Skip to main content
SpringerLink
Log in

Contact Modeling and Manipulation

  • Reference work entry
Springer Handbook of Robotics

Abstract

Robotic manipulators use contact forces to grasp and manipulate objects in their environments. Fixtures rely on contacts to immobilize workpieces. Mobile robots and humanoids use wheels or feet to generate the contact forces that allow them to locomote. Modeling of the contact interface, therefore, is fundamental to analysis, design, planning, and control of many robotic tasks.

This chapter presents an overview of the modeling of contact interfaces, with a particular focus on their use in manipulation tasks, including graspless or nonprehensile manipulation modes such as pushing. Analysis and design of grasps and fixtures also depends on contact modeling, and these are discussed in more detail in Chap. 28. Sections 27.2–27.5 focus on rigid-body models of contact. Section 27.2 describes the kinematic constraints caused by contact, and Sect. 27.3 describes the contact forces that may arise with Coulomb friction. Section 27.4 provides examples of analysis of multicontact manipulation tasks with rigid bodies and Coulomb friction. Section 27.5 extends the analysis to manipulation by pushing. Section 27.6 introduces modeling of contact interfaces, kinematic duality, and pressure distribution. Section 27.7 describes the concept of the friction limit surface and illustrates it with an example demonstrating the construction of a limit surface for a soft contact. Finally, Sect. 27.8 discusses how these more accurate models can be used in fixture analysis and design.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 309.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

CCW:

counterclockwise

COR:

center of rotation

CP:

cerebral palsy

CP:

closest point

CP:

complementarity problem

CW:

clockwise

DOF:

degree of freedom

LCSP:

linear constraint satisfaction program

References

  1. A. Bicchi: On the problem of decomposing grasp and manipulation forces in multiple whole-limb manipulation, Int. J. Robot. Auton. Syst. 13, 127–147 (1994)

    Article  Google Scholar 

  2. K. Harada, M. Kaneko, T. Tsuji: Rolling Based Manipulation for Multiple Objects, Proceedings of IEEE Int. Conf. on Robotics and Automation (San Francisco 2000) pp. 3888–3895

    Google Scholar 

  3. M.R. Cutkosky, I. Kao: Computing and Controlling The Compliance of a Robotic Hand, IEEE Trans. Robot. Autom., 5(2), 151–165 (1989)

    Article  Google Scholar 

  4. M.R. Cutkosky, S.-H. Lee: Fixture Planning with Friction for Concurrent Product/Process Design, NSF Process Planning (1989)

    Google Scholar 

  5. S.-H. Lee, M. Cutkosky: Fixture planning with friction, ASME J. Eng. Ind. 113(3), 320–327 (1991)

    Google Scholar 

  6. Q. Lin, J.W. Burdick, E. Rimon: A stiffness-based quality measure for compliant grasps and fixtures, IEEE Trans. Robot. Autom. 16(6), 675–688 (2000), ,

    Article  Google Scholar 

  7. P. Lötstedt: Coulomb friction in two-dimensional rigid body systems, Z. Angew. Math. Mech. 61, 605–615 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  8. P. Lötstedt: Mechanical systems of rigid bodies subject to unilateral constraints, SIAM J. Appl. Math. 42(2), 281–296 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  9. P.E. Dupont: The effect of Coulomb friction on the existence and uniqueness of the forward dynamics problem, International Conference on Robotics and Automation (Nice 1992) pp. 1442–1447

    Google Scholar 

  10. M.A. Erdmann: On a representation of friction in configuration space, Int. J. Robot. Res. 13(3), 240–271 (1994)

    Article  MathSciNet  Google Scholar 

  11. K.M. Lynch, M.T. Mason: Pulling by pushing, slip with infinite friction, and perfectly rough surfaces, Int. J. Robot. Res. 14(2), 174–183 (1995)

    Article  Google Scholar 

  12. J.S. Pang, J.C. Trinkle: Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with Coulomb friction, Math. Prog. 73, 199–226 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  13. J.C. Trinkle, J.S. Pang, S. Sudarsky, G. Lo: On dynamic multi-rigid-body contact problems with Coulomb friction, Z. Angew. Math. Mech. 77(4), 267–279 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  14. M.T. Mason: Mechanics of Robotic Manipulation (MIT Press, Cambrige 2001)

