Abstract
As described in Chaps. 2–5, neuroscientific studies showed that the control of the human hand is mainly realized in a synergistic way. Recently, taking inspiration from this observation, with the aim of facing the complications consequent to the high number of degrees of freedom, similar approaches have been used for the control of robotic hands. As Chap. 12 describes SynGrasp, a useful technical tool for grasp analysis of synergy-inspired hands, in this chapter recently developed analysis tools for studying robotic hands equipped with soft synergy underactuation (see Chap. 8) are exhaustively described under a theoretical point of view. After a review of the quasi-static model of the system, the Fundamental Grasp Matrix (FGM) and its canonical form (cFGM) are presented, from which it is possible to extract relevant information as, for example, the subspaces of the controllable internal forces, of the controllable object displacements and the grasp compliance. The definitions of some relevant types of manipulation tasks (e.g. the pure squeeze, realized maintaining the object configuration fixed but changing contact forces, or the kinematic grasp displacements, in which the grasped object can be moved without modifying contact forces) are provided in terms of nullity or non-nullity of the variables describing the system. The feasibility of such predefined tasks can be verified thanks to a decomposition method, based on the search of the row reduced echelon form (RREF) of suitable portions of the solution space. Moreover, a geometric interpretation of the FGM and the possibility to extend the above mentioned methods to the study of robotic hands with different types of underactuation are discussed. Finally, numerical results are presented for a power grasp example, the analysis of which is initially performed for the case of fully-actuated hand, and later verifying, after the introduction of a synergistic underactuation, which capacities of the system are lost, and which other are still present.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The dimension of the contact force vector c is related to the number of contact points and to the local characteristics of the contacts. More details about this will be provided in Sect. 13.2.3.
- 2.
Strictly speaking, the vector \(w\in \mathbb {R}^{\sharp w}\), in the present dissertation, represents a parametrization of an external wrench, abbreviated in the text simply as external wrench. Similarly, the object configuration is described by a parametrization vector \(u\in \mathbb {R}^{\sharp w}\). As a consequence, the object velocity \(\dot{u}\) in (13.3) is a parametrization of the object twist, and, for this reason, can be expressed as the time derivative of some physical variables. As an example, in a 3D case, a complete parametrization can be obtained considering a \(6-\)DoF virtual kinematic chain describing the configuration of the object frame with respect to a fixed one. In this case, the vectors \(\dot{u}\) and w will contain, respectively, the joint velocities and the joint torques of the virtual kinematic chain.
- 3.
More precisely, the vectors \(v_o\) and \(v_h\) contain the terms of the contact frame twists violating the (rigid) contact constraints between the hand and the object.
- 4.
Exceptions are analytically possible but they refer to pathological situations of poor practical interest.
- 5.
Other choices are possible, as for example considering to know the object displacement \(\delta u\), instead of the external wrench \(\delta w\), or the actuation force variation \(\delta \eta \), instead of the synergistic displacement variable \(\delta \sigma _r\). Many results of our analysis can be easily adapted to the above mentioned situations as well.
- 6.
This is a typical situation with the most popular computational platforms, e.g.: \(\texttt {rref}(X)\) in MATLAB and \(\texttt {RowReduce(X)}\) in Mathematica.
- 7.
More precisely, the equations related to the elasticity do not describe an equilibrium law, and, for this reason, we should, more properly, talk about a manifold describing the kineto-static behavior of the whole system. For the sake of compactness, this definition will be left implicit in the rest of the discussion.
