Finite-Time Trajectory Tracking Control for Uncertain Underactuated Marine Surface Vessels

Space manipulator is considered as one of the most promising technologies for future space activities owing to its important role in various on-orbit serving missions. In this study, a robust finite-time tracking control method is proposed for the rapid and accurate trajectory tracking control of an attitude-controlled free-flying space manipulator in the presence of parametric uncertainties and external disturbances. First, a baseline finite-time tracking controller is designed to track the desired position of the space manipulator based on the homogeneous method. Then, a finite-time disturbance observer is designed to accurately estimate the lumped uncertainties. Finally, a robust finite-time tracking controller is developed by integrating the baseline finite-time tracking controller with the finite-time disturbance observer. Rigorous theoretical analysis for the global finite-time stability of the whole closed-loop system is provided. The proposed robust finite-time tracking controller has a relatively simple structure and can guarantee the position and velocity tracking errors converge to zero in finite time even subject to lumped uncertainties. To the best of the authors’ knowledge, there are really limited existing controllers can achieve such excellent performance under the same conditions. Numerical simulations illustrate the effectiveness and superiority of the proposed control method.

Robust adaptive three-dimensional trajectory tracking control for unmanned underwater vehicles with disturbances and uncertain dynamics

In this paper, an adaptive neural network approach is developed based on the integral nonsingular terminal sliding mode control method, with the aim of fixed-time position tracking control of a wheelchair upper-limb exoskeleton robot system under external disturbance. The dynamical equation of the upper-limb exoskeleton robot system is obtained using a free and typical model of the robotic manipulator. Afterward, the position tracking error between the actual and desired values of the upper-limb exoskeleton robot system is defined. Then, the integral nonsingular terminal sliding surface based on tracking error is proposed for fixed-time convergence of the tracking error. Furthermore, the adaptive neural network procedure is proposed to compensate for the external disturbance which exists in the upper-limb exoskeleton robotic system. Finally, to demonstrate the effectiveness of the proposed method, simulation results using MATLAB/Simulink are provided.

A new adaptive controller for robot manipulators is proposed. The new approach uses only position measurements. The main conclusions derived from the closed-loop system analysis are in two main results. In the first one, the global convergence of the position and velocity tracking errors is stated by using a condition that relates the viscous friction damping and the desired joint speed. In the second one, such a condition is dropped out but the local exponential stability of the closed-loop system is shown. To confirm the theoretical conclusions, a detailed experimental study in a two degrees-of-freedom direct-drive manipulator is provided, where the performance of the new controller is compared with respect to a known output feedback adaptive controller.

Adaptive finite-time sliding mode control design for finite-time fault-tolerant trajectory tracking of marine vehicles with input saturation

This article proposes an enhanced adaptive time delay controller (ATDC) for robot manipulators subjected to external disturbances. This approach is model-free and uses time delay estimation (TDE) to estimate complex and unknown robot dynamics. First, to remove the reaching phase and improve the robustness of the control, an integral sliding surface (ISS) is used. Second, to speed up the convergence and compensate for the TDE errors and external disturbances, the gains of time delay control and the sliding mode have been made adaptive. In this article, we clearly point out using the Lyapunov method that the position and velocity tracking errors are guaranteed to be uniformly ultimately bounded (UUB). The effectiveness and the robustness of the designed controller over existing methods are experimentally verified on a parallel Delta robot. The novel model-free proposed control is robust and highly accurate, which is appropriate and recommended for industrial robotic applications.

For the trajectory following problem of a robot manipulator, a new linear learning control law, consisting of the conventional proportional‐integral‐differential (PID) control law, with respect to position tracking error, and an iterative learning term is provided. The learning part is a linear feedback control of position, velocity, and acceleration errors (PDD2). It has been shown that, under the proposed learning control, the position, velocity, and acceleration tracking errors are asymptotically stable in the presence of highly nonlinear dynamics. The proposed control is robust in the sense that exact knowledge about nonlinear dynamics is not required except for the bounding functions on their magnitudes. Further, neither is linear approximation of nonlinear dynamics nor repeatability of robot motion required.

Adaptive fuzzy tracking control for a class of uncertain nonaffine nonlinear systems with dead-zone inputs

This paper presents an online recorded data-based composite neural finite-time control scheme for underactuated marine surface vessels (MSVs) subject to uncertain dynamics and time-varying external disturbances. The underactuation problem of the MSVs was solved by introducing the line-of-sight (LOS) method. The uncertain dynamics of MSVs are approximated by the composite neural networks (NNs). A modified prediction error signal is designed by virtue of online recorded data. The weight updating law of NN is driven by both tracking error and prediction error, introducing additional correction information to the weights of NN, thus improving the learning ability of the NN. Furthermore, disturbance observers can be devised to estimate the compound disturbances consisting of the approximation errors of NNs and external disturbances. Moreover, the smooth function is inserted into the design of the control scheme, and the finite-time composite neural trajectory tracking control of MSVs is achieved. The stability of the MSVs trajectory tracking closed-loop control system is guaranteed rigorously by the Lyapunov approach, and the tracking error will converge to the set of residuals around zero within a finite time. The simulation tests on an MSV verify the effectiveness of the proposed control scheme.

