Design and Equilibrium Control of a Force-Balanced One-Leg Mechanism

  • Hiram PonceEmail author
  • Mario Acevedo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11289)


The problem of equilibrium is critical for planning, control, and analysis of legged robot. Control algorithms for legged robots use the equilibrium criteria to avoid falls. The computational efficiency of the equilibrium tests is critical. To comply with this it is necessary to calculate the horizontal momentum rotation for every moment. For arbitrary contact geometries, more complex and computationally-expensive techniques are required. On the other hand designing equilibrium controllers for legged robots is a challenging problem. Nonlinear or more complex control systems have to be designed, complicating the computational cost and demanding robust actuators. In this paper, we propose a force-balanced mechanism as a building element for the synthesis of legged robots that can be easily balance controlled. The mechanism has two degrees of freedom, in opposition to the more traditional one degree of freedom linkages generally used as legs in robotics. This facilitates the efficient use of the “projection of the center of mass” criterion with the aid of a counter rotating inertia, reducing the number of calculations required by the control algorithm. Different experiments to balance the mechanism and to track unstable set-point positions have been done. Proportional error controllers with different strategies as well as learning approaches, based on an artificial intelligence method namely artificial hydrocarbon networks, have been used. Dynamic simulations results are reported. Videos of experiments will be available at:


Mechanical design Legged robots Equilibrium Control systems Artificial hydrocarbon networks Reinforcement learning 


  1. 1.
    Wieber, P.-B., Tedrake, R., Kuindersma, S.: Modeling and control of legged robots. In: Siciliano, B., Khatib, O. (eds.) Springer Handbook of Robotics, 2nd edn, pp. 1203–1234. Springer, Cham (2016). Scholar
  2. 2.
    Rebula, J.R., Neuhaus, P.D., Bonnlander, B.V., Johnson, M.J., Pratt, J.E.: A controller for the LittleDog quadruped walking on rough terrain. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1467–1473 (2007)Google Scholar
  3. 3.
    Yoshida, E., Kanoun, O., Esteves, C., Laumond, J.P.: Task-driven support polygon reshaping for humanoids. In: Proceedings of the 2006 6th IEEE-RAS International Conference on Humanoid Robots, HUMANOIDS, pp. 208–213 (2006)Google Scholar
  4. 4.
    Del Prete, A., Tonneau, S., Mansard, N.: Fast algorithms to test static equilibrium for legged robots. In: IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, May 2016, pp. 1601–1607 (2016)Google Scholar
  5. 5.
    Najafi, E., Lopes, G.A.D., Babuska, R.: Balancing a legged robot using state-dependent Riccati equation control. IFAC Proc. Volumes 47(3), 2177–2182 (2014)CrossRefGoogle Scholar
  6. 6.
    Grasser, F., D’Arrigo, A., Colombi, S., Rufer, A.C.: JOE: a mobile, inverted pendulum. IEEE Trans. Ind. Electron. 49(1), 107–114 (2002)CrossRefGoogle Scholar
  7. 7.
    Kashki, M., Zoghzoghy, J., Hurmuzlu, Y.: Adaptive control of inertially actuated bouncing robot. IEEE Trans. Robot. 33(3), 509–522 (2017)CrossRefGoogle Scholar
  8. 8.
    Wensing, P., Wang, A., Seok, S., Otten, D., Lang, J., Kim, S.: Proprioceptive actuator design in the MIT Cheetah: impact mitigation and high-bandwidth physical interaction for dynamic legged robots. IEEE/ASME Trans. Mechatron. 22(5), 2196–2207 (2017)CrossRefGoogle Scholar
  9. 9.
    Komoda, K., Wagatsuma, H.: Energy-efficacy comparisons and multibody dynamics analyses of legged robots with different closed-loop mechanisms. Multibody Syst. Dyn. 40, 123–153 (2017)MathSciNetCrossRefGoogle Scholar
  10. 10.
    van der Wijk, V., Herder, J.L.: Synthesis of dynamically balanced mechanisms by using counter-rotary countermass balanced double pendula. ASME J. Mech. Des. 131(11), 111003-1–111003-8 (2009). Scholar
  11. 11.
    García de Jalón, J., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems: The Real-Time Challenge. Springer, New York (1994). Scholar
  12. 12.
    Munoz de Cote, E., Garcia, E.O., Morales, E.F.: Transfer learning by prototype generation in continuous spaces. Adapt. Behav. 24(6), 464–478 (2016)CrossRefGoogle Scholar
  13. 13.
    Molina, A., Ponce, H., Ponce, P., Tello, G., Ramirez, M.: Artificial hydrocarbon networks fuzzy inference systems for CNC machines position controller. Int. J. Adv. Manuf. Technol. 72(9–12), 1465–1479 (2014)CrossRefGoogle Scholar
  14. 14.
    Nagabandi, A., Yang, G., Asmar, T., Kahn, G., Levine, S., Fearing, R.S.: Neural network dynamics models for control of under-actuated legged millirobots. arXiv:1711.05253 (2017)
  15. 15.
    Sung-Kwun, O., Pedrycz, W., Rho, S.-B., Ahn, T.-C.: Parameter estimation of fuzzy controlle and its application to inverted pendulum. Eng. Appl. Artif. Intell. 17(1), 37–60 (2004)CrossRefGoogle Scholar
  16. 16.
    Ponce, H., Ponce, P.: Artificial organic networks. In: In 2011 IEEE Conference on Electronics, Robotics and Automotive Mechanics, pp. 29–34. IEEE, Cuernavaca (2011)Google Scholar
  17. 17.
    Ponce-Espinosa, H., Ponce-Cruz, P., Molina, A.: Artificial Organic Networks. SCI, vol. 521. Springer, Cham (2014). Scholar
  18. 18.
    Ponce, H., Ponce, P., Molina, A.: The development of an artificial organic networks toolkit for LabVIEW. J. Comput. Chem. 36(7), 478–492 (2015)CrossRefGoogle Scholar
  19. 19.
    Ponce, H.: A novel artificial hydrocarbon networks based value function approximation in hierarchical reinforcement learning. In: Pichardo-Lagunas, O., Miranda-Jiménez, S. (eds.) MICAI 2016. LNCS (LNAI), vol. 10062, pp. 211–225. Springer, Cham (2017). Scholar
  20. 20.
    Ponce, H., Ponce, P., Molina, A.: Artificial hydrocarbon networks fuzzy inference system. Math. Probl. Eng. 1–13, 2013 (2013)Google Scholar
  21. 21.
    Ponce, H., Ponce, P., Molina, A.: A novel robust liquid level controller for coupled-tanks systems using artificial hydrocarbon networks. Expert Syst. Appl. 42(22), 8858–8867 (2015)CrossRefGoogle Scholar
  22. 22.
    Rao, A.: A survey of numerical method for optimal control. Adv. Astronaut. Sci. 135, 497–528 (2009)Google Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Facultad de IngenieríaUniversidad PanamericanaMexico CityMexico

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