Purity: Walking During Wudu
Practical Laws of Islam as per the teachings of Ayatullah Sistani
Ruling 284:
There is no problem in walking while performing wuḍūʾ; therefore, if after washing the face and arms one walks a few steps and then wipes his head and feet, his wuḍūʾ is valid.
-Ayatullah Sistani, Practical Laws of Islam, Purification (Taharah)