Unless your employer is reporting income and state tax withheld from another state (Boxes 15 - 17 of Form W-2), you don't need to file any state tax returns.
For the vast majority of people who travel as part of their work, their income is considered as earned in the state where they are based, i.e. where their business travel starts and ends. Sales representatives and airline pilots are common examples of this approach.
(The most common exceptions for this rule are professional athletes and entertainers; they are required to calculate how much of their annual pay is earned in each place they play/perform).