Adaptive Shared Trajectory Tracking Control for Output-Constrained Euler–Lagrange Systems

In this paper, we investigate the trajectory tracking control problem of surface ships subject to unknown parameters, unknown time-varying disturbances, and input saturation. The input saturation is approximated using a Gaussian error function. The compounded uncertain term caused by the unknown parameters and disturbances is transformed into a linear parametric form with a single parameter called virtual parameter. Then, a novel robust adaptive ship trajectory tracking control law is designed using the adaptive vector-backstepping design method, where the adaptive law online provides the estimation of the virtual parameter. Further, a finite-time control scheme is developed injecting a power function vector of the position and velocity errors into the proposed control scheme such that the control performance is improved. Both our control schemes are simple to compute and easy to implement in engineering applications. Theoretical analysis indicates that the designed control laws can force the surface ship to track the desired trajectory while guaranteeing the global uniform ultimate boundedness of all the signals in the closed-loop trajectory tracking control system of surface ships. Simulation results and comparison verify the effectiveness of our novel robust adaptive trajectory tracking control schemes.

In this paper, an adaptive neural network (NN) trajectory tracking control scheme is developed for underactuated autonomous underwater vehicles (AUVs) subject to unknown dynamic parameters and unknown disturbances. A novel additional control based on Nussbaum function is proposed to handle the underactuation problem of AUVs. The radial basis function NNs with minimal learning parameter (MLP) are employed to online approximate the compounded uncertain item due to unknown dynamic parameters and unknown disturbances. On the basics of the above, an adaptive NN trajectory tracking control law is proposed using command filtered vector-backstepping design tool. As a result, the computational burden of the developed trajectory tracking control scheme is significantly reduced, Theoretical analysis indicates that the proposed control law can force the AUV track the desired trajectory and guarantee that all signals in the trajectory tracking closed-loop control system are bounded. Simulation results on an AUV verify the effectiveness of our developed control scheme.

This paper presented a novel adaptive cascade nonlinear trajectory tracking control scheme of over-actuated autonomous electric vehicles involving input saturation. First, a nonlinear vehicle dynamic model with input saturation is established, which can accurately describe the features of uncertainties and coupling of autonomous electric vehicles, and the hyperbolic tangent function is designed to estimate the saturation function for dealing with the input saturation problem. Then, a novel adaptive cascade trajectory tracking control scheme is designed. An adaptive neural network-based terminal sliding control law is proposed for producing the generalized force/moment in real-time, the asymptotic stability of this adaptive control system is proven by Lyapunov theory, and a quasi-newton distribution law is designed to determine the optimum tire forces that guarantee the actual generalized forces/moment are close to the desired values. Finally, simulation results demonstrate the effectiveness of the proposed control scheme.

In this paper, we investigate an adaptive output feedback trajectory tracking controller for an underactuated unmanned surface vehicle (USV) with position signals. Using Lyapunov stability theorem and backstepping strategy, a Neural Network (NN)-based adaptive trajectory tracking control scheme is proposed without the velocity informations. The NN is employed to approximate the unknown external disturbances and model parametric uncertainties. Also, a high-gain observer is applied to estimate the USV’ unmeasured velocities, and the NN-based output feedback tracking control is designed. Simulation results are carried out to verify the proposed controller.

The safety and optimality of underactuated autonomous underwater vehicles (AUVs) during operations are essential factors to consider. In this context, a three‐dimensional robust adaptive optimal trajectory tracking control method under position and velocity constraints, unknown dynamics, and environmental disturbances is proposed. The main features of the method are: (1) The outputs of an underactuated AUV system are redefined to handle the underactuation problem. (2) The system with position and velocity constraints is transformed into an unconstrained system by a nonlinear state‐dependent transformation. (3) A critic‐identifier architecture is constructed using adaptive dynamic programming and neural networks in a backstepping framework. Specifically, critic networks and weight update laws without requiring initial stability control are designed to solve Hamilton‐Jacobi‐Bellman equations in kinematic and dynamic subsystems, and optimal virtual and actual control laws are obtained. (4) A neural network identifier is developed to estimate unknown dynamics. Disturbances are overcome by improving the cost function and solving for optimal control of the nominal dynamic subsystem. By stability analysis, tracking errors in the AUV closed‐loop system can converge to an arbitrarily small compact set of the origin, and the other signals are uniformly ultimately bounded. Simulation comparisons demonstrate the effectiveness and superiority of the proposed method.

A quadrotor unmanned aerial vehicle (UAV) must achieve desired flight missions despite internal uncertainties and external disturbances. This paper proposes an adaptive trajectory tracking control method that attenuates unknown uncertainties and disturbances. Although the quadrotor is underactuated, a fully actuated controller is designed using backstepping control. To avoid repeated derivatives of control inputs, a dynamic surface method introduces a filter and auxiliary controller. Lyapunov criteria guide adaptive laws for tuning controller gain and filters. A low-power observer is integrated for state estimation. Additionally, a disturbance observer is developed and combined with the control scheme to handle unknown disturbances. Simulations on a DJI F450 quadrotor demonstrate that the proposed control algorithm offers strong trajectory-tracking performance and system stability under multiple uncertainties and external disturbances during flight.

