Trajectory tracking for robotic airships using sliding mode control based on neural network approximation and fuzzy gain scheduling

This article proposed a novel control approach for trajectory tracking of robotic airships. First, the nonlinear dynamics model of a robotic airship is derived and formulated. Second, a sliding mode controller is designed to track the commanded trajectory for its robustness against parametric variations and external disturbances. To address the chattering problem results from the sliding mode controller, a radial basis function neural network is adopted to construct the neural network self-gain-scheduling sliding mode controller in which the control gains are scheduled synchronously with the sliding surface via radial basis function neural network according to the learning algorithm, with switching sliding surface and its differential as radial basis function neural network inputs and control gains as radial basis function neural network outputs. In addition, the stability and convergence of the closed-loop controller are proven using the Lyapunov stability theorem. Finally, the effectiveness and robustness of the proposed controller are demonstrated via numerical simulations. Contrasting simulation results indicate that the neural network self-gain-scheduling sliding mode controller attenuates the chattering effectively and has better performance against the sliding mode controller.

The Delta robot is an over-actuated parallel robot with highly nonlinear kinematics and dynamics. Designing the control for a Delta robot to carry out various operations is a challenging task. Various advanced control algorithms, such as adaptive control, sliding mode control, and model predictive control, have been investigated for trajectory tracking of the Delta robot. However, these control algorithms require a reliable input–output model of the Delta robot. To address this issue, we have created a control-affine neural network model of the Delta robot with stepper motors. This is a completely data-driven model intended for control design consideration and is not derivable from Newton’s law or Lagrange’s equation. The neural networks are trained with randomly sampled data in a sufficiently large workspace. The sliding mode control for trajectory tracking is then designed with the help of the neural network model. Extensive numerical results are obtained to show that the neural network model together with the sliding mode control exhibits outstanding performance, achieving a trajectory tracking error below 5 cm on average for the Delta robot. Future work will include experimental validation of the proposed neural network input–output model for control design for the Delta robot. Furthermore, transfer learnings can be conducted to further refine the neural network input–output model and the sliding mode control when new experimental data become available.

Variable structure control with sliding mode, which is commonly known as sliding mode control (SMC), is a nonlinear control strategy that is well known for its robust characteristics (Utkin, 1977). The main feature of SMC is that it can switch the control law very fast to drive the system states from any initial state onto a user-specified sliding surface, and to maintain the states on the surface for all subsequent time (Utkin, 1977), (Phuah et al., 2005 a). The conventional SMC has two disadvantages (Ertugrul & Kaynak, 2000), (Slotine & Sastry, 1983), which are the chattering phenomenon (Slotine & Sastry, 1983), (Young et al., 1999) and the difficulty in calculating the equivalent control law of SMC that requires a thorough knowledge of the parameters and dynamics of the nominal controlled plant (Ertugrul & Kaynak, 2000), (Slotine & Sastry, 1983), (Hussain & Ho, 2004). Many methods of SMC using neural networks (NN) have been proposed (Phuah et al., 2005 a), (Ertugrul & Kaynak, 2000), (Hussain & Ho, 2004), (Phuah et al., 2005 b), (Yasser et al., 2007), (Topalov et al., 2007). In this paper, sliding mode controls using NN are proposed to deal with the problem of eliminating the chattering effect and the difficulty in calculating the equivalent control law of SMC that requires a thorough knowledge of the parameters and dynamics of the nominal controlled plant. The first method of this method applies a method using a simplified form of the distance function proposed in (Phuah et al., 2005 a), (Phuah et al., 2005 b). Furthermore, the simplified distance function of our method uses a sliding surface in the space of the output error and its derivations, as proposed in (Yasser et al., 2006 a), (Yasser et al., 2006 c), instead of the space of the states error to construct a corrective control input. Thus, no observer is required in the proposed method. Moreover, we also propose the application of an NN to construct the equivalent control input of SMC. The weights of the NN are adjusted using a backpropagation algorithm as in (Yasser et al., 2006 b). Hence, a thorough knowledge of the parameters and dynamics of the nominal controlled plant is not required for calculating the equivalent control law. Finally, a stability analysis is carried out, and the effectiveness of this first control method is confirmed through computer simulations. This first method has been previously discussed in (Yasser et al., 2007). The second method of this paper applies an NN to produce the gain of the corrective control of SMC. Furthermore, the output of the switching function the corrective control of SMC is applied for the learning and training of the NN. There is no equivalent control of SMC is used in this second method. As in the first method, this second method applies a method using a sliding surface in the space of the output error and its derivations, as proposed in

