Series Snake robots possess strong adaptability for unstructured environments, but their trajectory tracking control is hindered by nonlinear dynamics and model uncertainties. This article proposes an optimal tracking control strategy based on an actor–critic reinforcement learning framework. The method integrates line-of-sight guidance with serpentine gait generation, while a neural network identification system approximates the solution of the Hamilton–Jacobi–Bellman equation for unknown dynamics. Actor and critic networks are employed to update control policies and cost functions online, reducing dependence on precise models. Rigorous theoretical analysis proves that position and velocity errors achieve semi-global uniform ultimate boundedness. Both simulations and prototype experiments were conducted based on a servo-driven yaw-pitch linkage alternating series snake robot. The results verify that the proposed method can achieve accurate trajectory tracking, rapid convergence, and stable joint control, demonstrating its effectiveness and superiority compared to existing methods.

This study investigates the trajectory tracking strategy of a snake robot with sideslip disturbance and unknown model parameters. To guide the robot to track the ideal trajectory faster and more accurately, an adaptive anti-sideslip strategy for a snake robot with the Integral Line-of-Sight (ILOS) function is reported. This technique eliminates direction sideslip and error fluctuation by using auxiliary integral terms and shortens the convergence time of state variables. Following the position and angle control objectives, the proposed controller considers the negative effects caused by the uncertainty and time variability of environmental parameters and compensates for the joint input using the adaptive update laws. The environment adaptability and tracking efficiency are improved. The stability analysis indicates that the state errors converge to the origin. The simulation and experiment data verifies the effectiveness and strength of the work.Note to Practitioners—This article was motivated by the problem of robust trajectory tracking for a snake robot in an environment with sideslip disturbance and unknown model parameters. In this environment, information of the motion space (for example, the coefficient of ground friction) cannot be obtained. In addition, there may be other system limitations (for example, motion sideslip limitations) and other operational limitations. These limitations are caused by the requirements of various common trajectory tracking objectives. These cases should also be considered in the control strategy. However, based on the existing methods of tracking control for snake robots, there is still a lack of a complete and reliable autonomous control scheme that can consider the above problems. On this basis, we present a reliable control strategy, which considers the above problems and the dynamic uncertainty of the model. In the future, we will extend the proposed method to the field of formation tracking control for multiple robots.

This article proposes a robotic fish formation control scheme that is based on finite-time terminal sliding mode to achieve coordinated tracking of multiple target paths under external disturbances and internal parameter perturbations. The method explores the lateral sliding mechanism of each body in the surge and sway directions by constructing a directional compensation guidance strategy that is based on a finite-time disturbance observer, thus enabling the precise coordinated movement of multiple robotic fish. Furthermore, this article acknowledges that the highly coupled dynamics of the robotic fish are susceptible to external environmental influences and modeling accuracy. Hence, a rapid global terminal sliding mode fuzzy controller that considers tangential displacement is introduced, and fuzzy adaptive methods are utilized to fit complex uncertainties. This approach mitigates the chattering problems commonly associated with traditional sliding mode control and enhances the error convergence speed and accuracy of the robotic fish formation system.

This work presents a butterfly spiral propulsion mode of snake robots to realize the tracking control on the objective trajectory in multiple scenarios. This method investigates the force mechanism of each body element in the yaw and pitch directions. The butterfly spiral gait mechanic and friction models are constructed to offset the lateral torque force caused by joint rotation. In addition, this work combines an integral part of improving the line of sight guidance scheme, which eliminates the robot's sideslip when tracking the curve track and enhances the body's adaptability to different scenarios. Lyapunov's theory proves the stability of the designed guidance strategy. Simulation and experimental results illustrate that the designed butterfly spiral gait and guidance scheme can provide the snake robot faster tracking results and more stable error performance than the cylindrical and conical spiral gait.

To address the complicated modeling process and inadequate explainability of current methods for improving the contour accuracy of ultraprecision machining (UPM), this study presented an Internet of Things (IoT)–based contour error compensation (CEC) framework. To achieve a convincing and real-time compensation solution, a hybrid mechanism-data-driven CEC model was created that integrated the 1DCNN-BiLSTM-attention model for predicting the axis actual positions, contour error estimation, and bidirectional compensation algorithms. Bayesian hyperparameter optimization and sensitivity analysis were used in the proposed models to improve the prediction accuracy of the actual position of each axis, with high-quality training datasets from well-designed experiments. Finally, validating the system on a three-axis ultraprecision milling machine demonstrated its superior performance. This study first demonstrated the feasibility of a deep learning approach for improving UPM accuracy, which will assist in accelerating digitalization and intellectualization for UPM.

Three-dimensional spiral gait enables a snake robot to climb over obstacles, cross caves, and adapt to complex environments. This article reports an antidisturbance path-following control method for a snake robot with a spiral gait. This method reduces the deviation of the robot's position in following the ideal path by estimating the time-varying parameters, the external disturbances, and the viscous friction coefficients. The estimations are used to compensate for the control inputs of the system, which can improve the adaptability of the robot to the environment. Then, the attitude and position errors can rapidly converge to the origin. An appropriate Lyapunov function is adopted to explore the stability of following errors. Experimental results show that the proposed method can accelerate the convergence rate of errors, reduce the fluctuation peak, and improve the following stability of snake robots.

This article reports a trajectory tracking control technique for snake robots with sideslip elimination and coefficient approximation. By introducing an integral part and virtual input variables to optimize the line-of-sight guidance law, a closed-loop trajectory tracking system with the functions of canceling disturbance and sideslip is designed. Besides, the method constructs the time-varying predicted values of virtual model variables and viscous friction coefficients to approximate the system's unmeasurable states. The approximation value can compensate for a snake robot's joint offset and torque input. Then, it is proved via the Lyapunov approach that the designed system is stable. The remarkable advantage of this strategy is that the accuracy of a snake robot tracking the ideal trajectory is optimized, which can improve the error's stability and the body's adaptability to the surroundings. The simulation and experimental results confirm the usefulness of the proposed technique.

To eliminate the influence of nonlinear state terms in the highly-coupled unmanned aerial vehicle (UAV) model and improve the aircraft’s ability to suppress wind field interferences, this work presents a path-following scheme for UAVs. This method uses the radial basis neural network (RBNN) to develop an adaptive approximation law for the gyroscopic effect function to balance for the influence of system uncertainty and nonlinear state terms on UAV modeling and reduce the dependence of the UAV’s roll and pitch control orders on attitude velocity information. In addition, the adaptive update laws of the disturbance predictions are designed to compensate for the control input and repress the chattering and deviation of the drone. The stability of the proposed controller was proven by using the Lyapunov theorem. Simulations and experiments have shown that the controller can perform faster convergence speed and higher following accuracy of the flight position and attitude errors.

This work reports an adaptive path-following controller for a multijoint snake robot (MSR) to improve the adaptability of the robot to the environment. The new strategy estimates the time-varying parameters of the system and the external interference to adjust the motion state of the robot in real time. Estimations are used to compensate for the joint torque of an MSR, thus reducing the fluctuation peak of path-following errors. In addition, this work designs an anti-sideslip line-of-sight (LOS) guidance strategy to avoid the deviation of the direction angle. The method can improve the tracking accuracy of an MSR, and the position errors enable the system to achieve uniformly ultimate boundedness (UUB). The angle errors converge to the origin to achieve stability. Experimental results demonstrate that the novel method can accurately estimate the time-dependent parameters, sideslip, and interference, raise the convergent speed of errors, and reduce the fluctuation peak.

This article studies the formation and trajectory tracking control of multiagent systems. We present a novel multilayer graph for the multiagent system to enable extensibility of the interaction network. Based on the multilayer graph, a formation control law by using the potential function approach is developed for autonomous formation, formation maintenance, collision, and obstacle avoidance. When the desired formation is achieved, the barycentric of the formation shape is viewed as a virtual leader, and a model predictive control (MPC) scheme is applied to the virtual leader for tracking a reference trajectory; meanwhile, the agents will maintain the desired angles and distances via the formation control law. By applying the proposed schemes, the tasks of formation maintenance and trajectory tracking in a constrained space are fulfilled. Comprehensive simulation studies under different environmental constraints and trajectories confirm the effectiveness of the proposed approaches in addressing the formation and trajectory tracking problems.

This work designs an adversarial Bayesian deep network to solve the cognitive detection of pilot fatigue. Batch normalization and data enhancement are adopted in the posterior inference of the proposed model parameters to effectively improve the generalization of neural networks. The generator is used to enhance the brain power map generated from three cognitive indicators and improve the accuracy of fatigue state recognition. This work also adds adversarial noise in the vicinity of each brain electrode to form an adversarial image, which further reveals the correlation between the cognitive state of brain and the location of brain regions. Compared with other deep models and parameter optimization methods, our model achieves better detection accuracy.