Quadruped robots are machines intended for challenging and harsh environments. Despite the progress in locomotion strategy, safely recovering from unexpected falls or planned drops is still an open problem. It is further made more difficult when high horizontal velocities are involved. In this work, we propose an optimization-based reactive Landing Controller that uses only proprioceptive measures for torque-controlled quadruped robots that free-fall on a flat horizontal ground, knowing neither the distance to the landing surface nor the flight time. Based on an estimate of the Center of Mass horizontal velocity, the method uses the Variable Height Springy Inverted Pendulum model for continuously recomputing the feet position while the robot is falling. In this way, the quadruped is ready to attain a successful landing in all directions, even in the presence of significant horizontal velocities. The method is demonstrated to dramatically enlarge the region of horizontal velocities that can be dealt with by a naive approach that keeps the feet still during the airborne stage. To the best of our knowledge, this is the first time that a quadruped robot can successfully recover from falls with horizontal velocities up to 3 m/s in simulation. Experiments prove that the used platform, Go1, can successfully attain a stable standing configuration from falls with various horizontal velocity and different angular perturbations.

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