Animal locomotion exhibits all the features of complex non linear systems such as multi-stability, critical fluctuation, limit cycle behavior and chaos. Studying these aspects on real robots has been proved difficult and therefore results mostly rely on the use of computer simulation. Simple control approaches – based on phase oscillators – have been proposed and exhibit several of these features. In this work, we compare two types of controllers: (a) an open loop control approach based on phase oscillators and (b) the Tegotae-based closed loop extension of this controller. The first controller has been shown to exhibit synchronization features between the body and the controller when applied to a quadruped robot with compliant leg structures. In this contribution, we apply both controllers to the locomotion of a stiff quadruped structure. We show that the Tegotae-controller exhibits self-organizing behavior, such as spontaneous gait transition and critical fluctuation. Moreover, it exhibits features such as the ability to stabilize both asymmetric and symmetric morphological changes, despite the lack of compliance in the leg.