References
Jacobsen S, Wood J, Knutt D, Biggers K (1984) The Utah/MIT dextrous hand: work in progress. Int J Robot Res 3(4):21–50
Lovchik C, Diftler M (1999) The robonaut hand: a dexterous robot hand for space. In: Proceedings of 1999 IEEE International conference on robotics and automation, vol 2. pp 907–912
Shadow Robot Company Ltd. (2009) Shadow hand. http://shadowhand.com
Grebenstein M, Chalon M, Friedl W, Haddadin S, Wimbck T, Hirzinger G, Siegwart R (2012) The hand of the dlr hand ARM system: designed for interaction. Int J Robot Res 31(13):1531–1555
Fish J, Soechting JF (1992) Synergistic finger movements in a skilled motor task. Exp Brain Res 91(2):327–334
Angelaki DE, Soechting JF (1993) Non-uniform temporal scaling of hand and finger kinematics during typing. Exp Brain Res 92(2):319–329
Soechting JF, Flanders M (1997) Flexibility and repeatability of finger movements during typing: analysis of multiple degrees of freedoms. J Comput Neurosci 4(1):29–46
Santello M, Flanders M, Soechting J (1998) Postural hand synergies for tool use. J Neurosci 18:10105–10115
Latash, ML, Krishnamoorthy V, Scholz JP, Zatsiorsky VM (2005) Postural synergies and their development. Neural Plast 12:119–130, discussion 263–272
Thakur PH, Bastian AJ, Hsiao SS (2008) Multidigit movement synergies of the human hand in an unconstrained haptic exploration task. J Neurosci 28:1271–1281
Castellini C, van der Smagt P (2013) Evidence of muscle synergies during human grasping. Biol Cybern 107:233–245
Ciocarlie M, Goldfeder C, Allen P (2007) Dexterous grasping via eigengrasps: a low-dimensional approach to a high-complexity problem. In: Proceedings of the robotics: science and systems 2007 workshop-sensing and adapting to the real world. Electronically Published
Brown CY, Asada HH (2007) Inter-finger coordination and postural synergies in robot hands via mechanical implementation of principal components analysis. In: 2007 IEEE/RSJ international conference on intelligent robots and system, pp 2877–2882
Gabiccini M, Bicchi A, Prattichizzo D, Malvezzi M (2011) On the role of hand synergies in the optimal choice of grasping forces. Auton Robots [special issue on RSS2010] 31(2–3):235–252
Prattichizzo D, Malvezzi M, Bicchi A (2010) On motion and force controllability of grasping hands with postural synergies. In: Robotics: science and systems, vol VI. The MIT Press, Zaragoza, pp 49–56
Gabiccini M, Farnioli E, Bicchi A (2012) Grasp and manipulation analysis for synergistic underactuated hands under general loading conditions. In: International conference of robotics and automation—ICRA 2012, Saint Paul, MN, USA, pp 2836–2842, 14–18 May 2012
Gabiccini M, Farnioli E, Bicchi A (2013) Grasp analysis tools for synergistic underactuated robotic hands. Int J Robot Res 32:1553–1576
Farnioli E, Gabiccini M, Bonilla M, Bicchi A (2013) Grasp compliance regulation in synergistically controlled robotic hands with VSA. In: IEEE/RSJ international conference on intelligent robots and systems, IROS 2013, Tokyo, Japan, pp 3015–3022. 3–7 Nov 2013
Meyer CD (2000) Matrix analysis and applied linear algebra. Society for Industrial and Applied Mathematics, Philadelphia
Bicchi A, Melchiorri C, Balluchi D (1995) On the mobility and manipulability of general multiple limb robotic systems. IEEE Trans Robot Autom 11:215–228
Bonilla M, Farnioli E, Pallottino L, Bicchi A (2015) Sample-based motion planning for soft robot manipulators under task constraints. In: Accepted to international conference of robotics and automation—ICRA 2015
Birglen L, Laliberté T, Gosselin C (2008) Underactuated robotic hands. Springer tracts in advanced robotics, vol 40. Springer, Berlin
Catalano MG, Grioli G, Serio A, Farnioli E, Piazza C, Bicchi A (2012) Adaptive synergies for a humanoid robot hand. In: IEEE-RAS international conference on humanoid robots, Osaka, Japan
Acknowledgments
This work was supported by the European Commission under the CP-IP grant no. 248587 “THE Hand Embodied”, within the FP7-2007-2013 program “Cognitive Systems and Robotics”, the ERC Advanced Grant no. 291166 “SoftHands: A Theory of Soft Synergies for a New Generation of Artificial Hands”, and by the grant no. 600918 “PaCMan” - Probabilistic and Compositional Representations of Objects for Robotic Manipulation - within the FP7-ICT-2011-9 program “Cognitive Systems”.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Farnioli, E., Gabiccini, M., Bicchi, A. (2016). Quasi-Static Analysis of Synergistically Underactuated Robotic Hands in Grasping and Manipulation Tasks. In: Bianchi, M., Moscatelli, A. (eds) Human and Robot Hands. Springer Series on Touch and Haptic Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-26706-7_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-26706-7_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26705-0
Online ISBN: 978-3-319-26706-7
eBook Packages: Computer ScienceComputer Science (R0)