Hostname: page-component-cb9f654ff-hqlzj Total loading time: 0 Render date: 2025-08-26T23:43:58.864Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal path crossing the orientation exclusion zone of a robot with offset wrist

Published online by Cambridge University Press:  21 June 2021

Paul Milenkovic Open the ORCID record for Paul Milenkovic [Opens in a new window]
Paul Milenkovic*
Affiliation:
Department of Electrical and Computer Engineering, University of Wisconsin-Madison, 1415 Engineering Drive, Madison, Wisconsin 53706, USA
*
Email: phmilenk@wisc.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An unexpected path reversal is discovered for a serial robot with an offset-axis wrist over a finite range of proximity to the wrist singularity. This is replicated by a kinematic model. A prior spherical-wrist method transits the singularity with limited joint rate and acceleration under a constant rate of tool traversal. Accurate position is maintained by controlling a small deviation in orientation. Extensions to the method for an offset wrist (1) find the least-maximum deviation, (2) identify and locate where a path reversal occurs, and (3) use this point to control step size in a high-order predictor-correction path following procedure.

Keywords

Robotic wristNonsphericalOffset wristTurning pointSingularity avoidanceAlgorithmic differentiationPower series expansion

Information

Type
Article
Information
Robotica , Volume 40 , Issue 1 , January 2022 , pp. 191 - 212
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0), which permits non-commercial re-use, distribution, and reproduction in any medium, provided that no alterations are made and the original article is properly cited. The written permission of Cambridge University Press must be obtained prior to any commercial use and/or adaptation of the article.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

