This study investigates the trajectory-tracking control problem of a two-degree-of-freedom underwater manipulator operating in a complex disturbance environment. A dynamic model of the multi-link serial manipulator is first established. In this study, water resistance and additional mass forces acting on the manipulator are analyzed and calculated using differential analysis and the Morrison formula. To account for coupling between joints, the concept of equivalent gravity is introduced to precisely calculate the underwater manipulator’s buoyancy and gravity. As a result, a relatively accurate dynamic model of the underwater manipulator is established. To mitigate the influences of external disturbances and unmodeled parts on the manipulator, a finite-time extended state observer (FTESO) is designed to estimate system quantities that are difficult to measure directly. The robustness of the controller is enhanced using a feedforward compensation mechanism, and it is demonstrated that the observation error of the observer converges in finite time. Finally, a global fast terminal sliding mode controller (GFTSMC) is developed for trajectory tracking, integrated with the aforementioned observer, and designed to smooth and limit the controller’s output. The controller’s stability is proven using Lyapunov stability theory, and its effectiveness is verified through simulation-based comparison experiments.

To address the rapid population diversity loss and premature convergence of the Artificial Lemming Algorithm (ALA) in complex optimization problems, this paper proposes an Improved Artificial Lemming Algorithm (IALA) with multi-strategy enhancements inspired by lemming behavior. First, a non-uniform mutation operator and a nonlinear step-size strategy are introduced to strengthen local optima escape capability and optimization precision. Second, inspired by the foraging and positioning behavior of lemmings, a relative advantage learning strategy is designed to reduce dependence on the global best individual, further enhancing the algorithm’s exploration ability. Finally, a Q-learning-based adaptive mechanism is integrated to intelligently orchestrate five lemming-inspired behavioral modes through a nonlinear reward function, enabling adaptive switching among search patterns. Comparative experiments on the CEC2022 benchmark suite demonstrate that IALA achieves a Friedman mean rank of 1.25, ranking first with a significant margin. Compared with the original ALA and other six classical and state-of-the-art metaheuristic algorithms, and four recently proposed improved ALA variants (EALA, IALA_Tan, DMSALAs, and MsIALA), the Wilcoxon rank-sum test confirms that IALA is significantly outperformed in only 2 out of 120 pairwise comparisons, exhibiting remarkable advantages in optimization accuracy, convergence speed, and robustness. Ablation experiments validate the synergistic necessity of all three strategies, with the Q-learning adaptive mechanism identified as the most critical contributor. Exploration–exploitation balance analysis and search history visualization further confirm that IALA achieves a smooth adaptive transition from global exploration to local exploitation. Space complexity analysis reveals that the Q-table introduces only approximately 19.5 KB of fixed additional overhead, which becomes negligible for high-dimensional problems. Furthermore, IALA is successfully applied to the parameter tuning of underwater manipulator controllers, verifying its efficiency and reliability in real-world engineering applications.

This paper addresses the trajectory tracking problem for a six-degree-of-freedom (6-DOF) underwater manipulator subject to complex disturbances and input saturation. It proposes a fixed-time preset performance sliding mode control method considering input saturation (FT-PP-SMC-IS), aiming to achieve rapid and stable tracking performance under these constraints. Firstly, to improve modeling accuracy, the Newton–Euler method and Morison’s equation are integrated to establish a more precise dynamic model of the underwater manipulator. Secondly, to balance dynamic and steady-state performance, a preset performance function is designed to constrain the tracking error boundaries. Based on dual-limit homogeneous theory, a fixed-time sliding mode surface is constructed, significantly enhancing the convergence speed and fixed-time stability. Furthermore, to suppress the effects of input saturation, a fixed-time auxiliary system is designed to compensate in real-time for deviations caused by actuator saturation. By separately constructing the sliding mode reaching law and equivalent control law, global fixed-time convergence of the system states is ensured. Based on Lyapunov stability theory, the fixed-time stability of the closed-loop system is rigorously proven. Finally, comparative simulation experiments verify the effectiveness and superiority of the proposed method.

This research study proposes a heuristic hybrid deep neural network (DNN) gait sub-phase recognition model based on multi-source heterogeneous motion data fusion which quantifies gait phases and is applied in balance disorder rehabilitation control, achieving a recognition accuracy exceeding 99%. Building upon this model, a motion control strategy for a novel rehabilitation training robot is designed and developed. For patients with some degree of independent movement, an active training strategy is introduced; it combines gait recognition with a variable admittance control strategy. This strategy provides assistance during the stance phase and moderate support during the swing phase, effectively enhancing the patient’s autonomous movement capabilities and increasing engagement in the rehabilitation process. The gait phase recognition system not only provides rehabilitation practitioners with a comprehensive tool for patient assessment but also serves as a theoretical foundation for collaborative control in rehabilitation robots. Through the innovative active–passive training control strategy and its application in the novel rehabilitation robot, this research study overcomes the limitations of traditional rehabilitation robots, which typically operate in a single functional mode, thereby expanding their functional boundaries and enabling more precise, personalized rehabilitation training programs tailored to the needs of patients in different stages of recovery.