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Investigation on Dynamic Modeling of SURENA III Humanoid Robot with Heel-Off and Heel-Strike Motions

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Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

The understudy SURENA III humanoid robot was designed and fabricated at the Center of Advanced Systems and Technologies (CAST) located in the University of Tehran. In this paper, a full dynamic model of SURENA III in different walking phases including heel-off and heel-strike motions is presented. To this end, first a trajectory planning method based on robot kinematics is introduced. Then, the multi-body dynamics of the robot links are calculated using Lagrange and Kane approaches which are then verified. In this model, the power transmission system is considered to be ideal. Afterward, system identification routine is adopted to model the dynamic behavior of the power transmission system. By adding the calculated actuating torques obtained from analytical model to the required torques for the drive system, the whole dynamic model of the humanoid robot is computed. Comparing the simulation results and experimental results of SURENA III for different types of gaits, the presented dynamic model is verified. Finally, these gaits are studied from several points of view, including joint energy consumption, range of motion (RoM) and maximum velocity, torque and power. It is shown that by adding heel-off and heel-strike motions to the gait 7.34 and 13.95% less energy is consumed, respectively. Also, the heel-off motion improves the gait performance in terms of ankle energy consumption, RoM and velocity, while the heel-strike motion enhances the gait functionality in terms of knee and hip energy consumption and velocity.

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Abbreviations

DS:

Double support

SS:

Single support

DoF:

Degree of freedom

RoM:

Range of motion

ZMP:

Zero moment point

\(\left[ {\begin{array}{*{20}c} {x_{ar} } & {y_{ar} } & {z_{ar} } \\ \end{array} } \right]\) :

Position of right ankle

\(\left[ {\begin{array}{*{20}c} {\alpha_{fr} } & {\beta_{fr} } & {\gamma_{fr} } \\ \end{array} } \right]\) :

Orientation of right foot

\(\left[ {\begin{array}{*{20}c} {x_{pl} } & {y_{pl} } & {z_{pl} } \\ \end{array} } \right]\) :

Position of pelvis

\(\left[ {\begin{array}{*{20}c} {\alpha_{tr} } & {\beta_{tr} } & {\gamma_{tr} } \\ \end{array} } \right]\) :

Orientation of trunk

\(q = \left[ {\begin{array}{*{20}c} {q_{r} } & {q_{l} } & {q_{pl} } \\ \end{array} } \right]^{\text{T}}\) :

Vector of generalized coordinates

\(\left[ {q_{hx}\,\,q_{hy}\,\,q_{hz}\,\,q_{ky}\,\,q_{ax}\,\,q_{ay} } \right]\) :

Hip, knee and ankle joint angles in X, Y and Z directions

\(M\left( q \right)\) :

Generalized inertia matrix

\(V\left( {q,\dot{q}} \right)\) :

Vector of centrifugal and coriolis terms

\(G\left( q \right)\) :

Vector of gravity forces

\(Q\) :

Generalized force vector

\(B\) :

Matrix of actuating torque selection

\(\tau\) :

Actuating joint torques vector

\(J\left( q \right)\) :

Jacobian matrix

\(F_{sr} = \left[ {F_{{x_{r} }} ,F_{{y_{r} }} ,F_{{z_{r} }} ,M_{{x_{r} }} ,M_{{y_{r} }} ,M_{{z_{r} }} } \right]^{\text{T}}\) :

Ground reactions of right sole

\(F_{sl} = \left[ {F_{{x_{l} }} ,F_{{y_{l} }} ,F_{{z_{l} }} ,M_{{x_{l} }} ,M_{{y_{l} }} ,M_{{z_{l} }} } \right]^{\text{T}}\) :

Ground reactions of left sole

\(F_{tr} = \left[ {F_{{x_{r} }} ,F_{{y_{r} }} ,F_{{z_{r} }} ,M_{{x_{r} }} ,M_{{z_{r} }} } \right]^{\text{T}}\) :

Ground reactions of right toe

\(F_{hl} = \left[ {F_{{x_{l} }} ,F_{{y_{l} }} ,F_{{z_{l} }} ,M_{{x_{l} }} ,M_{{z_{l} }} } \right]^{T}\) :

Ground reactions of left heel

\(A^{\dag }\) :

Moore–Penrose pseudo-inverse of matrix \(A\)

\(\left[ {\begin{array}{*{20}c} {X_{r} } & {Y_{r} } \\ \end{array} } \right]\) :

Position of the right-foot ground reactions

\(\left[ {\begin{array}{*{20}c} {X_{l} } & {Y_{l} } \\ \end{array} } \right]\) :

Position of the left-foot ground reactions

\(I\) :

Motor current

\(K_{i}\) :

Motor torque constant

t :

Time

\(V\) :

Walking velocity of the robot

\(D_{c}\) :

Stride length

\(T_{c}\) :

Walking cycle time

\(T_{d}\) :

DS time

\(T_{s}\) :

SS time

\(T_{sm}\) :

Middle time in SS in which the position of ankle in Z direction is maximum

\(T_{dm1}\) :

First middle time in DS in which the foot rotation around heel ends

\(T_{dm2}\) :

Second middle time in DS in which the foot rotation around toe starts

\(Z_{am}\) :

Position of ankle in Z direction at \(T_{sm}\) Angle of swing foot with respect to the ground at \(T_{sm}\)

\(Q_{fb}\) :

Angle of toe rotation at the end of DS

\(Q_{ff}\) :

Angle of heel rotation at the start of DS

\(X_{ed}\) :

Distance of the pelvis and stance ankle in X direction at the end of SS

\(X_{sd}\) :

Distance of the pelvis and stance ankle in X direction at the start of SS

\(Y_{{pl_{\hbox{max} } }}\) :

Position of pelvis in Y direction at the middle of SS which is maximum

\(Y_{{pl_{d} }}\) :

Position of pelvis in Y direction at the start of DS

\(Z_{{pl_{\hbox{max} } }}\) :

Position of pelvis in Z direction at the middle of SS which is maximum

\(Z_{{pl_{\hbox{min} } }}\) :

Position of pelvis in Z direction at the middle of DS which is minimum

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Acknowledgements

The authors would like to express deep gratitude to the Industrial Development and Renovation Organization of Iran (IDRO) and Iran National Science Foundation (INSF) for their financial support (Project Number: 94000927) to develop the SURENA III humanoid robot. We further thank the members of the Center of Advanced Systems and Technologies (CAST) for their valuable participation in design and fabrication of SURENA III humanoid robot.

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Authors and Affiliations

  1. Center of Advanced Systems and Technologies (CAST), School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Majid Sadedel & Aghil Yousefi-Koma

  2. Center of Excellence in Robotics and Control, Advanced Robotics & Automated Systems (ARAS) Lab, Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran

    Majid Khadiv

  3. Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    Saeed Mansouri

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  1. Majid Sadedel
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  2. Aghil Yousefi-Koma
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  3. Majid Khadiv
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  4. Saeed Mansouri
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Correspondence to Aghil Yousefi-Koma.

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Sadedel, M., Yousefi-Koma, A., Khadiv, M. et al. Investigation on Dynamic Modeling of SURENA III Humanoid Robot with Heel-Off and Heel-Strike Motions. Iran J Sci Technol Trans Mech Eng 41, 9–23 (2017). https://doi.org/10.1007/s40997-016-0042-4

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