Adaptive Trajectory Tracking Control Research Articles

Adaptive Trajectory Tracking Control of a Cable-Driven Underwater Vehicle on a Tension Leg Platform

This paper focuses on the dynamic modeling, controller design, and simulation verification of a new cable-driven underwater vehicle model system, which is proposed for future application on a tension leg platform. Compared with conventional underwater vehicles, the proposed cable-driven underwater vehicle model system has a unique structure and subjects to not only unknown underwater disturbances but also time-varying nonlinear cable tractions. To achieve accurate and robust trajectory tracking control, a universal high-order nonlinear dynamic model is established with multisource uncertainties, and an integrated estimation-based adaptive backstepping terminal sliding mode controller is designed. The proposed controller utilizes the integrated estimation method to handle the multisource unknown uncertainties, where recurrent radial basis function neural network and disturbance observer are employed for the estimations of uncertainties, and adaptive robust methods are utilized for compensations of estimation errors. The backstepping terminal sliding mode control method is utilized to improve the tracking performance and converging rate. In addition, the issue of “explosion of complexity” occurred in a traditional backstepping design is tackled by an adaptive control method, and the input saturation problem is solved by anti-windup compensator. Based on the Lyapunov analysis, all closed-loop signals are proved to be uniformly ultimately bounded. The numerical simulations show that the developed controller is not only robust against environmental disturbances and adaptive to unknown time-varying uncertainties but also able to steer the trajectory tracking errors along the prescribed transient, thus leading to effective cable-driven underwater vehicle model system control.

Robust Adaptive Trajectory Linearization Control for Tracking Control of Surface Vessels With Modeling Uncertainties Under Input Saturation

This paper develops a novel adaptive trajectory tracking control strategy to enhance the tracking performance for surface vessels with unmodeled dynamics and unknown time-varying disturbances. A high robustness and precision trajectory tracking controller is presented by using trajectory linearization control (TLC) technology, neural network, extended state observer (ESO), nonlinear tracking differentiator, and auxiliary dynamic system. First, the greatest advantage of this paper is that the TLC technology is first introduced into the field of surface vessels motion control, which provides a new direction for TLC technology research. Then, to further enhance the control performance and robustness of the system, the neural network with minimum learning parameter is used to replace the classical radial basis function neural network to approximate unmodeled dynamics, which can reduce the burden of computing. A novel reduced-order ESO is constructed to estimate unknown time-varying disturbances to achieve real-time compensation. Meanwhile, nonlinear tracking differentiator is employed to realize the derivative of virtual control command, as well as to provide command filtering. In addition, an auxiliary dynamic system is designed to reduce the risk of actuator saturation. The stability of the closed-loop system is guaranteed based on the Lyapunov criteria. Lastly, the comparison results demonstrate the superior performance of the proposed approach.

Adaptive model predictive control‐based attitude and trajectory tracking of a VTOL aircraft

A novel adaptive model-based predictive controller for attitude and trajectory tracking of a vertical take-off and landing (VTOL) aircraft in the simultaneous presence of model uncertainties and external disturbances is introduced in this study. An important challenge of designing the model-based controllers is developing an accurate model, especially in the presence of model uncertainties. In this study, first, the nominal model of a ducted-fan air vehicle, which is a multi-input multi-output nonlinear system with non-minimum phase behaviour, is given as the test case of this research. After that, two modified robust and adaptive model predictive controllers are proposed for tracking a predefined path in the presence of external gusts and model uncertainties. The design is performed by introducing two novel observers to estimate the model uncertainties and external disturbances, simultaneously. Different types of input constraints, as well as the time delay of the system inputs, can be considered effectively in the design steps of the proposed control strategy. The stability of the closed-loop system is proved under a few realistic assumptions. The simulation results demonstrate the great capability of the proposed method for attitude and trajectory tracking of the VTOL aircraft under model uncertainties and wind turbulence.

Adaptive sliding mode control for trajectory tracking of nonholonomic mobile robot with uncertain kinematics and dynamics

ABSTRACT This article designs a novel adaptive trajectory tracking controller for nonholonomic wheeled mobile robot under kinematic and dynamic uncertainties. A new velocity controller, in which kinematic parameter is estimated, produces velocity command of the robot. The designed adaptive sliding mode dynamic controller incorporates an estimator term to compensate for the external disturbances and dynamic uncertainties and a feedback term to improve the closed-loop stability and account for the estimation error of external disturbances. The system stability is analyzed using Lyapunov theory. Computer simulations affirm the robustness of the designed control scheme.

