Skip to main content
SpringerLink
Log in

Computing the best grasp in a discrete point set with wrench-oriented grasp quality measures

  • Published:
Autonomous Robots Aims and scope Submit manuscript

Abstract

This paper presents a novel solution to the problem of computing the best grasp in a discrete point set where the performance quality of a grasp is measured by its capability to apply wrenches to the grasped object. First, it is revealed that various wrench-oriented grasp quality measures, considering different physical properties of a grasp, can be written in a unified form as the maximum scale factor of a gauge set in a grasp wrench set. Also, it has been deduced that the maximum scale factor is equal to the minimum value of the support function of the grasp wrench set over all directions and can be computed by evaluating the support function in a sequence of directions. On this basis, we can quickly determine that a new grasp is worse than the current best grasp if the support function of its grasp wrench set in any direction in the sequence or any particular direction is less than the quality value of the current best grasp. In this way, there is no need to calculate the exact quality value of the new grasp. Furthermore, we enumerate candidate grasps in the point set in an adaptive way such that grasps that are more likely to outperform the current best grasp will be checked first, which helps find the best grasp earlier and significantly reduce the number of candidate grasps to be fully examined. With the aid of the quick grasp comparison and the adaptive grasp enumeration, the proposed algorithm takes tens of seconds to several hours on a normal PC to compute the best grasp in tens to hundreds of points on 3-D objects and it is two to several orders of magnitude faster than the brute-force search. Moreover, the wrench-oriented grasp quality measures and the proposed algorithm are extended to the real scenario involving robot hands to predict and compute the best grasps on objects in reachable contact point sets of fingertips by given hand poses.

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

Similar content being viewed by others

References

  • Bicchi, A. (1994). On the problem of decomposing grasp and manipulation forces in multiple whole-limb manipulation. Robotics and Autonomous Systems, 13(2), 127–147.

    Article  MathSciNet  Google Scholar 

  • Borst, C., Fischer, M., & Hirzinger, G. (1999). A fast and robust grasp planner for arbitrary 3D objects. In Proceedings of the IEEE international conference on mechatronics and automation, Detroit, Michigan (pp. 1890–1896).

  • Borst, C., Fischer, M., & Hirzinger, G. (2004). Grasp planning: How to choose a suitable task wrench space. In Proceedings of the IEEE international conference on robotics and automation, New Oeleans, LA (pp. 319–325).

  • Calli, B., Singh, A., Bruce, J., Walsman, A., Konolige, K., Srinivasa, S., et al. (2017). Yale-CMU-Berkeley dataset for robotic manipulation research. International Journal of Robotics Research, 36(3), 261–268.

    Article  Google Scholar 

  • Chen, I. M., & Burdick, J. W. (1993). Finding antipodal point grasps on irregular shaped objects. IEEE Transactions on Robotics and Automation, 9(4), 507–512.

    Article  Google Scholar 

  • Cornellà, J., & Suárez, R. (2009). Efficient determination of four-point form-closure optimal constraints of polygonal objects. IEEE Transactions on Automation Science and Engineering, 6(1), 121–130.

    Article  Google Scholar 

  • Dai, H. K., Majumdar, A., & Tedrake, R. (2015). Synthesis and optimization of force closure grasps via sequential semidefinite programming. In International symposium on robotics research.

  • Ding, D., Liu, Y. H., & Wang, S. G. (2001). Computation of 3-D form-closure grasps. IEEE Transactions on Robotics and Automation, 17(4), 515–522.

    Article  Google Scholar 

  • El-Khoury, S., Li, M., & Billard, A. (2012). Bridging the gap: One shot grasp synthesis approach. In Proceedings of the IEEE/RSJ international conference on intelligent robots and systems, Vilamoura, Portugal (pp. 2027–2034).

  • El-Khoury, S., Li, M., & Billard, A. (2013). On the generation of a variety of grasps. Robotics and Autonomous Systems, 61(12), 1335–1349.

    Article  Google Scholar 

  • Ferrari, C., & Canny, J. F. (1992). Planning optimal grasps. In Proceedings of the IEEE international conference on robotics and automation, Nice, France (pp. 2290–2295).

  • Han, L., Trinkle, J. C., & Li, Z. X. (2000). Grasp analysis as linear matrix inequality problems. IEEE Transactions on Robotics and Automation, 16(6), 663–674.

