This paper develops a theoretical framework for grasping objects using customized effectors that have curved contact surfaces, and presents its application to the problem of robotic whole-arm grasping. We present a collection of immobilizing grasps and cages that can effectively restrain the mobility of a wide range of object shapes including polyhedra. Each of the grasps or cages is formed by at most three effectors with appropriate contact surfaces in contrast to customary point fingertips. We also discuss the morphology of the curved contact surfaces that can realize the grasps and cages; the surfaces can simply be planar, cylindrical, or spherical. Stable grasps are obtained by simple motion planning and control. Our theory is based on a conservative assumption that all contacts are frictionless, rigid, unilateral. Finally, we present a robotic system, comprised of a software suite and a modular reconfigurable manipulator outfitted with exchangeable end-effectors and arm links, demonstrating the theory and our approach to whole-arm grasping.
AichholzerODemaineEDEricksonJHurtadoFOvermarsMSossMA. (2001) Reconfiguring convex polygons. Computational Geometry: Theory and Applications20(1–2): 85–95.
2.
AllenTBurdickJRimonE (2012) Two-fingered caging of polygons via contact-space graph search. In: 2012 IEEE international conference on robotics and automation (ICRA‘12), St. Paul, MN, USA, 14–18 May 2012, pp. 4183–4189. Piscataway: IEEE Press.
3.
BermanSLindseyQSakarMSKumarVPrattSC (2011) Experimental study and modeling of group retrieval in ants as an approach to collective transport in swarm robotic systems. Proceedings of the IEEE99(9): 1470–1481.
4.
BernardMKondakKMazaIOlleroA (2011) Autonomous transportation and deployment with aerial robots for search and rescue missions. Journal of Field Robotics28(6): 914–931.
5.
BicchiAKumarV (2000) Robotic grasping and contact: A review. In: 2000 IEEE international conference on robotics and automation (ICRA‘00), San Francisco, USA, 24–28 April 2000. Piscataway: IEEE Press.
6.
BorstCFischerMHirzingerG (1999) A fast and robust grasp planner for arbitrary 3D objects. In: 1999 IEEE international conference on robotics and automation (ICRA‘99), vol. 3, Detroit, USA, 10–15 May 1999, pp. 1890–1896Piscataway: IEEE Press.
7.
BosePBremnerDToussaintGT (1996) All convex polyhedra can be clamped with parallel jaw grippers. Computational Geometry: Theory and Applications6(5): 291–302.
8.
BowerT (1970) Demonstration of intention in the reaching behaviour of neonate humans. Nature228(5272): 679–681.
9.
BowersDLLumiaR (2003) Manipulation of unmodeled objects using intelligent grasping schemes. IEEE Transactions on Fuzzy Systems11(3): 320–330.
10.
BrostRCGoldbergKY (1996) A complete algorithm for designing planar fixtures using modular components. IEEE Transactions on robotics and Automation12(1): 31–46.
11.
BrownKQ (1979) Geometric transforms for fast geometric algorithms. PhD Thesis, Carnegie-Mellon University Pittsburgh, USA.
12.
CappelleriDJFatovicMFuZ (2011a) Caging grasps for micromanipulation & microassembly. In: IEEE/RSJ international conference on intelligent robots and systems (IROS‘11), San Francisco, USA, 25–30 September 2011, pp. 925–930. Piscataway: IEEE Press.
13.
CappelleriDJFatovicMShahU (2011b) Caging micromanipulation for automated microassembly. In: 2011 IEEE international conference on robotics and automation (ICRA‘11), Shanghai, China, 9–13 May 2011, pp. 3145–3150. Piscataway: IEEE Press.
14.
ChengPFinkJKumarVPangJS (2009) Cooperative towing with multiple robots. Journal of Mechanisms and Robotics1(1): 011008.
CutkoskyMRKaoI (1989) Computing and controlling compliance of a robotic hand. IEEE Transactions on Robotics and Automation5(2): 151–165.
17.
CzyzowiczJStojmenovicIUrrutiaJ (1991) Immobilizing a polytope. In: DehneFSackJ-RSantoroN (eds) Algorithms and Data Structures. Berlin Heidelberg: Springer, pp. 214–227.
18.
DaveyJSastraJPiccoliMYimM (2012) Modlock: A manual connector for reconfigurable modular robots. In: IEEE/RSJ international conference on intelligent robots and systems (IROS‘12), Vilamoura, Portugal, 7–12 October 2012, pp. 3217–3222. Piscataway: IEEE Press.
19.
DavidsonCBlakeA (1998a) Caging planar objects with a three-finger one-parameter gripper. In: 1998 IEEE international conference on robotics and automation (ICRA‘98), vol. 3, Leuven, Belgium, 16–21 May 1998, pp. 2722–2727. Piscataway: IEEE Press.
