To walk slowly with a lot of effort, especially over a difficult surface or while carrying something heavy. (Cambridge Dictionary)
Walk slowly and with heavy steps, typically because of exhaustion or harsh conditions. (Oxford Dictionaries)
A difficult or laborious walk. (Oxford Dictionaries)
To walk or march steadily and usually laboriously. (Merriam – Webster)
Trudge – Paperblog.
Vector Stock. Upstairs trudge.