Humanoid Loco-Manipulation

Carrying something while walking couples two problems. The load in the arms shifts the center of mass forward, so the robot must lean back or bring the load closer to stay balanced, and its walking controller must account for the extra mass. Humanoid robots doing warehouse work face exactly this.

Box mass How far the box is held out Lean back to compensate

Keeping the center of mass over the feet

For a body of mass $M$ with its own center of mass at $x_b$, carrying a load $m$ held at $x_l$, the combined center of mass is

$$x_c = \frac{M\,x_b + m\,x_l}{M + m}$$

To keep $x_c$ over the support foot, the body must shift back by $\Delta x_b = -\frac{m}{M}\,(x_l - x_b)$, by leaning or by stepping differently.

What to notice

With compensation off, a heavy box pushes the center of mass in front of the foot and the robot tips forward. With it on, the torso leans back and the readout shows how much. Holding the box closer reduces the lean needed, which is why people hug heavy loads to their chest. Real humanoids also plan footsteps and arm motions together, often in one whole-body optimization, so the hands keep their grip while the legs keep their balance.