A Sliding Mode Controler of Hips Actuated for Passive Walking Robots

Document Type : Original Research (Full Papers)


1 Mechanical Engineering Department, Islamic Azad University Tehran North Branch, Tehran, Iran

2 Management Engineering Department, Azad University Science and Research Branch, Tehran, Iran

3 Mechanical Engineering Department, Azad University Science and Research Branch, Tehran, Iran


This paper addresses the application of using pneumatic force actuators at the hips of a five-link robotic system to provide a controllable input torque. The goal of this research is to provide a base to build upon to eventually produce an ” active” biped walking robot that utilizes the benefits of the passive walking cycle. A reduced-order mathematical model of the system consisting of the pneumatic proportional valve and actuators is utilized in designing the force controller. The model takes into account tube links, valve friction, piston friction, and valve mechanics. The five-link robot is also modeled, including moments of inertia, masses, and centers of mass to design the trajectory controller. The mathematical models provide the equations necessary to develop the nonlinear control laws based on Sliding Mode Control Theory for both the force and trajectory controller. The controllers receive input signals from both pressure and position sensors located at the hips and position sensors at the knees. These signals are then converted into digital signals and processed by the computer using numerical analysis to obtain ethical values. Once the signals are input into the controllers, the experimental results of the actual system track the desired force and position trajectories defined for each controller within desired limits.


[1] Razzaghi, P.; Assadian, N., "Study of the triple-mass tethered satellite system under aerodynamic drag and j2 perturbations", Advances in Space Research, vol. 56, no. 10, pp. 2141–2150 (2015). 
[2] Razzaghi, P.; Al Khatib, E.; Bakhtiari, S., "Sliding mode and SDRE control laws on a tethered satellite system to de-orbit space debris", Advances in Space Research, vol. 64, no. 1, pp. 18–27 (2019). 
[3] Khiabani, A. G.; Babazadeh, R., "Design of robust fractional-order lead–lag  controller  for  uncertain  systems",  IET  Control  Theory  & Applications, vol. 10, no. 18, pp. 2447–2455 (2016). 
[4] Navabi, M.; Mirzaei, H., "Robust optimal adaptive trajectory tracking control of quadrotor helicopter", Latin American Journal of Solids and Structures, vol. 14, no. 6, pp. 1040–1063 (2017). 
[5] Navabi,  M.;  Mirzaei,  H.,  "θd  based  nonlinear  tracking  control  of quadcopter", in 2016 4th International Conference on Robotics and Mechatronics (ICROM). IEEE, pp. 331–336 (2016). 
[6] Al Khatib, E. I.; Al-Masri, W. M.; Mukhopadhyay, S.; Jaradat, M. A.; Abdel-Hafez,  M.,  "A  comparison  of  adaptive  trajectory  tracking controllers  for  wheeled  mobile  robots",  in  Mechatronics  and  its Applications (ISMA), 2015 10th International Symposium on. IEEE, pp. 1–6 (2015). 
[7] Al  Khatib,  E.  I.;  Jaradat,  M.  A.;  Abdel-Hafez,  M.;  Roigari,  M., "Multiple sensor fusion for mobile robot localization and navigation using  the  extended  kalman  filter",  in  Mechatronics  and  its Applications (ISMA), 2015 10th International Symposium on. IEEE, pp. 1–5 (2015). 
[8] Nateghi, S.; Shtessel, Y.; Barbot, J.-P.; Zheng, G.; Yu, L., "Cyber-attack  reconstruction  via  sliding  mode  differentiation  and  sparse recovery algorithm: Electrical power networks application", in 2018 15th  International  Workshop  on  Variable  Structure  Systems  (VSS). IEEE, pp. 285–290 (2018). 
[9] Nateghi, S.; Shtessel, Y.; Barbot, J.-P.; Edwards, C., "Cyber attack reconstruction  of  nonlinear  systems  via  higher-order  sliding-mode observer and sparse recovery algorithm", in 2018 IEEE Conference on Decision and Control (CDC). IEEE, 2018, pp. 5963–5968 (2018). 
[10] McGeer,  T.,  "Passive  dynamic  walking",  International  Journal  of Robotic Research., vol. 9, no. 2, pp. 62–82 (1990). 
[11] McGeer,  T.,  "Passive  walking  with  knees",  in  Proceedings.,  IEEE International  Conference  on  Robotics  and  Automation,  May  1990, vol. 3, pp. 1640–1645 (1990). 
[12] Camp,  J.,  "Powered  “passive”  dynamic  walking",  Masters  of Engineering Project Report, Cornell University (1997). 
[13] Coleman, M. J.; Ruina, A., "An uncontrolled walking toy that cannot stand still", Physical Review Letters, vol. 80, no. 16, pp. 3658-3661 (1998). 
[14] Garcia, M.; Chatterjee, A.; Ruina, A.; Coleman, M., "The simplest walking  model:  stability,  complexity,  and  scaling",  Journal  of biomechanical engineering, vol. 120, no. 2, pp. 281–288 (1998). 
[15] Van Der Linde, R. Q., "Active leg compliance for passive walking", in Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No. 98CH36146), vol. 3, pp. 2339–2344 (1998). 
[16] Van Der Linde, R. Q., "Passive bipedal walking with phasic muscle contraction",  Biological  cybernetics,  vol.  81,  no.  3,  pp.  227–237 (1999). 
[17] Spong, M. W., "Passivity based control of the compass gait biped", in Proc. of IFAC World Congress, pp. 19–23 (1999). 
[18] Goswami,  A.;  Espiau,  B.;  Keramane,  A.,  "Limit  cycles  and  their stability  in  a  passive  bipedal  gait",  in  Proceedings  of  IEEE International Conference on Robotics and Automation, vol. 1. IEEE, 1996, pp. 246–251 (1996). 
[19]  Kuo,  A.  D.,  "Stabilization  of  lateral  motion  in  passive  dynamic walking", The International journal of robotics research, vol. 18, no. 9, pp. 917–930 (1999). 
[20]  Wisse, M.; Schwab, A. L., "A 3d passive dynamic biped with yaw and roll compensation", Robotica, vol. 19, no. 3, pp. 275–284 (2001). 
[21]  Collins, S. H.; Wisse, M.; Ruina, A., "A three-dimensional passive-dynamic walking robot with two legs and knees", The International Journal of Robotics Research, vol. 20, no. 7, pp. 607–615 (2001). 
[22]  Nikkhah,  M.;  Ashrafiuon,  H.;  Fahimi,  F.,  "Robust  control  of underactuated bipeds using sliding modes", Robotica, vol. 25, no. 3, pp. 367-374 (2007). 
[23]  Rahmani, M.; Ghanbari, A.; Ettefagh, M., "A novel adaptive neural network  integral  sliding-mode  control  of  a  biped  robot  using  bat algorithm",  Journal of  Vibration and Control, vol.  24, no. 10,  pp. 2045-2060 (2019). 
[24]  Taherkhorsandi, M.; Mahmoodabadi, M. J.; Talebipour, M.; Castillo-Villar, K. K., "Pareto design of an adaptive robust hybrid of PID and sliding control for a biped robot via genetic algorithm optimization", Nonlinear dynamics, vol. 79, no. 1, pp. 251-263 (2015). 
[25]   Slotine, J.-J. E.; Li, W., "Applied nonlinear control", Prentice hall Englewood Cliffs, NJ, vol. 199, no. 1 (1991). 
Volume 12, Issue 1
June 2019
Pages 103-112
  • Receive Date: 07 June 2019
  • Revise Date: 07 August 2019
  • Accept Date: 04 November 2019
  • First Publish Date: 04 November 2019