SummaryThis paper studies the problem of stabilizing reference trajectories (also called as the trajectory tracking problem) for underactuated marine vehicles under predefined tracking error constraints. The boundary functions of the predefined constraints are asymmetric and time‐varying. The time‐varying boundary functions allow us to quantify prescribed performance of tracking errors on both transient and steady‐state stages. To overcome difficulties raised by underactuation and nonzero off‐diagonal terms in the system matrices, we develop a novel transverse function control approach to introduce an additional control input in backstepping procedure. This approach provides practical stabilization of any smooth reference trajectory, whether this trajectory is feasible or not. By practical stabilization, we mean that the tracking errors of vehicle position and orientation converge to a small neighborhood of zero. With the introduction of an error transformation function, we construct an inverse‐hyperbolic‐tangent‐like barrier Lyapunov function to show practical stability of the closed‐loop systems with prescribed transient and steady‐state performances. To deal with unmodeled dynamic uncertainties and external disturbances, we employ neural network (NN) approximators to estimate uncertain dynamics and present disturbance observers to estimate unknown disturbances. Subsequently, we develop adaptive control, based on NN approximators and disturbance estimates, that guarantees the prescribed performance of tracking errors during the transient stage of on‐line NN weight adaptations and disturbance estimates. Simulation results show the performance of the proposed tracking control.

A spherical robot is a nonlinear, nonholonomic, and unstable system which increases the difficulty of the direction and trajectory tracking problem. In this study, we propose a new direction controller Hierarchical Terminal Sliding Mode Controller (HTSMC), an instruction planning controller called Model Prediction Control-based Planner (MPCBP), and a trajectory tracking framework named MPCBP-HTSMC-HSMC (MHH). The HTSMC is designed by integrating a fast terminal algorithm, a hierarchical method, the motion features of a spherical robot, and its dynamics. In addition, the new direction controller has an excellent control effect with a quick response speed and strong stability. MPCBP can obtain optimal commands that are then transmitted to the velocity and direction controller. Since the two torque controllers in MHH are all Lyapunov-based sliding mode controllers, the MHH framework may achieve optimal control performance while assuring stability. Finally, the two controllers eliminate the requirement for MPCBP's stability and dynamic constraints. Finally, hardware experiments demonstrate the efficacy of the HTSMC, MPCBP, and MHH.

This paper proposed a sliding mode angle control with neural network estimator design for a fan-plate system. The neural network estimator is based on radial basis function and it estimates the unknown lumped bounded uncertainty of parameter variations and external disturbances in real-time. The abilities of anti-disturbance and anti-chattering are better than conventional sliding mode controller and adaptive sliding mode controller. The Lyapunov stability theorem is employed to ensure the stability of the proposed controller. The convergence and signal tracking properties are better than the conventional sliding mode controller. Finally, we employed the experiment to validate the proposed method is feasible.

The key attributes of Two Wheeled Balancing Mobile Robots (TWBMRs) are nonholonomic constraints and inherent instability. This paper deals with the problem of balancing and trajectory tracking of TWBMR using backstepping Sliding Mode Controller (SMC). First, the mathematical representation of TWBMR is derived using Lagrangian method by incorporating the dynamics of DC motors. Then, a decoupling approach is applied for simplifying the dynamic equations. The backstepping SMC technique is finally adopted to achieve the balancing and trajectory tracking of the TWBMR, whereas both model uncertainties and exogenous disturbance are taken into account in the controller design methodology. In order to determine the velocity, the trajectory tracking is achieved by the kinematic control, which is a common backstepping controller. For the velocity convergence of TWBMR to the generated desired value, two SMCs are designed, in which the motors voltage are directly controlled as the control laws. Simplicity in practical implementation and control law, ability to overcome uncertainties and appropriate performance are the main advantages of the proposed controller. The effectiveness of the proposed controller is verified through simulation and experimental results.

