Systems and methods are presented that enable a legged robot to maintain its balance when subjected to an unexpected force. In the reflex phase, the robot withstands the immediate effect of the force by yielding to it. In one embodiment, during the reflex phase, the control system determines an instruction that will cause the robot to perform a movement that generates a negative rate of change of the robot's angular momentum at its centroid in a magnitude large enough to compensate for the destabilizing effect of the force. In the recovery phase, the robot recovers its posture after having moved during the reflex phase. In one embodiment, the robot returns to a statically stable upright posture that maximizes the robot's potential energy. In one embodiment, during the recovery phase, the control system determines an instruction that will cause the robot to perform a movement that increases its potential energy.