The week's pick
Reseach Article
Dynamic Modeling of Biped Robot using Lagrangian and Recursive Newton-Euler Formulations
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 101 - Number 3 |
| Year of Publication: 2014 |
| Authors: Hayder F. N. Al-shuka, Burkhard J. Corves, Wen-hong Zhu |
10.5120/17664-8485
|
Hayder F. N. Al-shuka, Burkhard J. Corves, Wen-hong Zhu . Dynamic Modeling of Biped Robot using Lagrangian and Recursive Newton-Euler Formulations. International Journal of Computer Applications. 101, 3 ( September 2014), 1-8. DOI=10.5120/17664-8485
Abstract
The aim of this paper is to derive the equations of motion for biped robot during different walking phases using two well-known formulations: Euler-Lagrange (E-L) and Newton-Euler (N-E) equations. The modeling problems of biped robots lie in their varying configurations during locomotion; they could be fully actuated during the single support phase (SSP) and over-actuated during the double support phase (DSP). Therefore, first, the E-L equations of 6-link biped robot are described in some details for dynamic modeling during different walking phases with concentration on the DSP. Second, the detailed description of modified recursive Newton-Euler (N-E) formulation (which is very useful for modeling complex robotic system) is illustrated with a novel strategy for solution of the over-actuation/discontinuity problem. The derived equations of motion of the target biped for both formulations are suitable for control laws if the analyzer needs to deal with control problems. As expected, the N-E formulation is superior to the E-L concerning dealing with high degrees-of-freedom (DoFs) robotic systems (larger than 6 DoFs).
References
- Al-Shuka, Hayder F. N. ; Corves, B. ; Zhu, W. -H. ; Vanderborght, B. 2014. Multi-level control of zero-moment point (ZMP)-based humanoid biped robots: A review. Robotica (accepted).
- Al-Shuka, H. ; Allmendinger, F. ; Corves, B. ; Zhu, W. -H. 2014. Modeling, stability and walking pattern generators of biped robots: a review. Robotica, 32(06): 907-934.
- Sato, T. ; Sakaino, S. ; Ohnishi, K. 2010. Trajectory planning and control for biped robot with toe and heel joint. IEEE International Workshop on Advanced Motion Control, Nagaoka, Japan, pp. 129-136.
- Vanderborght, B. ; Ham, R. V. ; Verrelst, B. ; Damme, M. V. ; Lefeber, D. 2008. Overview of the Lucy project: Dynamic stabilization of a biped powered by pneumatic artificial muscles. Advanced Robotics: 22 (10), 1027-1051.
- Featherstone, R. ; Orin, D. 2000. Robot dynamics: Equations and algorithms. IEEE International Conference on Robotics and Automation, ICRA'00, vol. 1, pp. 826-834.
- Saha, S. K. 2007. Recursive dynamics algorithms for serial, parallel and closed-chain multibody systems. Indo-US Workshop on Protein Kinematics and Protein Conformations, IISC, Bangalore.
- Khalil, W. 2011. Dynamic modeling of robots using recursive Newton-Euler formulations. J. A. Cettoet al. (Eds. ): Informatics in Control, Automation and Robotic, LNEE 89, pp. 3-20, Springer-Verlag Berlin Heidelberg.
- Fu, K. S. ; Gonzalez, R. C. ; C. Lee, S. G. 1987. Robotics: control, sensing, vision, and intelligence. USA: McGraw-Hill Book Company.
- Zhu, W. -H. 2010. Virtual decomposition control: towards hyper degrees of freedom. Berlin, Germany: Springer–Verlag.
- Al-Shuka, Hayder F. N. ; Corves, B. 2013. On the walking pattern generators of biped robot. Journal of automation and control, 1(2): 149-155.
- Chen, X. ; Watanabe, K. ; Kiguchi, K. ; Izumi, K. 1999. Optimal force distribution for the legs of a quadruped robot. Machine Intelligence and Robotic Control: 1(2), 87-94.
- Hamon, A. ; Aoustin, Y. 2010. Cross four-bar linkage for the knees of a planar bipedal robot. 10th IEEE-RAS International Conference on Humanoid Robots, Nashville, TN, pp. 379-384.
- Tzafests, S. ; Raibert, M. ; Robust sliding mode control applied to 5-link biped robot. Journal of Intelligent and Robotic Systems: vol. 15, pp. 67-133.
- Li, Z. ; Yang, C. ; Fan, L. 2013. Advanced control of wheeled inverted pendulum systems. London: Springer-Verlag London.
- Spong, Mark. W. ; Vidyasagar, M. 1989. Robot dynamics and control. USA: John Wiley & Sons.
- Tsai, Lung-Wen. 1999. Robot analysis: the mechanics of serial and parallel manipulators. New York: John Wiley and Sonc Inc.
- Blajer, W. ; Bestle, D. ; Schiehlen, W. 1994. An orthogonal complement matrix formulation for constrained multibody systems. Journal of Mechanical Design: vol. 116.
- Pennestri, E. ; Valentini, P. P. 2007. Coordinate reduction strategies in multibody dynamics: a review. In Atti Conference on Multibody System Dynamics.
- Mitobe, K. ; Mori, N. ; Nasu, Y. ; Adachi, N. 1997. Control of a biped walking robot during the double support phase. Autonomous Robots: 4(3), 287-296.
- Su, C. -Y. ; Leung, T. P. ; Zhou, Q. -J. 1990. Adaptive control of robot manipulators under constrained motion. Proceedings of the 29th Conference on Decision and Control, pp. 2650-2655.
- Zarrugh, M. Y. 1981. Kinematic prediction of intersegment loads and power at the joints of the leg in walking. J. Biomechanics: 10 (10), 713-725.
- Alba, A. G. ; Zielinska, T. 2012. Postural equilibrium criteria concerning feet properties for biped robot. Journal of Automation, mobile robotics and Intelligent Systems: 6 (1), 22-27.
- Al-Shuka, Hayder F. N. ; Corves, B. ; Vanderborght, B. ; Zhu, W. -H. 2013. Finite difference-based suboptimal trajectory planning of biped robot with continuous dynamic response. International Journal of Modeling and Optimization, 3(4):337-343.
- Arora, J. S. 2012. Introduction to optimum design. USA: Elsevier.
Index Terms
Keywords