Adaptive Trajectory Tracking Control of a Fully Actuated Surface Vessel With Asymmetrically Constrained Input and Output

This brief addresses the trajectory tracking control problem of a fully actuated surface vessel subjected to asymmetrically constrained input and output. The controller design process is based on the backstepping technique. An asymmetric time-varying barrier Lyapunov function is proposed to address the output constraint. To overcome the difficulty of nondifferentiable input saturation, a smooth hyperbolic tangent function is employed to approximate the asymmetric saturation function. A Nussbaum function is introduced to compensate for the saturation approximation and ensure the system stability. The command filters and auxiliary systems are integrated with the control law to avoid the complicated calculation of the derivative of the virtual control in backstepping. In addition, the bounds of uncertainties and disturbances are estimated and compensated with an adaptive algorithm. With the proposed control, the constraints will never be violated during operation, and all system states are bounded. Simulation results and comparisons with standard method illustrate the effectiveness and advantages of the proposed controller.

Adaptive trajectory tracking control for VTOL‐UAVs with unknown inertia, gyro‐bias, and actuator LOE

SummaryThis paper proposes an adaptive controller for the trajectory tracking problem of vertical take‐off and landing unmanned aerial vehicles with unknown inertia and gyro‐bias, in the presence of external disturbances and actuator loss of effectiveness. To achieve our control objective, first, an a priori bounded virtual control law, providing an a priori bounded thrust and desired attitude, is designed for the translational dynamics. Thereafter, the torque input is designed for the rotational dynamics to track the desired orientation derived in the first stage. The stability of the overall hierarchical closed‐loop system and the global convergence of the tracking errors to zero are rigorously established. Finally, numerical simulations are performed to validate the effectiveness of the proposed control scheme.

Adaptive dynamical tracking control under uncertainty of shunt DC motors

A new adaptive velocity trajectory tracking control scheme for nonlinear shunt DC electric motors subjected to unmeasurable variable load torque and parametric uncertainty is proposed. Artificial neural networks and dynamical tracking error compensators are synergically combined to avoid dependence on detailed mathematical models of uncertain nonlinear systems and significantly improve the controller robustness and efficiency. The introduced robust tracking control approach can efficiently adapt to diverse uncertain operating scenarios. A priori knowledge or real-time estimation of disturbances and system parameters are unnecessary. The proposed output feedback dynamical tracking control can be extended to a wide class of controllable electric power systems operating under uncertainty. Analytical and numerical results prove the robust and efficient performance of the dynamical tracking control.

Adaptive trajectory tracking controller design for a quadrotor UAV with payload variation

PurposeThe purpose of this paper is to enhance the quadrotor’s capability of short-distance delivery to satisfy the large demand for quadrotor, which is used for goods distribution in huge warehouses, under time-varying payload and external wind disturbance.Design/methodology/approachA trajectory tracking controller design based on the combination of an adaptive sliding mode control (ASMC) method and the active disturbance rejection control (ADRC) technique is proposed. Besides, an inner–outer loop control system structure is adopted.FindingsSimulation results of different trajectory tracking verify the effectiveness and robustness of the proposed tracking control method under various conditions, including parameter uncertainty and external wind disturbance. The proposed control strategy ensures that quadrotor UAV is capable of tracking linear and spiral trajectory well whether it loads or unloads goods in the presence of the external wind disturbance.Originality/valueThe proposed method of designing a trajectory tracking controller is based on an integral ADRC and ASMC scheme so as to deal with the trajectory tracking problem for a quadrotor with payload variation.

Optimized adaptive tracking control for an underactuated vibro-driven capsule system

This paper studies the issue of adaptive trajectory tracking control for an underactuated vibro-driven capsule system and presents a novel motion generation framework. In this framework, feasible motion trajectory is derived through investigating dynamic constraints and kernel control indexes that underlie the underactuated dynamics. Due to the underactuated nature of the capsule system, the global motion dynamics cannot be directly controlled. The main objective of optimization is to indirectly control the friction-induced stick–slip motions to reshape the passive dynamics and, by doing so, to obtain optimal system performance in terms of average speed and energy efficacy. Two tracking control schemes are designed using a closed-loop feedback linearization approach and an adaptive variable structure control method with an auxiliary control variable, respectively. The reference model is accurately matched in a finite-time horizon. The key point is to define an exogenous state variable whose dynamics is employed as a control input. The tracking performance and system stability are investigated through rigorous theoretic analysis. Extensive simulation studies are conducted to demonstrate the effectiveness and feasibility of the developed trajectory model and optimized adaptive control system.

