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Parameter Estimation for Deformable Objects in Robotic Manipulation Tasks

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Part of the Springer Proceedings in Advanced Robotics book series (SPAR,volume 27)


We consider the problem of identifying material parameters of a deformable object, such as elastic moduli, by non-destructive robotic manipulation. We assume known geometry and mass, a reliable fixed grasp, and the ability to track the positions of a few points on the object surface. We collect a dataset of grasp pose sequences and corresponding point position sequences. We represent the object by a tetrahedral Finite Element Method (FEM) mesh and optimize the material parameters to minimize the difference between the real and predicted observations. We use a collocation-type formulation where the sequence of FEM mesh states are decision variables, and the dynamics are encoded as constraints. Sparsity patterns in the constraints make this problem tractable despite the large number of variables. Experiments show that our approach is computationally feasible and able to adequately re-identificy simulated material parameters.


  • Dynamical systems
  • Parameter estimation
  • Deformable objects

G.S. Sukhatme holds concurrent appointments as a Professor at USC and as an Amazon Scholar. This paper describes work performed at USC and is not associated with Amazon. This work was supported by a NASA Space Technology Research Fellowship, grant number 80NSSC19K1182.

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  1. Akkaya, I., et al.: Solving Rubik’s Cube with a Robot Hand (2019)

    Google Scholar 

  2. Armstrong, B., Khatib, O., Burdick, J.: The explicit dynamic model and inertial parameters of the PUMA 560 arm. In: Proceedings of the 1986 IEEE International Conference on Robotics and Automation, vol. 3, pp. 510–518. IEEE

    Google Scholar 

  3. Barbič, J., James, D.L.: Real-time subspace integration for St. Venant-Kirchhoff deformable models. In: ACM Transactions on Graphics (TOG), vol. 24, no. 3, pp. 982–990 (2005)

    Google Scholar 

  4. Belytschko, T., et al.: Nonlinear Finite Elements for Continua and Structures. John Wiley & Sons, Hoboken (2014)

    Google Scholar 

  5. Bezanson, J., et al.: Julia: a fresh approach to numerical computing. In: SIAM Review, vol. 59, no. 1, pp. 65–98 (2017).

  6. Coumans, E., Bai, Y.: PyBullet, a Python module for physics simulation for games, robotics and machine learning (2016).

  7. de Avila Belbute-Peres, F., et al.: End-to-end differentiable physics for learning and control. In: Advances in Neural Information Processing Systems, vol. 31 (2018)

    Google Scholar 

  8. Elmqvist, H., Mattsson, S.E., Otter, M.: Modelica-a language for physical system modeling, visualization and interaction. In: Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design (Cat. No. 99TH8404), pp. 630–639. IEEE

    Google Scholar 

  9. Ha, H., Song, S.: Flingbot: the unreasonable effectiveness of dynamic manipulation for cloth unfolding. In: Conference on Robot Learning. PMLR, pp. 24–33 (2022)

    Google Scholar 

  10. Hager, W.W., Zhang, H.: Algorithm 851: CG\(_{D}\)ESCENT, a conjugate gradient method with guaranteed descent. In: ACM Transactions on Mathematical Software, vol. 32, no. 1, pp. 113–137 (2006). ISSN: 0098-3500.

  11. Hahn, D., et al.: Real2sim: visco-elastic parameter estimation from dynamic motion. In: ACM Transactions on Graphics (TOG), vol. 38, no. 6, pp. 1–13 (2019)

    Google Scholar 

  12. Heiden, E., et al.: Disect: a differentiable simulation engine for autonomous robotic cutting. In: Robotics: Science and Systems (2021)

    Google Scholar 

  13. Holzapfel, G.A.: Nonlinear Solid Mechanics: A Continuum Approach for Engineering. Wiley. ISBN: 978-0-471-82304-9

    Google Scholar 

  14. Hu, Y., et al.: DiffTaichi: differentiable programming for physical simulation. In: ICLR (2020)

    Google Scholar 

  15. Koenig, N., Howard, A.: Design and use paradigms for gazebo, an open-source multi-robot simulator. In: 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No. 04CH37566), vol. 3, pp. 2149–2154.

