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In complex environments, a spherical robot has great application value. When the pendulum spherical robot is stopped or disturbed, there will be a periodic oscillation. This situation will seriously affect the stability of the spherical robot. Therefore, this paper aims to propose a control method based on backstepping and disturbance observers for oscillation suppression.

This paper analyzes the mechanism of oscillation. The oscillation model of the spherical robot is constructed and the relationship between the oscillation and the internal structure of the sphere is analyzed. Based on the oscillation model, the authors design the oscillation suppression control of the spherical robot using the backstepping method. At the same time, a disturbance observer is added to suppress the disturbance.

It is found that the control system based on backstepping and disturbance observer is simple and efficient for nonlinear models. Compared with the PID controller commonly used in engineering, this control method has a better control effect.

The proposed method can provide a reliable and effective stability scheme for spherical robots. The problem of instability in real motion is solved.

In this paper, the oscillation model of a spherical robot is innovatively constructed. Second, a new backstepping control method combined with a disturbance observer for the spherical robot is proposed to suppress the oscillation.

This study aims to promote the anti-disturbance and tracking accuracy performance of the servo systems, in which a modified active disturbance rejection control (MADRC) scheme is proposed.

An adaptive radial basis function (ARBF) neural network is utilized to estimate and compensate dominant friction torque disturbance, and a parallel high-gain extended state observer (PHESO) is employed to further compensate residual and other uncertain disturbances. This parallel compensation structure reduces the burden of single ESO and improves the response speed of permanent magnet synchronous motor (PMSM) to hybrid disturbances. Moreover, the sliding mode control (SMC) rate is introduced to design an adaptive update law of ARBF.

Simulation and experimental results show that as compared to conventional ADRC and SMC algorithms, the position tracking error is only 2.3% and the average estimation error of the total disturbances is only 1.4% in the proposed MADRC algorithm.

The disturbance parallel estimation structure proposed in MADRC algorithm is proved to significantly improve the performance of anti-disturbance and tracking accuracy.

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.

Autonomous underwater vehicle (AUV) is widely used in resource prospection and underwater detection due to its excellent performance. This study considers input saturation, nonlinear model uncertainties and external ocean current disturbances. The containment errors can be limited to a small neighborhood of zero in finite time by employing control strategy. The control strategy can keep errors within a certain range between the trajectory followed by AUVs and their intended targets. This can mitigate the issues of collisions and disruptions in communication which may arise from AUVs being in close proximity or excessively distant from each other.

The tracking errors are constrained. Based on the directed communication topology, a cooperative formation control algorithm for multi-AUV systems with constrained errors is designed. By using the saturation function, state observers are designed to estimate the AUV’s velocity in six degrees of freedom. A new virtual control algorithm is designed through combining backstepping technique and the tan-type barrier Lyapunov function. Neural networks are used to estimate and compensate for the nonlinear model uncertainties and external ocean current disturbances. A neural network adaptive law is designed.

The containment errors can be limited to a small neighborhood of zero in finite time so that follower AUVs can arrive at the convex hull consisting of leader AUVs within finite time. The validity of the results is indicated by simulations.

The state observers are designed to approximate the speed of the AUV and improve the accuracy of the control method. The anti-saturation function and neural network adaptive law are designed to deal with input saturation and general disturbances, respectively. It can ensure the safety and reliability of the multiple AUV systems.

Fully-actuated unmanned aerial vehicles (UAVs) are a growing and promising field of research, which shows advantages for aerial physical interaction. The purpose of this paper is to construct a force sensor-denied control method for a fully-actuated hexarotor to conduct aerial interaction with accurate force exerted outward.

First, by extending single-dimension impedance model to the fully-actuated UAV model, an impedance controller is designed for compliant UAV pose/force control. Then, to estimate the interaction force between UAV end-effector and external environment accurately, combined with super-twisting theory, a nonlinear force observer is constructed. Finally, based on impedance controller and estimated force from observer, an interaction force regulation method is proposed.

The presented nonlinear observer-based impedance control approach is validated in both simulation and environments, in which the authors try to use a fully-actuated hexarotor to accomplish the task of aerial physical interaction finding that a specified force is able to be exerted to environment without any information from force sensors.

