###### Abstract  
Some challenging issues exist in trajectory tracking control of an uncertain bilaterally symmetrical hybrid robot (UBSHR) with variational desired trajectories, mainly the uncertainty problem of UBSHR, the synchronization problem of UBSHR's active joints and bilateral symmetrical hybrid mechanisms, and the flexible control problem of active adaption to different technological requirements without artificially adjusting the control parameters or switching the hardware system. To solve these problems, an adaptive fuzzy neural network in conjunction with subtractive clustering algorithm (SC-AFNN) for UBSHR is proposed. More specifically, a novel composite error is incorporated into the second-order sliding mode control method to generate ideal training data samples and to improve the uncertain system robustness and synchronization performance simultaneously. Furthermore, the SC-AFNN is introduced to realize self-learning and self-adjusting of control rules and control parameters and to enhance the flexible control performance of UBSHR with variational desired trajectories. Strict theoretical proof of the defined errors' relationship and the stability of the proposed control method is given. Ultimately, simulations and experiments for the prototype system of an UBSHR are conducted to verify the effectiveness of the proposed control method. intelligent control; adaptive fuzzy neural network; sliding mode control; composite error; hybrid robot +
Footnote †: 2021: 11  
without artificially adjusting the control parameters or switching the hardware system. Firstly, analyzed from the closed-chain structure of UBSHR and the actual operation environment, system uncertainties exist in UBSHR, i.e., modeling errors, and the internal friction and external disturbances. These uncertainties may influence the trajectory tracking control performance of a UBSHR. Moreover, the control security, dependability, and precision are influenced by the synchronization performance among active joints and the synchronization performance between UBSHR's bilateral symmetrical hybrid mechanisms due to multiple active joints of UBSHR. Thus, the trajectory tracking performance under system uncertainties and the synchronization performance should be considered simultaneously. In addition, the controller parameters need to be adjusted artificially to satisfy the actual control requirements due to variational desired trajectories caused by different technological requirements in practice. As a result, the flexibility superiority of the mechanical structure cannot be exerted, which makes it difficult to realize the flexible control performance of active adaption to different technological requirements. For the uncertainty problem existing in a robot system, robust control methods have been presented, i.e., Ho control [3], backstepping control [4], and sliding mode control (SMC) [5]. The SMC method is insensitive to parameter changes and external disturbances. Hence, it has superiorities to dispose of the uncertainty problem for hybrid robots [6; 7]. In a previous study by our research group, problems of system uncertainties and synchronization performance have been handled by combining the SMC algorithm and synchronous control strategy [8; 9; 10]. Nevertheless, for the researched UBSHR, the defined synchronization errors in [8; 9; 10] could only guarantee the synchronization performance of active joints. The synchronization performance of an UBSHR's end-effector could not be considered. Therefore, a novel composite error was defined by considering synchronization errors and by tracking errors of the UBSHR's end-effector. Combined with the second-order non-singular fast terminal SMC (SOSMC) method [11; 12; 13], the composite error-based SOSMC (CE-SOSMC) for a hybrid robot was realized. Compared with the synchronization error in [8; 9; 10], the defined composite error could ensure the synchronization performance not only of active joints but also of the end-effector.