Skip to main content
Log in

Compliant landing of a trotting quadruped robot based on hybrid motion/force robust control

  • Mechanical Engineering, Control Science and Information Engineering
  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

A compliant landing strategy for a trotting quadruped robot on unknown rough terrains based on contact force control is presented. Firstly, in order to lower the disturbance caused by the landing impact force, a landing phase is added between the swing phase and the stance phase, where the desired contact force is set as a small positive constant. Secondly, the joint torque optimization of the stance legs is formulated as a quadratic programming (QP) problem subject to equality and inequality/bound constraints. And a primal-dual dynamical system solver based on linear variational inequalities (LVI) is applied to solve this QP problem. Furthermore, based on the optimization results, a hybrid motion/force robust controller is designed to realize the tracking of the contact force, while the constraints of the stance feet landing angles are fulfilled simultaneously. Finally, the experiments are performed to validate the proposed methods.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. PLAYTER R, BUEHLER M, RAIBERT M. BIGDOG. Unmand systems technology [M]. 2006: 1–6.

    Google Scholar 

  2. RAIBERT M, BLANKESPOOR K, NELSON. G. BIGDOG, the rough-terrain quadruped robot [C]// Proceeding of the 17th World Congress. Seoul, Korea, 2008: 10822–10825.

    Google Scholar 

  3. MICHAEL K. Meet boston dynamics. Ls3-the latest robotic war machine [R]. Boston Dynamics Company, 2012.

    Google Scholar 

  4. BOAVENTURA T, SEMINI C, BUCHLI J, FRIGERO M, FOCCHI M, CALDWELL D G. Dynamic torque control of a hydraulic quadruped robot [C]// IEEE Conference on Robotics and Automation. St, Paul, USA, 2012: 1889–1894.

    Google Scholar 

  5. UGURLU B, HAVOUTIS I, SEMINI C, CALDWELL D G. Dynamic trot-walking with the hydraulic quadruped robot-hyq: Analytical trajectory generation and active compliance control [C]// IEEE Conference on Intelligent Robots and Systems. Tokyo, Japan, 2013: 6044–6051.

    Google Scholar 

  6. CHUNG J W, LEE I H, CHO B K, OH J H. Posture stabilization strategy for a trotting point-foot quadruped robot [J]. Journal of Intelligent Robots Systems, 2013, 72(3/4): 325–341.

    Article  Google Scholar 

  7. KAZEMI H, MAJD V J, MOGHADDAM M M. Modeling and robust backstepping control of an underactuated quadruped robot in bounding motion [J]. Robotica, 2013, 31: 423–439.

    Article  Google Scholar 

  8. LONG Teng, WU Xing-ming, CHEN Wei-hai, WANG Jian-hua. Center of gravity balance approach based on CPG algorithm for locomotion control of a quadruped robot [J]. IEEE Transactions on Advanced Intelligent Mechatronics, 2013, 82(12): 325–329.

    Google Scholar 

  9. SEBASITEM G, JOSE S V, AUKE I. Learning robot gait stability using net works as sensing feedback function for central pattern generators [C]// IEEE International Conference on Intelligent Robots and Systems. Tokyo, 2013: 142–201.

    Google Scholar 

  10. KALAKRISHNAN M, BUCHLI J, PASTOR P, MISTRY M, SCHAAL S. Contact consistent control framework for humanoid robots [J]. International Journal of Robotics Research, 2011, 30(2): 236–258.

    Article  Google Scholar 

  11. DEISENROTH M, CALANDRA R, SEYFARTH A, PETERS J. Toward fast policy search for learning legged locomotion [C]// IEEE International Conference on Intelligent Robots and Systems. Portugal, 2012.

    Google Scholar 

  12. FANKHAUSER P, HUTTER M, GEHRING C, BLOESCH M. Reinforcement learning of single legged locomotion [C]// International Conference on Intelligent Robots and Systems. Tokyo, Japan, 2013: 188–193.

    Google Scholar 

  13. LANG Lin, WANG Jian, MA Hong-xu, WEI Qing. Dynamic stability analysis of a trotting quadruped robot on unknown rough terrains [C]// China Automatic Congress. Wuhan, 2015.

