SpringerLink
Log in

Traction control design for off-road mobility using an SPH-DAE cosimulation framework

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

We describe an analytical framework implemented in a general-purpose mobility simulation platform for enabling the design of control policies for improved rover mobility in granular terrain environments. We employ a homogenization of the granular material and use an elasto-plastic continuum model to capture the dynamics of the deformable terrain. The solution of the continuum problem is obtained using the smoothed particle hydrodynamics method. The Curiosity rover wheel geometry is defined through a mesh. The interaction between each wheel and the granular terrain is handled via cosimulation using so-called boundary conditions enforcing particles attached to the rover wheel. A traction control algorithm is implemented to reduce wheel slip and battery drain in hill-climbing scenario. Several parametric studies are carried out to assess rover simulation robustness for operation in uphill mobility scenario with different heights and friction coefficients. The analysis is carried out in an in-house developed simulation framework called Chrono. The implementation of the methods and models described herein is available on GitHub as open source for free use, modification, and redistribution, as well as reproducibility studies.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27

Similar content being viewed by others

References

  1. Johnson, J.B., Kulchitsky, A.V., Duvoy, P., Iagnemma, K., Senatore, C., Arvidson, R.E., Moore, J.: Discrete element method simulations of Mars exploration rover wheel performance. J. Terramech. 62, 31–40 (2015)

    Article  Google Scholar 

  2. Ucgul, M., Fielke, J., Saunders, C.: Three-dimensional discrete element modeling (DEM) of tillage: accounting for soil cohesion and adhesion. Biosyst. Eng. 129, 298–306 (2015)

    Article  Google Scholar 

  3. Zhao, C.-L., Zang, M.-Y.: Application of the FEM/DEM and alternately moving road method to the simulation of tire-sand interactions. J. Terramech. 72, 27–38 (2017)

    Article  Google Scholar 

  4. Recuero, A.M., Serban, R., Peterson, B., Sugiyama, H., Jayakumar, P., Negrut, D.: A high-fidelity approach for vehicle mobility simulation: nonlinear finite element tires operating on granular material. J. Terramech. 72, 39–54 (2017)

    Article  Google Scholar 

  5. Negrut, D., Mazhar, H.: Sand to mud to fording: modeling and simulation for off-road ground vehicle mobility analysis. In: International Workshop on Bifurcation and Degradation in Geomaterials, pp. 235–247. Springer, Berlin (2017)

    Google Scholar 

  6. Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)

    Article  Google Scholar 

  7. Bertrand, F., Leclaire, L., Levecque, G.: DEM-based models for the mixing of granular materials. Chem. Eng. Sci. 60(8–9), 2517–2531 (2005)

    Article  Google Scholar 

  8. Longmore, J.-P., Marais, P., Kuttel, M.M.: Towards realistic and interactive sand simulation: a GPU-based framework. Powder Technol. 235, 983–1000 (2013)

    Article  Google Scholar 

  9. Hou, Q., Dong, K., Yu, A.: DEM study of the flow of cohesive particles in a screw feeder. Powder Technol. 256, 529–539 (2014)

    Article  Google Scholar 

  10. Gan, J., Zhou, Z., Yu, A.: A GPU-based DEM approach for modeling of particulate systems. Powder Technol. 301, 1172–1182 (2016)

    Article  Google Scholar 

  11. He, Y., Evans, T., Yu, A., Yang, R.: A GPU-based DEM for modeling large scale powder compaction with wide size distributions. Powder Technol. 333, 219–228 (2018)

    Article  Google Scholar 

  12. Toson, P., Siegmann, E., Trogrlic, M., Kureck, H., Khinast, J., Jajcevic, D., Doshi, P., Blackwood, D., Bonnassieux, A., Daugherity, P.D., et al.: Detailed modeling and process design of an advanced continuous powder mixer. Int. J. Pharm. 552(1–2), 288–300 (2018)

    Article  Google Scholar 

  13. Chauchat, J., Médale, M.: A three-dimensional numerical model for dense granular flows based on the \(\mu \) (i) rheology. J. Comput. Phys. 256, 696–712 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  14. Ionescu, I.R., Mangeney, A., Bouchut, F., Roche, O.: Viscoplastic modeling of granular column collapse with pressure-dependent rheology. J. Non-Newton. Fluid Mech. 219, 1–18 (2015)

