# Design of a Predictive RBF Compensation Fuzzy PID Controller for 3D Laser Scanning System
## 1 Introduction  
With the development of laser technology, 2D Lidar has been widely used in various fields such as map navigation [1; 2], simultaneous localization and mapping (SLAM) [3; 4] and robots [5; 6]. However, the exploration of the environment requires more information dimensions and a more comprehensive perspective with the advancement of navigation and robot technology. Therefore, 3D Lidar technology emerges [7; 8; 9; 10], but mature multi-line 3D Lidar is too expensive to be widely used. By contrast, a 3D laser scanning system formed by 2D Lidar with the pitching motion mechanism is more cost-effective, which can be reasonably applied to multiple fields [11; 12; 13; 14; 15]. For the 3D laser scanning system, many researchers focus only on the optimization of the calibration process [16; 17; 18; 19; 20], while neglecting the influence of 2D Lidar motion control on the scanning results. In fact, there is a deviation between the actual pitching motion of the 2D Lidar and the ideal motion. The size of the deviation directly affects the scanning results of the system. The speed of the 2D Lidar pitching motion should be adapted to different objects or environments, so the accuracy of the obtained data information can be improved, and the phenomenon of target point loss and overlap can be reduced. In short, it is important to design a control method that can effectively and accurately control the pitching motion of the 2D Lidar. Proportional integral derivative (PID) control is one of the most commonly used control methods in various fields. Since 1942, researchers have put forward many PID control methods [21; 22]. However, the controlled object generally has great uncertainty or complex nonlinearity in practical applications. For the pitching motion of the 2D Lidar in the article, the 2D Lidar rotates around the central axis of thesystem, so the torque generated by gravity will change nonlinearly with the pitching angle. Moreover, the pitching motion is accompanied by nonlinear and unknown friction torque. Therefore, the model of Lidar pitching motion is a complex system with unknown nonlinearity. For this kind of model, how to adjust PID parameters properly is not an easy task. Most tuning methods are mainly determined by the system model [23; 24]. [PERSON] aimed at a linear motor system to put forward a PID tuning method, which used particle swarm optimization (PSO) to tune PID parameters [25]. [PERSON] used the internal model control (IMC) to adjust PID parameters for integrator/dead-time processes [26], but it cannot deal with an unknown disturbance. [PERSON] proposed a unified approach to tune PID controllers for stable, integrative and unstable dead-time processes [27], which further optimizes the robustness of the system. However, its control performance for nonlinear systems is still poor. Although traditional PID control is widely applied in various industrial processes, its performance may not always be satisfactory due to unknown and nonlinear effects. At present, many intelligent control algorithms have been proposed and widely used. Many of these algorithms can be used to reasonably improve the PID controller. [PERSON] firstly put forward fuzzy set theory [28]. Its core is to establish a mathematical model of language analysis for complex systems or processes. Thus, the modeling problem of the system, which cannot be accurately described by a rigorous mathematical method, is solved. Since nonlinear systems often occur in practical applications, fuzzy control is required to solve these control problems [29; 30]. [PERSON] used PSO to effectively search the optimal fuzzy PID controller parameters of an active automobile suspension system, which improved the nonlinear defects in the system [31]. [PERSON] proposed a fuzzy adaptive adjustment method for PID parameters in a nonlinear process [32]. However, the fuzzy rules above are all based on long-term practical experience accumulated by the operators; such practical experience is not easy to obtain, which is a key issue in fuzzy adaptive PID control.