20.
DavidsonCBlakeA (1998b) Error-tolerant visual planning of planar grasp. In: 6th international conference on computer vision, Bombay, India, 4–7 January 1998, pp. 911–916. Piscataway: IEEE Press.
21.
de BergMVan KreveldMOvermarsMSchwarzkopfOC (2000) Computational Geometry. Berlin Heidelberg: Springer.
22.
DiankovRSrinivasaSSFergusonDKuffnerJ (2008) Manipulation planning with caging grasps. In: 8th IEEE-RAS international conference on humanoid robots, Daejeon, Korea, 1–3 December 2008, pp. 285–292. Piscataway: IEEE Press.
23.
DogarMSrinivasaS (2011) A framework for push-grasping in clutter. Robotics: science and systems VII, Los Angeles, USA, pp. 65–72. Cambridge, MA: MIT Press.
24.
DollarAMHoweRD (2010) The highly adaptive SDM hand: Design and performance evaluation. International Journal of Robotics Research29(5): 585–597.
25.
FerreELaumondJP (2004) An iterative diffusion algorithm for part disassembly. In: 2004 IEEE international conference on robotics and automation (ICRA‘04), vol. 3, New Orleans, USA, 26 April –1 May 2004, pp. 3149–3154. Piscataway: IEEE Press.
26.
FinkJHsiehMAKumarV (2008) Multi-robot manipulation via caging in environments with obstacles. In: 2008 IEEE international conference on robotics and automation (ICRA‘08), Pasadena, USA, 19–23 May 2008, pp. 1471–1476. Piscataway: IEEE Press.
27.
FinkJMichaelNKimSKumarV (2011) Planning and control for cooperative manipulation and transportation with aerial robots. International Journal of Robotics Research30(3): 324–334.
28.
FruchardA (2012) Small holding circles. Geometriae Dedicata157(1): 397–405.
29.
GallowayKCClarkJEYimMKoditschekDE (2011) Experimental investigations into the role of passive variable compliant legs for dynamic robotic locomotion. In: 2011 IEEE international conference on robotics and automation (ICRA‘11), Shanghai, China, 9–13 May 2011, pp. 1243–1249. Piscataway: IEEE Press.
30.
GopalakrishnanKGGoldbergK (2002) Gripping parts at concave vertices. In: 2002 IEEE international conference on robotics and automation (ICRA‘02), vol. 2, Washington DC, USA, 11–15 May 2002, pp. 1590–1596. Piscataway: IEEE Press.
31.
HanafusaHAsadaH. (1977) Stable prehension by a robot hand with elastic fingers. In: 7th international symposium on industrial robots, Tokyo, Japan, pp. 361–368.
32.
HowardWSKumarV (1996) On the stability of grasped objects. IEEE Transactions on Robotics and Automation12(6): 904–917.
33.
HsiaoKLozano-PerezT (2006) Imitation learning of whole-body grasps. IEEE/RSJ international conference on intelligent robots and systems (IROS‘06), Beijing, China, 9—15 October 2006, pp. 5657–5662. Piscataway: IEEE Press.
34.
HudsonNHowardTMaJJainABajracharyaMMyintS.(2012) End-to-end dexterous manipulation with deliberate interactive estimation. In: 2012 IEEE international conference on robotics and automation (ICRA‘12), St. Paul, USA, 14–18 May 2012, pp. 2371–2378. Piscataway: IEEE Press.
JacobsenSIversenEKnuttiDJohnsonRBiggersK (1986) Design of the Utah/MIT dextrous hand. In: 1986 IEEE international conference on robotics and automation (ICRA‘86), vol. 3, San Francisco, USA, 7–10 April 1986, pp. 1520–1532. Piscataway: IEEE Press.
37.
JohnsonAMKoditschekDE (2013) Toward a vocabulary of legged leaping. In: 2013 IEEE international conference on robotics and automation (ICRA‘13), Karlsruhe, Germany, 6–10 May 2013, pp. 2568–2575. Piscataway: IEEE Press.
38.
KosugeKHirataYAsamaHKaetsuHKawabataK (1999) Motion control of multiple autonomous mobile robots handling a large object in coordination. In: 1999 IEEE international conference on robotics and automation (ICRA‘99), vol. 4, Detroit, USA, 10–15 May 1999, pp. 2666–2673. Piscataway: IEEE Press.
39.
KragtenGBarilMGosselinCHerderJ (2011) Stable precision grasps by underactuated grippers. IEEE Transactions on Robotics27(6): 1056–1066.
40.
