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Angioplasty is a frequently performed clinical procedure in which a catheter is inserted into a blood vessel under image guidance to open narrowed or blocked arteries and to allow normal blood flow to resume. This paper is concerned with the development of algorithms for a robot-assisted method for a more accurate, safer and more reliable approach for catheter insertion that can reduce the potential for injury to patients and radiation exposure or discomfort to clinicians. A force control algorithm is presented for a robot to control the force of insertion of a catheter and prevent the catheter from buckling or “bunching up” during insertion. In addition, the paper also describes a master—slave control strategy to precisely control the bending angle of the tip of an active catheter instrumented with Shape Memory Alloy (SMA) actuators. A novel model for SMAs and a robust H∞ loop-shaping controller have been implemented to guarantee robust performance of the active catheter. The algorithms for catheter insertion developed in this paper may help to prevent damage to the epithelial cells of an artery and enable easier guidance of the catheter into appropriate branches. In addition, a robotics-based approach could make it possible for a clinician to remotely perform the insertion of the active catheter from a safe and comfortable environment, thereby reducing exposure to harmful X-ray radiation. Experimental results are presented to illustrate the performance of the algorithms.