Acts 16:10

‘And when he had seen the vision, straightway we sought to go forth into Macedonia, concluding that God had called us to preach the gospel to them.'

Paul was immediately responsive. This call explained the prohibitions that they had been facing, and was a clear message from God. So concluding that God had called him to proclaim the Good News to the Macedonians he prepared to embark.

We note at this point that the pronoun changes to ‘we'. It is apparent that Luke has joined the party, and feels himself an essential part of it. He was a physician and if the hindrances to Paul had been because of his health may well have ministered to Paul. He travelled with them to Philippi and went with them to the place of prayer, but seemingly remained in Philippi when they moved on, being still there when they returned and returning to Troas with them (Acts 20:5). From then on he remained with Paul on his journey to Jerusalem, and was again with him from Caesarea to Rome (Acts 27:1 - Acts 28:16).