A constant plunge depth control strategy for robotic FSW based on online trajectory generation

Highlights

• A method of FSW constant plunge depth control based on online trajectory generation is proposed.

• The proposed method can realize the autonomous tracking with a rough reference welding path.

• An online S-curve error compensator is proposed to track changing targets and meet the velocity, acceleration, and jerk constraints.

• The core of the S-curve planning is to calculate the initial jerk of each planning step.

Abstract

Robotic friction stir welding (RFSW) usually comes with a huge upsetting force, and the stiffness of the welding system distributes unevenly over the position, which leads to a large deviation of the plunge depth of the tool at the end of the robot. The conventional constant distance tracking control suffers from the problem of unsmooth compensation leading to the vibration of the robot and thus degrading the weld quality. For this problem, a constant plunge depth control based on online trajectory generation for RFSW is studied, which can generate an accurate welding trajectory according to the rough initial reference path and smoothly compensate for the plunge deviation. Initially, three laser-ranging sensors are utilized to measure the pose deviation of the tool in real-time and generate the ideal welding trajectory according to the projection vector method. Then, a deformation compensation model is established to realize the real-time prediction of the correct value. To ensure the smoothness and rapidity of the dynamic tracking process of displacement deviation, we adopt an online trajectory generator as the core of optimization control to meet the process constraints such as speed, acceleration, and jerk during the compensation process. Finally, simulation and experiment are carried out. The results show that the proposed method can effectively reduce the vibration caused by compensation during the welding process and reduce flash, which can improve the welding quality.

Introduction

Friction stir welding (FSW) is a solid-state welding technology that has been widely used in aerospace, marine equipment, and road traffic industries [1,2]. With the development of industrial robot, its applications for FSW have received much attention due to its greater flexibility, larger working space, and lower cost relative to traditional welding equipment dedicated to FSW. It is especially suitable for welding large-scale complex parts with three-dimensional curves [2]. Therefore, robotic FSW (RFSW) has great application prospects.

However, RFSW is a complex thermal-mechanical coupling nonlinear process [3,4], and there are numerous difficulties in its practical application. First, inaccurate calibration of the workpiece coordinate system will produce static errors on the weld track [5]. Second, the insufficient stiffness of the robot-workpiece system and excessive forge force will cause deformation of the workpiece and the robot, resulting in transverse and longitudinal dynamic deviations of the expected welding path [3,6,7]. Third, the welding parameters such as spindle speed, welding speed, and welding pin shape directly affect the metal heat flow and stress change [3,8]. The above factors impact the quality of RFSW. Uncompensated robot machining trajectories lead to defects such as poor quality of welding joints, low bending strength, and even non-penetrating welds, thus failing to use [9,10].

To overcome the above challenges, notice that the RFSW usually works with a low welding speed [11], which allows manual online intervention [12]. The operator adjusts the compensation value of the robot tool center point (TCP) to improve the welding quality by observing the welding condition and shaking the handwheel. Nevertheless, this manual observation is inaccurate and has large hysteresis, which cannot fundamentally enhance the welding quality. For welding a super-long seam on a large thin-walled tank, this qualitative manual adjustment of the TCP requires many human strengths, which is impractical.

In view of the defects of manual compensation, methods such as constant depth control and constant downforce, torque, or power control [13], [14], [15], to adjust the welding process trajectory automatically to ensure RFSW quality. The PID control can meet the requirements of control accuracy and fast response. However, the overly rapidly unsmooth compensation will cause oscillations in the RFSW system. Certain scholars [16] have adapted fuzzy PID to realize constant process force welding to reduce the fluctuation of upsetting force during welding. Since the heat of the weldment is difficult to monitor, and the welding force is related to the welding parameters, the workpiece is heated and softened, resulting in a change in force. When the shoulder fully plunges into the workpiece, if the force sensor detects that it is less than the set value, it will continue to press down, thus failing the downforce control [17]. The constant depth control is different from force control in principle and can avoid the defects of the force control. Therefore, this paper mainly focuses on the constant plunge depth control and will solve the inconsistency of pressing depth caused by insufficient rigidity of the robot-weldment system through trajectory compensation.

To compensate for the error and improve the machining quality, a series of studies have been conducted on each source of deviation in the robot-workpiece system. The sources of deviation are mainly attributed to low robot joint stiffness and workpiece deformation. Based on the calibration of the kinematic parameters of the mechanism [18], some solutions focus on building robot configuration error models and attribute the TCP deformation to insufficient joint stiffness [11]. These solutions mainly include offline or online trajectory corrections [19], for example, deformation prediction from joint stiffness estimation [[20], [21], [22], [23]] and the neural network [10], adopting dual encoders to measure the error of each joint [7], online diagnostics of joint deviations based on information fusion [24] and using sensorless external observers [25]. Guillo and Dubourg [9] compensated the trajectory of the robot by analyzing joint stiffness and applying the feedforward compensation to improve the machining accuracy. Jing et al. [26] introduced an overall flexible stiffness index, which improved the overall stiffness of the serial RFSW process trajectory. Although these studies can predict the joint deformation of a robot and compensate it to some extent, for the parallel robot studied in this paper, it is difficult to establish an accurate stiffness model when the dynamics and stiffness parameters are inaccurate or unknown [9]. As a result, the end deformation cannot be compensated accurately in real-time.