    Google Scholar 

  15. Y.-T. Wang, V. Kumar, J. Abel: Dynamics of Rigid Bodies Undergoing Multiple Frictional Contacts, Proceedings of IEEE Int. Conf. on Robotics and Automation (Nice, France 1992) pp. 2764–2769

    Chapter  Google Scholar 

  16. T.H. Speeter: Three-dimensional finite element analysis of elastic continua for tactile sensing, Int. J. Robot. Res. 11(1), 1–19 (1992)

    Article  Google Scholar 

  17. K. Dandekar, A.K. Srinivasan: A 3-Dimensional Finite Element Model of the Monkey Fingertip for Predicting Responses of Slowly Adapting Mechanoreceptors, ASME Bioengineering Conference, Vol. 29 (1995) pp. 257–258

    Google Scholar 

  18. N. Xydas, M. Bhagavat, I. Kao: Study of Soft-Finger Contact Mechanics Using Finite Element Analysis and Experiments, Proc. IEEE Int. Conf. on Robotics and Automation, ICRA (San Francisco, California 2000)

    Google Scholar 

  19. K. Komvopoulos, D.-H. Choi: Elastic finite element analysis of multi-asperity contacts, J. Tribol. 114, 823–831 (1992)

    Article  Google Scholar 

  20. L.T. Tenek, J. Argyris: Finite Element Analysis for Composite Structures (Kluwer Academic, Bosten 1998)

    MATH  Google Scholar 

  21. Y. Nakamura: Contact Stability Measure and Optimal Finger Force Control of Multi-Fingered Robot Hands, Crossing Bridges: Advances in Flexible Automation and Robotics - The Proceedings of the USA-Japan Symposium on Flexible Automation (ASME, 1988) pp. 523–528

    Google Scholar 

  22. Y.C. Park, G.P. Starr: Optimal Grasping Using a Multifingered Robot Hand, Proceedings of the 1990 IEEE International Conference on Robotics and Automation (IEEE, Cincinnati, Ohio 1990) pp. 689–694

    Google Scholar 

  23. E. Rimon, J. Burdick: On force and form closure for multiple finger grasps, IEEE International Conference on Robotics and Automation (1996) pp. 1795–1800

    Google Scholar 

  24. E. Rimon, J.W. Burdick: New bounds on the number of frictionless fingers required to immobilize planar objects, J. Robot. Sys. 12(6), 433–451 (1995)

    Article  MATH  Google Scholar 

  25. E. Rimon, J.W. Burdick: Mobility of bodies in contact—part I: A 2nd-order mobility index for multiple-finger grasps, IEEE Trans. Robot. Autom. 14(5), 696–708 (1998)

    Article  Google Scholar 

  26. D.J. Montana: The kinematics of contact and grasp, Int. J. Robot. Res. 7(3), 17–32 (1988)

    Article  Google Scholar 

  27. C.S. Cai, B. Roth: On the planar motion of rigid bodies with point contact, Mechanism Machine Theory 21(6), 453–466 (1986)

    Article  Google Scholar 

  28. C. Cai, B. Roth: On the spatial motion of a rigid body with point contact, IEEE International Conference on Robotics and Automation (1987) pp. 686–695

    Google Scholar 

  29. A.B.A. Cole, J.E. Hauser, S.S. Sastry: Kinematics and control of multifingered hands with rolling contact, IEEE Trans. Autom. Control 34(4), 398–404 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  30. R.M. Murray, Z. Li, S.S. Sastry: A Mathematical Introduction to Robotic Manipulation (CRC, Boca Raton 1994)

    MATH  Google Scholar 

  31. F. Reuleaux: The Kinematics of Machinery (Dover, New York 1963), , reprint of MacMillan, 1876

    Google Scholar 

  32. C.A. Coulomb: Theorie des machines simples en ayant egard au frottement de leurs parties et a la roideur des cordages. In: Memoires des mathematique et de physique presentes a lʼAcademie des Sciences (Bachelier, Paris 1821)

    Google Scholar 

  33. Y. Maeda, T. Arai: Planning of graspless manipulation by a multifingered robot hand, Adv. Robot. 19(5), 501–521 (2005)

