Why is the ZMP reference position below the ankle?

[stephane-caron]

I'm reproducing here the discussion from jrl-umi3218#33.

There are two common choices of ZMP reference in the MPC, depending on the robot's most prominent constraint:

• Minimize ankle joint torques: the optimal solution is then to select the ZMP at the "ankle" frame. (We call it the ankle frame but it lies on the sole.) See Optimizing foot centers of pressure through force distribution in a humanoid robot (Wensing et al., 2013) for details. This approach results in lower ankle torques but a higher risk of foot tilting.
• Maximize distance to sole edges: in that case, the optimal solution is indeed to select to foot center frame. Reduces the risk of foot tilting but increases ankle torques.

The appropriate solution depends on your system. On HRP robot, there is one extra reason for keeping the ZMP at the ankle frame: it reduces the restoring wrench of the foot flexibility mechanism (Fig. 3.11 of Introduction to Humanoid Robotics, Kajita et al., 2014) and thus the deflection of the unobserved joint between the ankle frame and the ground.