Skip to main content
SpringerLink
Log in

Input torque sensitivity to uncertain parameters in biped robot

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

Input torque is themain power to maintain bipedal walking of robot, and can be calculated from trajectory planning and dynamic modeling on biped robot. During bipedal walking, the input torque is usually required to be adjusted due to some uncertain parameters arising from objective or subjective factors in the dynamical model to maintain the pre-planned stable trajectory. Here, a planar 5-link biped robot is used as an illustrating example to investigate the effects of uncertain parameters on the input torques. Kinematic equations of the biped robot are firstly established by the third-order spline curves based on the trajectory planning method, and the dynamic modeling is accomplished by taking both the certain and uncertain parameters into account. Next, several evaluation indices on input torques are introduced to perform sensitivity analysis of the input torque with respect to the uncertain parameters. Finally, based on the Monte Carlo simulation, the values of evaluation indices on input torques are presented, from which all the robot parameters are classified into three categories, i.e., strongly sensitive, sensitive and almost insensitive parameters.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kuppuswamy, N., Alessandro, C.: Impact of body parameters on dynamic movement primitives for robot control. Procedia Computer Science 7, 166–168 (2011)

    Article  Google Scholar 

  2. Gritli, H., Khraief, N., Belghith, S.: Period-three route to chaos induced by a cyclic-fold bifurcation in passive dynamic walking of a compass-gait biped robot. Communications in Nonlinear Science and Numerical Simulation 17, 4356–4372 (2012)

    Article  MathSciNet  Google Scholar 

  3. Singh, H.P., Sukavanam, N.: Stability analysis of robust adaptive hybrid position/force controller for robot manipulators using neural network with uncertainties. Neural Computing & Applications DOI: 10.1007/s00521-012-0966-6 (2012)

    Google Scholar 

  4. Plestan, F., Grizzle, J.W., Westervelt, E.R., et al.: Stable walking of a 7-DOF biped robot. IEEE Transactions on Robotics and Automation 19, 653–668 (2003)

    Article  Google Scholar 

  5. Chevallereau, C., Grizzle, J.W., Shih, C.L.: Asymptotically stable walking of a five-link underactuated 3D bipedal robot. IEEE Transactions on Robotics 25, 37–50 (2009)

    Article  Google Scholar 

  6. Hashemi, E., Jadidi, G.M.: Dynamic modeling and control study of the NAO biped robot with improved trajectory planning. Materials with complex behavior II, Advanced Structured Materials 16, 671–688 (2012)

    Article  Google Scholar 

  7. Channon, P.H., Hopkins, S.H., Phan, D.T.: Derivation of optimal walking motions for a biped walking robot. Robotica 10, 165–172 (1992)

    Article  Google Scholar 

  8. Kurazume, R., Tanaka, S., Yamashita, M., et al.: Straight legged walking of a biped robot. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, 3095–3101 (2005)

    Google Scholar 

  9. Seyfarth, A., Geyer, H., Gunther, M., et al.: A movement criterion for running. Journal of Biomechanics 35, 649–655 (2002)

    Article  Google Scholar 

  10. Hosoda, K., Takuma, T., Nakamoto, A., et al.: Biped robot design powered by antagonistic pneumatic actuators for multimodal locomotion. Robotics and Autonomous Systems 56, 46–53 (2008)

    Article  Google Scholar 

  11. Rossi, C., Savino, S.: Robot trajectory planning by assigning positions and tangential velocities. Robotics and Computer-Integrated Manufacturing 29, 139–156 (2013)

    Article  Google Scholar 

  12. Tang, Z., Zhou, C., Sun, Z.: Trajectory planning for smooth transition of a biped robot. In: Proceedings of the 2003 IEEE International Conference on Robotics & Automation 2455–2460 (2003)

    Chapter  Google Scholar 

  13. Shih, C.: Gait synthesis for a biped robot. Robotica 15, 599–607 (1997)

    Article  Google Scholar 

  14. Xiong, Y., Pan, G., Yu, L.: Speed control for under-actuated planar biped robot. Advances in Intelligent and Soft Computing. 123, 165–172 (2011)

