Hadith: When the Messenger of Allah (may Allah's peace and blessings be upon him) encamped to sleep at night during a journey, he would lie down on his right side, and when he wanted to sleep before dawn, he would extend his forearm and place his head on his palm

عن أبي قتادة الأنصاري رضي الله عنه قال: كان رسول الله صلى الله عليه وسلم إذا كان في سفر، فعَرَّس بليل اضطجع على يمينه، وإذا عَرَّس قُبَيْل الصُّبْح نصَب ذراعه، ووضَع رَأْسه على كَفِّه.
[صحيح] - [رواه مسلم]

Abu Qatādah al-Ansāri (may Allah be pleased with him) reported: When the Messenger of Allah (may Allah's peace and blessings be upon him) encamped to sleep at night during a journey, he would lie down on his right side, and when he wanted to sleep before dawn, he would extend his forearm and place his head on his palm.
[Authentic hadith] - [Narrated by Muslim]

Explanation

It was from his custom (may Allah's peace and blessings be upon him) that whenever he would encamp to sleep or rest at night while on a journey, he would place his right side on the ground, and if it was just before dawn, he would lean on his extended hand. He would sleep on his right side in the beginning of the night in order to give himself enough sleep. If it was close to the time of the Fajr prayer, he would extend his hand and sleep on it, so that he may not fall into a deep sleep and miss the Fajr prayer.