This paper presents the complete system architecture of a robotic biopsy system for real-time operations. The system has individual functional blocks working simultaneously including a 5 DoF parallel robot, ultrasound (US) imaging machine, two robotic manipulators, and a motion capturing system. Details of the real-time functionality of the robotic system components working with spatial and computational synchronization are presented. This paper also deals with a scenario in which the target tissue is moving due to the breathing of the patient. The motion of the needle tip and the target is tracked using US images as feedback. Two types of control laws for target tracking are discussed: traditional feedback control and an optimal control method. Motion compensation is demonstrated by tracking a moving target with the needle tip motion with an RMS error of 0.25 mm.