How did Louis I become Charlemagne’s successor?

Louis I, also known as Louis the Pious, became Charlemagne’s successor primarily because he was the only surviving legitimate son of the emperor at the time of Charlemagne's death in 814.12

Earlier, in 806, Charlemagne had planned to divide his empire among his three legitimate sons—Charles, Pippin, and Louis—but the deaths of the two elder brothers left the undivided inheritance to Louis. In September 813, Charlemagne formally associated Louis with him in the exercise of imperial power. This act was conducted in the imperial chapel at Aachen without papal consultation or approval, deliberately contrasting with the Roman ceremony of 800 to emphasize the Frankish view of imperial authority. Following Charlemagne's death five months later, Louis succeeded him as the sole ruler of the empire.12