Humanoid locomotion requires deciding where to step and how to distribute contact forces. However, a disturbance can invalidate the nominal plan, requiring coordinated revision under constraints that switch with every footfall. To solve this online, the proposed approach employs the single-rigid-body model, which retains attitude dynamics and the full contact wrench. An iterative linear-quadratic-regulator MPC (iLQR-MPC) then jointly optimizes contact forces and footstep locations in a single receding-horizon problem, without a separate step planner. Specifically, contact and motion constraints are incorporated into the backward pass through augmented-Lagrangian and relaxed-barrier penalties. A whole-body controller subsequently maps the plan to joint torques at 500 Hz while preserving contact feasibility. The model-based formulation makes disturbance responses interpretable through explicit costs and constraints, and requires no platform-specific policy training. In MuJoCo simulations, the iLQR-MPC replans at 100 Hz (mean solve time 8.9 ms); the Unitree G1 sustains steady-state walking and recovers from impulsive 245 N forward and 175 N lateral pushes.

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