Calculating the full contact wrench from the ZMP

[wyqsnddd]

In eq. (9) of the paper Stair Climbing Stabilization of the HRP-4 Humanoid Robot using Whole-body Admittance Control, we obtained force from ZMP. Is it a straight forward result by injecting zmp to eq. (2)?

[stephane-caron]

Basically yes, you get it as follows:

• Start from eq. (1)
• Force: replace the CoM acceleration by eq. (3)
• Moment: the rate of change of the angular momentum around the CoM is zero because we are in the inverted pendulum mode

This gets you to eq. (9).

The relevant part of the code related to this is the final step of computeDesiredWrench(), where the desired CoM acceleration is converted to a spatial force vector (a.k.a. wrench) in the inertial frame.