How did Charlemagne’s empire pass to Louis the Pious?

Charlemagne’s empire passed to his only surviving son, Louis I (the Pious), following the deaths of Charlemagne’s other legitimate sons.123

In 813, several months before his death, Charlemagne took deliberate steps to ensure the succession by associating Louis with him in the exercise of imperial power. Unlike the papal-led coronation Charlemagne received in 800, this ceremony was held in the imperial chapel at Aachen without the presence of the pope. The act was confirmed by the acclamation of the gathered Frankish nobility, and Louis received the imperial diadem either directly from his father or by taking it himself from the altar. This process was intended to assert a Frankish view of imperial authority, independent of papal intervention. Upon Charlemagne's death in 814, Louis succeeded him as emperor.4256