The goal of this clinical trial is to test a personalized intervention aiming to optimize the mechanical ventilator settings in morbidly obese patients suffering from moderate to severe Acute Respiratory Distress Syndrome (ARDS). The intervention consists of personalized measurements and calculations of the different pressures inside the thorax. The main question to answer is: • Will the evaluated esophageal pressure-guided strategy lead to different mechanical ventilator settings than suggested by a strategy largely used in ARDS patients in France? A specific nasogastric probe permitting to measure esophageal pressure will monitor participants. Esophageal pressure will act as an indicator of the pleural pressure. Other respiratory signals displayed by the mechanical ventilators will also be acquired. Further, ventilator settings will be adjusted to the evaluated esophageal pressure-guided strategy, with possible benefit of this personalized approach.