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Directional drilling has become increasingly important as a means for better exploitation of oil and gas reservoirs as well as part of a drive to increase the level of automation in the industry. Typically, a well plan is created for a variety of reasons, such as maximizing productive drilling, minimizing well tortuosity, collision avoidance, or navigating the tool to strategic points within a pay zone. Following a nominal well plan created to satisfy these requirements whilst drilling leads to a clear need for automated trajectory-controlled drilling. This paper builds on the authors' earlier work on generalized attitude control of directional drilling to develop a path-following algorithm incorporating optimized geometric Hermite space curves as a means of generating the correction path from the instantaneous tool position to the well plan whilst minimizing the drillstring strain energy. The proposed scheme is tested in simulation and shown to perform satisfactorily for a typical set of drilling operating parameters for converging towards a target position and attitude.