Skip to main content

Advertisement

SpringerLink
Log in

Inverse Kinematics of High Dimensional Robotic Arm-Hand Systems for Precision Grasping

  • Regular Paper
  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

Conventionally, the arm and the hand are considered separately for robotic manipulation and grasp. The hand configuration and the wrist pose are obtained during grasp planning and afterwards, the arm configuration is found to accommodate the wrist pose. However, without considering the arm during grasp planning, this approach can become very inefficient as significant time and computation power are spent on evaluating and planning grasps that are simply unreachable. This paper presents an efficient method for obtaining a desired configuration of the arm and the hand simultaneously for precision grasping. Our method assumes that contact points and contact normals are given for the desired grasp. Inspired by the human grasp strategy, our approach implements a thumb-first strategy to narrow down the search space and increase the success rate. To precisely fulfill all fingers’ requirements, the inverse kinematics (IK) solution for the position and orientation of each finger are regarded as independent tasks. These tasks are organized in a well-designed hierarchy and the resulting joint movements from each level are combined through nullspace projection with a nullspace enlargement method to ensure the correctness of the results. Comprehensive simulation results will demonstrate that the proposed method can significantly improve the performance of classic IK algorithms.

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

Similar content being viewed by others

Materials Availability

All data and materials related to this paper are available by sending requests to the authors.

Abbreviations

\(\mathbb {R}\) :

Set of real numbers

J :

Task-related Jacobian matrix

Δ 𝜃 :

Joint movement for achieving a task

e :

Task-related error vector

λ :

Nonzero damping factor

Σ :

Rectangular diagonal matrix obtained from singular value decomposition

σ i :

i-th singular value of a matrix obtained from singular value decomposition

U,V :

Orthogonal matrices obtained from singular value decomposition

u i, v i :

i-th column of U and V, respectively

v i,j :

j-th element of vi

r :

Rank of the Jacobian matrix (J)

\(\|\cdot \|_{\infty }\) :

Maximum absolute values of a vector’s components

n j :

The number of joints in a robot manipulator

J j :

j-th column vector of the Jacobian matrix (J)

\(\gamma _{\max \limits }\) :

Maximum joint movement threshold in a single iteration in Selectively Damped Least Squares (SDLS) method [1]

n i :

Normal vector direction of the i-th finger’s tip

X palm, Y palm, Z palm :

Coordinate frame axes attached to the palm

\(\mathbf {p}_{i_{b}}\) :

Base point of the i-th finger

J t+p :

Augmented Jacobian matrix of the tasks related to the thumb and the palm

\(J_{t_{pos}}, J_{t_{ori}}\) :

Jacobian matrix related to the thumb’s position and orientation, respectively

\(J_{p_{ori}}\), J f2pos :

Jacobian matrix related to the palm’s orientation and Finger 2’s position, respectively

(⋅)‡ :

Moore-Penrose inverse of a matrix

\(\mathcal {N}_{t+p}, \mathcal {N}_{f2pos}\) :

Projector into the nullspace of Jt+p and Jf2pos, respectively

\(\mathcal {N}_{t+p+f2pos}\) :

Projector into the nullspace of Jt+p and Jf2pos

r a n(⋅):

Range of a matrix

d i m(⋅):

Dimension of a matrix

n u l l(⋅):

Nullspace of a matrix

{T new}:

New coordinate frame

q 0 :

Initial configuration of the arm-hand system

\(\mathbf {p}_{i_{d}}, \mathbf {p}_{i}\) :

Desired and current contact point for the i-th finger, respectively

\(\mathbf {n}_{i_{d}}, \mathbf {n}_{i}\) :

Desired and current contact normal for the i-th finger, respectively

ϕ i :

Unoriented angle between ni and \(\mathbf {n}_{i_{d}}\)

q d :

Desired configuration of the arm-hand system

O palm(α d,β d,γ d):

Desired palm orientation described using Euler angles

q t :

Thumb reaching configuration of the arm-hand system

\(\mathbf {e}_{p_{i}}\) :

Position error vector for the i-th finger

\(\mathbf {e}_{o_{i}}\) :

Orientation error vector for the i-finger

Δ q m :

Joint movement for the m-th task

n :

Number of tasks

Δ q :

Overall joint movement at the end of each iteration

\(\mathcal {N}_{m}\) :

Nullspace projector for the m-th task

𝜖 p,𝜖 o :

Preset error tolerances for the position and orientation, respectively

q t,q d :

Inverse kinematics solution of the Thumb Reaching phase and the hand alignment, respectively

References

  1. Buss, S.R., Kim, J.-S.: Selectively damped least squares for inverse kinematics. Journal of Graphics Tools 10(3), 37–49 (2005)

    Article  Google Scholar 

  2. Siciliano, B., Khatib, O.: Springer Handbook of Robotics. Springer, Berlin (2016)

    Book  Google Scholar 

  3. Calandra, R., Owens, A., Jayaraman, D., Lin, J., Yuan, W., Malik, J., Adelson, E.H., Levine, S.: More than a feeling: learning to grasp and regrasp using vision and touch. IEEE Robotics and Automation Letters 3(4), 3300–3307 (2018)