In this article, a practical fixed-time adaptive neural network (NN) trajectory tracking control scheme for underactuated autonomous underwater vehicles (AUVs) subject to uncertain dynamics, unknown time-varying disturbances, an unknown dead zone, actuator faults and input quantization is developed for the first time. Here, a hysteresis quantizer is introduced to decrease the oscillation in the signal quantization process. Then, the radial basis function NN is employed to compensate the uncertainty term in the AUVs trajectory tracking control system. By incorporating the bounded estimate, smoothing functions and parameter adaptive technique, the problem of unknown dead zone, actuator fault and input quantization are addressed. The restrictive conditions of boundedness for the disturbance-like item in conventional sector bounded quantizer is resolved. Subsequently, a practical fixed-time adaptive NN trajectory tracking control law is designed does not require any parameter information of the quantizer under the backstepping design framework. The theoretical analysis further confirms that all signals in the AUV trajectory tracking closed-loop control system remain bounded, and the developed control scheme is shown to be effective through simulation results.

Trajectory tracking problem of autonomous vehicle under lane change is considered in this paper. To improve trajectory tracking performance in real scene, an adaptive tracking controller with finite time convergence performance is proposed to deal with the uncertain factors in the lane change scenario. The effectiveness and advantages of the proposed adaptive finite time control strategy (AFTCS) are illustrated by the simulation comparison results with the conventional PID tracking controller.

Adaptive trajectory tracking control for underwater vehicle based on hierarchical compensation

Existing adaptive optimal tracking controllers for linear continuous-time systems rely on a formulation that hinders learning control policies for general reference trajectories; generalizing approaches are currently limited to discrete-time systems. In addition, existing results usually rely on globally discounted objective functions. We demonstrate that global discounting potentially leads to unstable controllers and propose a partially discounted objective function instead, which we show to have a unique, globally asymptotically stabilizing solution in the linear-quadratic case. Based on this result, we present a model-free adaptive tracking control architecture for linear continuous-time systems. Once trained, the controller can be used to track flexible reference trajectories. We demonstrate the functionality of our approach with an example.

SUMMARYThis paper presents an adaptive trajectory tracking controller for a non-holonomic wheeled mobile robot (WMR) in the presence of parametric uncertainty in the kinematic and dynamic models of the WMR and actuator dynamics. The adaptive non-linear control law is designed based on input–output feedback linearization technique to get asymptotically exact cancellation for the uncertainty in the given system parameters. In order to evaluate the performance of the proposed controller, a non-adaptive controller is compared with the adaptive controller via computer simulation results. The results show satisfactory trajectory tracking performance by virtue of SPR-Lyapunov design approach. In order to verify the simulation results, a set of experiments have been carried out on a commercial mobile robot. The experimental results also show the effectiveness of the proposed controller.

This paper proposes an adaptive fuzzy fixed-time control (AF-FxT-C) scheme for a piezoelectric-driven microinjector. The inherent hysteresis of the piezoelectric actuator is treated as an unknown nonlinearity. A fuzzy logic system is employed to approximate this hysteresis, along with other lumped disturbances, while an adaptive law is designed to improve approximation accuracy. To address the challenge of inconsistent initial states caused by frequent start-stop operations, a fixed-time control law is developed via a second-order backstepping approach. This guarantees that the upper bound of the system’s settling time is independent of the initial conditions, which is a claim rigorously substantiated by a theoretical stability analysis. The simulation and experimental results validate the effectiveness of the proposed method. The method also maintains robust tracking performance across reference signals of varying frequencies and amplitudes, demonstrating its potential for industrial microinjection applications.

The adaptive trajectory and force tracking control is considered for a new mobile manipulator under both holonomic and affine constraints with the presence of uncertainties and disturbances in this paper. A new state transformation is proposed to deal with the affine constraints, and then based on a suitable reduced dynamic model, adaptive controller is presented to ensure that the states of closed-loop system asymptotically track to desired trajectories while the constraint force remains bounded by tuning design parameters. Detailed simulation results confirm the effectiveness of the control strategy.

Uncertainties are prevalent in real-world applications of bipedal walking robots, which may deteriorate the robot’s locomotion performance and even cause instability. However, designing controllers to address uncertainties for bipedal robotic walking is challenging mainly due to the high complexity of the hybrid walking dynamics under uncertainties. In this paper, an adaptive robust control strategy is proposed by combining control Lyapunov functions and the construction of multiple Lyapunov functions for provably guaranteeing the stability and trajectory tracking performance of fully actuated bipedal robots in the presence of uncertainties such as modeling errors and unmodeled disturbances. Simulation results on a three-dimensional bipedal robot with nine revolute joints were conducted to illustrate that the proposed adaptive robust control law can ensure stability and satisfactory tracking performance in the presence of parametric modeling uncertainties and unmodeled nonlinearities.

Trajectory tracking control problems for a given desired trajectory q/t) in joint space are treated on the basis of passivity analysis of residual error robot dynamics. Owing to the physical property that dynamic parameters appear linearly in Lagrange’s equation, a concept named a ‘regressor’ is introduced, which renders the system description more flexible. Model-based adaptive control for trajectory tracking is then devised by defining an update law of parameter estimation. This method is extended to cope with adaptive hybrid trajectory tracking control for dynamics under holonomic constraint. The effectiveness of this adaptive scheme is finally verified by experimental data.