    Article  Google Scholar 

  34. M.T. Mason: Two graphical methods for planar contact problems, IEEE/RSJ International Conference on Intelligent Robots and Systems (Osaka, Japan November 1991) pp. 443–448

    Google Scholar 

  35. R. Howe, I. Kao, M. Cutkosky: Sliding of Robot Fingers Under Combined Torsion and Shear Loading, Proceedings of 1988 IEEE International Conference on Robotics and Automation, Vol. 1 (Philadelphia, Pennsylvania 1988) pp. 103–105

    Chapter  Google Scholar 

  36. I. Kao, M.R. Cutkosky: Dextrous manipulation with compliance and sliding, Int. J. Robot. Res. 11(1), 20–40 (1992)

    Article  Google Scholar 

  37. R.D. Howe, M.R. Cutkosky: Practical force-motion models for sliding manipulation, Int. J. Robot. Res. 15(6), 555–572 (1996)

    Article  Google Scholar 

  38. N. Xydas, I. Kao: Modeling of contact mechanics and friction limit surface for soft fingers with experimental results, Int. J. Robot. Res. 18(9), 941–950 (1999)

    Article  Google Scholar 

  39. I. Kao, F. Yang: Stiffness and contact mechanics for soft fingers in grasping and manipulation, IEEE Trans. Robot. Autom. 20(1), 132–135 (2004), ,

    Article  Google Scholar 

  40. J. Jameson, L. Leifer: Quasi-Static Analysis: A Method for Predicting Grasp Stability, Proceedings of 1986 IEEE International Conference on Robotics and Automation (1986) pp. 876–883

    Google Scholar 

  41. S. Goyal, A. Ruina, J. Papadopoulos: Planar sliding with dry friction: Part 2. Dynamics of motion, Wear 143, 331–352 (1991)

    Article  Google Scholar 

  42. P. Tiezzi, I. Kao: Modeling of viscoelastic contacts and evolution of limit surface for robotic contact interface, IEEE Trans. Robot. 23(2), 206–217 (2007)

    Article  Google Scholar 

  43. M. Anitescu, F. Potra: Formulating multi-rigid-body contact problems with friction as solvable linear complementarity problems, ASME J. Nonlin. Dyn. 14, 231–247 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  44. S. Berard, J. Trinkle, B. Nguyen, B. Roghani, J. Fink, V. Kumar: daVinci code: A multi-model simulation and analysis tool for multi-body systems, IEEE International Conference on Robotics and Automation (2007)

    Google Scholar 

  45. P. Song, J.-S. Pang, V. Kumar: A semi-implicit time-stepping model for frictional compliant contact problems, Int. J. Numer. Methods Eng. 60(13), 2231–2261 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  46. D. Stewart, J. Trinkle: An implicit time-stepping scheme for rigid body dynamics with inelastic collisions and Coulomb friction, Int. J. Numer. Methods Eng. 39, 2673–2691 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  47. R.W. Cottle, J.-S. Pang, R.E. Stone: The Linear Complementarity Problem (Academic, New York 1992)

    MATH  Google Scholar 

  48. S.N. Simunovic: Force information in assembly processes, International Symposium on Industrial Robots (1975)

    Google Scholar 

  49. V.-D. Nguyen: Constructing force-closure grasps, Int. J. Robot. Res. 7(3), 3–16 (1988), ,

    Article  Google Scholar 

  50. K.M. Lynch: Toppling manipulation, IEEE International Conference on Robotics and Automation (1999)

    Google Scholar 

  51. M.T. Zhang, K. Goldberg, G. Smith, R.-P. Berretty, M. Overmars: Pin design for part feeding, Robotica 19(6), 695–702 (2001)

    Google Scholar 

  52. D. Reznik, J. Canny: The Coulomb pump: a novel parts feeding method using a horizontally-vibrating surface, IEEE International Conference on Robotics and Automation (1998) pp. 869–874

    Google Scholar 

  53. A.E. Quaid: A miniature mobile parts feeder: Operating principles and simulation results, IEEE International Conference on Robotics and Automation (1999) pp. 2221–2226

