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Foot Shape-Dependent Resistive Force Model for Bipedal Walkers on Granular Terrains

Xunjie Chen, Aditya Anikode, Jingang Yi, Tao Liu

Abstract

Legged robots have demonstrated high efficiency and effectiveness in unstructured and dynamic environments. However, it is still challenging for legged robots to achieve rapid and efficient locomotion on deformable, yielding substrates, such as granular terrains. We present an enhanced resistive force model for bipedal walkers on soft granular terrains by introducing effective intrusion depth correction. The enhanced force model captures fundamental kinetic results considering the robot foot shape, walking gait speed variation, and energy expense. The model is validated by extensive foot intrusion experiments with a bipedal robot. The results confirm the model accuracy on the given type of granular terrains. The model can be further integrated with the motion control of bipedal robotic walkers.

Foot Shape-Dependent Resistive Force Model for Bipedal Walkers on Granular Terrains

Abstract

Legged robots have demonstrated high efficiency and effectiveness in unstructured and dynamic environments. However, it is still challenging for legged robots to achieve rapid and efficient locomotion on deformable, yielding substrates, such as granular terrains. We present an enhanced resistive force model for bipedal walkers on soft granular terrains by introducing effective intrusion depth correction. The enhanced force model captures fundamental kinetic results considering the robot foot shape, walking gait speed variation, and energy expense. The model is validated by extensive foot intrusion experiments with a bipedal robot. The results confirm the model accuracy on the given type of granular terrains. The model can be further integrated with the motion control of bipedal robotic walkers.
Paper Structure (12 sections, 12 equations, 6 figures, 1 table)

This paper contains 12 sections, 12 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Dynamic RFT Model for Bipedal Foot
  3. 3D RFT Configuration
  4. Dynamic RFT with Intrusion Depth Correction
  5. Foot Intrusion Motion of Bipedal Walking
  6. Experiments
  7. Force Model Experiments
  8. Bipedal Robotic Walker Experiments
  9. Experimental Results
  10. Force Model Validation
  11. Robotic Foot-Terrain Interactions
  12. Conclusion

Figures (6)

  • Figure 1: (a) The general 3D plate intrusion configuration of plate $dS_i$. (b) The schematic of horizontal intrusion with the height difference of the free surfaces in the leading and trailing zones.
  • Figure 2: Bipedal robot walks on the granular terrain (single stance phase).
  • Figure 3: The experimental setups. (a) RFT calibrations including vertical penetration tests for scale factor $\zeta$ and horizontal penetration tests for $f_1$ and $f_{23}$. (b) Humanoid walking gait capture using Vicon system. (c) Bipedal foot-terrain intrusions using a robotic leg. (d) Two selected non-flat foot models.
  • Figure 4: Plate calibration results. (a) Vertical penetration resistive force versus intrusion depth. (b) Tangential and normal force relationship. $f_1$ and $f_{23}$ were fitted by sigmoid functions. (c) Horizontal penetration results under different velocities.
  • Figure 5: Dynamic RFT for foot-terrain intrusion results. (a) Human walking gait re-construction. (b) Forces of the robotic foot (ellipse) in sands. Blue solid lines present simulation results using the proposed method with the structural correction term. The first, second and third columns are for $F_x$, $F_y$, and $F_z$, respectively. The top, middle, and bottom rows show the slow ($T_g=13.5$ s), medium ($T_g=4.5$ s) and fast ($T_g=2.3$ s) gait speed intrusions, respectively. (c) The forces of the robotic foot with three shapes.
  • ...and 1 more figures