Learning‐based iterative modular adaptive control for nonlinear systems

SummaryIn this paper, we study the problem of adaptive trajectory tracking control for a class of nonlinear systems with structured parametric uncertainties. We propose to use an iterative modular approach: we first design a robust nonlinear state feedback that renders the closed‐loop input‐to‐state stable (ISS). Here, the input is considered to be the estimation error of the uncertain parameters, and the state is considered to be the closed‐loop output tracking error. Next, we propose an iterative adaptive algorithm, where we augment this robust ISS controller with an iterative data‐driven learning algorithm to estimate online the parametric uncertainties of the model. We implement this method with two different learning approaches. The first one is a data‐driven multiparametric extremum seeking method, which guarantees local convergence results, and the second is a Bayesian optimization‐based method called Gaussian Process Upper Confidence Bound, which guarantees global results in a compact search set. The combination of the ISS feedback and the data‐driven learning algorithms gives a learning‐based modular indirect adaptive controller. We show the efficiency of this approach on a two‐link robot manipulator numerical example.

Adaptive Trajectory Tracking Control of Dynamics of Nonholonomic Mobile Robot based on Orthogonal Function Approximation Technique

Adaptive Trajectory Tracking Control of Dynamics of Nonholonomic Mobile Robot based on Orthogonal Function Approximation Technique

Adaptive neural finite-time trajectory tracking control of hydraulic excavators

This article is focused on the high-performance trajectory tracking control of single actuator of a hydraulic excavator. A novel adaptive neural finite-time controller without tedious offline parameter identification and the complex backstepping scheme is put forward. By employing a coordinate transform, the original system can be represented in a canonical form. Consequently, the control objective is retained by controlling the transformed system, which allows a simple controller design without using backstepping. To estimate the immeasurable states of the transformed system, a high-order sliding mode observer is employed, of which observation error is guaranteed to be bounded in finite time. To guarantee finite-time trajectory tracking performance, an adaptive neural finite-time controller based on neural network approximation and terminal sliding mode theory is synthesized. During its synthesis, an echo state network is used to approximate the lumped uncertain system functions, and it guarantees an improved approximation with online-updated output weights. Besides, to handle the lumped uncertain nonlinearities resulting from observation error and neural approximation error, a robust term is employed. The influences of the uncertain nonlinearities are restrained with a novel parameter adaption law, which estimates and updates the upper bound of the lumped uncertain nonlinearities online. With this novel controller, the finite-time trajectory tracking error convergence is proved theoretically. The superior performance and the practical applicability of the proposed method are verified by comparative simulations and experiments.

Adaptive Non-Strict Trajectory Tracking Control Scheme for a Fully Actuated Unmanned Surface Vehicle

This study presents a new adaptive trajectory tracking control scheme for a fully actuated Unmanned Surface Vehicle (USV) to track a common moving target region. In this control concept, the desired objective trajectory is specified as a moving region instead of a moving point, and so which is called non-strict trajectory tracking. Within this control scheme, a regression matrix is used to handle the parameter uncertainties, and region-based control scheme is used to track a desired moving region. A switching gain control term based on the exponential function is proposed to make the USV’s trajectory converge into the desired moving region rather than converge on the boundary of the moving region, and to reduce system chattering at the same time. A Lyapunov-like function is presented for stability analysis of the proposed control scheme. Numerical simulations are conducted to demonstrate the performance of the proposed non-strict trajectory tracking control scheme of the USV.

Adaptive Trajectory Tracking Control for Underactuated Unmanned Surface Vehicle Subject to Unknown Dynamics and Time-Varing Disturbances

This paper proposes an adaptive trajectory tracking control strategy for underactuated unmanned surface vehicles subject to unknown dynamics and time-varing external disturbances. In short, the goal of this paper is to provide a control strategy that allows an underactuated unmanned surface vehicle to track a time dependent trajectory. First, a first-order sliding surface is introduced into the design of surge control law to converge to surge tracking error, and then a second-order sliding surface is hired to design yaw control law to deal with sway motion tracking error. Meanwhile, neural network minimum learning parameter method, which has a smaller amount of computation than a multilayer neural network, is employed to preserve the control law robustness against unknown dynamics and time-varing disturbances induced by wind, waves and ocean currents. Furthermore, much effort is made to obtain uniform ultimate bounded stability for the closed-loop control system. Finally, the numerical simulation experiments of straight line and circle trajectory tracking have been given to prove the correctness and feasibility of the proposed control strategy.

