We address the problem of humanoid locomotion in 3D environments consisting of planar regions with arbitrary inclination and elevation, such as staircases, ramps, and multi-floor layouts. The proposed framework combines an offline randomized footstep planner with an online control pipeline that includes a model predictive controller for gait generation and a whole-body controller for computing robot torque commands. The planner efficiently explores the environment and returns the highest-quality plan it can find within a user-specified time budget, while the control layer ensures dynamic balance and adequate ground friction. The complete framework was evaluated via dynamic simulation in MuJoCo, placing the JVRC1 humanoid in four scenarios of varying complexity.

We address the problem of humanoid locomotion in a 3D environment composed of planar regions with arbitrary inclination and elevation, which includes staircases, ramps, and multi‑floor layouts. The proposed framework couples an off‑line randomized footstep planner with an on‑line control pipeline comprising a model predictive controller and a whole‑body controller which provides the robot torque commands. The planner efficiently explores the environment without predefined motion primitives and returns the highest-quality plan it can find within a user‑specified time budget, while the control layer ensures dynamic balance and adequate ground friction. The complete pipeline is evaluated in MuJoCo using the JVRC1 humanoid across four scenarios of increasing complexity.