ZMP Support Areas for Multi-contact Mobility Under Frictional Constraints

Stéphane Caron, Quang-Cuong Pham, Yoshihiko Nakamura. IEEE Transactions on Robotics. Submitted 12 October 2015. Accepted 6 September 2016. Published 14 December 2016.


We propose a method for checking and enforcing multi-contact stability based on the Zero-tilting Moment Point (ZMP). The key to our development is the generalization of ZMP support areas to take into account (a) frictional constraints and (b) multiple non-coplanar contacts. We introduce and investigate two kinds of ZMP support areas. First, we characterize and provide a fast geometric construction for the support area generated by valid contact forces, with no other constraint on the robot motion. We call this set the full support area. Next, we consider the control of humanoid robots using the Linear Pendulum Mode (LPM). We observe that the constraints stemming from the LPM induce a shrinking of the support area, even for walking on horizontal floors. We propose an algorithm to compute the new area, which we call pendular support area. We show that, in the LPM, having the ZMP in the pendular support area is a necessary and sufficient condition for contact stability. Based on these developments, we implement a whole-body controller and generate feasible multi-contact motions where an HRP-4 humanoid locomotes in challenging multi-contact scenarios.

Two kinds of ZMP support area


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doi 10.1109/TRO.2016.2623338


  title = {ZMP Support Areas for Multi-contact Mobility Under Frictional Constraints},
  author = {Caron, St{\'e}phane and Pham, Quang-Cuong and Nakamura, Yoshihiko},
  journal = {IEEE Transactions on Robotics},
  publisher = {IEEE},
  doi = {10.1109/TRO.2016.2623338}
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