    Google Scholar 

  14. ZHANG Y N, GE S S, LEE T H. A unified quadraticprogramming-based dynamical system approach to joint torque optimization of physically constrained redundant manipulators [J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 2004, 34(5): 2126–2132.

    Article  Google Scholar 

  15. ZHANG Y, WANG J, XIA Y. A dual neural network for redundancy resolution of kinematically redundant manipulators subject to joint limits and joint velocity limis [J]. IEEE Transactions on Neural Networks, 2003, 14: 658–667.

    Article  Google Scholar 

  16. ZHANG Y, WANG J. A dual neural network for constrained joint torque optimization of kinematically redundant manipulators [J]. IEEE Transactions on Syst, Man, Cybern B, 2002, 32: 654–662.

    Article  Google Scholar 

  17. LI W, SWETITS J. A new algorithm for solving strictly convex quadratic programs [J]. SIAM J on Optimiz, 1997, 7(3): 595–619.

    Article  MathSciNet  MATH  Google Scholar 

  18. LI Zhi-jun, GE S S. Contact-force distribution optimization and control for quadruped robots using both gradient and adaptive neural networks [J]. IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(8): 1460–1473.

    Article  Google Scholar 

  19. BERTSEKAS D P. Parallel and distributed computation: numerical methods [M]. Englewood Cliffs, NJ: Prentice-Hall, 1989.

    Google Scholar 

  20. FERRIS M C, PANG J S. Complementarity and variational problems: State of the art [M]. Philadelphia, PA: SIAM, 1997.

    Google Scholar 

  21. XIA Y, WANG J. A recurrent neural network for solving linear projection equations [J]. Neural Networks, 2000, 13: 337–350.

    Article  Google Scholar 

  22. HE B, YANG H. A neural network model for monotone linear asymmetric variational inequalities [J]. IEEE Transactions on Neural Networks, 2000, 11: 3–16.

    Article  Google Scholar 

  23. KINDERLEHRER D, STAMPCCHIA G. An introduction to variational inequalities and their applications [M]. New York: Academic, 1980.

    Google Scholar 

  24. RICHARD C, ROBERT D, BISHOP H. Modern control systems [M]. Addison-Wesley, 1998: 210–213.

    Google Scholar 

  25. XU Jia-qi, LANG Lin, MA Hong-xu, WEI Qing. Contact force based compliance control for a trotting quadruped robot [C]// Control and Decision Conference. Qingdao, China, 2015.

    Google Scholar 

  26. ZHANG Xian-peng, LANG Lin, WANG Jian, MA Hong-xu. The quadruped robot locomotion based on force control [C]// Chinese Control and Decision. Qingdao, China, 2015.

    Google Scholar 

  27. XU Jia-qi, GE Li-gang, WANG Jian, WEI Qing, MA Hong-xu. ZMP preview control based compliance control for a walking quadruped robot [C]// International Conference on Information and Automation. Lijiang, China, 2015.

    Google Scholar 

  28. XU, Ke LANG Lin, WEI Qing, MA Hong-xu. Design of single leg foot force controller for hydraulic actuated quadruped robot based on ADRC [C]// The 34th Chinese Conference. Hangzhou, China, 2015.

    Google Scholar 

  29. LIU Yi-zhang, WANG Jian, LANG Lin, MA Hong-xu. Hybrid position/force control of the planar trotting quadruped robot [C]// The 18th International Conference on Climbing and Walking Robots and The Support Technologies for Mobile Machines. Hangzhou, China, 2015.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jian Wang  (王剑).

Additional information

Foundation item: Project(61473304) supported by the National Natural Science Foundation of China; Project(2015AA042202) supported by Hi-tech Research and Development Program of China

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lang, L., Wang, J., Wei, Q. et al. Compliant landing of a trotting quadruped robot based on hybrid motion/force robust control. J. Cent. South Univ. 23, 1970–1980 (2016). https://doi.org/10.1007/s11771-016-3254-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-016-3254-2

Key words

Navigation