A new adaptive fuzzy sliding-mode control (FSMC) scheme was proposed, which incorporated the fuzzy logic into sliding-mode control using fuzzy logic to approximate the equivalent control and the upper bound of uncertainty which involved the disturbance and approximation error, thus the influence of modeling error was reduced and the gain of sliding-mode control part was more fitting, such that the chattering effects could be alleviated . Besides, inspired by the thought of fully tuned RBF neural networks, a fully tuned fuzzy logic was proposed which enhanced the approximating ability of fuzzy logic system. Lyapunov stability theorem was used to prove the stability of the system and the adaptive laws were deduced. Finally, simulation results of some BTT missile were included to illustrate the effectiveness of the adaptive fuzzy sliding-mode control scheme.

The robotic airship can be used as an aerostatic platform for many potential applications, for example, communication, hovering payload deliveries, data-gathering for research studies, etc. These applications require a fully autonomous perspective of an airship. One of the important aspects of airship autonomy is trajectory tracking control. An airship has complex and uncertain nonlinear dynamics which pose a major challenge for designing a precise trajectory tracking control. This paper addresses the airship trajectory tracking control problem under model uncertainties and wind disturbance. We propose a lumped model uncertainties and wind disturbance estimation approach based on an unscented Kalman filter. The estimated lumped uncertainty is used by the Sliding Mode Controller (SMC) for ultimate control of airship trajectory tracking. This comprehensive algorithm, Unscented Kalman filter-based Sliding Mode Controller (USMC), is used as a robust adaptive control solution to track the desired trajectory. The stability and convergence of the proposed method are investigated using the Lyapunov stability analysis. Simulation results show that the proposed method efficiently tracks the desired trajectory. The method solves the stability, convergence, and chattering problem of SMC without the bound constraint of model uncertainties and wind disturbance.

Trajectory tracking is an importance practice in ship motion control field. It attracts more attention recently due to its difficulties. Trajectory tracking requires the ship to arrive pinpoint location at exact time. It is a underactuated system because the degrees of freedom of control inputs are fewer than the degrees of freedom that needed to be controlled. In this paper, a hierarchical sliding mode controller and a common sliding mode controller are proposed to deal with the trajectory tracking problem of underactuated surface vessels. Simulation results validate the tracking performance of the proposed controllers. The closed-loop stability is testified by the Lyapunov stability theorem.

In this chapter an adaptive sliding mode controller for the Furuta pendulum is proposed. The Furuta pendulum is a class of underactuated mechanical systems commonly used in many control systems laboratories due to its complex stabilization which allows the analysis and design of different nonlinear and multivariable controllers that are useful in some fields such as aerospace and robotics. Sliding mode control has been extensively used in the control of mechanical systems as an alternative to other nonlinear control strategies such as backstepping, passivity based control etc. The design and implementation of an adaptive sliding mode controller for this kind of system is explained in this chapter, along with other sliding mode controller variations such as second order sliding mode (SOSMC) and PD plus sliding mode control (PD \(+\) SMC) in order to compare their performance under different system conditions. These control techniques are developed using the Lyapunov stability theorem and the variable structure design procedure to obtain asymptotically stable system trajectories. In this chapter the adaptive sliding mode consist of a sliding mode control law with an adaptive gain that makes the controller more flexible and reliable than other sliding mode control (SMC) algorithms and nonlinear control strategies. The adaptive sliding mode control (ASMC) of the Furuta pendulum, and the other SMC strategies shown in this chapter, are derived according to the Furuta’s pendulum dynamic equations making the sliding variables, position errors and velocity errors reach the zero value in a specified reaching time. The main reason of deriving two well known sliding mode control strategy apart from the proposed control strategy of this chapter (adaptive sliding mode control) is for comparison purposes and to evince the advantages and disadvantages of adaptive sliding mode control over other sliding mode control strategies for the stabilization of the Furuta pendulum. A chattering analysis of the three SMC variations is done, to examine the response of the system, and to test the performance of the ASMC in comparison with the other control strategies explained in this chapter.

Inspite of so much research, key technical problem, naming chattering of conventional, simple and robust SMC is still a challenge to the researchers and hence limits its practical application. However, newly developed soft computing based techniques can provide solution. In order to have advantages of conventional and heuristic soft computing based control techniques, in this paper various commonly used intelligent techniques, neural network, fuzzy logic and adaptive neuro fuzzy inference system (ANFIS) have been combined with sliding mode controller (SMC). For validation, proposed hybrid control schemes have been implemented for tracking a predefined trajectory by robotic manipulator, incorporating structured and unstructured uncertainties in the system. After reviewing numerous papers, all the commonly occurring uncertainties like continuous disturbance, uniform random white noise, static friction like coulomb friction and viscous friction, dynamic friction like Dhal friction and LuGre friction have been inserted in the system. Various performance indices like norm of tracking error, chattering in control input, norm of input torque, disturbance rejection, chattering rejection have been used. Comparative results show that with almost eliminated chattering the intelligent SMC controllers are found to be more efficient over simple SMC. It has also been observed from results that ANFIS based controller has the best tracking performance with the reduced burden on the system. No paper in the literature has found to have all these structured and unstructured uncertainties together for motion control of robotic manipulator.

An effective method, adaptive fuzzy sliding-mode (SM) PI Control to design full-bridge inverter is proposed in this paper. For practical applications, sliding mode control (SMC) with chattering phenomenon is a large hindrance. The modified model of the PI controller is built by the plant extension scheme, in order to relieve the chattering. Also, the fuzzy logic is applied to find the appropriate parameter values of the PI controller, and can adapt to plant parameter variations and external load disturbances. The proposed method has been realized for the actual full-bridge inverters controlled by DSP and CPLD. Simulation and experimental results of the closed-loop system show that the proposed method yields system performance improvement, such as low total harmonic distortion (THD), fast dynamic response, reduced steady-state error, and reduced chattering.

Mechatronic systems are becoming an intrinsic part of our daily life, and the adopted control approach in turn plays an essential role in the emulation of the intelligent behavior. In this paper, a framework for the development of intelligent controllers is proposed. We highlight that robustness, prediction, adaptation, and learning, which may be considered the most fundamental traits of all intelligent biological systems, should be taken into account within the project of the control scheme. Hence, the proposed framework is based on the fusion of a nonlinear control scheme with computational intelligence and also allows mechatronic systems to be able to make reasonable predictions about its dynamic behavior, adapt itself to changes in the plant, learn by interacting with the environment, and be robust to both structured and unstructured uncertainties. In order to illustrate the implementation of the control law within the proposed framework, a new intelligent depth controller is designed for a microdiving agent. On this basis, sliding mode control is combined with an adaptive neural network to provide the basic intelligent features. Online learning by minimizing a composite error signal, instead of supervised off-line training, is adopted to update the weight vector of the neural network. The boundedness and convergence properties of all closed-loop signals are proved using a Lyapunov-like stability analysis. Numerical simulations and experimental results obtained with the microdiving agent demonstrate the efficacy of the proposed approach and its suitableness for both stabilization and trajectory tracking problems.

The distributed trajectory tracking problem for multiple UAVs under unknown external disturbance is investigated. A new nonlinear robust trajectory tracking strategy for multiple UAVs is proposed. The dynamic model for the UAVs' formation is illustrated in the Tangent frame. For the trajectory tracking problem, a Robust formation tracking control strategy based on robust integral of the signum of error (RISE) is designed to compensate for the effects of unknown external disturbances, which improves the robustness of the UAVs' formation system. Based on the Lyapunov stability analysis, it is proved that the global asymptotic convergence of the coordination errors and the semi-global asymptotic convergence of the UAVs' position tracking errors are achieved. The proposed formation control strategy is validated via real-time experiments that are performed on the self-build UAVs' formation flight control testbed. Flights without wind disturbance and flights with disturbance are all performed. The performance comparison experiment with the conventional sliding mode control algorithm is performed. The experimental results show that the designed control strategy can achieve good coordinated trajectory tracking of multiple UAVs, and has better control performance compared with normal sliding mode control law.