  16. Kutz, J.N., et al.: Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems. SIAM, Philadelphia (2016)

    CrossRef  MATH  Google Scholar 

  17. Levine, S., et al.: Learning hand-eye coordination for robotic grasping with deep learning and large-scale data collection.

  18. Lim, V., et al.: Planar robot casting with real2sim2real self-supervised learning (2021)

    Google Scholar 

  19. MacNeal, R.H., McCormick, C.W.: The NASTRAN computer program for structural analysis. In: Computers & Structures, vol. 1, no. 3, pp. 389–412 (1971)

    Google Scholar 

  20. Mahnken, R.: Identification of material parameters for constitutive equations. In: Encyclopedia of Computational Mechanics 2nd edn. pp. 1–21. John Wiley & Sons, Ltd. ISBN: 978-1-119-17681-7.

  21. Mitrano, P., McConachie, D., Berenson, D.: Learning where to trust unreliable models in an unstructured world for deformable object manipulation. In: Science Robotics, vol. 6, no. 54, p. eabd8170 (2021).,

  22. Mogensen, P.K., Riseth, A.N.: Optim: a mathematical optimization package for Julia. J. Open Source Softw. 3(24), 615 (2018).

    CrossRef  Google Scholar 

  23. Müller, M., et al.: Detailed rigid body simulation with extended position based dynamics. In: Computer Graphics Forum, vol. 39, pp. 101–112. Wiley Online Library

    Google Scholar 

  24. Nathan, M.: Newmark. American Society of Civil Engineers, A Method of Computation for Structural Dynamics (1959)

    Google Scholar 

  25. Preiss, J.A., et al.: Tracking fast trajectories with a deformable object using a learned model. In: IEEE Conference on Robotics and Automation (2022)

    Google Scholar 

  26. Reece, A.R.: The fundamental equation of earth-moving mechanics. In: Proceedings of the Institution of Mechanical Engineers, Conference Proceedings, vol. 179, no. 6, pp. 16–22. SAGE Publications, London (1964)

    Google Scholar 

  27. Sharma, A., Azizan, N., Pavone, M.: Sketching curvature for efficient out-of-distribution detection for deep neural networks. In: de Campos, C., Maathuis, M.H. (ed.) Proceedings of the 37th Conference on Uncertainty in Artificial Intelligence, vol. 161. Proceedings of Machine Learning Research. PMLR, 27–30 July 2021, pp. 1958–1967.

  28. Slotine, J.J.E., Li, W., et al.: Applied Nonlinear Control, vol. 199. Prentice Hall Englewood Cliffs, New Jersey (1991)

    MATH  Google Scholar 

  29. Tassa, Y., Erez, T., Todorov, E.: Synthesis and stabilization of complex behaviors through online trajectory optimization. In: 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4906–4913. IEEE

    Google Scholar 

  30. Todorov, E., Erez, T., Tassa, Y.: Mujoco: a physics engine for model-based control. In: 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 5026–5033. IEEE

    Google Scholar 

  31. Wang, B., et al.: Deformation capture and modeling of soft objects. ACM Trans. Graph. 34(4), 1–94 (2015)

    Google Scholar 

  32. Wang, B., Zheng, M., Barbič, J.: Adjustable constrained soft-tissue dynamics. In: Computer Graphics Forum, vol. 39, no .7, pp. 69–79 (2020). ISSN: 1467-8659.,

  33. Weng, T., et al.: FabricFlowNet: bimanual cloth manipulation with a flow-based policy. In: Conference on Robot Learning (2021)

    Google Scholar 

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Correspondence to David Millard .

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Millard, D., Preiss, J.A., Barbič, J., Sukhatme, G.S. (2023). Parameter Estimation for Deformable Objects in Robotic Manipulation Tasks. In: Billard, A., Asfour, T., Khatib, O. (eds) Robotics Research. ISRR 2022. Springer Proceedings in Advanced Robotics, vol 27. Springer, Cham.

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