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Research Papers

A Fast and Robust Hybrid Method for the Solution of the 6-3 Stewart–Gough Platform Direct Position Analysis

[+] Author and Article Information
R. Vertechy

DIEM,  University of Bologna, Viale Risorgimento 2, 40136, Bologna, Italyrocco.vertechy@mail.ing.unibo.it

V. Parenti-Castelli

DIEM,  University of Bologna, Viale Risorgimento 2, 40136, Bologna, Italyvincenzo.parenti@unibo.it

J. Mechanisms Robotics 1(1), 011014 (Sep 02, 2008) (9 pages) doi:10.1115/1.2966389 History: Received January 04, 2008; Revised July 06, 2008; Published September 02, 2008

A robust and accurate hybrid method for the real-time estimation of the actual configuration of 6-3 Stewart–Gough platforms is presented. The method is hybrid since on one hand it requires the use of three extra sensors in addition to the six ones, which measure the lengths of the manipulator legs, and on the other hand it reduces the influence of sensor noise on the pose estimate by means of either an iterative procedure, which is based on the Newton–Raphson scheme, at regular configurations, or by means of a noniterative procedure, which is based on the study of the null-space of the manipulator Jacobian, in the vicinity of singular configurations. The method is robust since it does not fail near singular configurations and it detects the actual assembly mode of the manipulator. It is also accurate since it always provides a solution, which satisfies the kinematic constraint equations of the manipulator and is rather insensitive to sensor noise. The method is fast since the estimation of the actual configuration of the mechanism requires a limited number of operations, which can be executed in real-time. Analytical and numerical results are reported to show the robustness, accuracy, and computational efficiency of the proposed method.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Stewart-Gough platform of type 6-3

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Figure 2

Subsystem BiPiBi′ of the Stewart-Gough platform of type 6-3

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Figure 3

Condition number of the kinematic equation Jacobian

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Figure 4

Displacement error for the case: linear sensor error equal to zero, rotary sensor error equal to 12.5 mrad

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Figure 5

Orientation error for the case: linear sensor error equal to zero, rotary sensor error equal to 12.5 mrad

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Figure 6

Displacement error for the case: linear sensor error equal to 0.4 mm, rotary sensor error equal to 12.5 mrad

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Figure 7

Orientation error for the case: linear sensor error equal to 0.4 mm, rotary sensor error equal to 12.5 mrad

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Figure 8

Number of Iterations for the case: linear sensor error equal to zero, rotary sensor error equal to 12.5 mrad

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Figure 9

Number of Iterations for the case: linear sensor error equal to 0.4 mm, rotary sensor error equal to 12.5 mrad

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