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There are various uncertain and nonlinear problems in hydraulic legged robot systems, including parameter uncertainty, unmodeled dynamics and external disturbances. This study aims to eliminate uncertainties and improve the foot trajectory tracking control performance of hydraulic legged robots, a high-performance foot trajectory tracking control method based on fixed-time disturbance observers for hydraulic legged robots is proposed.

First, the robot leg mechanical system model and hydraulic system model of the hydraulic legged robot are established. Subsequently, two fixed-time disturbance observers are designed to address the unmatched lumped uncertainty and match lumped uncertainty in the system. Finally, the lumped uncertainties are compensated in the controller design, and the designed motion controller also achieves fixed-time stability.

Through simulation and experiments, it can be found that the proposed tracking control method based on fixed-time observers has better tracking control performance. The effectiveness and superiority of the proposed method have been verified.

Both the disturbance observers and the controller achieve fixed-time stability, effectively improving the performance of foot trajectory tracking control for hydraulic legged robots.

This study aimed to analyze the free vibration of a radially graded Ni-Al2O3-based functionally graded (FG) disk with uniform thickness.

Using the energy method, natural frequencies of rotating and non-rotating disks were determined at the limit elastic angular speed. Material properties were estimated using a modified rule of mixture. Both even and uneven porosity variation effects were considered in the material modeling. Finite element analysis validated the analytical approach.

The study explored limit angular speeds and natural frequencies across various grading indices, investigating the impact of porosity types and grading indices on these parameters.

Insights from this research are valuable for researchers and design engineers involved in modeling and fabricating porous FG disks, aiding in more effective design and manufacturing processes.

This study contributes to the field by providing a comprehensive analysis of free vibration behavior in radially graded Ni-Al2O3-based FG disks. The incorporation of material modeling considering both even and uneven porosity variation adds originality to the research. Additionally, the validation through finite element analysis enhances the credibility of the findings.

This study aims to improve the control accuracy and antidisturbance performance of the manipulator with the flexible link, a combined controller, which combines the novel backstepping sliding mode controller based on the extended state observer (ESO) and super-twisting sliding mode controller.

First, the dynamic of the system is constructed by Lagrange method and assumed mode method, and then the dynamic is decoupled by the singular perturbation theory to obtain the slow-varying subsystem and fast-varying subsystem. For the slow-varying subsystem, the novel backstepping sliding mode controller based on ESO is used to achieve joint tracking. For the fast-varying subsystem, the super-twisting sliding mode controller is used for vibration suppression. At the same time, to suppress chattering, the tanh function is used to replace the sign function in the reaching law.

The simulation results show that the combined control has better trajectory tracking performance, antiinterference performance and vibration suppression performance than traditional sliding mode control (SMC).

A novel backstepping sliding mode controller based on ESO is designed to guarantee the performance of the tracking trajectory. The new controller improves the converge rate. A super-twisting sliding mode controller, which can stabilize the fast-varying subsystem, is used to suppress the vibration of flexible link.