KubeCRBonabeauE (2000) Cooperative transport by ants and robots. Robotics and Autonomous Systems30(1): 85–101.
41.
LakshminarayanaK (1978) Mechanics of Form Closure. American Society of Mechanical Engineers.
42.
LaValleS (2006) Planning Algorithms. Cambridge: Cambridge University Press.
43.
LeDTCortésJSiméonT (2009) A path planning approach to (dis)assembly sequencing. In: 2009 IEEE international conference on automation science and engineering (CASE‘09), Bangalore, India, 22–25 August 2009, pp. 286–291. Piscataway: IEEE Press.
44.
MaeharaH (2011) On the diameter of a circle to hold a cube. In: AkiyamaJBoJKanoMTanX (eds) Computational Geometry, Graphs and Applications. Berlin Heidelberg: Springer, pp. 147–153.
45.
MarkenscoffXNiLPapadimitriouC (1990) The geometry of grasping. International Journal of Robotics Research9(1): 61–74.
46.
MasonMT (2001) Mechanics of Robotic Manipulation. Cambridge: MIT Press.
47.
MasonMTRodriguezASrinivasaSSVazquezAS (2012) Autonomous manipulation with a general-purpose simple hand. International Journal of Robotics Research31(5): 688–703.
48.
MasonMTSalisburyJK (1985) Robot Hands and the Mechanics of Manipulation. Cambridge: MIT Press.
49.
McDowellMA (2008) Anthropometric reference data for children and adults: United States, 2003-2006. Report for the US Department of Health and Human Services.
50.
MillerATKnoopSChristensenHIAllenPK (2003) Automatic grasp planning using shape primitives. In: 2003 IEEE international conference on robotics and automation (ICRA‘03), vol. 2, Taipei, Taiwan, 14–19 September 2003, pp. 1824–1829. Piscataway: IEEE Press.
51.
MontemayorGWenJT (2005) Decentralized collaborative load transport by multiple robots. In: 2005 IEEE international conference on robotics and automation (ICRA‘05), Barcelona, Spain, 18–22 April 2005, pp. 372–377. Piscataway: IEEE Press.
52.
MoralesASanzPJDel PobilAP (2002) Vision-based computation of three-finger grasps on unknown planar objects. In: IEEE/RSJ international conference on intelligent robots and systems (IROS‘02), vol. 2, Lausanne, Switzerland, 30 September–4 October 2002, pp. 1711–1716. Piscataway: IEEE Press.
53.
MurrayRM (1996) Trajectory generation for a towed cable system using differential flatness. In: IFAC world congress, San Francisco, USA, 30 June–5 July 1996, pp. 395–400.
54.
MurrayRMLiZSastrySS (1994) A Mathematical Introduction to Robotic Manipulation. Boca Raton: CRC Press.
55.
NapierJR (1956) The prehensile movements of the human hand. Journal of Bone and Joint Surgery38B(4): 902–913.
56.
Navarro-AlarconDLiuYhRomeroJGLiP (2014) On the visual deformation servoing of compliant objects: Uncalibrated control methods and experiments. International Journal of Robotics Research. Epub ahead of print 12 June 2014. DOI: 10.1177/0278364914529355.
57.
NguyenVD (1988) Constructing force-closure grasps. International Journal of Robotics Research7(3): 3–16.
58.
NguyenVD (1989) Constructing stable grasps. International Journal of Robotics Research8(1): 26–37.
59.
ParkMYimM (2009) Distributed control and communication fault tolerance for the CKbot. In: ASME/IFToMM international conference on reconfigurable mechanisms and robots (ReMAR‘09), London, UK, 22–24 June 2009, pp. 682–688. Piscataway: IEEE Press.
60.
PereiraGACamposMFKumarV (2004) Decentralized algorithms for multi-robot manipulation via caging. International Journal of Robotics Research23(7–8): 783–795.
61.
PeshkinMSandersonA (1986) Reachable grasps on a polygon: The convex rope algorithm. IEEE Transactions on Robotics and Automation2(1): 53–58.
62.
PollardNS (2004) Closure and quality equivalence for efficient synthesis of grasps from examples. International Journal of Robotics Research23(6): 595–613.
63.
PonceJ (1996) On planning immobilizing fixtures for three-dimensional polyhedral parts. In: 1996 IEEE international conference on robotics and automation (ICRA‘96), Minneapolis, USA, 22–28 April 1996, pp. 509–514. Piscataway: IEEE Press.
64.
PonceJSullivanSSudsangABoissonnatJDMerletJP (1997) On computing four-finger equilibrium and force-closure grasps of polyhedral objects. International Journal of Robotics Research16(1): 11–35.
65.
