A minimal-error-model based two-step kinematic calibration methodology for redundantly actuated parallel manipulators: An application to a 3-DOF spindle head

2022 ◽  
Vol 167 ◽  
pp. 104532
Author(s):  
Shujia Jiang ◽  
Changcheng Chi ◽  
Hanliang Fang ◽  
Tengfei Tang ◽  
Jun Zhang
Keyword(s):  
Parallel Manipulators ◽  
Error Model ◽  
Kinematic Calibration ◽  
Minimal Error ◽  
Model Based ◽  
Redundantly Actuated

Kinematic calibration of the 3-degree-of-freedom redundantly actuated spatial parallel module of a five-axis hybrid machine

2020 ◽  
Vol 234 (9) ◽  
pp. 1185-1197
Author(s):  
Xuan Luo ◽  
Fugui Xie ◽  
Xin-Jun Liu
Keyword(s):  
Error Model ◽  
Error Modeling ◽  
Kinematic Calibration ◽  
Bilinear Interpolation ◽  
Position Errors ◽  
Redundantly Actuated ◽  
Parallel Module ◽  
Hybrid Machine ◽  
Five Axis ◽  
Active Joints

As a new type of manufacturing equipment, redundant hybrid machines have the theoretical advantage over the traditional serial machines in efficiently processing large structural parts with high material removal ratio and complex parts with curved surfaces. In order to solve the accuracy problem of the redundantly actuated spatial parallel module of a five-axis hybrid machine, an improved kinematic calibration method is proposed in this article. First, different from error modeling for the corresponding non-redundant parallel module, the geometric error model of the redundantly actuated spatial parallel module considers the deformations at active joints caused by actuation redundancy as an error source. Then, the applicable error model is developed using projection technique to remove the need of active joints’ stiffness measurement or modeling. Later, the practical error model is derived from model reduction method to avoid using additional sensors or gratings. Finally, three forms of relative measurement and step identification are adopted for the calibration work, and the bilinear interpolation compensation function is introduced to ensure the calibration effect. On this basis, the kinematic calibration of the redundantly actuated spatial parallel module is conducted. The max position errors are reduced from original −0.192 to 0.075 mm after RM1 and SI1, and then further reduced to 0.014 mm after bilinear interpolation compensation, while the max orientation errors are reduced from −0.017° and 0.249° to −0.005° and −0.007° after RM2 and SI2, and RM3 and SI3, respectively. A contrasting experiment is also carried out with the previous method for the corresponding non-redundant parallel module. As a result, the proposed method shows better convergence value and speed in identifying error parameters, and therefore the effectiveness and efficiency of the proposed method for the redundantly actuated spatial parallel module are validated.

Complete, Minimal and Continuous Kinematic Error Models of Perfect Multi-DOF Joints for Parallel Manipulators

2020 ◽  
Author(s):  
Lingyu Kong ◽  
Genliang Chen ◽  
Zhuang Zhang ◽  
Anhuan Xie ◽  
Hao Wang ◽  
...  
Keyword(s):  
Parallel Manipulators ◽  
Error Model ◽  
Parallel Robots ◽  
Kinematic Error ◽  
Kinematic Calibration ◽  
Calibration Result ◽  
Calibration Methods ◽  
Manufacturing Errors ◽  
The One ◽  
Serial Chains

Abstract Kinematic error model plays an important role in improving the positioning accuracy of robot manipulators by kinematic calibration. In order to get a better calibration result, the error model should satisfy complete, minimal and continuous criteria. In order to meet the complete requirement, the multi degree-of-freedom (DOF) joints, such as universal or spherical joint in parallel robots, have to be regarded as serial chains formed by multiple independent single DOF joints, such that the manufacturing errors of these joints can be considered. However, several previous work found that these manufacturing errors for some parallel manipulators have little effect on the accuracy improvement. Besides, considering these kind of errors will cause the kinematics to be much more complicated. Therefore, under the assumptions of perfectly manufactured universal, spherical and cylinder joints, a complete, minimal and continuous (CMC) error model is presented in this paper. The identifiability of the kinematic errors of these multi-DOF joints are analytically analyzed. In order to verify the correctness and effectiveness of the proposed method, a numerical simulation of kinematic calibration is conducted on a 6-UPS parallel manipulator. The calibration result is also compared to the one derived from the error model with 138 error parameters. Since the error model and calibration methods are described uniformly, it can be applied to most parallel manipulators.

