This paper presents the design and control of a two-link lightweight robotic arm using Shape Memory Alloy wires as actuators. Both, a single wire actuated system and an antagonistic configuration system are tested in open and closed-loop. The mathematical model of the SMA wire, as well as the kinematics and dynamics of the robotic arm, are presented. The Operational Space Control of the robotic arm is performed by using a Joint Space control in the inner loop and Closed Loop Inverse Kinematics in the outer loop. In order to choose the best Joint Space Control approach, a comparative study of four different control approaches (Proportional Derivative, Sliding Mode, Adaptive and Adaptive Sliding Mode Control) is carried out for the proposed model. From this comparative analysis, the adaptive controller was chosen to perform Operational Space Control. This control helps us to perform accurate positioning of the endeffector of SMA wire based robotic arm. The complete Operational Space control was successfully tested through simulation studies performing position reference tracking in the end-effector space. Through simulation studies the proposed control solution is successfully verified to control the hysteretic robotic arm.