During the past 20 years, tremendous advancements have been made in the fields of minimally invasive surgery (MIS) and minimally invasive robotic assisted (MIRA) surgery. The technologies associated with these advancements have their own drawbacks, however. The surgical robots used in MIRA procedures are large, costly, and do not offer the miniaturized articulation necessary to facilitate additional advancements. This research tests the hypothesis that miniature actuation can overcome some of the limitations of current robotic systems by demonstrating accurate, repeatable control of a small end-effector. A simple two link manipulator is designed and fabricated, using antagonistic shape memory alloy (SMA) tendons as actuators, to simulate motions of a surgical end-effector. Artificial neural networks (ANNs) are used in conjunction with real-time visual feedback to "learn" the inverse system dynamics and control the manipulator endpoint trajectory. Experimental results are presented for indirect, on-line learning and control. Manipulator tip trajectories are shown to be accurate and repeatable to within 0.5 mm. These results confirm that SMAs can be effective actuators for miniature surgical robotic systems, and that intelligent control can be used to accurately control the trajectory of these systems.