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

is fine and neither formal nor particularly colloquial.

“On” matches “one” 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.