# Saturation Based Nonlinear FOPD Motion Control Algorithm Design for Autonomous Underwater Vehicle
## 1 Introduction  
Autonomous Underwater Vehicle (AUV) is one of the most important research fields of marine science and technology [1; 2; 3]. Different from other underwater vehicles, AUV has some specific advantages. In intelligence, AUV is relatively small and has no physical connection with the mother ship, so it has certain autonomous decision-making and control capabilities. In safety, AUV can replace human beings in underwater operation, avoiding the defects of high risk factor, high strength and low efficiency of manual operation. In addition, compared with other underwater equipment, AUVs have lower manufacturing and operating costs, making it more economical and sustainable. Therefore, AUVs have broad application prospects in civil areas such as marine salvage, marine resources exploration and development, underwater engineering construction, and in some military tasks such as underwater weapon delivery and deployment, intelligence collection and investigation, anti-submarine, underwater combat, etc. [4; 5; 6]. With the increasing application of AUV, the requirement for its autonomy increases. One of the keys to improve the autonomy of AUVs is enhancing the dynamic performance of its motion control system. However, there are many difficulties in AUV motion control, including the strong nonlinearity and multi-degree freedom of AUV motion control system, which makes it difficult to obtain an accurate model; the ocean environment, which is complex and vulnerable to the interference of waves, currents and other unknown factors; the load and parameter perturbations; components aging or damage; andsensor noise, transmission channel delay and other unmeasurable factors, which may also affect the motion control performance. PID controller is one of the most widely applied controllers in practical applications, as well as in underwater vehicles motion control. Until now, it still appears frequently in the underwater vehicles equipped with high precision sensors and navigation equipments. [PERSON] et al. designed an improved nonlinear PID and experimented on the VORTEX underwater vehicle to overcome the nonlinearity and suppress the external interference [7]. The scheme was compared experimentally with conventional PID controller. A PID controller with the shallow water wave disturbance rejection ability was applied on the ODIN underwater vehicle [8]. [PERSON] et al. applied a PID controller considering the effect of ocean currents on the MKII underwater vehicle [9]. [PERSON] et al. designed a PID depth controller based on the nonlinear model of an underwater vehicle [10]. Compared with conventional PID controller, these improved PID controllers have superior abilities of suppressing specified interference and fast response. However, the dynamic control performances of AUVs with the existed PID and improved PID controllers are usually not good enough. The controller parameters are also hard to adjust in order to satisfy different control requirements. In recent years, fractional calculus has attracted great attention in both academic and engineering fields [11; 12; 13; 14; 15; 16; 17]. The development of fractional-order control algorithms provides more possibilities in achieving challenging control requirements [18; 19; 20]. The traditional PID type controllers only have at most three parameters, namely proportional, integral and differential parameters. Except from these three parameters, fractional-order PID type controllers may have two extra parameters, namely the integral and differential orders [21]. Benefiting from these two parameters, systems controlled by FOPID type controllers are proved to be capable in achieving better transient performance as well as robustness [22; 23; 24; 25]. A fractional sliding mode control algorithm for a fully actuated underwater vehicle subjected to the non-differentiable disturbance was proposed in [26]. Another fractional-order PI controller was also presented for REMUS AUV to improve its maneuvering precision [27].