References

Milenkovic, P., “Continuous path control for optimal wrist singularity avoidance in a serial robot,” Mech. Mach. Theory 140, 809–824 (2019). doi: 10.1016/j.mechmachtheory.2019.05.004 0094-114XCrossRefGoogle Scholar
ÖzgÖren, M. K., “Kinematic analysis of a manipulator with its position and velocity related singular configurations,” Mech. Mach. Theory 34(7), 1075–1101 (1999).CrossRefGoogle Scholar
Huang, B. and Milenkovic, V., “Method to Avoid Singularity in a Robot Mechanism,” U.S. Patent and Trademark Office patent US 4,716,350 (1987).Google Scholar
Cheng, S. K., Jean, M. R., McGee, H. D., Tsai, C. K. and Xiao, D., “Method of Controlling a Robot through a Singularity,” U.S. Patent and Trademark Office patent US 6,845,295 (2005).Google Scholar
Association, R. I., ANSI/RIA r15. 06 American National Standard for Industrial Robots and Robot Systems—Safety Requirements (Robotics Industries Association, Ann Arbor, 1999).Google Scholar
Trinh, C., Zlatanov, D., Zoppi, M. and Molfino, R., “A Geometrical Approach to the Inverse Kinematics of 6r Serial Robots with Offset Wrists,” ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (2015) pp. 1–10.Google Scholar
Wu, M.-K., Kung, Y.-S., Lee, F.-C. and Chen, W.-C., “Inverse Kinematics of Robot Manipulators with Offset Wrist,” 2015 International Conference on Advanced Robotics and Intelligent Systems (ARIS) (2015) pp. 1–6.Google Scholar
Corinaldi, D., Callegari, M. and Angeles, J., “Singularity-free path-planning of dexterous pointing tasks for a class of spherical parallel mechanisms,” Mech. Mach. Theory 128, 47–57 (2018). doi: 10.1016/j.mechmachtheory.2018.05.006 0094-114XCrossRefGoogle Scholar
Sun, T., Liang, D. and Song, Y., “Singular-perturbation-based nonlinear hybrid control of redundant parallel robot,” IEEE Trans. Ind. Electron. 65(4), 3326–3336 (2018).CrossRefGoogle Scholar
Ozgoren, M. K., “Kinematic and kinetostatic analysis of parallel manipulators with emphasis on position, motion, and actuation singularities,” Robotica 37(4), 599–625 (2019).CrossRefGoogle Scholar
Huang, Y., Yong, Y. S., Chiba, R., Arai, T., Ueyama, T. and Ota, J., “Kinematic control with singularity avoidance for teaching-playback robot manipulator system,” IEEE Trans. Automat. Sci. Eng. 13(2), 729–742 (2016).CrossRefGoogle Scholar
Wampler, C. W., “Manipulator inverse kinematic solutions based on vector formulations and damped least-squares methods,” IEEE Trans. Syst. Man Cybernet. 16(1), 93–101 (1986).CrossRefGoogle Scholar
Nakamura, Y. and Hanafusa, H., “Inverse kinematic solutions with singularity robustness for robot manipulator control,” ASME J. Dyn. Syst. Meas. Cont. 108(3), 163–171 (1986).CrossRefGoogle Scholar
Tsai, L. W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators (John Wiley and Sons, New York, 1999).Google Scholar
Chiaverini, S., Siciliano, B. and Egeland, O., “Review of the damped least-squares inverse kinematics with experiments on an industrial robot manipulator,” IEEE Trans. Cont. Syst. Technol. 2(2), 123–134 (1994).CrossRefGoogle Scholar
Maciejewski, A. A. and Klein, C. A., “Numerical filtering for the operation of robotic manipulators through kinematically singular configurations,” J. Robot. Syst. 5(6), 527–552 (1988).CrossRefGoogle Scholar
Wang, X., Zhang, D., Zhao, C., Zhang, H. and Yan, H., “Singularity analysis and treatment for a 7r 6-dof painting robot with non-spherical wrist,” Mech. Mach. Theory 126, 92–107 (2018). doi: 10.1016/j.mechmachtheory.2018.03.018 0094-114XGoogle Scholar
Wan, Y., Kou, Y. and Liang, X., “Closed-Loop Inverse Kinematic Analysis of Redundant Manipulators with Joint Limits,” International Conference on Mechanical Design (2017) pp. 1241–1255.Google Scholar
Nakamura, Y., Advanced Robotics: Redundancy and Optimization (Addison-Wesley Longman Publishing Co., Inc., Reading, Massachusetts, 1991).Google Scholar
Kim, D.-E., Park, D.-J., Park, J.-H. and Lee, J.-M., “Collision and Singularity Avoidance Path Planning of 6-DOF Dual-Arm Manipulator,” International Conference on Intelligent Robotics and Applications (2018) pp. 195–207.Google Scholar
Chembuly, V. and Voruganti, H. K., “An Optimization Based Inverse Kinematics of Redundant Robots Avoiding Obstacles and Singularities,” Proceedings of the Advances in Robotics (2017) p. 24.Google Scholar
Buss, S. R. and Kim, J.-S., “Selectively damped least squares for inverse kinematics,” J. Graph. GPU, Game Tools 10(3), 37–49 (2005).CrossRefGoogle Scholar
Chiaverini, S. and Egeland, O., “A Solution to the Singularity Problem for Six-Joint Manipulators,” IEEE International Conference on Robotics and Automation, vol. 1 (1990) pp. 644–649.Google Scholar
Oetomo, D. and Ang, M. H., Jr., “Singularity robust algorithm in serial manipulators,” Robot. Comput. Integr. Manufact. 25, 122–134 (2009). doi: 10.1016/j.rcim.2007.09.007CrossRefGoogle Scholar
Milenkovic, V. and Huang, B., “Development On an Algorithm Negotiating Wrist Singularities,” Robot 11/17th ISIR (1987) pp. 13-1–13-6.Google Scholar
Aboaf, E. W. and Paul, R. P., “Living with the Singularity of Robot Wrists,” IEEE International Conference on Robotics and Automation (1987) pp. 1713–1717.Google Scholar
