Skip to main content

A Hill Muscle Actuated Arm Model with Dynamic Muscle Paths

  • Conference paper
  • First Online:
Multibody Dynamics 2019 (ECCOMAS 2019)

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 53))

Abstract

This contribution presents the optimal control of a musculoskeletal multibody model with Hill muscle actuation and dynamic muscle paths. In particular, the motion of a human arm and its muscle paths is described via constrained variational dynamics. The optimal control problem in this work is based on the direct transcription method DMOCC [4], where the optimal control problem is discretised in time, and the resulting nonlinear constrained finite dimensional optimisation problem is solved. To take a step towards finding global or multiple minima, we utilize the Matlab multistart framework for global optimisation. With the help of an example, we outline a framework to find feasible solutions and analyse several minima to which the nonlinear programming solver converges.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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

Similar content being viewed by others

Notes

  1. 1.

    https://de.mathworks.com/help/gads/how-globalsearch-and-multistart-work.html.

References

  1. Andersson, J.A., Gillis, J., Horn, G., Rawlings, J.B., Diehl, M.: CasADi: a software framework for nonlinear optimization and optimal control. Math. Program. Comput. 11(1), 1–36 (2019)

    Article  MathSciNet  Google Scholar 

  2. Betsch, P., Leyendecker, S.: The discrete null space method for the energy consistent integration of constrained mechanical systems. Part II: multibody dynamics. Int. J. Numer. Meth. Eng. 67(4), 499–552 (2006)

    Article  Google Scholar 

  3. Leyendecker, S., Marsden, J.E., Ortiz, M.: Variational integrators for constrained dynamical systems. ZAMM J. Appl. Math. Mech. 88(9), 677–708 (2008)

    Article  MathSciNet  Google Scholar 

  4. Leyendecker, S., Ober-Blöbaum, S., Marsden, J.E., Ortiz, M.: Discrete mechanics and optimal control for constrained systems. Optim. Control Appl. Meth. 31(6), 505–528 (2010)

    Article  MathSciNet  Google Scholar 

  5. Marsden, J.E., West, M.: Discrete mechanics and variational integrators. Acta Numerica 10, 357–514 (2001)

    Article  MathSciNet  Google Scholar 

  6. Maas, R., Leyendecker, S.: Biomechanical optimal control of human arm motion. Proc. Inst. Mech. Eng. Part K J. Multi-body Dyn. 227(4), 375–389 (2013)

    Google Scholar 

  7. Penner, J., Leyendecker, S.: Multi-obstacle muscle wrapping based on a discrete variational principle. In: Proceedings of the European Consortium for Mathematics in Industry (ECMI) Conference, Budapest, Hungary (2018, in review)

    Google Scholar 

  8. Scholz, A., Sherman, M., Stavness, I., Delp, S., Kecskeméthy, A.: A fast multi-obstacle muscle wrapping method using natural geodesic variations. Multibody Syst. Dyn. 36(2), 195–219 (2016)

    Article  MathSciNet  Google Scholar 

  9. Thielhelm, H., Vais, A., Brandes, D., Wolte, F.E.: Connecting geodesics on smooth surfaces. Vis. Comput. 28(6–8), 529–539 (2012)

    Article  Google Scholar 

  10. Ugray, Z., Lasdon, L., Plummer, J., Glover, F., Kelly, J., Martí, R.: Scatter search and local NLP solvers: a multistart framework for global optimization. INFORMS J. Comput. 19(3), 328–340 (2007)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work is funded by the Federal Ministry of Education and Research (BMBF) as part of the project 05M16WEB - DYMARA.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Johann Penner .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Penner, J., Leyendecker, S. (2020). A Hill Muscle Actuated Arm Model with Dynamic Muscle Paths. In: Kecskeméthy, A., Geu Flores, F. (eds) Multibody Dynamics 2019. ECCOMAS 2019. Computational Methods in Applied Sciences, vol 53. Springer, Cham. https://doi.org/10.1007/978-3-030-23132-3_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-23132-3_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-23131-6

  • Online ISBN: 978-3-030-23132-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics