Exegesis:

poreuomenou de autou ‘as he went on,’ or, in a more specialized meaning, ‘as he rode on.’

hupestrōnnuon ta himatia autōn en tē hodō ‘they spread their clothes on the road.’ The subject of hupestrōnnuon is best understood as referring to the people that were present.

hupostrōnnumi ‘to spread out under.’

Translation:

They spread their garments on the road i.e. in token of reverence. If it would not be understood as such, an explanatory note will be necessary. — They, having indefinite force here, is often better rendered ‘people’ (Ekari, Kituba), ‘there were some who’ (Tzeltal). On the road, or, “before him on the road” (The Four Gospels – a New Translation), ‘on the road he went/rode over’ (Javanese).

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.