## 1 Introduction  
In many manufacturing fields, the processing of free-form surfaces is a challenging problem [1] (e.g., in aircraft engines, marine propellers, and sanitary equipment). In fact, poor working conditions have a negative impact on the health of workers. Robot grinding can reduce labor costs, reduce safety accidents, improve grinding quality, and work efficiency [2]. The free-form surface grinding robot (FFSGR) shown in Figure 1 was the result of a research project at the National Engineering Laboratory for robot visual perception and control. The FFSGR consisted of an industrial robot and its controller, an abrasive band, workpiece, and pens [3]. Automatic grinding robot systems have been widely studied by researchers [2; 3; 4; 5; 6]. In practice, actuator non-linearities, including dead zones, backlashes, and saturation, are quite common [7]. Especially, actuator dead zones may lead to undesired performance, such as excessive steady-state errors, poor transient responses, and a large overshoot [8]. Hence, the compensation of actuator non-linearities is essential for the precise motion and adaptability of the system's control scheme [9], and the study of how to deal with actuator dead zones remains an important topic for the design of FFSGR control. Control methods for non-linear systems with dead zones have been extensively studied [10; 11; 12; 13; 14; 15; 16; 17]. Early research in this field can be traced back to reference [11], where a general control framework for a non-linear system with an unknown dead zone was established. In the last two decades, many control schemes have been developed, such as robust adaptive control [18; 19; 20; 21; 22], backstepping control [23; 24; 25; 26], fuzzy logic control [15; 16; 27; 28; 29; 30; 31; 32], and neural network (NN) control [14; 17; 33; 34; 35; 36; 37; 38; 39]. As an effective method for non-linear systems, many studies have proven that artificial neural networks can approximate a wide range of non-linear functions accurately. Compared with other neural network structures, radial basis function neural network (RBFNN)-based control algorithms usually require fewer calculation resources and achieve the desired trajectory faster [36]. Because of these advantages, RBFNNs are widely used for dead zone estimation [10; 34; 35; 36; 37; 38; 39]. In Reference [35], an approach for constructing common virtual control functions was proposed for the studied system, and a backstepping-based adaptive control methodology with low computation burden was systematically developed. The simulation studies of a ship maneuvering system were used to illustrate the effectiveness of the proposed method. In Reference [36], the RBFNN was introduced to mitigate the impact of input dead zones, and an adaptive neural network controller based on the state feedback and output feedback method was also designed for a non-linear affine system. In Reference [37], an adaptive predictive control algorithm was employed to control a continuously stirred tank reactor (CSTR) system, and the unknown functions were approximately obtained via RBFNNs. In Reference [38], RBFNNs were used to model packaged unknown non-linearities, and an adaptive neural controller was systematically derived. The study in Reference [39] proposes a dynamic TSK (Takagi-Sugeno-Kang)-type RBF-based  
Figure 1: A free-form surface grinding robot system. neural-fuzzy (DTRN) system, in which the learning algorithm can not only generate and prune fuzzy rules online but also adjust the control parameters. Its effectiveness is also verified for a chaotic system and an inverted pendulum. In Reference [40], a backstepping sliding mode control algorithm with fuzzy wavelet neural networks was developed for a non-linear dynamic system. A neural network was used to identify dead zones, and the robustness of the control system was guaranteed via sliding mode control.