# Model-Free Tracking Control with Prescribed Performance for a Shape Memory Alloy-Based Robotic Hand
## 1 Introduction  
In recent years, developing service robots for human beings has been a prospective trend that has attracted the attention of scholars. As the main kind of service robotic system, the robotic hand has been extensively studied [1, 2, 3]. Robotic hands, conventionally composed of cumbersome mechanical components and rigid actuators, can produce accurate displacements and forces. However, conventional robotic hands are unsafe and exhibit poor adaptability when they interact with humans or the surrounding environment. With the development of smart materials, robotic hands have been actuated by different actuation techniques such as shape memory alloy (SMA) actuation [4, 5, 6], pneumatic actuation [6, 7], and dielectric elastomer actuation [8, 9]. Compared with other robotic hands, SMA-based robotic hands have shown dramatic potential for application because of the significant features of SMA, including a high power-to-weight ratio, low noise, and compact configuration [10]. Moreover, SMA can be easily actuated by a low driving electric current to achieve safe interactions between humans and robots. For these reasons, various prototypes of SMA-based hands have been proposed. [PERSON] et al. developed an SMA-based robotic hand in [11], which was a lightweight and compact robotic hand that had all the SMA wires and returning springs embedded in the palm. Each finger has two degrees of freedom (DOF) and the thumb is completely passive. To ensure compactness and sufficient stroke, the SMA wires were wrapped around some pulleys. However, the structure of the proposed robotic hand is complex. [PERSON] et al. presented in [12] a four DOF biomimetic finger actuated by SMA wires arranged in an antagonist-protagonist configuration. In the paper, an abduction/adduction motion is added, and a passive compliance is introduced in the tendon's cables by connecting a spring in series to each SMA wire and in parallel to a slack tendon wire. Each phalanx can perform a motion of 40 deg with a bending and stretching time of 25-30 s. A fingertip force of 0.4 N has been measured, while the grasping force is small. [PERSON] et al. developed in [13] a miniature five fingered hand designedfor surgeries using 0.05 mm diameter SMA wires. This 20 DOF prototype shows a finger motion range of 30 deg. The measure fingertip force is 0.75 N. The motion range is small. In [14], a concept for an SMA-actuated gripper has been developed. In the structure, SMA wires are integrated in protagonist-antagonist muscle pair configurations. The maximum force is 1.4 N, which is small for the robotic hand, and the weight is large. In [15], an SMA-based robotic gripper is proposed for grasping. The gripper is composed of three fingers with variable stiffness. The maximum gripping force of the gripper is 6N. However, the production process needs a long time. As the essential component of the SMA-based robotic hand, the robotic finger is designed by the SMA actuator embedded into a polymeric matrix [15; 16]. The structure and the driving method of the SMA-based robotic finger are simple, whereas SMA has the characteristic of nonlinearity. The \"shape memory effect\" of SMA, between a low-temperature martensite phase and a high temperature austenite phase, can lead to the complexity and difficulty of controlling the robotic hand. The existing research focuses more on the method of controlling the SMA actuator, which can be separated including: (1) constructing models, for instance, mathematical models [17; 18] and the \"black box\" model [19; 20], to represent the SMA dynamics for further control; (2) designing a controller to improve the tracking ability of the SMA actuator, such as sliding mode control [21], PID [22] and fuzzy logic [23]. Generally, the SMA-based robotic hand can produce movements through the embedded SMA actuator [5; 7; 16], which can result in the complication of control. Moreover, the SMA-based robotic hand system is subjected to the parameter uncertainties and imprecise models [24; 25].