Complete, minimal and continuous error models for the kinematic calibration of parallel manipulators based on POE formula

Chen, Genliang; Kong, Lingyu; Li, Qinchuan; Wang, Hao; Lin, Zhongqin

doi:10.1016/j.mechmachtheory.2017.11.003

Cited by 70 publications

(31 citation statements)

References 24 publications

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“…Given the reliability index β varies from 0.5 to 3.0, the reliability R and the allocated tolerance ±σ [η c,i ] of each uncompensatable geometric error can be obtained using Eqs. (14) and (20). The tolerance allocation results are listed in Table III.…”

Section: Error Analysis and Tolerance Allocationmentioning

confidence: 99%

A Systematic Approach for Accuracy Design of Lower-Mobility Parallel Mechanism

Tian¹,

Shen²,

Lv³

et al. 2020

Robotica

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SUMMARY Geometric accuracy is a critical performance factor for parallel robots, and regardless of error compensation, accuracy design or tolerance allocation is another way to ensure the pose accuracy of a robot at design stage. A general method of both geometric error modeling and accuracy design of lower-mobility parallel mechanisms is presented. First, a general approach for error modeling of lower-mobility parallel mechanism is proposed based on screw theory, and then the geometric errors affecting the compensatable and uncompensatable accuracy of the end-effector are separated using the properties of dual vector space. The pose error aroused by compensatable geometric errors can be compensated via kinematic calibration, while the uncompensatable geometric errors should be minimized during the manufacturing and assembly processes. Based on that, the tolerance allocation method is presented, giving each uncompensatable geometric error a proper tolerance by the use of reliability theory. Compared with the traditional tolerance allocation method, the advantages of the proposed method are as follows: the number of geometric errors to be allocated is greatly reduced; the results of serialized tolerance allocation can be obtained according to different reliability indices of pose accuracy of end-effector for designers to choose; on the premise of guaranteeing the same pose accuracy of end-effector, the allocated tolerances are loose and easy to realize. Finally, the proposed methods are successfully applied to an R(2-RPS&RP)&UPS lower-mobility parallel robot, and the effectiveness and practicability of the proposed method are verified.

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Section: Error Analysis and Tolerance Allocationmentioning

confidence: 99%

A Systematic Approach for Accuracy Design of Lower-Mobility Parallel Mechanism

Tian¹,

Shen²,

Lv³

et al. 2020

Robotica

View full text Add to dashboard Cite

show abstract

“…Since the initial pose coordinate system in the local POE formula can be established at any point on the link, the initial pose T(0) is floating. Therefore, the kinematic error is regarded as only due to the deviation of the initial poses T(0), while the joint twists and joint variables are regarded as being accurate [12]. Therefore, (9) and (10) are simplified to:…”

Section: Establishment Of the Kinematic Error Model From A Single Bramentioning

confidence: 99%

“…In the above error model, it has a total of 60 error parameters to describe the kinematic error. Through the discernibility analysis of the error model deduced from the POE formula, the maximum number of independent motion parameters of a universal non-over-constrained parallel manipulator after eliminating redundant error components is 4r + 2p + 6, where r and p represent equivalent rotation joints and translation joints, respectively [12]. In the 3T1R parallel manipulator, there are six equivalent rotation joints and two translation joints.…”

Section: Establishment Of the Overall Kinematic Error Modelmentioning

confidence: 99%

“…Although many modeling methods involving parallel manipulators have been proposed, the modeling method of kinematic error for such a 3T1R complex symmetrical parallel manipulator has not been mentioned yet. Compared with traditional manipulators' calibration methods such as the Denavit-Hartenberg (D-H) model based method [9] and the zero-position reference model method [10], the error model based on the local product of exponentials (POE) formula has some advantages [11,12]. First, the parameters of the kinematic model on the POE formula change smoothly with the change of the joint axis.…”

Section: Introductionmentioning

confidence: 99%

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A Kinematic Calibration Method of a 3T1R 4-Degree-of-Freedom Symmetrical Parallel Manipulator

Zhang

Chen

et al. 2020

Symmetry

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This paper proposes a method for kinematic calibration of a 3T1R, 4-degree-of-freedom symmetrical parallel manipulator driven by two pairs of linear actuators. The kinematic model of the individual branched chain is established by using the local product of exponentials formula. Based on this model, the model of the end effector’s pose error is established from a pair of symmetrical branched chains, and a recursive least square method is applied for the parameter identification. By installing built-in sensors at the passive joints, a calibration method for a serial manipulator is eventually extended to this parallel manipulator. Specifically, the sensor installed at the second revolute joint of each branched chain is saved, replaced by numerical calculation according to kinematic constraints. The simulation results validate the effectiveness of the proposed kinematic error modeling and identification methods. The procedure for pre-processing compensation on this 3T1R parallel manipulator is eventually given to improve its absolute positioning accuracy, using the inverse of the calibrated kinematic model.

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“…Liu estimation [9] was used in the calibration process to resolve the multicollinearity in the identification Jacobian. To simplify the calculation difficulty and to decrease the value range of the calibrated parameters, the product of exponential (POE) formula was used to describe the closed-chain structure of the parallel mechanism [10]. But, some imperfect geometric errors, such as the axes offset in the universal joints [11], cannot be taken into account in the system calibration models.…”

Section: Introductionmentioning

confidence: 99%

Accuracy Improvement Calibrations for the Double-Position 4-PPPS Aircraft Docking System

Tang

Zhang

2020

Mathematical Problems in Engineering

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A double-positions 4-PPPS parallel mechanism is used for the aircraft fuselage assembly process to improve the docking efficiency and reduce the labor intensity. However, the accuracy is hard to guarantee, for the mechanism is large and redundant and has manufacturing and assembly errors. To improve the accuracy of the 4-PPPS parallel aircraft fuselage docking system, firstly, an averaging iteration method is proposed to calibrate the datum points in the airplane coordinate which are the references of the entire docking system. And secondly, a kinematic calibration method based on the derivative of the spatial pose transformation is proposed to calibrate up to 42 kinematic parameters. By these two methods, the final maximum position error reduced from 2.2 mm to 0.035 mm and the maximum pointing error reduced from 0.08 degree to 0.018 degree. The accuracy measurement and docking experiment prove the efficiency of the proposed methods.

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Complete, minimal and continuous error models for the kinematic calibration of parallel manipulators based on POE formula

Cited by 70 publications

References 24 publications

A Systematic Approach for Accuracy Design of Lower-Mobility Parallel Mechanism

A Systematic Approach for Accuracy Design of Lower-Mobility Parallel Mechanism

A Kinematic Calibration Method of a 3T1R 4-Degree-of-Freedom Symmetrical Parallel Manipulator

Accuracy Improvement Calibrations for the Double-Position 4-PPPS Aircraft Docking System

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