# Accuracy of Robotic Elastic Object Manipulation as a Function of Material Properties

## Abstract

We deal with the problem of thin string (1D) or plate (2D) elastic material folding and its modeling. The examples could be metallic wire, metal, kevlar or rubber sheet, fabric, or as in our case, garment. The simplest scenario attempts to fold rectangular sheet in the middle. The quality of the fold is measured by relative displacement of the sheet edges. We use this scenario to analyse the effect of the inaccurate estimation of the material properties on the fold quality. The same method can be used for accurate placing of the elastic sheet in applications, e.g. the industrial production assembly.

In our previous work, we designed a model simulating the behavior of homogeneous rectangular garment during a relatively slow folding by a dual-arm robot. The physics based model consists of a set of differential equations derived from the static forces equilibrium. Each folding phase is specified by a set of boundary conditions. The simulation of the garment behavior is computed by solving the boundary value problem. We have shown that the model depends on a single material parameter, which is a weight to stiffness ratio. For a known weight to stiffness ratio, the model is solved numerically to obtain the folding trajectory executed by the robotic arms later.

The weight to stiffness ratio can be estimated in the course of folding or manually in advance. The goal of this contribution is to analyse the effect of the ratio inaccurate estimation on the resulting fold. The analysis is performed by simulation and in a real robotic garment folding using the CloPeMa dual-arm robotic testbed. In addition, we consider a situation, in which the weight to stiffness ratio cannot be measured exactly but the range of the ratio values is known. We demonstrate that the fixed value of the ratio produces acceptable fold quality for a reasonable range of the ratio values. We show that only four weight to stiffness ratio values can be used to fold all typical fabrics varying from a soft (e.g. sateen) to a stiff (e.g. denim) material with the reasonable accuracy. Experiments show that for a given range of the weight to stiffness ratio one has to choose the value on the pliable end of the range to achieve acceptable results.

## Keywords

Robotic soft material folding Physical elastic flat material model Robotic fold accuracy## Notes

### Acknowledgment

This work was supported by the Technology Agency of the Czech Republic under Project TE01020197 Center Applied Cybernetics, the Grant Agency of the Czech Technical University in Prague, grant No. SGS15/203/OHK3/3T/13.

## References

- 1.Bellman, R.E., Kalaba, R.E.: Quasilinearization and nonlinear boundary-value problems. Technical report, RAND Corporation, Santa Monica (1965)Google Scholar
- 2.van den Berg, J., Miller, S., Goldberg, K.Y., Abbeel, P.: Gravity-based robotic cloth folding. In: Hsu, D., Isler, V., Latombe, J.-C., Lin, M.C. (eds.) Algorithmic Foundations of Robotics (WAFR), vol. 68, pp. 409–424. Springer, Heidelberg (2010)CrossRefGoogle Scholar
- 3.Kierzenka, J.A., Shampine, L.F.: A BVP solver that controls residual and error. J. Numer. Anal. Ind. Appl. Math (JNAIAM)
**3**, 1–2 (2008)MathSciNetzbMATHGoogle Scholar - 4.Lahey, T.: Modelling hysteresis in the bending of fabrics (2002)Google Scholar
- 5.Li, Y., Yue, Y., Xu, D., Grinspun, E., Allen, P.K.: Folding deformable objects using predictive simulation and trajectory optimization. In: Proceedings of International Conference on Intelligent Robots and Systems (IROS). IEEE/RSJ (2015)Google Scholar
- 6.Petrík, V., Smutný, V., Krsek, P., Hlaváč, V.: Robotic garment folding: precision improvement and workspace enlargement. In: Dixon, C., Tuyls, K. (eds.) TAROS 2015. LNCS, vol. 9287, pp. 204–215. Springer, Heidelberg (2015)CrossRefGoogle Scholar
- 7.Petrík, V., Smutný, V., Krsek, P., Hlaváč, V.: Physics-based model of rectangular garment for robotic folding. Research report CTU-CMP-2016-06, Center for Machine Perception, K13133 FEE Czech Technical University, Prague, Czech Republic, May, 2016Google Scholar
- 8.Plaut, R.H.: Formulas to determine fabric bending rigidity from simple tests. Text. Res. J.
**85**(8), 884–894 (2015)CrossRefGoogle Scholar - 9.Stuart, I.: A loop test for bending length and rigidity. Br. J. Appl. Phys.
**17**(9), 1215 (1966)CrossRefGoogle Scholar - 10.Wang, L.Z., Yuan, F., Guo, Z., Li, Ll: Numerical analysis of pipeline in J-lay problem. J. Zhejiang Univ. Sci. A
**11**(11), 908–920 (2010)CrossRefzbMATHGoogle Scholar - 11.Zeng, X.G., Duan, M.L., An, C.: Mathematical model of pipeline abandonment and recovery in deepwater. J. Appl. Math.
**2014**, 1–7 (2014)Google Scholar