The facts are these: about 57 A.D., give or take, the apostle Paul traveled to Jerusalem, where he was arrested something less than seven days after his arrival. Initially at least, he was (falsely or mistakenly) accused by the Jewish religious authorities of profaning the temple. Later he was also accused of disturbing the peace, a charge more likely to be taken seriously by the Romans than any merely religious disagreement between members of a subject people group. His Roman custodians took him first to Caesarea and finally to Rome when he made an appeal to have his case heard by Caesar himself. He was imprisoned there for approximately two years.
Contrary to what I thought as a teen and young adult, Paul did not die in Rome. Not that time at least. I had my chronology muddled for years. In any case, even if martyrdom was not the result, we can reasonably conclude these four-plus years in Roman custody were not exactly fun and games.
And they were entirely voluntary.