structural parameters of the manipulator and performance parameters of components [9]; the operational reliability is a character to maintain the performance ability shown in the actual use process of a product, which considers not only the influence factors of inherent reliability but also those which impacts product installation, operation, and repair support, and so forth [10, 11].

Currently, researches on reliability of space manipulator mainly focus on the inherent reliability, and related research achievements mainly include evaluating the reliability of a manipulator with a certain method, reliability design of manipulators, and fault-tolerant techniques of manipulators [12–18]. Because the space manipulator is a kind of controllable space mechanism, its operational reliability is closely related to its control method. Currently, the mainstream control methods for space manipulator, such as task planning method, path planning method, robust control method, and neural network method, take into account many factors, but the operational reliability of a manipulator is not considered from the system level [19–27]. This may cause a low reliability of the system and cannot guarantee a manipulator to complete the task sustainably and reliably. Therefore, in order to further improve the operational reliability of space manipulator, system control method comprehensive multiple factors of operational reliability should be considered, building control methods and adjustment strategies to maintain its operational reliability from the system level. When the space manipulator performs specified tasks, through the adjustment of control strategies and self-adaptive changes, the ability of completing a task successfully with specified control method is maintained to improve the operational reliability of the system under the condition of constant inherent reliability.

A method to construct the operational reliability system control model for space manipulator based on the particle filter is proposed in this paper. Combining reliability theory with control characteristics of space manipulator, based on the given definition of the operational reliability and the degree of operational reliability for space manipulator, the state space equations of the control system are established. Combined with the principle of particle filter algorithm and features of the control system, the estimation of the terminal position error distribution and real time calculation of the operational reliability for space manipulator under any distribution of observed noise are realized. Control process performance model based on the principle of quality loss is constructed, and the control performance function is obtained, according to which the calculation of the terminal position adjustment amount for space manipulator is achieved. In this method, the operational reliability of space manipulator is calculated at the same time as the execution of specified tasks, and the control of manipulator is adjusted according to the degree of operational reliability; thus operational reliability and working efficiency of space manipulator are improved. Simulation results show that, compared with traditional control method and that based on Bayesian estimation, successful rate of tasks is increased significantly and the operational reliability of manipulator is improved effectively by the proposed control method.

#### 2. Construction of Operational Reliability Control Model for Space Manipulator

##### 2.1. Description of Operational Reliability for Space Manipulator

The operational reliability of space manipulator is the reliability shown in the process of its actual use, and it depends on its control method because it is a kind of controllable device. In this paper, the operational reliability of space manipulator is defined as the ability to complete the task successfully with specified control method when it performs the specified task, which is quantified by the degree of the operational reliability, and specifically reflected as the probability of completing the task for space manipulator according to specified requirements [28].

According to the control characteristics of space manipulator, its work consists of a series of tasks, which is denoted by ,

For any given task , factors which determine the success or failure of the task are denoted by ,

For each of any given task , it has a prescribed accuracy requirement, which is denoted by the following interval:where is the expectation of and presents the error allowance of . So if when is finished, task is considered executed successfully.

After the task is completed using a specified control method, a nonnegative random variable is used to describe the value of , the distribution function of which is described as

On this basis, the probability of meeting accuracy requirements of task can be obtained as follows:where is the operational reliability degree of space manipulator. From formula (5), the operational reliability degree of a manipulator is the probability that each factor meets specified accuracy requirement when it performs a task. Therefore, the operational reliability of a space manipulator can also be defined as the probability of successful completing of specified task when using specified control method to control the manipulator. So can also be called the reliability influence factor, and it can have different definitions such as terminal position and terminal force, according to different tasks.

##### 2.2. Basic Components of the Operational Reliability Control System for the Manipulator

As is shown in Figure 1, the operational reliability control system for the space manipulator is constructed based on its general control system, and the real time calculation of the operational reliability degree is a feedback unit of the control system. The basic working principle of the control system is as follows: the error value between the terminal position and the specified position of the space manipulator is measured after the movement control unit by the System Condition Detection Module, according to which the operational reliability degree of the space manipulator system is estimated and then the adjustment amount of its control variables is calculated. So the control variables can be fine-tuned to reduce the error and improve the system reliability.