Adaptive fixed-time trajectory tracking control of a stratospheric airship

This paper addresses the fixed-time trajectory tracking control problem of a stratospheric airship. By extending the method of adding a power integrator to a novel adaptive fixed-time control method, the convergence of a stratospheric airship to its reference trajectory is guaranteed to be achieved within a fixed time. The control algorithm is firstly formulated without the consideration of external disturbances to establish the stability of the closed-loop system in fixed-time and demonstrate that the convergence time of the airship is essentially independent of its initial conditions. Subsequently, a smooth adaptive law is incorporated into the proposed fixed-time control framework to provide the system with robustness to external disturbances. Theoretical analyses demonstrate that under the adaptive fixed-time controller, the tracking errors will converge towards a residual set in fixed-time. The results of a comparative simulation study with other recent methods illustrate the remarkable performance and superiority of the proposed control method.

Robust adaptive trajectory tracking control of underactuated surface vessel in fields of marine practice

To enhance the control system robustness of an underactuated surface vessel with model uncertainties and environmental disturbances, a robust adaptive trajectory tracking algorithm based on proportional integral (PI) sliding mode control and the backstepping technique is proposed. In this algorithm, a continuous adaptive term is constructed to reduce the chattering magenta phenomenon of the system due to the sliding mode surface, and the backstepping technique is employed to force the ship position and the orientation on the desired values. In addition, we have proved the Lyapunov stability of the closed-loop system under the discontinuous environment disturbances or the thruster discontinuity. Finally, numerical simulations are performed to demonstrate the effectiveness of this novel methodology.

Fractional Order Model Reference Adaptive Control for SCARA Robot Trajectory Tracking

This paper proposes a new control strategy to the problem of trajectory tracking of SCARA robotic manipulator system by using a fractional order model reference adaptive controller (FMRAC) for sufficiently smooth trajectories. Over the few last years the idea of introducing fractional calculus and systems in adaptive control has found a great interest, for the benefits one can win in the performances given by such systems. The main contribution of this paper, is to show that the proposed fractional adaptive controller is able to reduce the delay time and the overshoot existing in classical control approach. Simulation results illustrate the effectiveness of the proposed control approach comparatively to the classical integer order one.

A new adaptive tracking control scheme of wheeled mobile robot without longitudinal velocity measurement

SummaryThis paper proposes a new adaptive trajectory tracking control scheme of the wheeled mobile robot without longitudinal velocity measurement. First, based on a kinematic controller, we obtain a new tracking error equation, which is suitable to develop an adaptive controller. Then, we develop a new adaptive trajectory tracking controller, which does not need any accurate values of the wheeled mobile robot parameters, including the driving motor parameters. Moreover, as the longitudinal velocity measurement is still difficult, this controller is developed without longitudinal velocity measurement. In addition, this new adaptive controller introduces a method to improve the control performance. The stability of the closed‐loop system is presented using the direct Lyapunov method. Finally, numerous simulations verify the effectiveness of the new controller.

Adaptive fault tolerant control for trajectory tracking of a quadrotor helicopter

In this paper, an adaptive fault tolerant controller based on [Formula: see text] control is developed and applied to the trajectory tracking for a quadrotor helicopter. Both multiplicative and additive actuator faults are considered. The proposed design is based on nonlinear feed-forward compensations and a typical nonlinear quadrotor model with uncertain inertial parameters and external disturbances. The [Formula: see text] adaptive control design is slightly modified to adapt with the position and the attitude error dynamics. The proposed adaptive controller yields uniformly verifiable bounds on the transient and the steady-state tracking error for any designated bounded reference trajectory. In the presence of fast adaptation, the adaptive controller compensates for actuator fault and disturbances in a particular frequency range. Finally, simulation results are included to validate the effectiveness of the proposed design.

Nussbaum-Based Adaptive Fuzzy Tracking Control of Unmanned Surface Vehicles with Fully Unknown Dynamics and Complex Input Nonlinearities

In this paper, subject to both fully unknown dynamics and complex input nonlinearities including unknown control directions and dead zones, a Nussbaum-based adaptive fuzzy trajectory tracking control scheme of an unmanned surface vehicle is addressed by combining adaptive fuzzy backstepping technique with Nussbaum approach. The dead-zone input nonlinearity is firstly divided into input-dependent functions and time-varying input coefficients which can be treated as system uncertainties. Together with disturbances, unknown dynamics and uncertainties, the lumped nonlinearity is online approximated by employing an adaptive fuzzy approximator. Within the backstepping framework, a Nussbaum gain function is further designed to tackle unknown control directions, and thereby devising an adaptive fuzzy trajectory tracking control scheme which is constructed recursively to deal with complex input nonlinearities and fully unknown dynamics. Theoretical analysis reveals that all signals of the closed-loop tracking system are bounded and tracking errors can converge to an arbitrarily small neighborhood of zero. Simulation studies demonstrate the effectiveness and superiority of the proposed approach.