In this paper we present a novel controller for Shape Memory Alloy (SMA) actuated robotic systems. The new controller, called BAC (B-spline based Adaptive Control), is based on a hybrid combination of gain scheduling, B-spline approximation, variable structure control and integral control. The proposed controller shows excellent positioning accuracy and speed throughout the full range of motion of a SMA actuated robotic system in large-scale applications. To demonstrate the validity of BAC, a novel anthropomorphic SMA Actuated forearm/wrist mechanism is utilized in real-time PC based control experiments. BAC is experimentally compared to PID and integral variable structure controllers and it is shown that its performance is superior.