    Article  Google Scholar 

  15. Gasparetto, A., Zanotto, V.: A technique for time-jerk optimal planning of robot trajectories. Robotics and Computer-Integrated Manufacturing 24, 415–426 (2008)

    Article  Google Scholar 

  16. Cong, M., Xu, X., Xu, P.: Time-jerk synthetic optimal trajectory planning of robot based on fuzzy genetic algorithm. In: Proc. of International Conference on Mechatronics and Machine Vision in Practice 269–274 (2008)

    Chapter  Google Scholar 

  17. Zhang, L., Zhou, C.: Smooth and energy saving gait planning for humanoid robot using geodesics. Applied Bionics and Biomechanics 8, 1–11 (2011)

    Google Scholar 

  18. Piazzi, A., Visioli, A.: Global minimum-time trajectory planning of mechanical manipulators using interval analysis. International Journal of Control 71, 631–652 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  19. Lengagne, S., Ramdani, N., Fraisse, P.: Planning and fast replanning safe motions for humanoid robots. IEEE Transactions on Robotics 27, 1095–1106 (2011)

    Article  Google Scholar 

  20. Iwamura, M., Eberhard, P., Schiehlen, W., et al.: A general purpose algorithm for optimal trajectory planning of closed loop multibody systems. Multibody Dynamics: Computational Methods and Applications, ComputationalMethods in Applied Sciences 23, 173–193 (2011)

    Article  Google Scholar 

  21. Acosta Calderon, C.A., Mohan, R.E., Hu, L., et al.: Generating human-like soccer primitives from human data. Robotics and Autonomous Systems 57, 860–869 (2009)

    Article  Google Scholar 

  22. Chevallereau, C., Grizzle, J.W., Shih, C.L.: Asymptotically stable walking of a five-link underactuated 3-D bipedal robot. IEEE Transactions on Robotics 25, 37–50 (2009)

    Article  Google Scholar 

  23. Westervelt, E.R., Grizzle, J.W., Chevallereau, C., et al.: Feedback Control of Dynamic Bipedal Robot Locomotion. CRC Press, BocaRaton (2007)

    Book  Google Scholar 

  24. Hong, S., Oh, Y., Chang, Y.H., et al.: An omni-directional walking pattern generation method for humanoid robots with quartic polynomials. In: Proceedings of the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, 4213–4219 (2007)

    Google Scholar 

  25. Firmani, F., Park, E.J.: A framework for the analysis and synthesis of 3D dynamic human gait. Robotica 30, 145–157 (2012)

    Article  Google Scholar 

  26. Huang, Q., Kajita, S., Koyachi, N., et al.: Walking patterns and actuator specifications for a biped robot. In: Proceedings of the 1999 IEEE/RSJ International Conference on Intelligent Robots and Systems, 1462–1468 (1999)

    Google Scholar 

  27. Huang, Q., Yokoi, K., Kajita, S., et al.: Planning walking patterns for a biped robot. IEEE Transactions on Robotics and Automation 17, 280–289 (2001)

    Article  Google Scholar 

  28. Gu, F.: Design and control of a 6 DOF biped robot. [Ms Thesis], Lakehead University, Thunder Bay 19–57 (2006)

    Google Scholar 

  29. Lee, T.T., Chen, Y.C.: Minimum-fuel path planning of a 5-link biped robot. In: Proceedings of the Twentieth Southeastern Symposium on System Theory, 459–463 (1988)

    Chapter  Google Scholar 

  30. Hays, J., Sandu, A., Sandu, C., et al.: Motion planning of uncertain ordinary differential equation systems. Computer Science Technical Report. TR-11-04, 1–26 (2011)

    Google Scholar 

  31. Muscolino, G., Sofi, A.: Response statistics of linear structures with uncertain-but-bounded parameters under Gaussian stochastic input. International Journal of Structural Stability and Dynamics 11, 775–804 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  32. Cacciola, P., Colajanni, P., Muscolino, G.: A modal approach for the evaluation of the response sensitivity of structural systems subjected to non-stationary random process. Computer Methods in Applied Mechanics and Engineering 194, 4344–4361 (2005)