Milenkovic, P., “Effect of the Coordinate Frame on High-Order Expansion of Serial-Chain Displacement,” Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics (2019) pp. 840–855.Google Scholar
Kieffer, J., “Manipulator inverse kinematics for untimed end-effector trajectories with ordinary singularities,” Int. J. Robot. Res. 11(3), 225–237 (1992).CrossRefGoogle Scholar
Luo, X., Li, S., Liu, S. and Liu, G., “An optimal trajectory planning method for path tracking of industrial robots,” Robotica 37(3), 502–520 (2019).CrossRefGoogle Scholar
Tourajizadeh, H. and Gholami, O., “Optimal control and path planning of a 3PRS robot using indirect variation algorithm,” Robotica 38(5), 903–924 (2020).CrossRefGoogle Scholar
Vezvari, M. R., Nikoobin, A. and Ghoddosian, A., “Perfect torque compensation of planar 5R parallel robot in point-to-point motions, optimal control approach,” Robotica, 39, 1–18 (2020).Google Scholar
Mansouri, S., Sadigh, M. J. and Fazeli, M., “A computationally efficient algorithm to find time-optimal trajectory of redundantly actuated robots moving on a specified path,” Robotica 37(1), 62–79 (2019).CrossRefGoogle Scholar
Griewank, A. and Walther, A., “On the Efficient Generation of Taylor Expansions for DAE Solutions by Automatic Differentiation,” In: Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004 (Dongarra, J., Madsen, K. and Wasniewski, J., eds.) (Springer, Berlin, Heidelberg, 2006) pp. 1089–1098.Google Scholar
Milenkovic, P., “Series solution for finite displacement of single-loop spatial linkages,” ASME J. Mech. Robot. 4(2), 021016 (2012).CrossRefGoogle Scholar
Di Gregorio, R., “Acceleration and higher-order analyses solved by extending the superposition principle: The incipient motion technique,” Mech. Mach. Theory 153, 103953 (2020). doi: 10.1016/j.mechmachtheory.2020.1039530094-114XCrossRefGoogle Scholar
Hassan, A. A., El-Habrouk, M. and Deghedie, S., “Inverse kinematics of redundant manipulators formulated as quadratic programming optimization problem solved using recurrent neural networks: A review,” Robotica 38(8), 1495–1512 (2020).CrossRefGoogle Scholar
Huber, G. and Wollherr, D., “An online trajectory generator on se (3) for human–robot collaboration,” Robotica 38(10), 1756–1777 (2020).CrossRefGoogle Scholar
Blanes, S., Casas, F., Oteo, J.-A. and Ros, J., “The magnus expansion and some of its applications,” Phys. Rep. 470(5–6), 151–238 (2009).CrossRefGoogle Scholar
Achilles, R. and Bonfiglioli, A., “The early proofs of the theorem of campbell, baker, hausdorff, and dynkin,” Arch. His. Exact Sci. 66(3), 295–358 (2012).CrossRefGoogle Scholar
Kang, Z.-H., Cheng, C.-A. and Huang, H.-P., “A singularity handling algorithm based on operational space control for six-degree-of-freedom anthropomorphic manipulators,” Int. J. Adv. Robot. Syst. 16(3), 1729881419858910 (2019).CrossRefGoogle Scholar
Lloyd, J. E. and Hayward, V., “Singularity-robust trajectory generation,” Int. J. Robot. Res. 20(1), 38–56 (2001).CrossRefGoogle Scholar
Pohl, E. D. and Lipkin, H., “A New Method of Robotic Rate Control near Singularities,” IEEE International Conference on Robotics and Automation (1991) pp. 1708–1713.Google Scholar
Lloyd, J. E., “Desingularization of nonredundant serial manipulator trajectories using puiseux series,” IEEE Trans. Robot. Automat. 14(4), 590–600 (1998).CrossRefGoogle Scholar
“Motoman-ma1400 instructions” (n.d.).Google Scholar
Pashkevich, A., “Real-time inverse kinematics for robots with offset and reduced wrist,” Cont. Eng. Pract. 5(10), 1443–1450 (1997).CrossRefGoogle Scholar
Snyder, J. P., Map Projections: A Working Manual (US Government Printing Office, 1987).Google Scholar
What Are the Singularities of a Typical Collaborative Robot (Cobot) (École de Technologie SupÉrieure, 2018).Google Scholar
Milenkovic, P., “Solution of the forward dynamics of a single-loop linkage using power series,” ASME J. Dyn. Syst. Meas. Cont. 133(6), 061002 (2011).CrossRefGoogle Scholar
Milenkovic, P., “Projective constraint stabilization for a power series forward dynamics solver,” ASME J. Dyn. Syst. Meas. Cont. 135(3), 031004 (2013).CrossRefGoogle Scholar
Featherstone, R., Rigid Body Dynamics Algorithms (Springer, New York, 2008).CrossRefGoogle Scholar
Featherstone, R., “Plucker Basis Vectors,” Proceedings 2006 IEEE International Conference on Robotics and Automation (2006) pp. 1892–1897.Google Scholar
Garcia, C. B. and Zangwill, W. I., Pathways to Solutions, Fixed Points, and Equilibria (Prentice-Hall, Englewood Cliffs, New Jersey, 1981).Google Scholar
Ambike, S. and Schmiedeler, J. P., “A methodology for implementing the curvature theory approach to path tracking with planar robots,” Mech. Mach. Theory 43(10), 1225–1235 (2008).CrossRefGoogle Scholar
Ambike, S., Schmiedeler, J. P. and Stanisic, M. M., “Trajectory tracking via independent solutions to the geometric and temporal tracking subproblems,” ASME J. Mech. Robot. 3(2), 021008 (2011).CrossRefGoogle Scholar
Bickley, W. G., “1587. An extension of newton’s formula for approximating to the roots of equations,” Math. Gazette 26(269), 102–104 (1942).Google Scholar
Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T., Numerical Recipes in Pascal (Cambridge University Press, New York, 1989).Google Scholar