    Google Scholar 

  54. D. Reznik, J. Canny: A flat rigid plate is a universal planar manipulator, IEEE International Conference on Robotics and Automation (1998) pp. 1471–1477

    Google Scholar 

  55. D. Reznik, J. Canny: Cʼmon part, do the local motion!, IEEE International Conference on Robotics and Automation (2001) pp. 2235–2242

    Google Scholar 

  56. T. Vose, P. Umbanhowar, K.M. Lynch: Vibration-induced frictional force fields on a rigid plate, IEEE International Conference on Robotics and Automation (2007)

    Google Scholar 

  57. M.T. Mason: Mechanics and planning of manipulator pushing operations, Int. J. Robot. Res. 5(3), 53–71 (1986)

    Article  Google Scholar 

  58. K.Y. Goldberg: Orienting polygonal parts without sensors, Algorithmica 10, 201–225 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  59. R.C. Brost: Automatic grasp planning in the presence of uncertainty, Int. J. Robot. Res. 7(1), 3–17 (1988)

    Article  Google Scholar 

  60. J.C. Alexander, J.H. Maddocks: Bounds on the friction-dominated motion of a pushed object, Int. J. Robot. Res. 12(3), 231–248 (1993)

    Article  Google Scholar 

  61. M.A. Peshkin, A.C. Sanderson: The motion of a pushed, sliding workpiece, IEEE J. Robot. Autom. 4(6), 569–598 (1988)

    Article  Google Scholar 

  62. M.A. Peshkin, A.C. Sanderson: Planning robotic manipulation strategies for workpieces that slide, IEEE J. Robot. Autom. 4(5), 524–531 (1988)

    Article  Google Scholar 

  63. M. Brokowski, M. Peshkin, K. Goldberg: Curved fences for part alignment, IEEE International Conference on Robotics and Automation (Atlanta 1993) pp. 467–473

    Google Scholar 

  64. K.M. Lynch: The mechanics of fine manipulation by pushing, IEEE International Conference on Robotics and Automation (Nice 1992) pp. 2269–2276

    Google Scholar 

  65. K.M. Lynch, M.T. Mason: Stable pushing: Mechanics, controllability, and planning, Int. J. Robot. Res. 15(6), 533–556 (1996)

    Article  Google Scholar 

  66. K. Harada, J. Nishiyama, Y. Murakami, M. Kaneko: Pushing multiple objects using equivalent friction center, IEEE International Conference on Robotics and Automation (2002) pp. 2485–2491

    Google Scholar 

  67. J.D. Bernheisel, K.M. Lynch: Stable transport of assemblies: Pushing stacked parts, IEEE Trans. Autom. Sci. Eng. 1(2), 163–168 (2004)

    Article  Google Scholar 

  68. J.D. Bernheisel, K.M. Lynch: Stable transport of assemblies by pushing, IEEE Trans. Robot. 22(4), 740–750 (2006)

    Article  Google Scholar 

  69. H. Mayeda, Y. Wakatsuki: Strategies for pushing a 3D block along a wall, IEEE/RSJ International Conference on Intelligent Robots and Systems (Osaka, Japan 1991) pp. 461–466

    Google Scholar 

  70. H. Hertz: On the Contact of Rigid Elastic Solids and on Hardness. In: 6: Assorted Papers by H. Hertz, ed. by H. Hertz (MacMillan, New York 1882)

    Google Scholar 

  71. K.L. Johnson: Contact Mechanics (Cambridge Univ. Press, Cambridge 1985)

    MATH  Google Scholar 

  72. S.P. Timoshenko, J.N. Goodier: Theory of Elasticity, 3rd edn. (McGraw-Hill, New York 1970)

    MATH  Google Scholar 

  73. E. Wolf: Progress in Optics (North-Holland, Amsterdam 1992)

    Google Scholar 

  74. E.J. Nicolson, R.S. Fearing: The Reliability of Curvature Estimates from Linear Elastic Tactile Sensors, the Proceedings of the 1995 IEEE International Conference on Robotics and Automation (IEEE Press 1995)

    Google Scholar 

  75. M. Abramowitz, I. Stegun: Handbook of Mathematical Functions with formulas, graphs, and mathematical tables, 7th edn. (Dover, New York 1972)

