Optimal Stair Climbing Pattern Generation for Humanoids Using Virtual Slope and Distributed Mass Model

  • Ahmadreza Shahrokhshahi
  • Aghil Yousefi-KomaEmail author
  • Majid Khadiv
  • Saeed Mansouri
  • Seyed Saeid Mohtasebi


This study addresses optimal walking pattern generation for SURENA III humanoid robot in a stair-climbing scenario. To this end, the kinematic configuration of the 31-DOF humanoid robot is studied. Integrating the detailed dynamic properties of the robot, a comprehensive and precise dynamic model is developed for its lower-limb. In order to generate the optimal walking pattern for the considered humanoid robot, trajectories for feet and pelvis are first designed, and then joint angles are derived by means of inverse kinematics. Such a complete model provides the designer with the necessary tools to optimize the trajectory generation. Using two different types of objective functions, namely joints maximum torque and overall energy consumption, several optimization processes have been carried out to account for different stair-climbing speeds as well as different stair heights. Subsequently, the optimal walking patterns are obtained by applying the Genetic Algorithm (GA). The simulation results are verified experimentally by implementing the proposed walking patterns on SURENA III, a humanoid robot designed and fabricated in CAST (Center of Advanced Systems and Technologies). This paper provides insight into how an optimized gait for climbing stairs can be realized for a human-size humanoid robot from two different viewpoints and at several walking speeds and stair heights by assuming each stair as a virtual slope.


Humanoid robot Distributed mass model Stair Trajectory generation Virtual slope Zero-Moment Point (ZMP) 


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The authors would like to thank CAST members who provided insight and expertise that greatly assisted this research and Iran National Science Foundation (INSF) for their financial support.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Ahmadreza Shahrokhshahi
    • 1
  • Aghil Yousefi-Koma
    • 2
    Email author
  • Majid Khadiv
    • 3
  • Saeed Mansouri
    • 4
  • Seyed Saeid Mohtasebi
    • 5
  1. 1.Mechatronic Systems EngineeringSimon Fraser UniversityBritish ColumbiaCanada
  2. 2.Department of Mechanical Engineering, School of EngineeringUniversity of TehranTehranIran
  3. 3.Max Planck Institute for Intelligent SystemsStuttgartGermany
  4. 4.Department of Mechanical EngineeringSharif University of TechnologyTehranIran
  5. 5.Department of Mechanical Engineering of Agricultural MachineryUniversity of TehranAlborzIran

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