    Article  MathSciNet  Google Scholar 

  15. Liu, G.R., Liu, M.B.: Smoothed Particle Hydrodynamics: A Meshfree Particle Method. World Scientific, Singapore (2003)

    Book  MATH  Google Scholar 

  16. Sulsky, D., Chen, Z., Schreyer, H.L.: A particle method for history-dependent materials. Comput. Methods Appl. Mech. Eng. 118(1–2), 179–196 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  17. Bardenhagen, S.G., Brackbill, J.U., Sulsky, D.: The material point method for granular materials. Comput. Methods Appl. Mech. Eng. 187(3), 529–541 (2000)

    Article  MATH  Google Scholar 

  18. Yue, Y., Smith, B., Chen, P.Y., Chantharayukhonthorn, M., Kamrin, K., Grinspun, E.: Hybrid grains: adaptive coupling of discrete and continuum simulations of granular media. ACM Trans. Graph. 37(6), 1–19 (2018)

    Article  Google Scholar 

  19. Soga, K., Alonso, E., Yerro, A., Kumar, K., Bandara, S.: Trends in large-deformation analysis of landslide mass movements with particular emphasis on the material point method. Geotechnique 66(3), 248–273 (2016)

    Article  Google Scholar 

  20. Baumgarten, A.S., Kamrin, K.: A general fluid–sediment mixture model and constitutive theory validated in many flow regimes. J. Fluid Mech. 861, 721–764 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  21. Lucy, L.B.: A numerical approach to the testing of the fission hypothesis. Astron. J. 82, 1013–1024 (1977)

    Article  Google Scholar 

  22. Gingold, R.A., Monaghan, J.J.: Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181(1), 375–389 (1977)

    Article  MATH  Google Scholar 

  23. Bui, H.H., Fukagawa, R., Sako, K., Ohno, S.: Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic–plastic soil constitutive model. Int. J. Numer. Anal. Methods Geomech. 32(12), 1537–1570 (2008)

    Article  MATH  Google Scholar 

  24. Wei, C., Qiu, T.: Numerical simulations for large deformation of granular materials using smoothed particle hydrodynamics method. Int. J. Geomech. 12(2), 127–135 (2012)

    Article  MathSciNet  Google Scholar 

  25. Nguyen, C.T., Nguyen, C.T., Bui, H.H., Nguyen, G.D., Fukagawa, R.: A new SPH-based approach to simulation of granular flows using viscous dam** and stress regularisation. Landslides 14(1), 69–81 (2017)

    Article  Google Scholar 

  26. Hurley, R.C., Andrade, J.E.: Continuum modeling of rate-dependent granular flows in SPH. Comput. Part. Mech. 4(1), 119–130 (2017)

    Article  Google Scholar 

  27. Hu, W., Rakhsha, M., Yang, L., Kamrin, K., Negrut, D.: Modeling granular material dynamics and its two-way coupling with moving solid bodies using a continuum representation and the SPH method. Comput. Methods Appl. Mech. Eng. 385, 114022 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  28. Pazouki, A., Negrut, D.: A numerical study of the effect of particle properties on the radial distribution of suspensions in pipe flow. Comput. Fluids 108, 1–12 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  29. Rakhsha, M., Pazouki, A., Serban, R., Negrut, D.: Using a half-implicit integration scheme for the SPH-based solution of fluid-solid interaction problems. Comput. Methods Appl. Mech. Eng. 345, 100–122 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  30. Hu, W., Tian, Q., Hu, H.: Dynamic simulation of liquid-filled flexible multibody systems via absolute nodal coordinate formulation and sph method. Nonlinear Dyn. 75(4), 653–671 (2014)

    Article  MathSciNet  Google Scholar 

  31. Pazouki, A., Serban, R., Negrut, D.: A high performance computing approach to the simulation of fluid-solid interaction problems with rigid and flexible components. Arch. Mech. Eng. 61(2), 227–251 (2014)