    Article  Google Scholar 

  • Hang, K., Li, M., Stork, J. A., Bekiroglu, Y., Pokorny, F. T., Billard, A., et al. (2016). Hierarchical fingertip space: A unified framework for grasp planning and in-hand grasp adaptation. IEEE Transactions on Robotics, 32(4), 960–972.

    Article  Google Scholar 

  • Hang, K., Pokorny, F. T., & Kragic, D. (2013). Friction coefficients and grasp synthesis. In Proceedings of the IEEE/RSJ international conference on intelligent robots and systems, Tokyo, Japan (pp. 3520–3526).

  • Hang, K., Stork, J. A., Pollard, N. S., & Kragic, D. (2017). A framework for optimal grasp contact planning. IEEE Robotics and Automation Letters, 2(2), 704–711.

    Article  Google Scholar 

  • Harada, K., Tsuji, T., Uto, S., Yamanobe, N., Nagata, K., & Kitagaki, K. (2014). Stability of soft-finger grasp under gravity. In Proceedings of the IEEE international conference on robotics and automation, Hong Kong, China (pp. 883–888).

  • Haschke, R., Steil, J. J., Steuwer, I., & Ritter, H. (2005). Task-oriented quality measures for dextrous grasping. In Proceedings of IEEE international conference on computational intelligence in robotics and automation, Espoo, Finland (pp. 689–694).

  • Haustein, J. A., Hang, K., & Kragic, D. (2017). Integrating motion and hierarchical fingertip grasp planning. In Proceedings of the IEEE international conference on robotics and automation, Singapore (pp. 3439–3446).

  • Howe, R. D., Kao, I., & Cutkosky, M. R. (1988). The sliding of robot fingers under combined torsion and shear loading. In Proceedings of the IEEE international conference on robotics and automation, Philadephia, PA (pp. 103–105).

  • Lay, S. R. (1982). Convex sets and their applications. New York, NY: Wiley.

    MATH  Google Scholar 

  • Li, J. W., Liu, H., & Cai, H. G. (2003). On computing three-finger force-closure grasps of 2-D and 3-D objects. IEEE Transactions on Robotics and Automation, 19(1), 155–161.

    Article  Google Scholar 

  • Li, M., Hang, K., Kragic, D., & Billard, A. (2016). Dexterous grasping under shape uncertainty. Robotics and Autonomous Systems, 75, 352–364.

    Article  Google Scholar 

  • Li, Z. X., & Sastry, S. S. (1988). Task-oriented optimal grasping by multifingered robot hands. IEEE Journal on Robotics and Automation, 4(1), 32–44.

    Article  Google Scholar 

  • Lin, Y., & Sun, Y. (2015). Grasp planning to maximize task coverage. International Journal of Robotics Research, 34(9), 1195–1210.

    Article  Google Scholar 

  • Lippiello, V., Siciliano, B., & Villani, L. (2011). Online dextrous-hand grasping force optimization with dynamic torque constraints selection. In Proceedings of the IEEE international conference on robotics and automation, Shanghai, China (pp. 2831–2836).

  • Lippiello, V., Siciliano, B., & Villani, L. (2012). A grasping force optimization algorithm for dexterous robotic hands. In Proceedings of the IEEE international conference on robotics and automation, Saint Paul, MN (pp. 4170–4175).

  • Liu, G. F., Xu, J. J., & Li, Z. X. (2004a). On quality functions for grasp synthesis, fixture planning, and coordinated manipulation. IEEE Transactions on Automation Science and Engineering, 1(2), 146–162.

    Article  Google Scholar 

  • Liu, Y. H. (1999). Qualitative test and force optimization of 3-D frictional form-closure grasps using linear programming. IEEE Transactions on Robotics and Automation, 15(1), 163–173.

    Article  Google Scholar 

  • Liu, Y. H. (2000). Computing $n$-finger form-closure grasps on polygonal objects. International Journal of Robotics Research, 19(2), 149–158.

    Article  Google Scholar 

  • Liu, Y. H., Lam, M. L., & Ding, D. (2004b). A complete and efficient algorithm for searching 3-D form-closure grasps in the discrete domain. IEEE Transactions on Robotics, 20(5), 805–816.