An improved minimal error model for the robotic kinematic calibration based on the POE formula

Robotica ◽  
2021 ◽  
pp. 1-20
Author(s):  
Ruiqing Luo ◽  
Wenbin Gao ◽  
Qi Huang ◽  
Yi Zhang
Keyword(s):  
Least Squares Method ◽  
Industrial Robot ◽  
Kinematic Model ◽  
Error Model ◽  
Coordinate Frame ◽  
Exponential Map ◽  
Kinematic Calibration ◽  
Minimal Error ◽  
Serial Robots ◽  
Calibration Algorithm

Summary The conventional product of exponentials $\left(\rm POE\right)$ -based methods dissatisfy the parametric minimality for the kinematic calibration of serial robots due to overlooking the magnitude and pitch constraints. Thus, the minimal kinematic model is presented to solve this problem, which can be developed further. This paper puts forward an improved algorithm for the minimal parameter calibration. An actual kinematic model with the minimal parameters $\left(\rm MP\right)$ is constructed according to the geometric properties of actual joint twists in the auxiliary frames established on the basis of the nominal joint axes. Then, the initial pose error is defined in the tool coordinate frame, which is expressed as the exponential map of the twist, and all twist descriptions are unified, so as to give a unified kinematic model in mathematics. By differentiating the kinematic model, a minimal error model is derived in explicit form. Subsequently, we propose a novel parameter identification method, which identifies the orientation error and position error parameters separately by the iterative least-squares method and updates the MP uniformly. Finally, the simulations and experiments on the different serial robots are conducted to verify the correctness and effectiveness of the proposed algorithm. The simulation results show our calibration algorithm outperforms the existing ones in the accuracy aspect, and the experiment result shows that the absolute pose accuracy of the UR5 industrial robot is upgraded about 9 times under a statistics sense after the calibration.

A New Method for Error Modeling in the Kinematic Calibration of Redundantly Actuated Parallel Kinematic Machine

2020 ◽  
Author(s):  
Lei-Ying He ◽  
Zhen-Dong Wang ◽  
Qin-Chuan Li ◽  
Xin-Xue Chai
Keyword(s):  
Error Model ◽  
Error Modeling ◽  
New Method ◽  
Forward Kinematics ◽  
Kinematic Calibration ◽  
Parallel Kinematic Machine ◽  
Orientation Error ◽  
Redundantly Actuated ◽  
Parallel Kinematic ◽  
Moving Platform

Abstract This paper presents a new method for error modeling and studies the kinematic calibration of redundantly actuated parallel kinematic machines (RA-PKM). First, a n-DOF RA-PKM is split into several n-DOF non-redundantly actuated sub-mechanisms by removing actuators in limbs in an ergodic manner without changing the DOF. The error model of the sub-mechanisms is established by differentiating the forward kinematics. Then, the complete error model of the RA-PKM is obtained by a weighted summation of errors for all sub-mechanisms. Finally, a kinematic calibration experiments are performed on a 3-DOF RA-PKM to verify the method of error modeling. The positioning and orientation error of the moving platform is replaced by the positioning error of the tool center point, which was reduced considerably from 3.427 mm to 0.177 mm through kinematic calibration. The experimental results demonstrate the improvement of the kinematic accuracy after kinematic calibration using the proposed error modeling method.

Kinematic calibration of a 3-PRRU parallel manipulator based on the complete, minimal and continuous error model

2021 ◽  
Vol 71 ◽  
pp. 102158
Author(s):  
Lingyu Kong ◽  
Genliang Chen ◽  
Hao Wang ◽  
Guanyu Huang ◽  
Dan Zhang
Keyword(s):  
Parallel Manipulator ◽  
Error Model ◽  
Kinematic Calibration

Integrated Kinematic Calibration for All the Parameters of a Planar 2DOF Redundantly Actuated Parallel Manipulator

2009 ◽  
Vol 1 (3) ◽  
Author(s):  
Chunshi Feng ◽  
Shuang Cong ◽  
Weiwei Shang
Keyword(s):  
Parallel Manipulator ◽  
Closed Loop ◽  
Open Loop ◽  
Kinematic Calibration ◽  
Constraint Equations ◽  
Integrated Method ◽  
Uniqueness Of The Solution ◽  
Redundantly Actuated ◽  
Loop Constraint ◽  
Two Degree Of Freedom

In this paper, the kinematic calibration of a planar two-degree-of-freedom redundantly actuated parallel manipulator is studied without any assumption on parameters. A cost function based on closed-loop constraint equations is first formulated. Using plane geometry theory, we analyze the pose transformations that bring infinite solutions and present a kinematic calibration integrated of closed-loop and open-loop methods. In the integrated method, the closed-loop calibration solves all the solutions that fit the constraint equations, and the open-loop calibration guarantees the uniqueness of the solution. In the experiments, differential evolution is applied to compute the solution set, for its advantages in computing multi-optima. Experimental results show that all the parameters involved are calibrated with high accuracy.

Tracking-error model-based PDC control for mobile robots with acceleration limits

2009 ◽  
Author(s):  
El-Hadi Guechi ◽  
Jimmy Lauber ◽  
Michel Dambrine ◽  
Saso Blazic ◽  
Gregor Klancar
Keyword(s):  
Mobile Robots ◽  
Tracking Error ◽  
Error Model ◽  
Model Based

Kinematic calibration of a laser tracker based on nonlinear optimization of a refined geometric error model

Measurement ◽  
2022 ◽  
pp. 110672
Author(s):  
Xiaopeng Chen ◽  
Yanyang Liu ◽  
Yang Xu ◽  
Siyuan Gou ◽  
Siyan Ma ◽  
...  
Keyword(s):  
Nonlinear Optimization ◽  
Geometric Error ◽  
Error Model ◽  
Laser Tracker ◽  
Kinematic Calibration
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