> ***On** peut faire **ses** devoirs à la bibliothèque.*

is fine and neither formal nor particularly colloquial.

***On*** matches "**one**" meaning here (indefinite pronoun).

> Doing homework in the library is allowed. 

This sentence shouldn't be confused with:

> ***On** peut faire **nos** devoirs à la bibliothèque.*

which is standard spoken French for:

> *Nous pouvons faire nos devoirs à la bibliothèque.*  

i.e.:

> We can do our homework in the library.