Skip to main content
SpringerLink
Log in

History of Forward Dynamics Algorithms

  • Living reference work entry
  • First Online:
Encyclopedia of Robotics

  • 15 Accesses

Nomenclature and Acronyms

m :

Total number of independent system constraints.

n :

Total number of system generalized coordinates.

nl :

Total number of system generalized coordinates associated with the longest branch of the system (tracing the from the system base/root out to its terminal/leaf bodies).

N :

Newtonian reference frame.

\(\mathcal {O}\) :

Indicates the Order of the polynomial characterizing the number of mathematical operations involved in the described process.

p :

Number of processors available

ABA :

Articulated Body Algorithm.

DCA :

Divide and Conquer Algorithm.

DCAe :

Divide and Conquer Algorithm – efficient.

GPU :

Graphics Processing Unit.

Definitions

Multibody System

Any system which may be thought of and modelled as a system of bodies (which may be either rigid or flexible) whose motions are often constrained with respect to one another through some form of kinematic relationship. These motion constraints can be viewed as a form of joint.

Such multibody systems...

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

Access this chapter

Log in via an institution

Institutional subscriptions

Notes

  1. 1.

    www.motiongenesis.com

References

  • Anderson KS (1992) An order-n formulation for motion simulation of general constrained multi-rigid-body systems. Comput Struct 43(3):565–572

    Article  MATH  Google Scholar 

  • Anderson KS, Critchley JH (2003) Improved order-n performance algorithm for the simulation of constrained multi-rigid-body systems. Multibody Syst Dyn 9:185–212

    Article  MathSciNet  MATH  Google Scholar 

  • Anderson KS, Duan S (2000) Highly parallelizable low order algorithm for the dynamics of complex multi rigid body systems. J Guid Control Dyn 23(2):355–364

    Article  Google Scholar 

  • Anderson KS, Hsu YH (2001) Low operational order analytic sensitivity analysis for tree-type multibody dynamic systems. J Guid Control Dyn 24(6):1133–1143

    Article  Google Scholar 

  • Armstrong WW (1979) Recursive solution to the equations of motion of an N-link manipulator. In: Fifth world congress on the theory of machines and mechanisms, vol 2, pp 1342–1346

    Google Scholar 

  • Bae DS, Haug EJ (1987) A recursive formation for constrained mechanical system dynamics: part II, Closed loop systems. Mech Struct Mach 15(4):481–506

    Article  Google Scholar 

  • Bae DS, Kuhl JG, Haug EJ (1988) A recursive formation for constrained mechanical system dynamics: part III, Parallel processing implementation. Mech Struct Mach 16:249–269

    Article  Google Scholar 

  • Bhalerao KD, Crean C, Anderson KS (2011) Hybrid complementarity formulations for robotics applications. ZAMM Z Angew Math Mech 91(5):386–399. https://doi.org/10.1002/zamm.201000093

    Article  MathSciNet  MATH  Google Scholar 

  • Bhalerao KD, Critchley JH, Oetomo D, Featherstone R, Khatib O (2014) Distributed operational space formulation of serial manipulators. J Comput Nonlinear Dyn 9(2):10. https://doi.org/10.1115/1.4025577

    Google Scholar 

  • Bhalerao KD, Critchley J, Anderson K (2012) An efficient parallel dynamics algorithm for simulation of large articulated robotic systems. Mech Mach Theory 53(0):86–98. https://doi.org/10.1016/j.mechmachtheory.2012.03.001

  • Bottasso CL (2008) Multibody dynamics. In: Font-Llagunes JM (ed) Multibody dynamics, Computational methods in applied sciences, vol. 12. Springer, Cham, Switzerland, pp 57–79. 978-1-4020-8828-5, https://doi.org/10.1007/978-1-4020-8829-2, http://www.springerlink.com/content/x402531511157642/

  • Chung S, Haug EJ (1993) Real-time simulation of multibody dynamics on shared memory multiprocessors. J Dyn syst Meas Control 115(4):627–637

    Article  MATH  Google Scholar 

  • Critchley JH, Anderson KS, Binani A, An efficient multibody divide and conquer algorithm and implementation. J Comput Nonlinear Dyn 4(2):021004. 0791848027, https://doi.org/10.1115/1.3079823

  • Eichberger A, Führer C, Schwertassek R, The benefits of parallel multibody simulation. Int J Numer Methods Eng 37:1557–1572

    Google Scholar 

  • Featherstone R (1983) The calculation of robotic dynamics using articulated body inertias. Int J Robot Res 2(1):13–30

