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Inverse kinematics solution of a new circumferential drilling machine for aircraft assembly

Published online by Cambridge University Press:  22 May 2014

Weidong Zhu ,
Biao Mei  and
Yinglin Ke
Weidong Zhu*
Affiliation:
The State Key Lab of Fluid Power Transmission and Control, Department of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China
Biao Mei
Affiliation:
The State Key Lab of Fluid Power Transmission and Control, Department of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China
Yinglin Ke
Affiliation:
The State Key Lab of Fluid Power Transmission and Control, Department of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China
*
*Corresponding author. E-mail: [email protected]
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Summary

Inverse kinematics solutions are the basis for position and orientation control of automated machines in their Cartesian workspace. This paper presents an efficient and robust inverse kinematics algorithm for a new circumferential drilling machine for aircraft fuselage assembly. After a brief introduction to the circumferential drilling machine and its forward kinematics, the paper discusses the nonlinear optimization method for solving inverse kinematics problems. The objective function is defined as a weighted combination of a position error function and an orientation error function. By representing orientation error as the geodesic distance between two points on a unit sphere, the paper proposes to define the orientation error function by using faithful geodesic distance functions, which are accurate approximations to the geodesic distance when it is small. For increased efficiency, robustness, and easy setting of initial values, the inverse kinematics problem is decomposed into two subproblems. The revolute joint coordinates are obtained by nonlinear optimization, and the prismatic joint coordinates are calculated with closed-form formulas. Numerical experiments show that the objective function defined with faithful geodesic distance functions is effective, and the proposed algorithm is efficient, robust, and accurate. The algorithm has been successfully integrated into the control system of the circumferential drilling machine. Preliminary drilling experiments show that the position accuracy of drilled holes is within ±0.5 mm, which is acceptable for the assembly of large aircrafts.

Keywords

Inverse kinematicsNonlinear optimizationOrientation error functionGeodesic distanceDrilling machineAircraft assembly
Type
Articles
Information
Robotica , Volume 34 , Issue 1 , January 2016 , pp. 98 - 117
Copyright
Copyright © Cambridge University Press 2014 

