Can an employer require you to travel?
Unless you have an employment contract or union agreement that prohibits this action, then your company can ask you to travel. Further, if you refuse you can be terminated. The fact it that, absent actionable discrimination/retaliation, an employer can set the conditions of work much as it sees fit. Accordingly, you can be fired for any reason or no reason at all, with or without notice. This is called "at will" employment.