Skip to main content
SpringerLink
Log in

Generation of the Self-motion Manifolds of a Functionally Redundant Robot Using Multi-objective Optimization

  • Conference paper
  • First Online:
Robotics for Sustainable Future (CLAWAR 2021)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 324))

Included in the following conference series:

  • 1111 Accesses

Abstract

Off-line analysis of path tracking of functionally redundant robot manipulators is essential for effective use of industrial robots. The kinematic redundancy of the robot with respect to specific task can be exploited to optimize a desired criterion. Recently, industrial serial robots of 6 DOF are being widely used for a variety of tasks that only require 5 DOF or less, which is causes functional redundancy. For the case of functional redundancy, where the redundant parameters are within the operational space, once the optimal parameters have been selected, the inverse mapping between the operational space and the joint space often corresponds to a closed solution, which means that there are a finite number of joints configurations. This is the case for the most commonly used non-redundant 6 DoF serial robot manipulators. Moreover, each configuration lies on a specific solution branch into joint space. Due to this characteristic, during the optimization process by means of the Pareto Front technique, a sufficiently diverse set of Pareto Optimum points is not obtained to ensure that a solution close to the best combination of the multiple objectives can be found for a global optimization of the robot path. To overcome this difficulty, in this work, the Pareto Front is used to determine the topology of the selfmotions generated by redundancy and from these to identify the invertible subregions between the operational space and the configuration space. Multi-Objective Genetic Algorithms, MOGA, is used to solve the Inverse Kinematics (IK) for global optimization of functionally redundant robots, for incomplete orientation constrained task.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Stavropoulos, P., Foteinopoulos, P., Papacharalampopoulos, A., Bikas, H.: Addressing the challenges for the industrial application of additive manufacturing: towards a hybrid solution. Int. J. Lightweight Mater. Manuf. 1(3), 157–168 (2018). https://doi.org/10.1016/j.ijlmm.2018.07.002

    Article  Google Scholar 

  2. Borboni, A., Bussola, R., Faglia, R., Magnani, P.L., Menegolo, A.: Movement optimization of a redundant serial robot for high-quality pipe cutting. ASME. J. Mech. Des. 130(8), 082301 (2008). https://doi.org/10.1115/1.2918907

    Article  Google Scholar 

  3. Huo, L.: Robotic joint motion optimization of functionally redundant task for joint limits and singularity avoidance. Ph.D. thesis. University of Montreal, Canada (2009)

    Google Scholar 

  4. Schappler, M., Tappe, S., Ortmaier, T.: Resolution of functional redundancy for 3T2R robot tasks using two sets of reciprocal Euler angles. In: Uhl, T. (ed.) Advances in Mechanism and Machine Science. IFToMM WC 2019. Mechanisms and Machine Science, vol. 73. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20131-9_168

  5. Shahabi, M., Ghariblu, H.: Optimal joint motion for complicated welding geometry by a redundant robotic system. Eng. Optim. 52(5), 875–895 (2020). https://doi.org/10.1080/0305215X.2019.1630400

    Article  MathSciNet  Google Scholar 

  6. Jiao, J., Tian, W., Liao, W., Zhang, L., Yin, B.: Processing configuration off-line optimization for functionally redundant robotic drilling tasks. Robot. Auton. Syst. 110, 112–123 (2018). https://doi.org/10.1016/j.robot.2018.09.002

    Article  Google Scholar 

  7. Gonul, B., Faruk Sapmaz, O., Taner Tunc, L.: Improved stable conditions in robotic milling by kinematic redundancy. Procedia CIRP 82, 485–490 (2019). https://doi.org/10.1016/j.procir.2019.04.334

    Article  Google Scholar 

  8. Subrin, K., Sabourin, L., Cousturier, R., Gogu, G., Mezouar, Y.: New redundant architectures in machining: serial and parallel robots. Procedia Eng. 63, 158–166 (2013). https://doi.org/10.1016/j.proeng.2013.08.203

    Article  Google Scholar 

  9. Lotz, M., Bruhm, H., Czinki, A., Zalewski, M.: A real-time motion control strategy for redundant robots improving dynamics and accuracy. In: 2011 3rd International Congress on Ultra-Modern Telecommunications and Control Systems and Workshops (ICUMT), pp. 1–6 (2011)

    Google Scholar 

  10. Zanchettin, A.M., Rocco, P.: On the use of functional redundancy in industrial robotic manipulators for optimal spray painting. IFAC Proc. Vol. 44(1), 11495–11500 (2011). https://doi.org/10.3182/20110828-6-IT-1002.00687

    Article  Google Scholar 

  11. Xu, P., Yao, X., Chen, L., Liu, K., Bi, G.: Heuristic kinematics of a redundant robot-positioner system for additive manufacturing. In: 2020 6th International Conference on Control, Automation and Robotics (ICCAR), pp. 119–123 (2020). https://doi.org/10.1109/ICCAR49639.2020.9108047

  12. Rodríguez, H., Banfield, I.: Inverse kinematic multiobjective optimization for a vehicle-arm robot system using evolutionary algorithms. Memorias De Congresos UTP 1(1), 193–200 (2018). http://revistas.utp.ac.pa/index.php/memoutp/article/view/1913

  13. Zhang, Y., Li, J., Zhang, Z.: A time-varying coefficient-based manipulability-maximizing scheme for motion control of redundant robots subject to varying joint-velocity limits. Optim. Control Appl. Methods 34, 202–215 (2013). https://doi.org/10.1002/oca.201