    Article  Google Scholar 

  32. Hu, W., Tian, Q., Hu, H.: Simulating coupled dynamics of a rigid-flexible multibody system and compressible fluid. Sci. China, Phys. Mech. Astron. 61(4), 044711 (2018)

    Article  Google Scholar 

  33. Dunatunga, S., Kamrin, K.: Continuum modelling and simulation of granular flows through their many phases. J. Fluid Mech. 779, 483 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  34. Gurtin, M.E., Fried, E., Anand, L.: The Mechanics and Thermodynamics of Continua. Cambridge University Press, Cambridge (2010)

    Book  Google Scholar 

  35. Monaghan, J.J.: SPH without a tensile instability. J. Comput. Phys. 159(2), 290–311 (2000)

    Article  MATH  Google Scholar 

  36. Gray, J.P., Monaghan, J.J., Swift, R.P.: SPH elastic dynamics. Comput. Methods Appl. Mech. Eng. 190(49–50), 6641–6662 (2001)

    Article  MATH  Google Scholar 

  37. Yue, Y., Smith, B., Batty, C., Zheng, C., Grinspun, E.: Continuum foam: a material point method for shear-dependent flows. ACM Trans. Graph. 34(5), 1–20 (2015)

    Article  Google Scholar 

  38. Monaghan, J.J.: Smoothed particle hydrodynamics. Rep. Prog. Phys. 68(1), 1703–1759 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  39. Fatehi, R., Manzari, M.T.: Error estimation in smoothed particle hydrodynamics and a new scheme for second derivatives. Comput. Math. Appl. 61(2), 482–498 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  40. Trask, N., Maxey, M., Kimb, K., Perego, M., Parks, M.L., Yang, K., Xu, J.: A scalable consistent second-order SPH solver for unsteady low Reynolds number flows. Comput. Methods Appl. Mech. Eng. 289, 155–178 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  41. Pan, W., Kim, K., Perego, M., Tartakovsky, A.M., Parks, M.L.: Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics. J. Comput. Phys. 334, 125–144 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  42. Hu, W., Pan, W., Rakhsha, M., Tian, Q., Hu, H., Negrut, D.: A consistent multi-resolution smoothed particle hydrodynamics method. Comput. Methods Appl. Mech. Eng. 324, 278–299 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  43. Hu, W., Guo, G., Hu, X., Negrut, D., Xu, Z., Pan, W.: A consistent spatially adaptive smoothed particle hydrodynamics method for fluid-structure interactions. Comput. Methods Appl. Mech. Eng. 347, 402–424 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  44. Bonet, J., Lok, T.-S.L.: Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Comput. Methods Appl. Mech. Eng. 180(1–2), 97–115 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  45. Takeda, H., Miyama, S.M., Sekiya, M.: Numerical simulation of viscous flow by smoothed particle hydrodynamics. Prog. Theor. Phys. 92(5), 939–960 (1994)

    Article  Google Scholar 

  46. Morris, J.P., Fox, P.J., Zhu, Y.: Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys. 136(1), 214–226 (1997)

    Article  MATH  Google Scholar 

  47. Holmes, D.W., Williams, J.R., Tilke, P.: Smooth particle hydrodynamics simulations of low Reynolds number flows through porous media. Int. J. Numer. Anal. Methods Geomech. 35(4), 419–437 (2011)

    Article  MATH  Google Scholar 

  48. Zhan, L., Peng, C., Zhang, B., Wu, W.: Three-dimensional modeling of granular flow impact on rigid and deformable structures. Comput. Geotech. 112, 257–271 (2019)

    Article  Google Scholar 

  49. Bian, X., Ellero, M.: A splitting integration scheme for the SPH simulation of concentrated particle suspensions. Comput. Phys. Commun. 185(1), 53–62 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  50. Monaghan, J.J.: On the problem of penetration in particle methods. J. Comput. Phys. 82(1), 1–15 (1989)

