MPC needs a model, a set of equations describing how the machine responds. At every cycle it solves an optimisation problem: which sequence of commands over the prediction horizon minimises deviation from the goal while respecting constraints such as joint limits, motor torque, or keeping the ground reaction force inside the foot.
Only the first command is executed; the whole calculation is redone with fresh sensor data milliseconds later. That constant replanning is what makes it robust to pushes and modelling errors.
Legged robots use MPC to decide footstep timing and body motion while balancing; it is also common in drone flight control and in process industries, where it has been used for decades. The cost is computation: the optimiser must finish before the next control cycle.