Adaptive neural network based position tracking control for Dual-master/Single-slave teleoperation system under communication constant time delays

In this paper, a new nonlinear controller for a quadrotor unmanned aerial vehicle (UAV) is proposed using neural networks (NNs) and output feedback. The assumption on the availability of UAV dynamics is not always practical, especially in an outdoor environment. Therefore, in this work, an NN is introduced to learn the complete dynamics of the UAV online, including uncertain nonlinear terms like aerodynamic friction and blade flapping. Although a quadrotor UAV is underactuated, a novel NN virtual control input scheme is proposed which allows all six degrees of freedom (DOF) of the UAV to be controlled using only four control inputs. Furthermore, an NN observer is introduced to estimate the translational and angular velocities of the UAV, and an output feedback control law is developed in which only the position and the attitude of the UAV are considered measurable. It is shown using Lyapunov theory that the position, orientation, and velocity tracking errors, the virtual control and observer estimation errors, and the NN weight estimation errors for each NN are all semiglobally uniformly ultimately bounded (SGUUB) in the presence of bounded disturbances and NN functional reconstruction errors while simultaneously relaxing the separation principle. The effectiveness of proposed output feedback control scheme is then demonstrated in the presence of unknown nonlinear dynamics and disturbances, and simulation results are included to demonstrate the theoretical conjecture.

A convergence analysis of the angular position and velocity tracking errors and parametric estimation errors for a 2-link robot dynamics in the absence of noise exist in the literature (Slotine and Li in Applied nonlinear control. Prentice- Hall Inc, Englewood Cliffs, NJ, 1991). In this paper, we consider the effect of noise on the robot dynamics as well as on the parameter update equation. Noise in the robot dynamics arises due to errors in reading \(q,\dot{q}\), i.e., the angular positions and velocities of the robot link that are used for calculating the errors e, \(\dot{e}\) used to generate the feedback torque via the PD controller. Noise is chosen as Gaussian because it is produced as the cumulative effect of several small independent random effects like electrons moving in the motor wire and dust friction, and we know from the central limit theorem that the sum of a large number of small independent effects has a Gaussian distribution. Noise in the parametric update equation arises due to finite register effects in the digital computer. Both of these noises are modeled as white Gaussian, and the robot and parametric update dynamics have thus been modeled as nonlinear coupled stochastic differential equations. Using linearization of this coupled SDE system around the non-random components of the trajectory estimation error and parametric estimation errors, we first derive stochastic integral expressions for the random components in these errors. We then evaluate the average rate of change of the Lyapunov energy function using Ito calculus and obtain conditions on the noise amplitude so that the limiting value of this average rate of change is negative, guaranteeing asymptotic average stability of the system and parametric estimation algorithm. One of the novelties of this work is the new algorithm for parameter estimation which enables us to improve on the algorithm convergence rate as compared to previous work (Slotine and Li 1991). Finally, our stochastic algorithm is verified by performing hardware experiments with the actual PHANToM Omni robot.

This paper presents a robust neural network with an extended state observer control methodology for a piezoelectric-actuator-based surgical device. This control methodology is proposed for tracking of desired motion trajectories in the presence of unknown or uncertain system parameters, nonlinearities including friction, hysteresis, and disturbances in the motion system. In particular, the radial basis function neural network, which serves as a function approximator, aims to create a model for an unknown function to find a relationship between input and output data. An extended state observer is utilized to assist in canceling disturbances and uncertainties of the system dynamically. The stability of the control approach is analyzed. The convergence of position and velocity tracking errors is proven theoretically. Experiments are conducted to demonstrate that the performance with an improved accuracy can be attained by the proposed control scheme. With the motion tracking capability, the control methodology helps the novel surgical device achieve higher success rate in operation, which is also suitable for similar piezoelectric ultrasonic actuator applications.

In unmanned aerial vehicle (UAV) operations, achieving precise rendezvous with maneuvering targets is final requirement for critical missions. Most of the rendezvous techniques existing in the current literature face significant limitations in simultaneously achieving position and velocity synchronization, often requiring separate control loops and restrictive assumptions about target motion patterns. To this end, this paper introduces a novel sliding mode-based guidance strategy for precise UAV rendezvous with maneuvering targets in three-dimensional environments, where the target is modeled as a generic continuous-time trajectory—representing a realistic and practical scenario. The proposed approach employs a nonlinear sliding vector that couples position and velocity tracking errors. Rigorous stability analysis using Lyapunov theory demonstrates finite-time convergence of both position and velocity errors to predefined tolerances, even in the presence of unknown but bounded sensing uncertainties. Extensive numerical simulations validate the performance of the developed guidance algorithm under different maneuvering target scenarios.

Achieving precise trajectory tracking with practical applicability for underactuated autonomous underwater vehicles (AUVs) is challenging due to uncertainties and inherent underactuation. This paper presents a finite-time control framework with continuous inputs to address this issue. By incorporating a sliding mode observer, the framework estimates lumped disturbances – including mismatched lateral velocity disturbances – to facilitate effective control law design. A key feature is the direct dependence of the control input on the sliding manifold, which avoids chattering and yields a continuous dynamical control law. Furthermore, the controller utilises an integral form to obtain the equivalent sign-function of sliding variables, eliminating the need for saturation function approximations. This design guarantees finite-time convergence and reduces the reliance on high-order state derivatives. Simulation on the REMUS AUV verifies that the proposed controller achieves favorable performance in the convergence of both position and velocity tracking errors. These results robustly validate the practical value of the proposed controller for real-world AUV applications.