Error Analysis and Compensation of 3‒PTT Parallel Robot
ObjectivePrecision design and kinematic calibration are two commonly utilized approaches to further improve the pose accuracy of parallel robots. Specifically, the cost of precision design is relatively high, and it is not suitable for some circumstances in which high precision is required. The most...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Editorial Department of Journal of Sichuan University (Engineering Science Edition)
2025-07-01
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| Series: | 工程科学与技术 |
| Subjects: | |
| Online Access: | http://jsuese.scu.edu.cn/thesisDetails#10.12454/j.jsuese.202300801 |
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| Summary: | ObjectivePrecision design and kinematic calibration are two commonly utilized approaches to further improve the pose accuracy of parallel robots. Specifically, the cost of precision design is relatively high, and it is not suitable for some circumstances in which high precision is required. The most effective method with the lowest cost is to calibrate the robot's kinematics. However, problems exist in traditional calibration methods, such as excessive error parameters, error accumulation, and difficulty in obtaining the optimal solution of statically indeterminate equations. Considering the above problems, this study considers the benchmark 3‒PTT parallel robot as the research object, whose error analysis and error compensation are studied to avoid the shortcomings of traditional methods and improve the robot's motion accuracy.MethodsInitially, a simplified mathematical model of the 3‒PTT parallel robot is built, and its kinematic coordinate system is established. Then, topological structure analysis combined with the principle of spiral theory is carried forward to analyze the degree of freedom of the robot. The 3‒PTT parallel robot only has translational degrees of freedom along the three coordinate axes by referring to the velocity characteristic polynomial. Secondly, based on the structural characteristics of the 3‒PTT parallel robot, i.e., the distance between the hinge point of the static platform and the hinge point of the mobile platform being fixed to a constant value <italic>L</italic> by the rigid connecting rod, the inverse kinematics model of the robot is established. Then, based on the inverse kinematics analytic formula of the 3‒PTT parallel robot, the joint input is regarded as a known quantity, the position of the mobile platform is regarded as an unknown quantity, and the forward kinematics interpretation of the robot is solved through the inverse solution. In addition, the error source of the robot mainly consists of parts machining, assembly positioning, and others, and it is proposed in this study that the 3‒PTT parallel robot contains a total of 21 error terms, hinge point installation coordination error, and link length error. Based on the aforementioned kinematics equation, the error model is established and divided into three categories: the error of a single branch chain, the error of link length, and the error of three branch chains. Thus, the influence of the coordinate error and the link length error on the pose accuracy of the mobile platform is analyzed.Results and DiscussionsThe results of error analysis show that the length error of the link and the <italic>z</italic>‒coordinate error of the hinge point of the static platform have significant effects on the pose accuracy of the mobile platform (the average position error of the mobile platform in the three degrees of freedom directions is more than 1 mm), and appropriate attention is paid to the machining and assembly of robot parts. In addition, in order to overcome the shortcomings of traditional methods mentioned above, i.e., excessive error parameters, error accumulation, and difficulty in obtaining the optimal solution of statically indeterminate equations, an inverse kinematics error compensation algorithm is proposed in this study. The algorithm uses the inverse kinematics model of the robot to convert the mechanism error that causes the low operation accuracy of the end-effector into the joint input error of the robot. It focuses on compensating the joint input error after transformation, reducing the parameters in the error compensation algorithm, greatly reducing the difficulty of solving the error correction objective function, and effectively avoiding the problem of error accumulation. Thus, the algorithm is more feasible. In addition, to improve the efficiency of the aforementioned error compensation algorithm, the standard particle swarm optimization algorithm is further enhanced by integrating the dynamic inertia weight value and dynamic learning factor, thus overcoming the problems of precocious convergence to a local optimum and slow convergence in the later iteration of the standard particle swarm optimization algorithm. Then, the improved particle swarm optimization algorithm is utilized to optimize the error correction objective function, where the slider compensation is obtained, and the servo driver is utilized to complete the error compensation. Finally, 31 mobile platform position sampling points on both linear and circular trajectories in the workspace of the 3‒PTT parallel robot are selected for simulation and experimental verification. The simulation results show that the pose errors of the compensated mobile platform converge to zero asymptotically. Experimental results show that the maximum error of the mobile platform in the <italic>x</italic>, <italic>y</italic>, and <italic>z</italic>‒axis directions decreases from 10.89, 12.42, and 2.12 mm to 0.97, 1.14, and 0.72 mm, respectively. In addition, the maximum distance error decreases from 15.35 mm to 1.36 mm after compensation, and the effect is obvious. The mean error decreases from 5.86, 8.02, and 1.12 mm to 0.45, 0.46, and 0.33 mm, respectively, and the mean distance error decreases to 0.82 mm, increasing the operating accuracy of the robot by 92.1%.ConclusionsTherefore, through simulation and experimental results, the maximum and average position errors of the mobile platform after compensation are significantly reduced by more than one order of magnitude, indicating the effectiveness of the proposed compensation method. The salient feature of this study is the improved pose accuracy and operational efficiency in robotic systems through error analysis and compensation. |
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| ISSN: | 2096-3246 |