Scooters on Shabbos

Question: Can my children ride their scooters on Shabbos where there is an eruv?
Answer: R’ Ovadia Yosef (Yechave Daas 2:52; Yabia Omer OC 7:37:3; 10:55:2) quotes the Ben Ish Chai (Rav Poalim OC 1:25) who permitted cycling on Shabbos though writes that the consensus of acharonim is that cycling is prohibited for various reasons.
R’ Ovadia Yosef quotes acharonim who are concerned that the tyres will leave grooves in the earth which is prohibited due to choresh plowing. The Kaf Hachaim (OC 404:8) writes that when riding a bike, it is very easy to mistakenly ride outside of the techum or carry it out of the eruv. In addition, it is common for things to break which could easily lead to the prohibition of tikkun mana, fixing things. R’ Eliezer Waldenberg (Tzitz Eliezer 1:21:27; 4:4:8; 7:30) adds that using a bike is also prohibited because it is uvdin dechol, a mundane, weekday activity.
As children’s tricycles are not used to ride long distances, R’ Yaakov Kamenetsky (OC 302:339) did not consider them to be the same issue of uvdin dechol and allowed children to ride them on Shabbos. Likewise, R’ Moshe Feinstein (quoted in Tiltulei Shabbos 1:n21) differentiated between bikes that are used for travels and kid’s tricycles that are not typically ridden for long distances (See Baer Moshe 6:16; Ohr Letzion 2:42:1). Similarly, R’ Yehoshua Neuwirth (Shemiras Shabbos Kehilchasa 16:18) forbids children from riding bikes though writes that they may ride tricycles and scooters.
In conclusion, while adults may not ride bikes on Shabbos, children may ride on scooters.