    Article  MATH  Google Scholar 

  33. Muscolino, G.. Dynamically modified linear structures: deterministic and stochastic response. Journal of Engineering Mechanics 122, 1044–1051 (1996)

    Article  Google Scholar 

  34. Burkan, R., Uzmay, I.: Upper bounding estimation for robustness to the parameter uncertainty in trajectory control of robot arm. Robotics and Autonomous Systems 45, 99–110 (2003)

    Article  Google Scholar 

  35. Pi, Y., Wang, X.: Trajectory tracking control of a 6-DOF hydraulic parallel robot manipulator with uncertain load disturbances. Control Engineering Practice 19, 185–193 (2011)

    Article  Google Scholar 

  36. Chen, H., Li, X., Shalom, Y.B.: On joint track initiation and parameter estimation under measurement origin uncertainty. IEEE Transactions on Aerospace and Electronic Systems 40, 675–694 (2004)

    Article  Google Scholar 

  37. Rout, B.K., Mittal, R.K.: Optimal manipulator parameter tolerance selection using evolutionary optimization technique. Engineering Applications of Artificial Intelligence 21, 509–524 (2008)

    Article  Google Scholar 

  38. Tang, J., Zhao, Q., Yang, R.: Stability control for a walkingchair robot with human in the Loop. International Journal of Advanced Robotic Systems 6, 47–52 (2009)

    Google Scholar 

  39. Wang, L., Liu, F., Xu, S., et al.: Design, modeling and control of a biped line-walking robot. International Journal of Advanced Robotic Systems 7, 39–47 (2010)

    Google Scholar 

  40. Li, Y.: A moving base mobile robot: kinematics, stability, and trajectory control. Physica D. 1, 18–34 (1987)

    Google Scholar 

  41. Grizzle, J.W., Abba, G., Plestan, F.: Asymptotically stable walking for biped robots: analysis via systems with impulse effects. IEEE Transactions on Automatic Control 46, 51–64 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  42. Wang, T., Chevallereau, C.: Stability analysis and time-varying walking control for an under-actuated planar biped robot. Robotics and Autonomous Systems 59, 444–456 (2011)

    Article  Google Scholar 

  43. Westervelt, E.R.: Toward a coherent framework for the control of planar biped locomotion. [Ph.D. Thesis]. University of Michigan, USA, 20–25 (2003)

    Google Scholar 

  44. Plestan, F., Grizzle, J.W., Westervelt, E.R., et al.: Stable walking of a 7-DOF biped robot. IEEE Transactions on Robotics and Automation 19, 653–668 (2003)

    Article  Google Scholar 

  45. Park, J.H.: Impedance control for biped robot locomotion. IEEE Transactions on Robotics and Automation 17, 870–882 (2001)

    Article  Google Scholar 

  46. Kuczera, G., Parent, E.: Monte Carlo assessment of parameter uncertainty in conceptual catchment models: The Metropolis algorithm. Journal of Hydrology 211, 69–85 (1998)

    Article  Google Scholar 

  47. Tzafestas, S.G., Krikochoritis, T.E., Tzafestas, C.S.: Robust sliding-mode control of nine-link biped robot walking. Journal of Intelligent and Robotic Systems 20, 375–402 (1997)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Zhejiang University, 310027, Hangzhou, China

    Chang-Tao Ding, Shi-Xi Yang & Chun-Biao Gan

Authors
  1. Chang-Tao Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shi-Xi Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chun-Biao Gan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chun-Biao Gan.

Additional information

The project was supported by the National Natural Science Foundation of China (11142013, 11172260 and 11072214), the Doctoral Fund of Ministry of Education of China (20110101110016), and the Fundamental Research Funds for the Central Universities of China (2011QNA4001).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ding, CT., Yang, SX. & Gan, CB. Input torque sensitivity to uncertain parameters in biped robot. Acta Mech Sin 29, 452–461 (2013). https://doi.org/10.1007/s10409-013-0025-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-013-0025-2

Keywords

Search

Navigation