RimonEBlakeA (1999) Caging planar bodies by one-parameter two-fingered gripping systems. International Journal of Robotics Research18(3): 299–318.
66.
RimonEBurdickJW (1998a) Mobility of bodies in contact. I. A 2nd-order mobility index for multiple-finger grasps. IEEE Transactions on Robotics and Automation14(5): 696–708.
67.
RimonEBurdickJW (1998b) Mobility of bodies in contact. II. How forces are generated by curvature effects. IEEE Transactions on Robotics and Automation14(5): 709–717.
68.
RodriguezAMasonMT (2009) Two finger caging: Squeezing and stretching. In: ChirikjianGChosetHMoralesMMurpheyT (eds) Algorithmic Foundation of Robotics VIII. Berlin Heidelberg: Springer, pp. 119–133.
69.
RodriguezAMasonMFerryS (2012) From caging to grasping. International Journal of Robotics Research31(7): 886–900.
70.
SaranliUBuehlerMKoditschekDE (2001) RHex: A simple and highly mobile hexapod robot. International Journal of Robotics Research20(7): 616–631.
71.
SaxenaADriemeyerJNgAY (2008) Robotic grasping of novel objects using vision. International Journal of Robotics Research27(2): 157–173.
72.
SeoJYimMKumarV (2013) Restraining objects with curved effectors and its application to whole-arm grasping. In: 16th international symposium on robotics research (ISRR‘13), Singapore, 16–19 December 2013.
73.
SreenathKKumarV (2013) Dynamics, control and planning for cooperative manipulation of payloads suspended by cables from multiple quadrotor robots. In: Robotics: science and systems, Berlin, Germany, 24–28June2013.
74.
SugarTKumarV (1999) Multiple cooperating mobile manipulators. In: 1999 IEEE international conference on robotics and automation (ICRA‘99), vol. 2, Detroit, USA, 10–15 May 1999, pp. 1538–1543. Piscataway: IEEE Press.
75.
SundaramSRemmlerIAmatoNM (2001) Disassembly sequencing using a motion planning approach. In: 2001 IEEE international conference on robotics and automation (ICRA‘01), vol. 2, Seoul, Korea, 21–26 May 2001, pp. 1475–1480. Piscataway: IEEE Press.
76.
TrinkleJC (1992) On the stability and instantaneous velocity of grasped frictionless objects. IEEE Transactions on Robotics and Automation8(5): 560–572.
77.
TrinkleJCAbelJMPaulRP (1988) An investigation of frictionless enveloping grasping in the plane. International Journal of Robotics Research7(3): 33–51.
78.
UlrichNPaulRBajcsyR (1988) A medium-complexity compliant end effector. In: 1988 IEEE international conference on robotics and automation (ICRA‘88), Philadelphia, USA, 24–29 April 1988, pp. 434–436. Piscataway: IEEE Press.
79.
VahediMvan der StappenAF (2008a) Caging polygons with two and three fingers. International Journal of Robotics Research27(11–12): 1308–1324.
80.
VahediMvan der StappenAF (2008b) Caging convex polygons with three fingers. In: IEEE/RSJ international conference on intelligent robots and systems (IROS‘08), Nice, France, 22–26 September 2008, pp. 1777–1783. Piscataway: IEEE Press.
81.
VahediMvan der StappenAF (2008c) Towards output-sensitive computation of two-finger caging grasps. In: 2008 IEEE international conference on automation science and engineering (CASE‘08), Arlington, USA, 23–26 August 2008, pp. 73–78. Piscataway: IEEE Press.
82.
VahediMvan der StappenAF (2009) On the complexity of the set of three-finger caging grasps of convex polygons. In: Robotics: science and systems, Seattle, USA, 28June–1July2009.
83.
van der StappenAFWentinkCOvermarsMH (1999) Computing form-closure configurations. In: 1999 IEEE international conference on robotics and automation (ICRA‘99), vol. 3, Detroit, USA, 10–15 May 1999, pp. 1837–1842. Piscataway: IEEE Press.
84.
WanWFukuiRShimosakaMSatoTKuniyoshiY (2012) On the caging region of a third finger with object boundary clouds and two given contact positions. In: 2012 IEEE international conference on robotics and automation (ICRA‘12), St. Paul, USA, 14–18 May 2012, pp. 4154–4161. Piscataway: IEEE Press.
85.
YokoiRKobayashiTMaedaY (2009) 2D Caging manipulation by robots and walls. In: IEEE international symposium on assembly and manufacturing (ISAM‘09), Seoul, Korea, 17–20 November 2009, pp. 16–21. Piscataway: IEEE Press.
86.
ZamfirescuT (1995) How to hold a convex body?Geometriae Dedicata54(3): 313–316.