    Article  Google Scholar 

  4. Yi, L i, Saut, J.-P., Pettré, J., Sahbani, A., Multon, F.: Fast grasp planning using cord geometry. IEEE Trans. Robot. 31(6), 1393–1403 (2015)

    Article  Google Scholar 

  5. Przybylski, M., Asfour, T., Dillmann, R.: Planning grasps for robotic hands using a novel object representation based on the medial axis transform. In: 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp 1781–1788. IEEE (2011)

  6. Song, P., Zhongqi, F u, Liu, L.: Grasp planning via hand-object geometric fitting. Vis. Comput. 34(2), 257–270 (2018)

    Article  Google Scholar 

  7. Miller, A.T., Allen, P.K.: Graspit! a versatile simulator for robotic grasping. IEEE Robotics and Automation Magazine (2004)

  8. Vahrenkamp, N., Kröhnert, M., Ulbrich, S., Asfour, T., Metta, G., Dillmann, R., Sandini, G.: Simox: a robotics toolbox for simulation, motion and grasp planning. In: Intelligent Autonomous Systems 12, pp 585–594. Springer (2013)

  9. Akinola, I., Varley, J., Chen, B., Allen, P.K.: Workspace aware online grasp planning. In: 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp 2917–2924. IEEE (2018)

  10. Wampler, C.W.: Manipulator inverse kinematic solutions based on vector formulations and damped least-squares methods. IEEE Transactions on Systems, Man, and Cybernetics 16(1), 93–101 (1986)

    Article  Google Scholar 

  11. Chiaverini, S.: Singularity-robust task-priority redundancy resolution for real-time kinematic control of robot manipulators. IEEE Trans. Robot. Autom. 13(3), 398–410 (1997)

    Article  Google Scholar 

  12. Pouydebat, E., Laurin, M., Gorce, P., Bels, V.: Evolution of grasping among anthropoids. Journal of Evolutionary Biology 21(6), 1732–1743 (2008)

    Article  Google Scholar 

  13. Young, R.W.: Evolution of the human hand: the role of throwing and clubbing. J. Anat. 202(1), 165–174 (2003)

    Article  Google Scholar 

  14. Lin, Y., Yu, S.: Robot grasp planning based on demonstrated grasp strategies. The International Journal of Robotics Research 34(1), 26–42 (2015)

    Article  Google Scholar 

  15. Cotugno, G., Althoefer, K., Nanayakkara, T.: The role of the thumb: study of finger motion in grasping and reachability space in human and robotic hands. IEEE Transactions on Systems, Man, and Cybernetics: Systems 47(7), 1061–1070 (2016)

    Article  Google Scholar 

  16. Flacco, F., Luca, A.D.: A reverse priority approach to multi-task control of redundant robots. In: 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp 2421–2427. IEEE (2014)

  17. Moe, S., Teel, A.R., Antonelli, G., Pettersen, K.Y.: Stability analysis for set-based control within the singularity-robust multiple task-priority inverse kinematics framework. In: 2015 54th IEEE conference on decision and control (CDC), pp 171–178. IEEE (2015)

  18. Moe, S., Antonelli, G., Pettersen, K.Y., Schrimpf, J.: Experimental results for set-based control within the singularity-robust multiple task-priority inverse kinematics framework. In: 2015 IEEE international conference on robotics and biomimetics (ROBIO), pp 1233–1239. IEEE (2015)

  19. Liu, W., Chen, D., Steil, J.: Analytical inverse kinematics solver for anthropomorphic 7-dof redundant manipulators with human-like configuration constraints. Journal of Intelligent & Robotic Systems 86(1), 63–79 (2017)

    Article  Google Scholar 

  20. Alibeigi, M., Rabiee, S., Ahmadabadi, M.N.: Inverse kinematics based human mimicking system using skeletal tracking technology. Journal of Intelligent & Robotic Systems 85(1), 27–45 (2017)

    Article  Google Scholar 

  21. Tutsoy, O.: Cpg based rl algorithm learns to control of a humanoid robot leg. Int. J. Robot. Autom. 30(1), 178–183 (2015)

    Google Scholar 

  22. Tutsoy, O., Barkana, D.E., Colak, S.: Learning to balance an nao robot using reinforcement learning with symbolic inverse kinematic. Trans. Inst. Meas. Control. 39(11), 1735–1748 (2017)

    Article  Google Scholar 

  23. Starke, S., Hendrich, N., Krupke, D., Zhang, J.: Evolutionary multi-objective inverse kinematics on highly articulated and humanoid robots. In: 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp 6959–6966. IEEE (2017)

  24. An, S.-I., Lee, D.: Prioritized inverse kinematics with multiple task definitions. In: 2015 IEEE International Conference on Robotics and Automation (ICRA), pp 1423–1430. IEEE (2015)

