Advertisement

A Computationally Efficient Inverse Dynamics Solution Based on Virtual Work Principle for Biped Robots

  • Majid KhadivEmail author
  • Mahdokht Ezati
  • S. Ali A. Moosavian
Research Paper

Abstract

This paper deals with proposing a computationally efficient solution for the inverse dynamics problem of biped robots. To this end, the procedure of developing a closed-form dynamic model using D’Alembert’s-based virtual work principle (VWP) for a biped robot is described. Then, a closed-form inverse dynamics solution is developed during different phases of walking. For a given motion, the closed-form solution is evaluated at each control cycle to yield the joint torques and interaction forces. This procedure is time-consuming for robots with a large number of degrees of freedom such as 3D biped robots. Alternatively, to improve the computational efficiency of the procedure, a method is proposed to solve inverse dynamics efficiently without the need to develop a closed-form solution. In order to show the computational efficiency of the proposed method, its calculation time is compared to the closed-form solutions obtained from the VWP and Lagrange approaches, while this comparison reveals the merit of the proposed method in terms of computational efficiency. For an example application of the proposed solution for inverse dynamics, a dynamic-based optimization procedure is carried out to show the significance of employing toe-off and heel-contact gait phases during biped walking.

Keywords

Biped robots Dynamic modeling D’Alembert’s principle Virtual work principle Gait planning 

