  This study deals with the balance of humanoid or multi-legged robots in a
multi-contact setting where a chosen subset of contacts is undergoing desired
sliding-task motions. One method to keep balance is to hold the center-of-mass
(CoM) within an admissible convex area. This area should be calculated based on
the contact positions and forces. We introduce a methodology to compute this
CoM support area (CSA) for multiple fixed and sliding contacts. To select the
most appropriate CoM position inside CSA, we account for (i) constraints of
multiple fixed and sliding contacts, (ii) desired wrench distribution for
contacts, and (iii) desired position of CoM (eventually dictated by other
tasks). These are formulated as a quadratic programming optimization problem.
We illustrate our approach with pushing against a wall and wiping and conducted
experiments using the HRP-4 humanoid robot.