Another approach is to treat the compensation of weld trajectory deviations caused by workpiece deformation as a path or force tracking problem under an unknown surface. Current solutions measure the weld surface to track the welding seam [6,27]. For example, use force sensors [29], distance sensors with 3D vision, and other measurement techniques [28] to perform real-time 3D surface exploration. Most of the solutions aim at arc welding, and their application scenarios are non-contact processing. Their TCPs are subject to zero force, thus they had not considered the end deformation caused by the end forces, which is different from the RFSW. Recently, Amersdorfer et al. [30] adopted three laser-ranging sensors and a force sensor to track an unknown surface and achieve constant force processing. It is worth noting that these sensor-based measurement technologies can realize online compensation control.

Based on the above reasons, to realize the quantitative automatic control of welding compensation, a control strategy evolved from the manual compensation is proposed to study the online error compensation of RFSW. The S-curve velocity profile is adopted to smooth the compensation to avoid the system oscillations. A stable error compensation command can be obtained when applying the S-curve velocity profile in the constant depth control process. There are many studies on the online S-curve velocity planning. Planning in the displacement-velocity phase plane can get a time-optimal S-curve velocity profile that satisfies the specified constraints [31,32]. However, the calculation accuracy is affected by the number of discrete points. As the number of discrete points increases, the calculation time will also increase. Besides, this method is only applicable to situations where the trajectory does not turn back. Since online trajectory generation (OTG) can perform time-optimal planning under multiple constraints, it can be applied to real-time compensation of deviations. OTG is essentially a procedure of shaping and constraining the jerk input. Liu [33] proposed an online trajectory generator that satisfies the jerk constraint when the target state changes in real-time. However, the target velocity and acceleration are zero. In order to realize online planning for more general problems, considering that the S-curve velocity profile has the uncertainty characteristics of segments, Kröger and Wahl [34] studied a process of determining the type of acceleration by classifying the basic acceleration profiles and solving for each class separately. Recently, in [35], the problem of online trajectory planning under jerk constraint with non-zero target acceleration has been studied.

The above works directly calculate in the continuous-time domain. Certain scholars extend the trajectory planning problem in the time domain to the frequency domain by using filters to realize online planning. For example, Biagiotti and Melchiorri [36], and Besset et al. [37] used multiple FIR filters to achieve velocity, acceleration, and jerk constraints of the planned trajectory. However, the filter methods will cause time lags and difficulty in calculating filter parameters. Therefore, based on the above research, considering that any complex motion can be approximated by limited base trajectory units such as the Taylor series expansion, the online S-curve velocity planning base units can be regarded as the core of the OTG to achieve constant depth control.

In this work, based on previous research [38], an online S-curve generator is proposed to generate RFSW compensation in real time. Unlike traditional solutions, this research performs online error compensation from the perspective of trajectory planning. There is no need to modify the internal algorithm of the robot control system, and the external input is only responsible for compensating the trajectory in the non-feed direction under the welding process constraints. The primary consideration is to make the actual RFSW path converge to the desired welding path as quickly as possible, eventually stabilizing the trajectory deviation within a reasonable range. For the purpose to avoid oscillations during the compensation process, which results in reduced welding quality, the compensation welding speed, acceleration, and jerk are constrained to produce a smooth and stable weld motion. Considering the lower welding speed of RFSW compared with other applications, the influence of joint torque limits is not considered here. The innovations of this paper are as follows:

• A method of constant plunge depth control for RFSW based on online trajectory generation is proposed, which can be applied to a closed robot controller without changing the internal program of the controller.

• The proposed control strategy can realize the autonomous tracking with a rough reference welding path, which reduces the accuracy requirements of the original welding trajectory.

• An online S-curve error compensator is proposed to track changing targets and meet the velocity, acceleration, and jerk constraints. It points out that the core of the online S-curve planning is to calculate the initial jerk of each planning step.

The following of this paper is organized as follows: Section 2 proposes a constant plunge depth control scheme for RFSW, and expounds on the real-time detection of trajectory deviation and autonomous tracking, respectively. Section 3 proposes a compensator based on the online S-curve velocity planner that can generate compensation commands according to the predicted target input. In Section 4, the trajectory tracking simulation of the proposed online S-curve velocity tracking is carried out. Then, a FSW experiment of constant plunge depth control was carried out on the self-developed hybrid robot TriMule 800. Section 5 summarizes the full text and looks forward to future work.