    Article  MathSciNet  MATH  Google Scholar 

  14. \(\breve{Z}\)lajpah, L.: On orientation control of functional redundant robots. In: 2017 IEEE International Conference on Robotics and Automation (ICRA), pp. 2475–2482 (2017). https://doi.org/10.1109/ICRA.2017.7989288

  15. Tang, Q., Liang, L., Xie, J., Li, Y., Deng, Z.: Task-priority redundancy resolution on acceleration level for underwater vehicle-manipulator system. Int. J. Adv. Robot. Syst. (2017). https://doi.org/10.1177/1729881417719825

    Article  Google Scholar 

  16. Baron, L.: A joint-limits avoidance strategy for arc-welding robots. In: International Conference on Integrated Design and Manufacturing in Mechanical Engineering, pp. 16–19 (200)

    Google Scholar 

  17. Farouki, R., Shiqiao, L.: Optimal tool orientation control for 5-axis CNC milling with ball-end cutters. Comput. Aided Geom. Des. 30, 226–239 (2013). https://doi.org/10.1016/j.cagd.2012.11.003

    Article  MathSciNet  MATH  Google Scholar 

  18. Rokbani, N., Alimi, A.M.: Inverse kinematics using particle swarm optimization, a statistical analysis. Procedia Eng. 64, 1602–1611 (2013). https://doi.org/10.1016/j.proeng.2013.09.242

    Article  Google Scholar 

  19. Madhav, M., Harry, I., Richard, S., Venkatesh, V.: Approximation algorithms for PSPACE-hard hierarchically and periodically specified problems. SIAM J. Comput. 27, 1237–1261 (1998). https://doi.org/10.1137/S0097539795285254

    Article  MathSciNet  MATH  Google Scholar 

  20. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002). https://doi.org/10.1109/4235.996017

    Article  Google Scholar 

  21. Lück, C.L.: Self-motion representation and global path planning optimization for redundant manipulators through topology-based discretization. J. Intell. Robot. Syst. 19, 23–38 (1997). https://doi.org/10.1023/A:1007989214364

    Article  Google Scholar 

  22. Peidró, A., Reinoso, O., Gil, A., Marín, J.M., Payá, L.: A method based on the vanishing of self-motion manifolds to determine the collision-free workspace of redundant robots. Mech. Mach. Theory 128, 84–109 (2018). https://doi.org/10.1016/j.mechmachtheory.2018.05.013

    Article  Google Scholar 

  23. Demers, D.E.: Learning to invert many-to-one mappings. Ph.D. thesis. University of California at San Diego, La Jolla, CA, USA (1993)

    Google Scholar 

  24. DeMers, D., Kreutz-Delgado, K.: Issues in learning global properties of the robot kinematic mapping. In: Proceedings of the 1993 IEEE International Conference on Robotics and Automation, pp. 205–212 (1993). https://doi.org/10.1109/ROBOT.1993.291984

  25. DeMers, D., Kreutz-Delgado, K.: Canonically parameterized families of inverse kinematic functions for redundant manipulators. In: Proceedings of the 1994 IEEE International Conference on Robotics and Automation, pp. 1881–1886 (1994). https://doi.org/10.1109/ROBOT.1994.351187

  26. DeMers, D., Kreutz-Delgado, K.: Inverse kinematics of dextrous manipulators. In: Neural Systems for Robotics, pp. 75–116 (2012). https://doi.org/10.1016/B978-0-08-092509-7.50008-7

  27. Wenlei, X., Henning, S., Torsten, L., Hans-Werner, H., Jürgen, H.: Closed-form inverse kinematics of 6R milling robot with singularity avoidance. Prod. Eng. 5, 103–110 (2011). https://doi.org/10.1007/s11740-010-0283-9

    Article  Google Scholar 

  28. Yoshikawa, T.: Manipulability of robotic mechanisms. Int. J. Robot. Res. 4(2), 3–9 (1985). https://doi.org/10.1177/027836498500400201

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Faculty, Universidad Tecnológica de Panamá, Panama City, Panama

    Ilka Banfield & Humberto Rodríguez

  2. LEADS-UTP, Universidad Tecnológica de Panamá, Panama City, Panama

    Ilka Banfield & Humberto Rodríguez

Authors
  1. Ilka Banfield
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Humberto Rodríguez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Humberto Rodríguez .

Editor information

Editors and Affiliations

  1. Department of Engineering, Kwansei Gakuin University, Hyogo, Japan

    Daisuke Chugo

  2. School of Engineering, London South Bank University, London, UK

    Mohammad Osman Tokhi

  3. School of Engineering, Polytechnic Institute of Porto, Porto, Portugal

    Manuel F. Silva

  4. Chuo University, Bunkyo-ku, Tokyo, Japan

    Taro Nakamura

  5. School of Engineering, University of Lincoln, Lincolnshire, UK

    Khaled Goher

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Banfield, I., Rodríguez, H. (2022). Generation of the Self-motion Manifolds of a Functionally Redundant Robot Using Multi-objective Optimization. In: Chugo, D., Tokhi, M.O., Silva, M.F., Nakamura, T., Goher, K. (eds) Robotics for Sustainable Future. CLAWAR 2021. Lecture Notes in Networks and Systems, vol 324. Springer, Cham. https://doi.org/10.1007/978-3-030-86294-7_39

Download citation

Publish with us

Policies and ethics

Search

Navigation