For their efficient and elegant locomotion, batoid fishes (e.g. the manta ray) have been widely studied in biology, and also taken as a source of inspiration by engineers and roboticists willing to replicate their propulsion mechanism in order to build efficient swimming machines. In this work, a new model of an under-actuated compliant wing is proposed, exhibiting both the oscillatory and undulatory behaviors underlying batoid propulsion mechanism. The proposed model allowed an investigation of the co-evolution of morphology and control, exploiting dynamics emergent from the interaction between the environment and the mechanical properties of the soft materials. Having condensed such aspects in a mathematical model, we studied the adaptability of a batoid-like morphology to different environments. As for biology, our main contribution is an exploration of the parameters linking swimming mechanics, morphology and environment. This can contribute to a deeper understanding of the factors that led various species of the batoid group to phylogenetically adapt to different environments. From a robotics standpoint, this work offers an additional example remarking the importance of morphological computation and embodied intelligence. A direct application can be an under-water soft robot capable of adapting morphology and control to reach the maximum swimming efficiency