A solution of aerial physical interaction for UAV system enabling accurate force exerted outward without any force sensors is proposed in this paper.

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.

This paper aims to investigate the relative translational control for multiple spacecraft formation flying. This paper proposes an engineering-friendly, structurally simple, fast and model-free control algorithm.

This paper proposes a tanh-type self-learning control (SLC) approach with variable learning intensity (VLI) to guarantee global convergence of the tracking error. This control algorithm utilizes the controller's previous control information in addition to the current system state information and avoids complicating the control structure.

The proposed approach is model-free and can obtain the control law without accurate modeling of the spacecraft formation dynamics. The tanh function can tune the magnitude of the learning intensity to reduce the control saturation behavior when the tracking error is large.

This algorithm is model-free, robust to perturbations such as disturbances and system uncertainties, and has a simple structure that is very conducive to engineering applications.

This paper verified the control performance of the proposed algorithm for spacecraft formation in the presence of disturbances by simulation and achieved high steady-state accuracy and response speed over comparisons.

This study aims to address the issue of random movement and non coordination between docking mechanisms and locking mechanisms, and proposes a comprehensive dynamic docking control architecture that integrates perception, planning, and motion control.

Firstly, the proposed dynamic docking control architecture uses laser sensors and a charge-coupled device camera to perceive the pose of the target. The sensor data are mapped to a high-dimensional potential field space and fused to reduce interference caused by detection noise. Next, a new potential function based on multi-dimensional space is developed for docking path planning, which enables the docking mechanism based on Stewart platform to rapidly converge to the target axis of the locking mechanism, which improves the adaptability and terminal docking accuracy of the docking state. Finally, to achieve precise tracking and flexible docking in the final stage, the system combines a self-impedance controller and an impedance control algorithm based on the planned trajectory.

Extensive simulations and experiments have been conducted to validate the effectiveness of the dynamic docking system and its control architecture. The results indicate that even if the target moves randomly, the system can successfully achieve accurate, stable and flexible dynamic docking.

This research can provide technical guidance and reference for docking task of unmanned vehicles under the ground conditions. It can also provide ideas for space docking missions, such as space simulator docking.

Mobile robots with independent wheel control face challenges in steering precision, motion stability and robustness across various wheel and steering system types. This paper aims to propose a coordinated torque distribution control approach that compensates for tracking deviations using the longitudinal moment generated by active steering.

Building upon a two-degree-of-freedom robot model, an adaptive robust controller is used to compute the total longitudinal moment, while the robot actuator is regulated based on the difference between autonomous steering and the longitudinal moment. An adaptive robust control scheme is developed to achieve accurate and stable generation of the desired total moment value. Furthermore, quadratic programming is used for torque allocation, optimizing maneuverability and tracking precision by considering the robot’s dynamic model, tire load rate and maximum motor torque output.

Comparative evaluations with autonomous steering Ackermann speed control and the average torque method validate the superior performance of the proposed control strategy, demonstrating improved tracking accuracy and robot stability under diverse driving conditions.

When designing adaptive algorithms, using models with higher degrees of freedom can enhance accuracy. Furthermore, incorporating additional objective functions in moment distribution can be explored to enhance adaptability, particularly in extreme environments.

By combining this method with the path-tracking algorithm, the robot’s structural path-tracking capabilities and ability to navigate a variety of difficult terrains can be optimized and improved.

To improve the robustness of carrier-based unmanned aerial vehicle (UAV) with actuator faults attitude tracking control system, this paper aims to propose a fixed-time backstepping (FXTBSC) fault-tolerant control based on a fixed-time extended state observer.

A fixed-time extended state observer (FXTESO) is designed to estimate the total disturbance including nonlinear, coupling, actuator faults and external disturbances. The integration of backstepping control and fixed-time technology ensures fixed-time convergence.

The simulation results of tracking the desired attitude angle show that the anti-interference, fault tolerance and tracking accuracy of FXTBSC-FXTESO are better than the BSC-ESO control method.

Different from the traditional BSC-ESO, the convergence speed and convergence accuracy of FXTBSC-FXTESO proposed in this paper are better than conventional extended state observer. And the fixed time controller has the advantages of high tracking accuracy, fault tolerance and anti-interference ability.