    Article  Google Scholar 

  • Featherstone R (1987) Robot dynamics algorithms. Kluwer Academic Publishing, Boston/Dordrecht/Lancaster

    Book  Google Scholar 

  • Featherstone R (1999) A divide-and-conquer articulated body algorithm for parallel \(O(\log (n))\) calculation of rigid body dynamics. Part I: basic algorithm. Int J Robot Res 18(9):867–875

    Google Scholar 

  • Featherstone R, Fijany A (1999) A technique for analyzing constrained rigid-body systems, and its application to the constraint force algorithm. IEEE Trans Robot Autom 15(6):1140–1144

    Article  Google Scholar 

  • Fijany A, Bejczy AK (1991) Techniques in parallel computation of mechanical manipulator dynamics. Part II: Forward dynamics. Appearing in Control of Dynamics Systems In: Leondes CT (ed) Advances in robotic systems and control, part 2 of 2, vol 20, part 2, Academic Press, Elsevier pp 357–410

    Google Scholar 

  • Fijany A, Sharf I, D’Eleuterio GMT (1995) Parallel O(log n) algorithms for computation of manipulator forward dynamics. IEEE Trans Robot Autom 11(3):389–400

    Article  Google Scholar 

  • Fisette P, Peterkenne JM (1998) Contribution to parallel and vector computation in multibody dynamics. Parallel Comput 24:717–728

    Article  MathSciNet  MATH  Google Scholar 

  • Hollars M, Rosenthal D, Sherman M (1994) SD/FAST user’s manual. Symbolic Dynamics, Inc.; Mountain View, CA

    Google Scholar 

  • Hooker WW, Margulies G (1965) The dynamical attitude equations for an n-body satellite. J Astronaut Sci 7(4):123–128

    MathSciNet  Google Scholar 

  • Hwang RS, Bae DS, Kuhl JG, Haug EJ (1990) Parallel processing for real-time dynamics systems simulations. J Mech Des 112(4):520–528

    Article  Google Scholar 

  • Jain A (1991) Unified formulation of dynamics for serial rigid multibody systems. J Guid Control Dyn 14(3):531–542

    Article  MATH  Google Scholar 

  • Kane TR, Wang CF (1965) On the derivation of equations of motion. J Soc Ind Appl Math 13(2):487–492

    Article  MathSciNet  MATH  Google Scholar 

  • Kasahara H, Fujii H, Iwata M (1987) Parallel processing of robot motion simulation. In: Proceedings IFAC 10th World Conference, Munich, Germany

    Google Scholar 

  • Kreutz-Delgado K, Jain A, Rodriguez G (1992) Recursive formulation of operational space control. Int J Robot Res 11(4):320–328

    Article  Google Scholar 

  • Kurdila AJ, Menon RG, Sunkel JW (1993) Nonrecursive order N formulation of multibody dynamics. J Guid Control Dyn 16(5):838–844

    Article  Google Scholar 

  • Lee CSG, Chang PR (1988) Efficient parallel algorithms for robot forward dynamics. IEEE Trans Syst Man Cybernet 18(2):238–251

    Article  MathSciNet  Google Scholar 

  • Luh JSY, Walker MW, Paul RPC (1980) On-line computational scheme for mechanical manipulators. J Dyn Syst Meas Control 102(2):69–76

    Article  MathSciNet  Google Scholar 

  • Malczyk P, Fraqczek J (2012) A divide and conquer algorithm for constrained multibody system dynamics based on augmented Lagrangian method with projections-based error correction. Nonlinear Dyn 70(1):871–889. https://doi.org/10.1007/s11071-012-0503-2, http://link.springer.com/10.1007/s11071-012-0503-2

  • Mukherjee RM, Crozier PS, Plimpton SJ, Anderson KS (2008) Substructured molecular dynamics using multibody dynamics algorithms. Int J Non-Linear Mech: Nonlinear Mech Dyn Macromol 43(10):1040–1055

    Article  MATH  Google Scholar 

  • Mukherjee RM, Anderson KS (2007) A logarithmic complexity divide-and-conquer algorithm for multi-flexible articulated body dynamics. J Comput Nonlinear Dyn 2(1):10–21. https://doi.org/10.1115/1.2389038, http://computationalnonlinear.asmedigitalcollection.asme.org/article.aspx?articleid=1394362

  • Orlandea N, Chace MA, Calahan DA (1977) A sparsity-oriented approach to the dynamics analysis and design of mechanical systems – Parts 1 & 2. J Eng Ind 43:773–784

    Article  Google Scholar 

  • Poursina M, Bhalerao KD, Flores S, Anderson KS, Laederach A (2011) Strategies for articulated multibody-based adaptive coarse grain simulation of RNA. Methods Enzymol 487:73–98

