"Perambulations" is a word that is not widely used in the twenty-first century. In order to consider the antonym of this word, it is first important to establish its meaning and derivations.
This derivative example should give an indication of the possible meaning of "perambulations." A perambulator is a word that derives from perambulate and that was shortened to "pram," which is at least a word that most people find familiar. The word pram calls up images of the large baby carriages in which babies were transported up to the 70s. By the 80s, prams had mostly been replaced by collapsible push-chairs, also known as "buggies," which folded neatly in to most vehicles.
Returning to the noun "perambulations": It is a plural noun derived from the verb perambulate and has the meaning to walk about or over, as in taking a stroll or walking around. Synonyms are amble, meander and saunter.
An antonym is "a word opposite in meaning to another" (Random House Dictionary). There are no commonly recognized antonyms for the noun "perambulations." There is one commonly recognized antonym for the verb perambulate, and that is the verb "runs": one doesn't walk about, one runs about.