Is there any specific word to describe walking the same path from one place to other. For e.g, 1 Km line, where someone walks from one end and turns back, goes to other end & Keeps repeating it.
'to and fro' is good enough - http://dictionary.cambridge.org/dictionary/british/to-and-fro - in one direction and then in the opposite direction
Back and forth is another common expression:
in one direction and then the other repeatedly; from one place to another repeatedly.
- The tiger paced back and forth in its cage.
if someone or something moves back and forth between two places, they move from one place to the other place again and again.
- Nurses went back and forth among the wounded, bringing food and medicine.
You might say a person doing this is shuttling between points. A shuttle bus or shuttle flight is one that repeatedly retraces the same route
PACER noun: 1. one that paces; specifically : a horse whose predominant gait is the pace.
from Merriam-Webster Dictionary online
PACE verb gerund or present participle: pacing
walk at a steady and consistent speed, especially back and forth and as an expression of one's anxiety or annoyance.
from Google link