  25. Lee, J., Chang, P.H., Jamisola, R.S.: Relative task prioritization for dual-arm with multiple, conflicting tasks derivation and experiments. In: 2013 IEEE International Conference on Robotics and Automation, pp 1928–1933. IEEE (2013)

  26. Hu, Y., Huang, B., Yang, G.-Z.: Task-priority redundancy resolution for co-operative control under task conflicts and joint constraints. In: 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp 2398–2405. IEEE (2015)

  27. Jarquín, G., Escande, A., Arechavaleta, G., Moulard, T., Yoshida, E., Parra-Vega, V.: Real-time smooth task transitions for hierarchical inverse kinematics. In: 2013 13th IEEE-RAS International Conference on Humanoid Robots (Humanoids), pp 528–533. IEEE (2013)

  28. Hong, S., Park, G., Lee, W., Kang, S.: Realization of the fast real-time hierarchical inverse kinematics for dexterous full body manipulation. In: 2018 18th International Conference on Control, Automation and Systems (ICCAS), pp 166–171. IEEE (2018)

  29. Hoffman, E.M., Polverini, M.P., Laurenzi, A., Tsagarakis, N.G.: A study on sparse hierarchical inverse kinematics algorithms for humanoid robots. IEEE Robotics and Automation Letters 5(1), 235–242 (2019)

    Article  Google Scholar 

  30. Brossette, S., Escande, A., Kheddar, A.: Multicontact postures computation on manifolds. IEEE Trans. Robot. 34(5), 1252–1265 (2018)

    Article  Google Scholar 

  31. Murooka, M., Okada, K., Inaba, M.: Optimization-based posture generation for whole-body contact motion by contact point search on the body surface. IEEE Robotics and Automation Letters 5(2), 2905–2912 (2020)

    Article  Google Scholar 

  32. Feix, T., Pawlik, R., Schmiedmayer, H.-B., Romero, J., Kragic, D.: A comprehensive grasp taxonomy. In: Robotics, science and systems: workshop on understanding the human hand for advancing robotic manipulation. Available: http://grasp.xief.net, vol. 2, pp 2–3 (2009)

  33. žlajpah, L.: On orientation control of functional redundant robots. In: 2017 IEEE International Conference on Robotics and Automation (ICRA), pp 2475–2482. IEEE (2017)

  34. Dietrich, A., Ott, C., Albu-Schäffer, A.: An overview of null space projections for redundant, torque-controlled robots. The International Journal of Robotics Research 34(11), 1385–1400 (2015)

    Article  Google Scholar 

  35. Sciavicco, L., Siciliano, B.: Modelling and Control of Robot Manipulators. Springer Science & Business Media (2012)

  36. Kahan, W.: How futile are mindless assessments of roundoff in floating-point computation? https://people.eecs.berkeley.edu/wkahan/Mindless.pdf (2006)

  37. Rohmer, E., Singh, Surya PN, Freese, M.: V-rep: a versatile and scalable robot simulation framework. In: 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp 1321–1326. IEEE (2013)

  38. Calli, B., Walsman, A., Singh, A., Srinivasa, S., Abbeel, P., Dollar, A.M.: Benchmarking in manipulation research: the ycb object and model set and benchmarking protocols. arXiv:1502.03143 (2015)

Download references

Funding

This research was supported in part through funds received from the Natural Sciences and Engineering Research Council of Canada, Canada Foundation for Innovation, and Ontario Centres of Excellence.

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Western University, London, ON, Canada

    Shuwei Qiu & Mehrdad R. Kermani

Authors
  1. Shuwei Qiu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mehrdad R. Kermani
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Shuwei Qiu: Conceptualization; Methodology; Formal analysis and investigation; Writing - original draft preparation. Mehrdad R. Kermani: Conceptualization; Methodology; Data analysis; Writing - review and editing; Financial support; Supervision.

Corresponding author

Correspondence to Shuwei Qiu.

Ethics declarations

Ethics approval and consent to participate

This manuscript has not be submitted to other journals for simultaneous consideration.

The submitted work is original and has not been published elsewhere in any form or language (partially or in full).

The submitted work is complete and has not be split up into several parts to increase the quantity of submissions.

The results in this paper are presented clearly, honestly, and without fabrication, falsification or inappropriate data manipulation.

No data, text, or theories by others are presented as if they were the author’s own.

The submitted work does not involve human participants and animals.

Consent for Publication

The submitted work does not involve human participants and animals.

Competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher’s Note

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

This research was supported in part through funds received from the Natural Sciences and Engineering Research Council of Canada, Canada Foundation for Innovation, and Ontario Centres of Excellence.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qiu, S., Kermani, M.R. Inverse Kinematics of High Dimensional Robotic Arm-Hand Systems for Precision Grasping. J Intell Robot Syst 101, 70 (2021). https://doi.org/10.1007/s10846-021-01349-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10846-021-01349-7

Keywords

Search

Navigation