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References

1.Williams, G., Chalupa, E. and Rahhal, S., “Automated positioning and alignment systems,” SAE Trans. 109, 737–745 (2000).Google Scholar
2.Qiu, B., Jiang, J. and Ke, Y., “A new principle and device for large aircraft components gaining accurate support by ball joint,” J. Zhejiang Univ.-Sci. A 12, 405–414 (2011).CrossRefGoogle Scholar
3.Thompson, P., Oberoi, H. and Draper, A., “Development of a multi spindle flexible drilling system for circumferential splice drilling applications on the 777 airplane,” SAE Technical Paper 2008-01-2298, 2008, doi:10.4271/2008-01-2298.CrossRefGoogle Scholar
4.Oberoi, H., Draper, A. and Thompson, P., “Production implementation of a multi spindle flexible drilling system for circumferential splice drilling applications on the 777airplane,” SAE Technical Paper 2009-01-3090 (2009) doi:10.4271/2009-01-3090.CrossRefGoogle Scholar
5.Bestaoui, Y., “An unconstrained optimization approach to the resolution of the inverse kinematic problem of redundant and nonredundant robot manipulators,” Robot. Auton. Syst. 7, 37–45 (1991).CrossRefGoogle Scholar
6.Goldenberg, A., Benhabib, B. and Fenton, R., “A complete generalized solution to the inverse kinematics of robots,” IEEE J. Robot. Autom. 1, 14–20 (1985).CrossRefGoogle Scholar
7.Kazerounian, K.. “On the numerical inverse kinematics of robotic manipulators,” ASME J. Mech. Transm. Autom. Des. 109, 8–13 (1987).CrossRefGoogle Scholar
8.Wang, L.-C.T. and Chen, C.C., “A combined optimization method for solving the inverse kinematics problems of mechanical manipulators,” IEEE Trans. Robot. Autom. 7, 489–499 (1991).CrossRefGoogle Scholar
9.Luh, J., Walker, M. and Paul, R., “Resolved-acceleration control of mechanical manipulators,” IEEE Trans. Autom. Control 25, 468–474 (1980).CrossRefGoogle Scholar
10.Freund, E., “Fast nonlinear control with arbitrary pole-placement for industrial robots and manipulators,” Int. J. Robot. Res. 1, 65–78 (1982).CrossRefGoogle Scholar
11.Manseur, R. and Doty, K. L., “A fast algorithm for inverse kinematic analysis of robot manipulators,” Int. J. Robot. Res. 7, 52–63 (1988).CrossRefGoogle Scholar
12.Pieper, D. L., The Kinematics of Manipulators Under Computer Control. Ph.D. dissertation (Stanford University, Stanford, CA, 1968).Google Scholar
13.Raghavan, M. and Roth, B., “Kinematic Analysis of the 6R Manipulator of General Geometry,” Proceedings of the 5th International Symposium on Robotics Research, MIT Press, Cambridge, MA, USA (1990) pp. 263–269.Google Scholar
14.Raghavan, M. and Roth, B., “Solving polynomial systems for the kinematic analysis and synthesis of mechanisms and robot manipulators,” J. Mech. Des. 117B, 71–79 (1995).CrossRefGoogle Scholar
15.Sasaki, S., “Feasibility studies of kinematics problems in the case of a class of redundant manipulators,” Robotica 13, 233–241 (1995).CrossRefGoogle Scholar
16.Elgazzar, S., “Efficient kinematic transformations for the PUMA 560 robot,” IEEE J. Robot. Autom. 1, 142–151 (1985).CrossRefGoogle Scholar
17.Hollerbach, J. M. and Sahar, G., “Wrist-partitioned, inverse kinematic accelerations and manipulator dynamics,” Int. J. Robot. Res. 2, 61–76 (1983).CrossRefGoogle Scholar
18.Tsai, L.-W. and Morgan, A. P., “Solving the kinematics of the most general six- and five- degree-of-freedom manipulators by continuation methods,” ASME J. Mech. Trans. Autom. Des. 107, 189–200 (1985).CrossRefGoogle Scholar
19.Ibarra, R. and Perreira, N. D., “Determination of linkage parameter and pair variable errors in open chain kinematic linkages using a minimal set of pose measurement data,” ASME J. Mech. Trans. Autom. Des. 108, 159–166 (1986).CrossRefGoogle Scholar
20.Uicker, J. J. Jr., Denavit, J. and Hartenberg, R. S., “An iterative method for the displacement analysis of spatial mechanisms,” ASME J. Appl. Mech. 31, 309–314 (1964).CrossRefGoogle Scholar
21.Wampler, C. W., “Manipulator inverse kinematic solutions based on vector formulations and damped least-squares methods,” IEEE Trans. Syst. Man Cybern. 16, 93–101 (1986).CrossRefGoogle Scholar
22.Chiaverini, S., Siciliano, B. and Egeland, O., “Review of the damped least-squares inverse kinematics with experiments on an industrial robot manipulator,” IEEE Trans. Control Syst. Technol. 2, 123–134 (1994).CrossRefGoogle Scholar
23.Nakamura, Y. and Hanafusa, H., “Inverse kinematic solutions with singularity robustness for robot manipulator control,” J. Dyn. Syst. Meas. Control 108, 163–171 (1986).CrossRefGoogle Scholar
24.Levenberg, K., “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math 2, 164–168 (1944).CrossRefGoogle Scholar
25.Marquardt, D. W., “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441 (1963).CrossRefGoogle Scholar
26.Goldenberg, A. A. and Lawrence, D. L., “A generalized solution to the inverse kinematics of robotic manipulators,” J. Dyn. Syst. Meas. Control 107, 103–106 (1985).CrossRefGoogle Scholar
27.Zhao, J. and Badler, N. I., “Inverse kinematics positioning using nonlinear programming for highly articulated figures,” ACM Trans. Graphics (TOG) 13, 313–336 (1994).CrossRefGoogle Scholar
28.Angeles, J., “On the numerical solution of the inverse kinematic problem,” Int. J. Robot. Res. 4, 21–37 (1985).CrossRefGoogle Scholar
29.Wolovich, W. A. and Elliott, H., “A Computational Technique for Inverse Kinematics,” Proceedings of the 23rd IEEE Conference on Decision and Control, vol. 23, pp. 1359–1363 (1984).Google Scholar
30.Balestrino, A., de Maria, G. and Sciavicco, L., “Robust Control of Robotic Manipulators,” Proceedings of the 9th IFAC World Congress, vol. 5, pp. 2435–2440 (1984).Google Scholar
31.Sugihara, T., “Solvability-unconcerned inverse kinematics by the Levenberg–Marquardt method,” IEEE Trans. Robot. 27, 984–991 (2011).CrossRefGoogle Scholar
32.Lumelsky, V. J., “Iterative coordinate transformation procedure for one class of robots,” IEEE Trans. Syst. Man Cybern. SMC-14, 500–505 (1984).CrossRefGoogle Scholar
33.Featherstone, R., “Position and velocity transformations between robot end-effector coordinates and joint angles,” Int. J. Robot. Res. 2, 35–45 (1983).CrossRefGoogle Scholar
34.Deo, A. S. and Walker, I. D., “Adaptive Non-Linear Least Squares for Inverse Kinematics,” Proceedings of IEEE International Conference on Robotics and Automation, vol. 1, pp. 186–193 (1993).Google Scholar
35.Siciliano, B. and Khatib, O., Springer Handbook of Robotics (Springer, Berlin, 2008).CrossRefGoogle Scholar