    MATH  Google Scholar 

  76. I. Kao, S.-F. Chen, Y. Li, G. Wang: Application of bio-engineering contact interface and MEMS in robotic and human augmented systems, IEEE Robot. Autom. Mag. 10(1), 47–53 (2003)

    Article  Google Scholar 

  77. S. Goyal, A. Ruina, J. Papadopoulos: Planar sliding with dry friction. Part 1. Limit surface and moment function, Wear 143, 307–330 (1991)

    Article  Google Scholar 

  78. S. Goyal, A. Ruina, J. Papadopoulos: Planar sliding with dry friction. Part 2. Dynamics of motion, Wear 143, 331–352 (1991)

    Article  Google Scholar 

  79. J.W. Jameson: Analytic Techniques for Automated Grasp. Ph.D. Thesis (Department of Mechanical Engineering, Stanford University 1985)

    Google Scholar 

  80. S. Goyal, A. Ruina, J. Papadopoulos: Limit Surface and Moment Function Description of Planar Sliding, Proceedings of 1989 IEEE International Conference on Robotics and Automation (IEEE Computer Society, Scottsdale, Arizona 1989) pp. 794–799

    Google Scholar 

  81. K.M. Lynch, M.T. Mason: Dynamic nonprehensile manipulation: Controllability, planning, and experiments, Int. J. Robot. Res. 18(1), 64–92 (1999)

    Google Scholar 

  82. A.J. Goldman, A.W. Tucker: Polyhedral convex cones. In: Linear Inequalities and Related Systems, ed. by H.W. Kuhn, A.W. Tucker (Princeton Univ. Press, Princeton 1956)

    Google Scholar 

  83. M.A. Erdman: A configuration space friction cone;, IEEE/RSJ International Conference on Intelligent Robots and Systems (Osaka, 1991) pp. 455–460

    Google Scholar 

  84. M.A. Erdmann: Multiple-point contact with friction: Computing forces and motions in configuration space, IEEE/RSJ International Conference on Intelligent Robots and Systems (Yokohama, 1993) pp. 163–170

    Google Scholar 

  85. S. Hirai, H. Asada: Kinematics and statics of manipulation using the theory of polyhedral convex cones, Int. J. Robot. Res. 12(5), 434–447 (1993)

    Article  Google Scholar 

  86. R.S. Ball: The Theory of Screws (Cambridge Univ. Press, Cambridge 1900)

    Google Scholar 

  87. K.H. Hunt: Kinematic Geometry of Mechanisms (Oxford Univ., Oxford 1978)

    MATH  Google Scholar 

  88. J.K. Davidson, K.H. Hunt: Robots and Screw Theory (Oxford Univ. Press, Oxfort 2004)

    MATH  Google Scholar 

  89. J.M. Selig: Geometric Fundamentals of Robotics, 2nd edn. (Springer, Berlin Heidelberg 2005)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, State University of New York at Stony Brook, 11794-2300, Stony Brook, NY, USA

    Imin Kao Prof

  2. Mechanical Engineering Department, Northwestern University, 2145 Sheridan Road, 60208, Evanston, IL, USA

    Kevin Lynch Prof

  3. Mechanical Engineering Department, California Institute of Technology, 1200 E. California Blvd., 91125, Pasadena, CA, USA

    Joel W. Burdick Prof

Authors
  1. Imin Kao Prof
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kevin Lynch Prof
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Joel W. Burdick Prof
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Imin Kao Prof , Kevin Lynch Prof or Joel W. Burdick Prof .

Editor information

Editors and Affiliations

  1. PRISMA Lab, Dipartimento di Informatica e Sistemistica, Universitá degli Studi di Napoli Federico II, 80125, Napoli, Italy, Via Claudio 21

    Bruno Siciliano Prof.

  2. Artificial Intelligence Laboratory, Department of Computer Science, Stanford University, 94305-9010, Stanford, CA, USA

    Oussama Khatib Prof.

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Kao, I., Lynch, K., Burdick, J.W. (2008). Contact Modeling and Manipulation. In: Siciliano, B., Khatib, O. (eds) Springer Handbook of Robotics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30301-5_28

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30301-5_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23957-4

  • Online ISBN: 978-3-540-30301-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation