Underactuated Subsystem Research Articles

A novel adaptive super-twisting trajectory tracking control with back propagation algorithm for a quadrotor UAV

This paper presents a new method for controlling a quadrotor unmanned aerial vehicle (UAV) with neural network adaptive adjustment combined with a super-twisting algorithm, which utilizes back-propagation algorithm in neural networks to design an adaptive method that can adjust the coefficients of the sliding mode surface as well as the control gain adjustment adaptive problem in the super-twisting to improve the stability and accuracy of the position and attitude control of the quadrotor UAV under uncertainty and external disturbances. Specifically, the adaptive neural network learns to dynamically adjust the sliding surface parameters and control gain, effectively inhibiting the sensitivity to parameter uncertainty and external disturbances, while the super-twisting sliding mode control ensures that the sliding trajectory converges in finite time and reduces the chattering phenomenon. In addition, the quadrotor UAV system is divided into a fully-actuated subsystem and an under-actuated subsystem, each of which contains two control inputs and the appropriate control algorithms are designed respectively, and the stability of the algorithm is demonstrated by means of a Lyapunov function in finite time. The proposed control method for quadrotor UAVs is validated through numerical simulations conducted in the Matlab/Simulink environment.

Adaptive fuzzy sliding-mode control of under-actuated systems with unknown input gain function

This research addresses the design of an Adaptive Fuzzy Sliding-Mode Control (AFSMC) for a group of nonlinear under-actuated systems with unknown input gain functions. In the proposed approach, to provide a structure for controlling the under-actuated subsystem, the sliding manifold corresponding to the whole dynamic system is derived based on the backstepping technique. In addition, two separate fuzzy inference systems are utilized for approximating the system’s internal dynamics and the unknown input gain function. In order to derive the robust part of the controller, a novel method is proposed to define the upper bound of the uncertain term in the form of a state-dependent second-degree polynomial. It should be mentioned that the output vectors of the fuzzy systems and the coefficients of the robust part of the controller are obtained by the designed adaptation laws. The asymptotic stability analysis for the proposed AFSMC structure is provided by the second theorem of Lyapunov and Barbalat’s lemma. In the end, the AFSMC effectuality is confirmed by the depth control of a REMUS Autonomous Underwater Vehicle (AUV).

A Novel Neural Network-Based Robust Adaptive Formation Control for Cooperative Transport of a Payload Using Two Underactuated Quadcopters

Designing a controller for the cooperative transport of a payload using quadcopter-type unmanned aerial vehicles (UAVs) is a very challenging task in control theory because these vehicles are underactuated mechanical systems. This paper presents a novel robust adaptive formation control design for the cooperative transport of a suspended payload by ropes using two underactuated quadcopters in the presence of external disturbances and parametric uncertainties. The structure of the proposed controller is divided into two subsystems: fully actuated and underactuated. An integral sliding mode adaptive control strategy is proposed for the fully actuated subsystem, and for the underactuated subsystem, an adaptive control strategy based on the combination of Backstepping and sliding mode is proposed. Then, the control parameters of the sliding surfaces of both control subsystems are adaptively tuned by a neural network. In addition, to improve the robustness of the proposed controller, a disturbance observer is incorporated to estimate and compensate the lumped disturbances. The asymptotic stability of the cooperative transport system is verified with the Lyapunov theorem. Finally, numerical simulations are performed in MATLAB/Simulink environment, and the results show that the proposed controller successfully transports the payload safely and without oscillations. Moreover, the desired formation pattern is maintained throughout the flight task, even with external disturbances and parametric uncertainties.

Nonlinear Extended State Observer Based Prescribed Performance Control for Quadrotor UAV with Attitude and Input Saturation Constraints

In this paper, a prescribed performance control scheme of the quadrotor unmanned aerial vehicle (UAV) under attitude and input saturation constraints is introduced. According to the underactuated feature, the quadrotor UAV system can be decomposed into an underactuated subsystem and a fully actuated subsystem. With the feedback linearization technique, a single nonlinear extended state observer (ESO) is proposed, and multiple observations are utilized to estimate both matched and unmatched disturbances, which not only can obtain a uniform convergence, but also reduces the complexity of the observer’s parameter adjustment. To improve system stability, an input saturation algorithm for each single rotor is introduced to modify the final control output. In addition, the limited attitude for the quadrotor UAV is also considered as a saturation constraint in the control scheme with a compensation auxiliary system. On this basis, dynamic surface control (DSC) with prescribed performance is adopted to guarantee the bounded convergence and steady-state error. All state errors of the closed-loop system are proven to be uniformly bounded using the Lyapunov theory, and the simulation results are given to demonstrate the stability, effectiveness, and superiority of the proposed control strategies at last.

Aerial photography trajectory-tracking controller design for quadrotor UAV

Quad-rotor unmanned aerial vehicles (UAV) are prone to external interference during aerial photography of farmland environments. For example, they are affected by external airflow and load, resulting in route deviation and irregular image overlap, which seriously affects image quality. An aerial trajectory tracking controller is designed for this aerial photography process. To ensure that a drone can fly according to the established route during the aerial photography process and meet the requirements of large-scale topographic map stereo mapping for the flight control accuracy of the drone platform, the system was divided into a full-drive subsystem and an underactuated subsystem. The full-drive subsystem uses a fast terminal sliding mode controller to ensure that the variable ([Formula: see text]) reaches the desired value. The under-actuated subsystem adopts the second-order sliding mode control was used to achieve effective position and attitude tracking of variables ([Formula: see text]). The flight controllers are derived by using Lyapunov theory. Finally, with the aerial trajectory of a farmland taken as an example, the flight path control of the UAV is simulated. Simulation results show that the designed control system can be applied to the aerial photography process of the UAV and has strong anti-system parameter perturbation, robustness and good trajectory tracking.

MATHEMATICAL MODELING WITH PARAMETER IDENTIFICATION FOR HEXAROTOR SYSTEM: A HAMILTONIAN APPROACH

This paper presents a mathematical modeling with parameters identification of Unmanned Aerial Vehicle (UAV) system or hexarotor system using the Hamiltonian approach. The mathematical model of the hexarotor is derived from the Hamiltonian approach which involved the storage, dissipation, and routing of energy elements from the UAV. This UAV model parameters identification method is proposed as an alternative to the commonly used wind tunnel testing, which is complex and tedious. This Hamiltonian model is made of a fully actuated subsystem with roll, pitch, and yaw angles as output, as well as an under-actuated subsystem with position coordinates as its output. Thrust constant, drag constant and speed of hexarotor are determined through the experimental setup while moment of inertia is determined by physical measurement and calculation. The outcome from this research works demonstrates an undemanding, yet effective method of modeling an UAV, and is useful for designing nonlinear controller to perform the important UAV tasks such as taking off, hovering, and landing.

Learning-Based Trajectory Tracking and Balance Control for Bicycle Robots With a Pendulum: A Gaussian Process Approach

This article presents a learning-based control framework for a class of underactuated bicycle robots with an active pendulum attached to the rear body as a balancer. In contrast with the extent methods that require the exact dynamic modeling, the proposed solution deals with the uncertainties, including the impacts of changing road environment, unmodeled dynamics, and external disturbances by virtue of Gaussian process and disturbance cancellation on control device. The tracking controller using traction and steering is presented based on Lyapunov redesign. The self-balancing control of the roll-pendulum underactuated subsystem is considered. This subsystem is first converted into a pure-feedback form, and a novel backstepping controller based on dynamic inversion technique is developed to maintain the roll and pendulum angles in the balance equilibrium manifold. By using an event-triggered update in the learning process, efficient prediction can be achieved, and the tracking error and the roll angle are limited to smaller bounds that are explicitly given. The simulation verifies that adjustable performance can be offered for tracking by tuning the control gains and the hyperparameters of the Gaussian process predictor. Finally, experiments are conducted on a real bicycle platform to illustrate the effectiveness of the control framework.

Robust flight control for a quadrotor under external disturbances based on generic second order sliding mode control

This paper presents a novel robust second order sliding mode control (RSOSMC) for tracking controller of a quadrotor with external disturbances. In addition, in order to perform the position and attitude tracking control of the quadrotor perfectly, the dynamical model of the quadrotor is divided into two subsystems, a subsystem fully actuated and an underactuated subsystem. The algorithm allows for rapid adaptation and stringent robustness of the quadrotor flight control in the presence of perturbations. Moreover, the proposed controller is based on the idea of second order sliding mode approach, which removes chattering in first-order sliding mode controllers. The finite-time stability and convergence of the proposed method are proved via the Lyapunov theory. To demonstrate the effectiveness of the suggested control approach, extensive simulation results are provided.

Tracking and vibration control of a free-floating space manipulator system with flexible links and joints

The problem of modeling and controlling of a free-floating space manipulator with flexures in both links and joints is addressed in this study. A mathematical model of the system is developed by combining Lagrange’s equations and momentum conservation. The finite element method is introduced to discretize multi-links with complex cross-sections. In order to reduce the dimensions and maintain the precision of a rigid-flexible coupled system, an iterated improved reduction system method is adopted. Then, a novel composite control scheme for the reduced system is presented that uses the concept of integral manifolds and singular perturbation theory. Finally, an augmented computed torque controller is applied to the under-actuated slow subsystem to realize trajectory tracking in joint space, while a linear-quadratic controller is designed to damp out the vibration of joints and links. Numerical simulation results verified that the proposed hybrid controller can successfully suppress vibration and track trajectory at the same time.

Udwadia-Kalaba Equation Based Adaptive Robust Control for Two-wheeled Inverted Pendulum System: Underactuation and Uncertainty

A new adaptive robust control method based on Udwadia-Kalaba(U-K) approach which can be applied to the underactuated system is designed and used to two-wheeled inverted pendulum system in this paper. We separate this typical underactuated system into two subsystems(forward subsystem and yaw subsystem), which are fully underactuated and actuated. For these different subsystems, we use different control methods. We apply an adaptive robust control method which has been proved many times to the fully actuated subsystem. Based on this adaptive robust method, a new control strategy can be redesigned and applied to the underactuated subsystem by modifying the adaptive law and other things. This adaptive robust control with a leakage-type adaptive law could guarantee the uniform boundedness and uniform ultimate boundedness of the system. Finally, the simulation is executed to demonstrate the advantage and simplicity of the proposed method.

Neuro-adaptive fast integral terminal sliding mode control design with variable gain robust exact differentiator for under-actuated quadcopter UAV

In this paper, a robust global fast terminal attractor based full flight trajectory tracking control law has been developed for the available regular form which is operated under matched uncertainties. Based on the hierarchical control principle, the aforesaid model is first subdivided into two subsystems, i.e., a fully-actuated subsystem and an under-actuated subsystem. In other words, the under-actuated subsystem is further transformed into a regular form whereby the under-actuated characteristics are decoupled in terms of control inputs. In the proposed design, the nonlinear drift terms, which certainly varies in full flight, are estimated via functional link neural networks to improve the performance of the controller in full flight. Besides, a variable gain robust exact differentiator (VG-RED) is designed to provide us with estimated flight velocities. It has consequently reduced the noise in system’s velocities and has mapped this controller as a practical one. The finite-time sliding mode enforcement and the states’ convergence are shown, for all flight loops, i.e., forward flight and backward flight, via the Lyapunov approach. All these claims are verified via numerical simulations and experimental implementation of the quadcopter system in a Matlab environment. For a more impressive presentation, the developed simulation results are compared with standard literature.

Research on a combinatorial control method for coaxial rotor aircraft based on sliding mode

Aiming at the position and attitude tracking of coaxial rotor aircraft (CRA), this paper proposes a combinatorial control method of sliding mode control (SMC) coupled with proportional-integral-derivative control (PIDC). Considering the complete description of flight dynamics, aerodynamics and airflow interference, the dynamical model of CRA is established. The dynamical model is simplified according to the actual flight, then the simplified dynamical model is divided into two subsystems: a fully-actuated subsystem and an under-actuated subsystem. The controller of the fully-actuated subsystem consists of a SMC controller coupled with a rate bounded PIDC controller, while the controller of the under-actuated subsystem is composed of a SMC controller. The sliding manifold is defined by combining the position and velocity tracking errors of the state variables for each subsystem. Lyapunov stability theory is used to verify the stability of the sliding mode controller, which ensures that all state trajectories of the system can reach and stay on the sliding mode surface, the uncertainty and external interference of the model are compensated. Simulation and experiment compared with the conventional PIDC are carried out, the results demonstrate the effectiveness and the robustness of the proposed control method of this paper.

Sliding mode control of a class of underactuated system with non-integrable momentum

In this paper, a sliding mode control scheme is developed to stabilise a class of nonlinear perturbed underactuated system with a non-integral momentum. In this scheme, by initially maintaining a subset of actuated variables on sliding manifolds, the underactuated system with the non-integrable momentum can be approximated by one with the integrable momentum in finite time. During sliding, a subset of the actuated variables converge to zero and a physically meaningful diffeomorphism is systematically calculated to transform the reduced order sliding motion into one in a strict feedback normal form in which the control signals are decoupled from the underactuated subsystem. Furthermore, based on the perturbed strict feedback form, it is possible to find a sliding mode control law to ensure the asymptotic stability of the remaining actuated and unactuated variables. The design efficacy is verified via a multi-link planar robot case study.

A novel sliding mode composite control design for fast time performance of quadrotor UAV

The dynamical model of a quadrotor unmanned aerial vehicle (UAV) is nonlinear, multivariable as well as unstable. Many control methods are available, but the existing controls are not sufficient to achieve stability and accuracy in a short time. This study presents a composite control approach to perform the attitude and position tracking of a UAV. The proposed control scheme has two steps. In the first step, the dynamical model is decomposed into two parts, i.e., fully actuated subsystem and underactuated subsystem. In the second step, the sliding mode control has been used to control the underactuated subsystem and terminal sliding mode control has been exploited to control the fully actuated subsystem. The application of terminal sliding mode guarantees the finite time convergence. The stability of the system has been ensured by obtaining the condition on control parameter using Lyapunov criterion. The performance of proposed control was evaluated and it has been found that there is substantive improvement over the performance of conventional methods.

A novel sliding mode composite control design for fast time performance of quadrotor UAV

The dynamical model of a quadrotor unmanned aerial vehicle (UAV) is nonlinear, multivariable as well as unstable. Many control methods are available, but the existing controls are not sufficient to achieve stability and accuracy in a short time. This study presents a composite control approach to perform the attitude and position tracking of a UAV. The proposed control scheme has two steps. In the first step, the dynamical model is decomposed into two parts, i.e., fully actuated subsystem and underactuated subsystem. In the second step, the sliding mode control has been used to control the underactuated subsystem and terminal sliding mode control has been exploited to control the fully actuated subsystem. The application of terminal sliding mode guarantees the finite time convergence. The stability of the system has been ensured by obtaining the condition on control parameter using Lyapunov criterion. The performance of proposed control was evaluated and it has been found that there is substantive improvement over the performance of conventional methods.

Disturbance suppression for quadrotor UAV using sliding-mode-observer-based equivalent-input-disturbance approach

This paper presents a new control scheme for quadrotor unmanned aerial vehicle attitude control and disturbance suppression. A quadrotor dynamic model is divided into two subsystems: fully-actuated and under-actuated. While the PID method is used to control the fully-actuated subsystem, a sliding-mode-observer-based equivalent-input-disturbance approach is used to control the under-actuated subsystem. The system design is simple, and it is globally uniformly ultimately bounded. Simulations and comparisons demonstrate the effectiveness of the method.

Robust Output Control of an Uncertain Underactuated 2DOF Mass-Spring-Damper System with Backlash Based on Active Disturbance Rejection Control Structure

We propose a strategy to solve the tracking and regulation problem for a 2DOF underactuated mass-spring-damper system with backlash on the underactuated joint, parametric uncertainties, and partial measurement of the state vector. The design of the controller is divided into two stages; in the first stage, it is assumed that the full state vector and all perturbations in the system are available. The model is divided into one actuated subsystem and one underactuated subsystem. The position of the actuated mass is defined as the control input of the underactuated subsystem, which is designed as an ideal controller that solves the tracking and regulation control problems for the underactuated mass. Finally, the control input of the actuated subsystem is designed to solve the tracking problem considering as a reference signal the control signal of the underactuated subsystem. The second stage solves the problem of the implementation of the previously designed ideal controller using the active disturbances rejection control structure (ADRC). Here state observers estimate the nonmeasured state variables and, at the same time, estimate perturbations and auxiliary signals for their compensation. The performance of the closed-loop system is illustrated by numerical simulations and experimental results.

Global fast dynamic terminal sliding mode control for a quadrotor UAV

A control method based on global fast dynamic terminal sliding mode control (TSMC) technique is proposed to design the flight controller for performing the finite-time position and attitude tracking control of a small quadrotor UAV. Firstly, the dynamic model of the quadrotor is divided into two subsystems, i.e., a fully actuated subsystem and an underactuated subsystem. Secondly, the dynamic flight controllers of the quadrotor are formulated based on global fast dynamic TSMC, which is able to guarantee that the position and velocity tracking errors of all system state variables converge to zero in finite-time. Moreover, the global fast dynamic TSMC is also able to eliminate the chattering phenomenon caused by the switching control action and realize the high precision performance. In addition, the stabilities of two subsystems are demonstrated by Lyapunov theory, respectively. Lastly, the simulation results are given to illustrate the effectiveness and robustness of the proposed control method in the presence of external disturbances.

Second order sliding mode control for a quadrotor UAV

A method based on second order sliding mode control (2-SMC) is proposed to design controllers for a small quadrotor UAV. For the switching sliding manifold design, the selection of the coefficients of the switching sliding manifold is in general a sophisticated issue because the coefficients are nonlinear. In this work, in order to perform the position and attitude tracking control of the quadrotor perfectly, the dynamical model of the quadrotor is divided into two subsystems, i.e., a fully actuated subsystem and an underactuated subsystem. For the former, a sliding manifold is defined by combining the position and velocity tracking errors of one state variable, i.e., the sliding manifold has two coefficients. For the latter, a sliding manifold is constructed via a linear combination of position and velocity tracking errors of two state variables, i.e., the sliding manifold has four coefficients. In order to further obtain the nonlinear coefficients of the sliding manifold, Hurwitz stability analysis is used to the solving process. In addition, the flight controllers are derived by using Lyapunov theory, which guarantees that all system state trajectories reach and stay on the sliding surfaces. Extensive simulation results are given to illustrate the effectiveness of the proposed control method.

Dynamic balance and motion control for wheeled inverted pendulum vehicle via hierarchical sliding mode approach

Dynamic balance and motion control for a class of underactuated wheeled inverted pendulum vehicles that are inherent unstable are investigated in this study. The control objective is to stable the posture of the vehicle platform (longitudinal and rotational position/velocity) as well as hold upright position of the pendulum (tilt angle stability), only with two control inputs generated by the left and right motors. The overall dynamic system is separated into two decoupled subsystems: one is a one-dimensional fully actuated subsystem while the other is a two-dimensional underactuated subsystem. A new hierarchical sliding mode control methodology is first developed to resolve the underactuated problem of this kind of unstable vehicles. The first layer sliding mode surfaces are established upon tilt angle and longitudinal displacement of the vehicle body, respectively; while the second layer sliding mode surface is constructed by the first layer sliding mode surfaces. Consequently, the total control law is deduced, and then the asymptotic stabilities for the overall closed-loop control system are addressed via Lyapunov stability theorem and Barbalat’s Lemma. Numerical simulations illustrate the effectiveness of the proposed control approaches and methodologies.