A humanoid robot with a body joined to an omnidirectional mobile ground base, equipped with: a body position sensor, a base position sensor and an angular velocity sensor to provide measures, actuators comprising at least 3 wheels located in the omnidirectional mobile base, extractors for converting sensored measures into useful data, a supervisor to calculate position, velocity and acceleration commands from the useful data, means for converting commands into instructions for the actuators, wherein the supervisor comprises: a no-tilt state controller, a tilt state controller and a landing state controller, each controller comprising means for calculating, position, velocity and acceleration commands based on a double point-mass robot model with tilt motion and on a linear model predictive control law, expressed as a quadratic optimization formulation with a weighted sum of objectives, and a set of predefined linear constraints.