Self-piercing rivets deployed in an elongated tape are moved into alignment with a rivet driving spindle using a processor-controlled servomotors. The tape is conveyed between a supply reel and an exhaust reel, the supply reel having a supply motor and the exhaust reel having an exhaust motor. The tape is moved under processor control in an advancing direction until the rivet has traveled past being in alignment with the spindle, by controlling the supply and exhaust motors using a first tension regimen. Thereafter the tape is moved under processor control in a retracting direction until the rivet is in alignment with the spindle by controlling the tape supply and exhaust motors using a second tension regimen.