Stability of Surface Contacts for Humanoid Robots

Closed-Form Formulae of the Contact Wrench Cone for Rectangular Support Areas

Stéphane Caron, Quang-Cuong Pham and Yoshihiko Nakamura. ICRA 2015, Seattle, USA, May 2015.


Humanoids locomote by making and breaking contacts with their environment. Thus, a crucial question for them is to anticipate whether a contact will hold or break under effort. For rigid surface contacts, existing methods usually consider several point-contact forces, which has some drawbacks due to the underlying redundancy. We derive a criterion, the Contact Wrench Cone (CWC), which is equivalent to any number of applied forces on the contact surface, and for which we provide a closed-form formula.

Illustration of the paper's contribution

It turns out that the CWC can be decomposed into three conditions: (i) Coulomb friction on the resultant force, (ii) CoP inside the support area, and (iii) upper and lower bounds on the yaw torque. While the first two are well-known, the third one is novel. It can, for instance, be used to prevent the undesired foot yaws observed in biped locomotion. We show that our formula yields simpler and faster computations than existing approaches for humanoid motions in single support, and assess its validity in the OpenHRP simulator.



  title = {Stability of Surface Contacts for Humanoid Robots: Closed-Form Formulae of the Contact Wrench for Rectangular Support Areas},
  author = {Caron, St{\'e}phane and Pham, Quang-Cuong and Nakamura, Yoshihiko},
  booktitle = {IEEE International Conference on Robotics and Automation},
  year = {2015},
  month = may,
  pages = {5107--5112},
  doi = {10.1109/ICRA.2015.7139910},
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