References

  1. Aoi S, Tsuchiya K (2011) Generation of bipedal walking through interactions among the robot dynamics, the oscillator dynamics, and the environment: stability characteristics of a five-link planar biped robot. Auton Robots 30:123–141CrossRefGoogle Scholar
  2. Aoustin Y, Formalskii A (2014) 3D walking biped: optimal swing of the arms. Multibody SysDyn 32:55–66MathSciNetCrossRefGoogle Scholar
  3. Baruh H (1999) Analytical dynamics. WCB/McGraw-Hill, BostonGoogle Scholar
  4. Buschmann T, Lohmeier S, Ulbrich H (2009) Humanoid robot lola: design and walking control. J Physiol Paris 103:141–148CrossRefzbMATHGoogle Scholar
  5. Carbone G, Ogura Y, H-o Lim, Takanishi A, Ceccarelli M (2004) Dynamic simulation and experiments for the design of a new 7-dofs biped walking leg module. Robotica 22:41–50CrossRefGoogle Scholar
  6. Englsberger J, Ott C, Albu-Schaffer A (2015) Three-dimensional bipedal walking control based on divergent component of motion. IEEE Trans Robot 31:355–368CrossRefGoogle Scholar
  7. Ezati M, Khadiv M, Moosavian SAA (2014) Dynamics modeling of a biped robot with active toe joints. In: 2014 Second RSI/ISM international conference on robotics and mechatronics (ICRoM), 2014. IEEE, pp 107–112Google Scholar
  8. Ezati M, Khadiv M, Moosavian SAA (2015) Effects of toe-off and heel-off motions on gait performance of biped robots. In: 2015 3rd RSI international conference on robotics and mechatronics (ICROM), 2015. IEEE, pp 007–012Google Scholar
  9. García DH, Monje CA, Balaguer C (2015) Adaptation of robot skills models to new task contraints. Int J Humanoid Robot 12:1550024CrossRefGoogle Scholar
  10. Herzog A, Righetti L, Grimminger F, Pastor P, Schaal S (2014) Balancing experiments on a torque-controlled humanoid with hierarchical inverse dynamics. In: 2014 IEEE/RSJ international conference on intelligent robots and systems (IROS 2014), 2014. IEEE, pp 981–988Google Scholar
  11. Herzog A, Rotella N, Mason S, Grimminger F, Schaal S, Righetti L (2016) Momentum control with hierarchical inverse dynamics on a torque-controlled humanoid. Auton Robots 40(3):473–491CrossRefGoogle Scholar
  12. Hollerbach JM (1980) A recursive lagrangian formulation of maniputator dynamics and a comparative study of dynamics formulation complexity. IEEE Trans Syst Man Cybern 10:730–736CrossRefGoogle Scholar
  13. Hopkins MA, Leonessa A, Lattimer BY, Hong DW (2015) Optimization-based whole-body control of a series elastic humanoid robot. Int J Humanoid Robot 13:1550034CrossRefGoogle Scholar
  14. Huang Q, Yokoi K, Kajita S, Kaneko K, Arai H, Koyachi N, Tanie K (2001) Planning walking patterns for a biped robot. IEEE Trans RobotAutom 17:280–289Google Scholar
  15. Kaiser P, Vahrenkamp N, Schültje F, Borràs J, Asfour T (2015) Extraction of whole-body affordances for loco-manipulation tasks. Int J Humanoid Rob 12:1550031CrossRefGoogle Scholar
  16. Khadiv M, Moosavian SA (2014) A low friction demanding approach in gait planning for humanoid robots during 3D manoeuvres. J Appl Mech 45:47–60Google Scholar
  17. Khadiv M, Moosavian SAA, Sadedel M (2014) Dynamics modeling of fully-actuated humanoids with general robot-environment interaction. In: 2014 Second RSI/ISM international conference on robotics and mechatronics (ICRoM), 2014. IEEE, pp 233–238Google Scholar
  18. Khadiv M, Moosavian SAA, Yousefi-Koma A, Sadedel M, Mansouri S (2017) Optimal gait planning for humanoids with 3D structure walking on slippery surfaces. Robotica 35(3):569–587CrossRefGoogle Scholar
  19. Kwon O, Park JH (2009) Asymmetric trajectory generation and impedance control for running of biped robots. Auton Robots 26:47–78CrossRefGoogle Scholar
  20. Kwon O, Jeon KS, Park JH (2006) Optimal trajectory generation for biped robots walking up-and-down stairs. J Mech Sci Technol 20:612–620CrossRefGoogle Scholar
  21. Löffler K, Gienger M, Pfeiffer F (2003) Sensors and control concept of walking “Johnnie”. Int J Robot Res 22:229–239Google Scholar
  22. Lohmeier S, Buschmann T, Ulbrich H (2009) Humanoid robot LOLA. In: IEEE international conference on robotics and automation, 2009. ICRA’09, 2009. IEEE, pp 775–780Google Scholar
  23. Park HA, Ali MA, Lee CG (2012) Closed-form inverse kinematic position solution for humanoid robots. Int J Humanoid Rob 9:1250022CrossRefGoogle Scholar
  24. Peasgood M, Kubica E, McPhee J (2007) Stabilization of a dynamic walking gait simulation. J Comput Nonlinear Dyn 2:65–72CrossRefGoogle Scholar
  25. Righetti L, Buchli J, Mistry M, Kalakrishnan M, Schaal S (2013) Optimal distribution of contact forces with inverse-dynamics control. Int J Robot Res 32:280–298CrossRefGoogle Scholar
  26. Siciliano B, Sciavicco L, Villani L, Oriolo G (2010) Robotics: modelling, planning and control. Springer, BerlinGoogle Scholar
  27. Tlalolini D, Chevallereau C, Aoustin Y (2009) Comparison of different gaits with rotation of the feet for a planar biped. Robot Auton Syst 57:371–383CrossRefGoogle Scholar
  28. Wang T, Chevallereau C, Rengifo CF (2012) Walking and steering control for a 3D biped robot considering ground contact and stability. Robot Auton Syst 60:962–977CrossRefGoogle Scholar
  29. Wensing PM, Orin DE (2016) Improved computation of the humanoid centroidal dynamics and application for whole-body control. Int J Humanoid Robot 13(01):1550039CrossRefGoogle Scholar

Copyright information

© Shiraz University 2017

Authors and Affiliations

  • Majid Khadiv
    • 1
    Email author
  • Mahdokht Ezati
    • 1
  • S. Ali A. Moosavian
    • 1
  1. 1.Center of Excellence in Robotics and Control, Advanced Robotics and Automated Systems (ARAS) Lab, Department of Mechanical EngineeringK. N. Toosi University of TechnologyTehranIran

Personalised recommendations