A calibration-based method for interval reliability analysis of the multi-manipulator system

Manipulators have a wide range of applications in industry because of their high efficiency, accuracy and easy operation. They are often used in the field of transportation, gripping and assembling etc. in which end-effector of the manipulator is designed to move from one point to another with the same position and orientation repetitively[1,4]. In practice, errors that originated from manufacturing and assembling process of the manipulator cannot be eliminated. The main uncertainties include joint clearance, dimensional deviations, material deformation et al. which can finally result in the erratic shocks, vibration and deterioration of motion capability over its service life [9, 13,22]. Therefore, analyzing the behavior of a manipulator with consideration of parameter uncertainties and evaluating the reliability appropriately can be significant issues. To calculate the reliability of a manipulator with reference to a particular point during a repetitive work. Rao and Bhatti [20] proposed a probabilistic method to measure the extent of influence caused by the joint clearance on the repeatability of the two-link manipulator. The instability of the behavior from the aspect of dynamics and kinematics are both analyzed. Kim et al. [12] focused on the analysis of impact caused by joint clearance, all the variables were treated as normally distributed and then the first order reliability method (FORM) was applied. With integration of the second order Taylor expansion and an entropy-based optimization approach, Wang et al. [27] analyzed the reliability of a manipulator when confronted with arbitrarily distributed joint clearance. Though the reproducibility of a manipulator outperforms its ability to reach an expected position [18], there are a lot of demands in which the motion should be controlled in the entire trajectory instead of only a few points, such as tasks of welding, sculpture, spraying etc. [4,29,31]. Pandey and Zhang[17]proposed a fractional moment estimation method, the drawback lies in that two layers of optimization process are required, which makes it complicated. Zhao et al. [30] developed an approximated approach to study the motion reliability of a parallel mechanism during a circle trajectory movement, in their work, the first passage method, Lie group and Lie algebra were utilized to describe the variables with time-variant character. Other popular methods like FOSM (first order second moment method) and MCS (Monte Carlo simulation) are also widely used [26]. The researches mentioned-above exhibit an obvious feature in common that only one failure mode is needed to be concerned. When the multi-agent system consists of many subsystems, the numerical The multiple manipulators can construct a special multi-agent system with the distinction that the type can be serial or parallel according to their cooperative way. We proposed a comprehensive method to handle the problem of reliability estimation. The wide and narrow bound method are applied to calculate the interval reliability respectively when multiple manipulators work as the series system. Aims to decrease the system complexity and enhance the dynamic adjustment capability, the base frame calibration technique is presented to convert the series system to a parallel one, naturally the reliability can be improved significantly. A system composed by three manipulators is utilized as an example to illustrate the feasibility of the proposed method. Highlights Abstract