# Rigid vs compliant contact: an experimental study on biped walking

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## Abstract

Contact modeling plays a central role in motion planning, simulation and control of legged robots, as legged locomotion is realized through contact. The two prevailing approaches to model the contact consider rigid and compliant premise at interaction ports. Contrary to the dynamics model of legged systems with rigid contact (without impact) which is straightforward to develop, there is no consensus among researchers to employ a standard compliant contact model. Our main goal in this paper is to study the dynamics model structure of bipedal walking systems with rigid contact and a *novel* compliant contact model, and to present experimental validation of both models. For the model with rigid contact, after developing the model of the articulated bodies in flight phase without any contact with environment, we apply the holonomic constraints at contact points and develop a constrained dynamics model of the robot in both single and double support phases. For the model with compliant contact, we propose a novel nonlinear contact model and simulate motion of the robot using this model. In order to show the performance of the developed models, we compare obtained results from these models to the empirical measurements from bipedal walking of the human-size humanoid robot Surena III, which has been designed and fabricated at CAST, University of Tehran. This analysis shows the merit of both models in estimating dynamic behavior of the robot walking on a semi-rigid surface. The model with rigid contact, which is less complex and independent of the physical properties of the contacting bodies, can be employed for model-based motion optimization, analysis as well as control, while the model with compliant contact and more complexity is suitable for more realistic simulation scenarios.

## Keywords

Bipedal locomotion Dynamics modeling Contact modeling Rigid and compliant contact models Foot–ground contact## Notes

### 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: 95849278) to develop the Surena III humanoid robot. We further thank to the members of CAST for their valuable participation in the design and fabrication of the robot.

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