###### Abstract
Compared with the existing SMC method based on linear sliding mode surface, the designed SOSMC method possesses superiorities such as small chattering, non-singularity, and fast convergence rate. Therefore, the presented CE-SOSMC algorithm can improve the trajectory tracking performance under system uncertainties and synchronization performance simultaneously. For the flexible control problem of active adaption to different technological requirements without constantly adjusting the control parameters or switching the hardware system, the existing related research achievements are few, and existing control methods are mostly suitable for systems with definite desired trajectories [14; 15]. For example, due to the condition limitations of sliding mode existence, the SMC could not satisfy the flexible control requirements of active adaption to different desired trajectories caused by different technological requirements. Recently, intelligent control theory has been introduced to track different desired trajectories for robot systems [16; 17]. In [16], for the KUKA industrial robot system, a learning from demonstration method was addressed to track different desired trajectories under unseen situations. The learning control method has strong nonlinear fitting ability and learning ability, but it needs a mass of training samples and does not possess the inferential and inductive capacity [18; 19]. In [17], for a 3-RPR parallel robot system with physical uncertainties, such as the mass of a robot end-effector and the inertia of robot cylinders, a robust optimal fuzzy controller was presented to track step-type trajectories with different heights as well as sinusoidal trajectories with different frequencies and phases. The fuzzy control method exhibits merits such as strong nonlinearity, self-adaptability, and better stability under time-varying system parameters. However, it needs to establish a mass of rules and could not obtain the rules that are used to make corresponding control decisions automatically [20; 21]. Consequently, the adaptive fuzzy neural network (AFNN) was introduced. Subtractive clustering in conjunction with evolutionary algorithm were applied to construct the fuzzy rule base with fewer rules automatically to avoid the rule base explosion problem for fuzzy control of the multivariable nonlinear hybrid robot system [22]. Furthermore, the Takagi-Sugeno model-based adaptive neural network (TSANN) based on the above fuzzy rules was constructed to realize self-learning and self-adjusting of control rules and control parameters [23; 24; 25]. Therefore, an adaptive fuzzy neural network in conjunction with subtractive clustering algorithm (SC-AFNN) for hybrid robot was constructed to improve the tracking performance under system uncertainties, synchronization performance, and flexible control performance of active adaption to variational desired trajectories caused by different technological requirements simultaneously. The main contributions of this paper are (1) combining the defined novel composite error of hybrid robot with SOSMC; (2) constructing an AFNN in conjunction with subtractive clustering algorithm for UBSHR; (3) realizing self-learning and self-adjusting of control rules and control parameters for the proposed control method; and (4) improving the trajectory tracking performance under system uncertainties, the synchronization performance, and the flexible control performance of active adaption to variational desired trajectories simultaneously. This paper is divided into five sections. A dynamic model of UBSHR and the problem formulation are covered in Section 2. In Section 3, the design and stability proofs of the developed control methods are presented. On the basis of a UBSHR prototype system, simulation and experimental research are carried out to further validate the validity of SC-AFNN in Sections 4 and 5. Finally, Section 6 summarizes the research conclusions.