    Article  Google Scholar 

  • Markenscoff, X., & Papadimitriou, C. H. (1989). Optimum grip of a polygon. International Journal of Robotics Research, 8(2), 17–29.

    Article  Google Scholar 

  • Miller, A. T., & Allen, P. K. (1999). Examples of 3D grasp quality computation. In Proceedings of the IEEE international conference on robotics and automation, Detroit, MI (pp. 1240–1246).

  • Miller, A. T., & Allen, P. K. (2004). GraspIt! a versatile simulator for robotic grasping. IEEE Robotics & Automation Magazine, 11(4), 110–122.

    Article  Google Scholar 

  • Mishra, B., Schwarz, J. T., & Sharir, M. (1987). On the existence and synthesis of multifingered positive grips. Algorithmica, 2(4), 541–558.

    Article  MathSciNet  MATH  Google Scholar 

  • Murray, R. M., Li, Z. X., & Sastry, S. S. (1994). A mathematical introduction to robotic manipulation. Boca Raton, FL: CRC Press.

    MATH  Google Scholar 

  • Nguyen, V. D. (1988). Constructing force-closure grasps. International Journal of Robotics Research, 7(3), 3–16.

    Article  MathSciNet  Google Scholar 

  • Park, Y. C., & Starr, G. P. (1992). Grasp synthesis of polygonal objects using a three-fingered robot hand. International Journal of Robotics Research, 11(3), 163–184.

    Article  Google Scholar 

  • Pollard, N. S. (1994). Parallel methods for synthesizing whole-hand grasps from generalized prototypes. Ph.D. Thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology.

  • Ponce, J., & Faverjon, B. (1995). On computing three-fingered force-closure grasps of polygonal objects. IEEE Transactions on Robotics and Automation, 11(6), 868–881.

    Article  Google Scholar 

  • Ponce, J., Stam, D., & Faverjon, B. (1993). On computing two-fingered force-closure grasps of curved 2d objects. International Journal of Robotics Research, 12(3), 263–273.

    Article  Google Scholar 

  • Ponce, J., Sullivan, S., Sudsang, A., Boissonnat, J. D., & Merlet, J. P. (1997). On computing four-fingered equilibrium and force-closure grasps of polyhedral objects. International Journal of Robotics Research, 16(1), 11–35.

    Article  MATH  Google Scholar 

  • Pozzi, M., Malvezzi, M., & Prattichizzo, D. (2017). On grasp quality measures: Grasp robustness and contact force distribution in underactuated and compliant robotic hands. IEEE Robotics and Automation Letters, 2(1), 329–336.

    Article  Google Scholar 

  • Prattichizzo, D., Malvezzi, M., Gabiccini, M., & Bicchi, A. (2013). On motion and force controllability of precision grasps with hands actuated by soft synergies. IEEE Transactions on Robotics, 29(6), 1440–1456.

    Article  Google Scholar 

  • Roa, M. A., & Suárez, R. (2009). Computation of independent contact regions for grasping 3-D objects. IEEE Transactions on Robotics, 25(4), 839–850.

    Article  Google Scholar 

  • Roa, M. A., & Suárez, R. (2015). Grasp quality measures: Review and performance. Autonomous Robots, 38(1), 65–88.

    Article  Google Scholar 

  • Shilane, F., Min, P., Kazhdan, M., & Funkhouser, T. (2004). The Princeton shape benchmark. In Shape modeling international.

  • Shimoga, K. B. (1996). Robot grasp synthesis algorithms: A survey. International Journal of Robotics Research, 15(3), 230–266.

    Article  Google Scholar 

  • Sintov, A., Menassa, R. J., & Shapiro, A. (2016). A gripper design algorithm for grasping a set of parts in manufacturing lines. Mechanism and Machine Theory, 105, 1–30.

    Article  Google Scholar 

  • Sintov, A., & Shapiro, A. (2017). An analysis of grasp quality measures for the application of sheet metal parts grasping. Autonomous Robots, 41(1), 145–161.

    Article  Google Scholar 

  • Strandberg, M., & Wahlberg, B. (2006). A method for grasp evaluation based on disturbance force rejection. IEEE Transactions on Robotics, 22(3), 461–469.