    Article  Google Scholar 

  • Poursina M, Anderson KS (20130) An extended divide-and-conquer algorithm for a generalized class of multibody constraints. Multibody Syst Dyn 29(3):235–254. https://doi.org/10.1007/s11044-012-9324-9, http://link.springer.com/10.1007/s11044-012-9324-9

  • Praprotnik M, Site LD, Kremer K (2005) Adaptive resolution molecular-dynamics simulation:changing the degrees of freedom on the fly. J Chem Phys 123(22):224106–224114

    Article  Google Scholar 

  • Redon S, Galoppo N, Lin MC (2005) Adaptive dynamics of articulated bodies. ACM Trans Graph (SIGGRAPH 2005) 24(3):936–945

    Article  Google Scholar 

  • Roberson RE, Wittenburg JA (1966) A dynamical formalism for an arbitrary number of interconnected rigid bodies, with reference to the problem of satellite attitude control. In: Proceedings of the Third International Congress on Automatic Control, London, England, pp 46–1469

    Google Scholar 

  • Rodriguez G (1987) Kalman filtering, smoothing, and recursive robot arm forward and inverse dynamics. IEEE J Robot Autom RA-3(6):624–639 (1987)

    Google Scholar 

  • Rosenthal DE (1990) An order n formulation for robotic systems. J Astronaut Sci 38(4):511–529

    Google Scholar 

  • Saha SK, Schiehlen WO (2001) Recursive kinematics and dynamics for parallel structured closed-loop multibody systems. Mech Struct Mach 29(2):143–175

    Article  Google Scholar 

  • Sharf I, D’Eleuterio GMT (1993) An iterative approach to multibody simulation dynamics suitable for parallel implementation. J Dyn Syst Meas Control 115:730–735

    Article  Google Scholar 

  • Stejskal V, Valaseǩ́ M (1996) Kinematics and dynamics of machinery. Marcel Dekker, New York/Basel/Hong Kong

    Google Scholar 

  • Uicker JJ (1965) On the dynamic analysis of spatial linkages using 4 × 4 matrices, Ph.D. dissertation by J.J. Uicker. Northwester University, 6602749

    Google Scholar 

  • Uicker JJ (1967) Dynamic force analysis of spatial linkages. Trans ASME J Appl Mech 34:418–424

    Article  Google Scholar 

  • Vereshchagin AF (1974) Computer simulation of the dynamics of complicated mechanisms of robot-manipulators. Eng Cybernet 12(6):65–70

    Google Scholar 

  • Walker MW, Orin DE (1982) Efficient dynamic computer simulation of robotic mechanisms. J Dyn Syst Meas Control 104(3):205–211

    Article  MATH  Google Scholar 

  • Yamane K, Nakamura Y (2002) Efficient parallel dynamics computation of human figures. In: Proceedings of International Conference on Robotics and Automation, vol 1. ICRA ’02. IEEE,0 pp 530–5371. https://doi.org/10.1109/ROBOT.2002.1013413

  • Yamane K, Nakamura Y (2006) Parallel O (log n) algorithm for dynamics simulation of humanoid robots. In: 2006 6th IEEE-RAS International Conference on Humanoid Robots, IEEE, pp 554–559

    Google Scholar 

  • Yamane K, Nakamura Y (2009) Comparative study on serial and parallel forward dynamics algorithms for kinematic chains*. Int J Robot Res 28(5):622–629

    Article  Google Scholar 

  • Zeid AA, Overholt JL (1995) Modeling of multibody systems connected by standard engineering joints. Mech Struct Mach 23(2):273–307

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rensselaer Polytechnic Institute, Troy, NY, USA

    Kurt S. Anderson

Authors
  1. Kurt S. Anderson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kurt S. Anderson .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, National University of Singapore, Singapore, Singapore

    Marcelo H. Ang

  2. Department of Computer Science, Stanford University, Stanford, CA, USA

    Oussama Khatib

  3. Department of Electrical Engineering, University of Naples Federico II, Naples, Italy

    Bruno Siciliano

Section Editor information

  1. Department of Advanced Robotics, Istituto Italiano di Tecnologia, Genova, Italy

    Roy Featherstone

Rights and permissions

Reprints and permissions

Copyright information

© 2023 Springer-Verlag GmbH Germany, part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Anderson, K.S. (2023). History of Forward Dynamics Algorithms. In: Ang, M.H., Khatib, O., Siciliano, B. (eds) Encyclopedia of Robotics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41610-1_51-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-41610-1_51-1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41610-1

  • Online ISBN: 978-3-642-41610-1

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation