Journal of Intelligent & Robotic Systems

, Volume 88, Issue 1, pp 37–56 | Cite as

Generating Feasible Solutions for Dynamically Crossing a Wide Ditch by a Biped Robot

  • Janardhan V.
  • Prasanth Kumar R.


The aim of this research work is to generate feasible motion for a biped robot to dynamically cross a wide ditch which is defined as a ditch with width more than or equal to the leg length. We propose an approach to obtain feasible solutions for dynamically crossing the wide ditch considering the dynamic balance of the biped robot, friction between the robot foot and ground, impact on the foot, limitations on the joint actuator torques and angular velocities. The biped robot is modeled as a seven link planar robot with the ditch crossing task consisting of two single support phases and a double support phase. An algorithm is developed to find the joint trajectories and the joint torques in each phase of ditch crossing by formulating the ditch crossing task as a constrained nonlinear optimization problem. In order to make the algorithm converge fast and to give feasible solutions, additional constraints called Adopted Constraints (ACs) are incorporated into the system of constraints. With time being one of the parameters, the developed algorithm adaptively adjusts the time for crossing a wide ditch. The significance of ground reaction force constraints in obtaining feasible solutions for crossing the wide ditch is shown through simulations. Feasible solutions obtained from simulation results provide not only the feasible joint angle trajectories, but also the joint torques required for the selection of actuators for a biped robot crossing the wide ditch.


Biped robot Ditch crossing Wide ditch Motion planning 


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  1. 1.
    Al-Shuka, H., Corves, B., Zhu, W.H.: Dynamic modeling of biped robot using lagrangian and recursive newton-euler formulations. Int. J. Comput. Appl. 101, 1–8 (2014)Google Scholar
  2. 2.
    Azevedo, C., Poignet, P., Espiau, B.: On line optimal control for biped robots. In: Proceedings of the IFAC 15th World Congress (2002)Google Scholar
  3. 3.
    Caballero, R., Armada, M.: Zero moment point modeling using harmonic balance. In: Climbing and Walking Robots, pp. 689–699. Springer (2005)Google Scholar
  4. 4.
    Cheng, J., Pan, J.: Ditch crossing control for quadruped walking robot. In: IROS’93. Proceedings of the 1993 IEEE/RSJ International Conference on Intelligent Robots and Systems’ 93, vol. 1, pp. 537–541. IEEE (1993)Google Scholar
  5. 5.
    Choi, B.S., Song, S.M.: Fully automated obstacle-crossing gaits for walking machines. IEEE Trans. Syst., Man Cybern. 18(6), 952–964 (1988)CrossRefGoogle Scholar
  6. 6.
    Doubliez, P.F., Bruneau, O., Ouezdou, F.B.: Dynamic obstacle crossing by a biped robot, based on control of the propulsion energy. In: 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 3144–3149. IEEE (2010)Google Scholar
  7. 7.
    Fattah, A., Fakhari, A.: Trajectory planning of walking with different step lengths of a seven-link biped robot. In: ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 1361–1369. American Society of Mechanical Engineers (2010)Google Scholar
  8. 8.
    Fu, C., Chen, K.: Gait synthesis and sensory control of stair climbing for a humanoid robot. IEEE Trans. Indust. Electron. 55(5), 2111–2120 (2008)CrossRefGoogle Scholar
  9. 9.
    Guan, Y., Neo, E.S., Yokoi, K., Tanie, K.: Stepping over obstacles with humanoid robots. IEEE Trans. Robot. 22(5), 958–973 (2006)CrossRefGoogle Scholar
  10. 10.
    Guan, Y., Yokoi, K., Sian, N.E., Tanie, K.: Feasibility of humanoid robots stepping over obstacles. In: 2004.(IROS 2004). Proceedings. 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 1, pp. 130–135. IEEE (2004)Google Scholar
  11. 11.
    Guan, Y., Yokoi, K., Tanie, K.: Feasibility: Can humanoid robots overcome given obstacles?. In: 2005. ICRA 2005. Proceedings of the 2005 IEEE International Conference on Robotics and Automation, pp. 1054–1059. IEEE (2005)Google Scholar
  12. 12.
    Guo, F., Mei, T., Luo, M., Ceccarelli, M., Zhao, Z., Li, T., Zhao, J.: Motion planning for humanoid robot dynamically stepping over consecutive large obstacles. Indust. Robot: Int. J. 43(2), 204–220 (2016)CrossRefGoogle Scholar
  13. 13.
    Heydari, R., Farrokhi, M.: Model predictive control for biped robots in climbing stairs. In: 2014 22nd Iranian Conference on Electrical Engineering (ICEE), pp. 1209–1214. IEEE (2014)Google Scholar
  14. 14.
    Huang, Q., Yokoi, K., Kajita, S., Kaneko, K., Arai, H., Koyachi, N., Tanie, K.: Planning walking patterns for a biped robot. IEEE Trans. Robot. Autom. 17(3), 280–289 (2001)CrossRefGoogle Scholar
  15. 15.
    Jafri, A.R., Huang, Q., Yang, J., Wang, Z., Xiao, T.: Motion planning for stepping on/off obstacles by humanoid robot. In: 2007. ICMA 2007. International Conference on Mechatronics and Automation, pp. 1154–1159. IEEE (2007)Google Scholar
  16. 16.
    Kajita, S., Kanehiro, F., Kaneko, K., Fujiwara, K., Harada, K., Yokoi, K., Hirukawa, H.: Resolved momentum control: Humanoid motion planning based on the linear and angular momentum. In: 2003. (IROS 2003). Proceedings. 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 2, pp. 1644–1650. IEEE (2003)Google Scholar
  17. 17.
    Kalamian, N., Farrokhi, M.: Dynamic walking of biped robots with obstacles using predictive controller. In: 2011 1st International eConference on Computer and Knowledge Engineering (ICCKE), pp. 105–110. IEEE (2011)Google Scholar
  18. 18.
    Kalamian, N., Farrokhi, M.: Stepping of biped robots over large obstacles using nmpc controller. In: 2011 2nd International Conference on Control, Instrumentation and Automation (ICCIA), pp. 917–922. IEEE (2011)Google Scholar
  19. 19.
    Kaneko, K., Kanehiro, F., Kajita, S., Hirukawa, H., Kawasaki, T., Hirata, M., Akachi, K., Isozumi, T.: Humanoid robot hrp-2. In: 2004. Proceedings. ICRA ’04. 2004 IEEE International Conference on Robotics and Automation, vol. 2, pp. 1083–1090. doi: 10.1109/ROBOT.2004.1307969 (2004)
  20. 20.
    Kaneko, T., Sekiya, M., Ogata, K., Sakaino, S., Tsuji, T.: Force control of a jumping musculoskeletal robot with pneumatic artificial muscles. In: 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 5813–5818. IEEE (2016)Google Scholar
  21. 21.
    Kapandji, I.: The Physiology of the Joints. Volume 2: Lower Limb. Churchill Livingstone (1974).
  22. 22.
    Kato, I.: The hydraulically powered biped walking machine with a high carrying capacity. In: Proceedings of the 4th Int. Symposium on External Control of Human Extremities, Dubrovnik, pp. 410–421 (1972)Google Scholar
  23. 23.
    Kushida, D., Takemori, F., Kitamura, A.: Stepping over excess of obstacle for biped robot based on hybrid control. In: IFAC World Congress, vol. 16 (2005)Google Scholar
  24. 24.
    Lathan, L., Rani, B., Vundavilli, P.R.: Analytical approach for generating dynamically balanced gaits for obstacle crossing biped robot. In: 2012 International Conference on Advances in Engineering, Science and Management (ICAESM), pp. 187–191. IEEE (2012)Google Scholar
  25. 25.
    Motahar, M.S., Veer, S., Huang, J., Poulakakis, I.: Integrating dynamic walking and arm impedance control for cooperative transportation. In: 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1004–1010. IEEE (2015)Google Scholar
  26. 26.
    Mu, X., Wu, Q.: Dynamic modeling and sliding mode control of a five-link biped during the double support phase. In: American Control Conference, 2004. Proceedings of the 2004, vol. 3, pp. 2609–2614. IEEE (2004)Google Scholar
  27. 27.
    Murray, R.M., Li, Z., Sastry, S.S., Sastry, S.S.: A mathematical introduction to robotic manipulation. CRC press (1994)Google Scholar
  28. 28.
    Nikravesh, P.E.: Planar multibody dynamics: Formulation, Programming and Applications. CRC press (2007)Google Scholar
  29. 29.
    Shih, C.L.: Ascending and descending stairs for a biped robot. IEEE Trans. Syst., Man Cybern., Part A: Syst. Hum. 29(3), 255–268 (1999)CrossRefGoogle Scholar
  30. 30.
    Siciliano, B., Khatib, O.: Springer handbook of robotics. Springer Science & Business Media (2008)Google Scholar
  31. 31.
    Smyth, G.K.: Polynomial approximation. Encyclopedia of Biostatistics (1998)Google Scholar
  32. 32.
    Stasse, O., Verrelst, B., Vanderborght, B., Yokoi, K.: Strategies for humanoid robots to dynamically walk over large obstacles. IEEE Trans. Robot. 25(4), 960–967 (2009)CrossRefGoogle Scholar
  33. 33.
    Tözeren, A.: Human body dynamics: classical mechanics and human movement. Springer Science & Business Media (2000)Google Scholar
  34. 34.
    Tzafestas, S., Raibert, M., Tzafestas, C.: Robust sliding-mode control applied to a 5-link biped robot. J. Intell. Robot. Syst. 15(1), 67–133 (1996)CrossRefGoogle Scholar
  35. 35.
    Verrelst, B., Stasse, O., Yokoi, K., Vanderborght, B.: Dynamically stepping over obstacles by the humanoid robot hrp-2. In: 2006 6th IEEE-RAS International Conference on Humanoid Robots, pp. 117–123. IEEE (2006)Google Scholar
  36. 36.
    Verrelst, B., Yokoi, K., Stasse, O., Arisumi, H., Vanderborght, B.: Mobility of humanoid robots: Stepping over large obstacles dynamically. In: Proceedings of the 2006 IEEE International Conference on Mechatronics and Automation, pp. 1072–1079. IEEE (2006)Google Scholar
  37. 37.
    Vukobratović, M., Borovac, B.: Zero-moment point—thirty five years of its life. Int. J. Humanoid Robot. 1(01), 157–173 (2004)CrossRefGoogle Scholar
  38. 38.
    Vundavilli, P.R., Pratihar, D.K.: Dynamically balanced optimal gaits of a ditch-crossing biped robot. Robot. Auton. Syst. 58(4), 349–361 (2010)CrossRefGoogle Scholar
  39. 39.
    Yuan, Q., Chen, I.M.: Planar jumping with stable landing through foot orientation design and ankle joint control. Front. Mech. Eng. 7(2), 100–108 (2012)CrossRefGoogle Scholar
  40. 40.
    Zhong, Q.B., Chen, F.: Trajectory planning for biped robot walking on uneven terrain—taking stepping as an example CAAI. Transactions on Intelligence Technology (2016)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of Mechanical & Aerospace EngineeringIndian Institute of Technology HyderabadKandiIndia

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