    Article  Google Scholar 

  • Teichmann, M. (1996). A grasp metric invariant under rigid motions. In Proceedings of the IEEE international conference on robotics and automation (pp. 2143–2148).

  • Tung, C. P., & Kak, A. C. (1996). Fast construction of force closure grasps. IEEE Transactions on Robotics and Automation, 12(4), 615–626.

    Article  Google Scholar 

  • Wang, M. Y. (2000). An optimal design for 3-D fixture synthesis in a point set domain. IEEE Transactions on Robotics and Automation, 16(6), 839–846.

    Article  Google Scholar 

  • Wang, M. Y., & Pelinescu, D. M. (2001). Optimizing fixture layout in a point-set domain. IEEE Transactions on Robotics and Automation, 17(3), 312–323.

    Article  Google Scholar 

  • Watanabe, T., & Yoshikawa, T. (2007). Grasping optimization using a required external force set. IEEE Transactions on Automation Science and Engineering, 4(1), 52–66.

    Article  Google Scholar 

  • Xue, Z. X., Woerner, P., Zoellner, J. M., & Dillmann, R. (2009). Efficient grasp planning using continuous collision detection. In Proceedings of the IEEE international conference on mechatronics and automation, Chengdu, China (pp. 2752–2758).

  • Xue, Z. X., Zoellner, J. M., & Dillmann, R. (2008). Automatic optimal grasp planning based on found contact points. In Proceedings of the IEEE/ASME international conference on advanced intelligent mechatronics, Xi’an, China (pp. 1053–1058).

  • Zheng, Y. (2013). An efficient algorithm for a grasp quality measure. IEEE Transactions on Robotics, 29(2), 579–585.

    Article  Google Scholar 

  • Zheng, Y. (2016). Computing the globally optimal frictionless fixture in a discrete point set. IEEE Transactions on Robotics, 32(4), 1026–1032.

    Article  Google Scholar 

  • Zheng, Y. (2017). Computing the best grasp in a discrete point set. In Proceedings of the IEEE international conference on robotics and automation, Singapore (pp. 2208–2214).

  • Zheng, Y., & Chew, C. M. (2009). Distance between a point and a convex cone in n-dimensional space: Computation and applications. IEEE Transactions on Robotics, 25(6), 1397–1412.

    Article  Google Scholar 

  • Zheng, Y., Lin, M. C., & Manocha, D. (2011). Efficient simplex computation for fixture layout design. Computer-Aided Design, 43(10), 1307–1318.

    Article  Google Scholar 

  • Zheng, Y., & Qian, W. H. (2009). Improving grasp quality evaluation. Robotics and Autonomous Systems, 57(6–7), 665–673.

    Article  Google Scholar 

  • Zheng, Y., & Yamane, K. (2013). Evaluation of grasp force efficiency considering hand configuration and using novel generalized penetration distance algorithm. In Proceedings of the IEEE international conference on robotics and automation, Karlsruhe, Germany (pp. 1580–1587).

  • Zheng, Y., & Yamane, K. (2015). Generalized distance between compact convex sets: Algorithms and applications. IEEE Transactions on Robotics, 31(4), 988–1003.

    Article  Google Scholar 

  • Zhu, X. Y., & Ding, H. (2006). Computation of force-closure grasps: An iterative algorithm. IEEE Transactions on Robotics, 22(1), 172–179.

    Article  Google Scholar 

  • Zhu, X. Y., & Ding, H. (2007). An efficient algorithm for grasp synthesis and fixture layout design in discrete domain. IEEE Transactions on Robotics, 23(1), 157–163.

    Article  Google Scholar 

  • Zhu, X. Y., & Wang, J. (2003). Synthesis of force-closure grasps on 3-D objects based on the $Q$ distance. IEEE Transactions on Robotics and Automation, 19(4), 669–679.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Michigan-Dearborn, Dearborn, MI, 48128, USA

    Yu Zheng

Authors
  1. Yu Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu Zheng.

Additional information

Publisher's Note

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

This work was partially supported by UM-Dearborn Scholars Grant (U056122).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zheng, Y. Computing the best grasp in a discrete point set with wrench-oriented grasp quality measures. Auton Robot 43, 1041–1062 (2019). https://doi.org/10.1007/s10514-018-9788-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10514-018-9788-4

Keywords

Search

Navigation