    Article  MATH  Google Scholar 

  51. Monaghan, J.J.: Simulating free surface flows with SPH. J. Comput. Phys. 110, 399 (1994)

    Article  MATH  Google Scholar 

  52. Xu, R., Stansby, P., Laurence, D.: Accuracy and stability in incompressible SPH (ISPH) based on the projection method and a new approach. J. Comput. Phys. 228(18), 6703–6725 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  53. Pazouki, A., Kwarta, M., Williams, K., Likos, W., Serban, R., Jayakumar, P., Negrut, D.: Compliant versus rigid contact: a comparison in the context of granular dynamics. Phys. Rev. E 96, 042905 (2017)

    Article  Google Scholar 

  54. Negrut, D., Serban, R., Tasora, A.: Posing multibody dynamics with friction and contact as a differential complementarity problem. ASME J. Comput. Nonlinear Dyn. 13(1), 014503 (2017)

    Article  Google Scholar 

  55. Melanz, D., Jayakumar, P., Negrut, D.: Experimental validation of a differential variational inequality-based approach for handling friction and contact in vehicle/granular-terrain interaction. J. Terramech. 65, 1–13 (2016)

    Article  Google Scholar 

  56. Brian Kumanchik, NASA, and JPL-Caltech: Curiosity clean,nasa 3d resources (2016). https://nasa3d.arc.nasa.gov/detail/curiosity-clean

  57. Gutierrez, F., Ricchio, C., Rakhsha, M., Pazouki, A., Hu, W., Negrut, D.: Investigation of mesh to point cloud conversion approaches for applications in SPH-based fluid-solid interaction simulations. Technical Report TR-2015-10, Simulation-Based Engineering Laboratory, University of Wisconsin-Madison (2015)

  58. Fraeman, A.: The rocks vs. stone cold aluminum wheels (2018). https://mars.nasa.gov/MSL/mission/mars-rover-curiosity-mission-updates/index.cfm?mu=sol-2032-2033-the-rocks-vs-stone-cold-aluminum-wheels

  59. Toupet, O., Biesiadecki, J., Rankin, A., Steffy, A., Meirion-Griffith, G., Levine, D., Schadegg, M., Maimone, M.: Traction control design and integration onboard the Mars science laboratory Curiosity rover. In: 2018 IEEE Aerospace Conference, pp. 1–20 (2018)

    Google Scholar 

  60. Hu, W., Zhou, J., Negrut, D.: Mobility simulations of Mars Curiosity rover with traction control on uphill granular material terrain with different friction. Simulation-Based Engineering Laboratory, University of Wisconsin Press-Madison, 2021. https://uwmadison.box.com/s/gszprtae2tbfnv70xbms33wm1pxfnvui

  61. Hu, W., Zhou, J., Negrut, D.: Mobility simulations of Mars Curiosity rover with traction control on uphill granular material terrain with different heights. Simulation-Based Engineering Laboratory, University of Wisconsin Press-Madison, 2021. https://uwmadison.box.com/s/as31kohnxj3cw6l9cre99zrwu9b9da6n

  62. Kelly, C., Olsen, N., Negrut, D.: Billion degree of freedom granular dynamics simulation on commodity hardware via heterogeneous data-type representation. Multibody Syst. Dyn. 50, 355–379 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  63. Chrono Project Development Team: Chrono: an Open Source Framework for the Physics-Based Simulation of Dynamic Systems. https://github.com/projectchrono/chrono. Accessed: 2019-12-07

Download references

Acknowledgements

This work was supported by NASA under a Sequential STTR contract 80NSSC20C0252. Support was also provided by National Science Foundation grant CISE1835674 and US Army Research Office under grants W911NF1910431 and W911NF1810476.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI, 53706, USA

    Wei Hu, Zhenhao Zhou, Radu Serban & Dan Negrut

  2. ProtoInnovations, LLC, Pittsburgh, PA, 15201, USA

    Samuel Chandler & Dimitrios Apostolopoulos

  3. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Ken Kamrin

Authors
  1. Wei Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhenhao Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Samuel Chandler
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dimitrios Apostolopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ken Kamrin
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Radu Serban
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Dan Negrut
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dan Negrut.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, W., Zhou, Z., Chandler, S. et al. Traction control design for off-road mobility using an SPH-DAE cosimulation framework. Multibody Syst Dyn 55, 165–188 (2022). https://doi.org/10.1007/s11044-022-09815-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-022-09815-2

Keywords

Search

Navigation