This paper solves the tracking control problem for a quadrotor system under the tasks of large-angle rotation and high-speed trajectory tracking. A quadrotor dynamic model is presented taking both disturbances and drag force into account. A reachability control strategy is developed for a quadrotor to track the planned attitude and position. Outdoor experiments of a circle trajectory tracking at different flight speeds validate the robustness of the proposed method. A task of flip is demonstrated to verify the effectiveness of the proposed controller under a large tilt angle.

In this paper, we present the positioning control problem for underactuated unmanned surface vehicles (USVs) in the presence of unknown external disturbances, such as the wind, waves, and currents. The three control objectives of positioning control for underactuated USVs are, firstly, to retain a predefined constant distance to a look-ahead point, secondly, to regulate the vehicle heading to point at the look-ahead point and, thirdly, to update the position of the look-ahead point to rotate the USVs. Particularly, a new guidance rule is proposed to update the look-ahead point based on the positioning error such that the predefined desired position is maintained and the vehicle heading is counter to the direction of resultant environmental force at the same time. To illustrate the stability of the positioning control system, the error dynamics driven by the component of resultant environmental force is derived and analyzed. In addition to the simulations, experiments were carried out offshore in the face of wind and waves to verify the validity and effectiveness of the proposed method.

This article presents two interrelated problems-along tracking and cross tracking-in guidance design for curved path following for unmanned surface vehicles. Since these two types of directional tracking are interactively constrained in most research work, an iteration mechanism is first put forward to optimize the path parameter in each closed loop such that along tracking will not affect cross tracking in the subsequent time period. An extended line-of-sight (ELOS) guidance principle is then proposed by varying the look-ahead distance with the cross-track error such that sideslip in cross tracking can be promptly compensated through vehicle heading amendment. Both simulation and experimental results verify the effectiveness of the proposed methods, which perform better than the conventional line-of-sight (LOS) and integral LOS (ILOS) guidance laws.

This paper presents an on-line estimator to evaluate the inertia-related parameters for a class of quasi-linear mechanical systems. The proposed estimator is established on the designed virtual acceleration error signal, and only the measurements for velocity and position are needed, therefore the usage of an accelerometer is avoided. The performance of the proposed estimator is verified on the numerical simulation of two mechanical systems. The simulation results of the linear spring-mass-damper system show that the proposed estimator could evaluate the constant mass well, even when the initial estimation contains large error values. And also another simulation conducted on a two-link planar robotic arm shows the proposed estimator can follow the time-varying inertia matrix with large initial estimation error.

This paper presents the development of a new type of robot capable of vertical and directional jumping. The robot uses soft silicone elastomer based pneumatic actuators as legs that accelerate the platform upwards by rapid pressurization. The robot is able to control and adjust the direction of the jumping by altering the timing patterns in which the individual legs are activated.

A new iterative learning control approach based on Fourier neural network (FNN) is presented for the tracking control of a class of nonlinear systems with deterministic uncertainties. The proposed controller consists of two loops. The inner loop is a feedback control action that decreases system variability and reduces the influence of random disturbances. The outer loop is an FNN-based learning controller that generates the system input to suppress the error caused by system nonlinearities and deterministic uncertainties. The FNN employs orthogonal complex Fourier exponentials as its activation functions. Therefore, it is essentially a frequency-domain method that converts the tracking problem in the time domain into a number of regulation problems in the frequency domain. Through a novel phase compensation technique, this model-free method makes it possible to use higher-frequency components in the FNN to improve the tracking performance. In addition, the structure of the FNN can be reconfigured according to the system output information to make the learning more efficient and increase the convergent speed of the tracking error. Experiments on both a commercial gear box and a belt-driven positioning table are conducted to show the effectiveness of the proposed controller.

This paper considers an output feedback learning control for a class of uncertain nonlinear systems with flexible components. The distinct time delay caused by system flexibility leads to the phase lag phenomenon and low system bandwidth. Therefore, the tracking problem of such systems is very difficult and challenging. To improve the tracking performance of such systems, an iterative learning control scheme using the Fourier neural network (FNN) is presented in this paper. This scheme uses only local output information for feedback. FNN employs orthogonal complex Fourier exponentials as its activation functions and the physical meaning of its hidden-layer neurons is clear. The FNN-based learning controller introduced here relies on the frequency-domain method, which converts the tracking problem in the time domain into a number of regulation problems in the frequency domain. A novel phase compensation method is introduced to deal with the phase lag phenomenon, so that the bandwidth of the closed-loop system is increased. Experiments on a belt-driven positioning table are conducted to show the effectiveness of the proposed controller.

An adaptive Fourier neural network (AFNN) control scheme is presented in this paper for the control of a class of uncertain nonlinear systems. Based on Fourier analysis and neural network (NN) theory, AFNN employs orthogonal complex Fourier exponentials as the activation functions. Due to the clear physical meaning of the neurons, the determination of the AFNN structure as well as the parameters of the activation functions becomes convenient. One salient feature of the proposed AFNN approach is that all the nonlinearities and uncertainties of the dynamical system are lumped together and compensated online by AFNN. It can, therefore, be applied to uncertain nonlinear systems without any a priori knowledge about the system dynamics. Derived from Lyapunov theory, a novel learning algorithm is proposed, which is essentially a frequency domain method and can guarantee asymptotic stability of the closed-loop system. The simulation results of a multiple-input-multiple-output (MIMO) nonlinear system and the experimental results of an X - Y positioning table are presented to show the effectiveness of the proposed AFNN controller.

The flexible joints in robotic manipulators may lower the bandwidth of the robotic system. Therefore, it is difficult to achieve good control performance on robots with flexible joints by the conventional control schemes. In this paper, we presented the implementation and improvement of the Fourier series based learning controller for tracking control of a belt-driving system which is one type of flexible joints. Experimental results demonstrate the effectiveness of the applied methodology.

A Takagi-Sugeno (T-S) fuzzy model is used to express non-linear dynamic systems with time-delay in this paper, and an on-line identification algorithm is presented regarding its parameters and structures. A multivariable fuzzy generalized predictive control approach is proposed based on the identified fuzzy model by means of the generalized predictive control principle. The closed-loop stability is analyzed in detail. A simulation study for the multivariable load system of a boiler-turbine unit shows that the approach is superior to convention load control systems.

In this article, a control problem for nonlinear single-input/single-output (SISO) systems with time-varying parameters is discussed. The control system consists of two parts. One part is a fuzzy control loop, which has feedback function designed to overcome random instant disturbances. The other part is a Fourier series-based control, which is a feedforward loop designed to overcome steady lasting deterministic types of uncertain disturbances. The former is a fast loop, in which feedback control rules are autotuned in each sample time. The latter is a slow loop, in which the feedforward control actions are computed at each pass. Stability of the nonlinear control system is guaranteed by means of Lyapunov stability. This approach has been applied to a simulation study of a control system of a superheated steam temperature process in a thermal power plant. The results of comparisons with PID and a fuzzy control show satisfactory performance.

This paper presents a new nonlinear adaptive tracking controller for a class of general time-variant nonlinear systems. The control system consists of an inner loop and an outer loop. The inner loop is a fuzzy sliding mode control that is used as the feedback controller to overcome random instant disturbances. The stability of the inner loop is designed by the sliding mode control method. The other loop is a Fourier integral-based control that is used as the feedforward controller to overcome the deterministic type of uncertain disturbance. The asymptotic convergence condition of the nonlinear adaptive control system is guaranteed by the Lyapunov direct method. The effectiveness of the proposed controller is illustrated by its application to composition control in a continuously stirred tank reactor system.

We proposed a new learning controller for decentralized tracking control of nonlinear robot manipulators. When the desired trajectory of each subsystem of the robot lasts for a finite duration, it can be approximated by a Fourier series with constant harmonic magnitudes. For each subsystem of the robot, a learning controller is designed to individually control each harmonic component of the actual output, although it is cross-related to other components in nonlinear systems. The learning algorithm is designed such that each harmonic magnitude of the actual output converges to that of the desired trajectory within the system bandwidth. Since this decentralized learning controller is designed in Fourier space instead of time domain, the system's time-delay could be easily compensated. This learning controller is only based on the local input and output information; no a priori structure or parameters of the system model are required. The experimental results on a 3-DOF direct-drive robot are presented.

In this paper, a new fuzzy basis function vector (FBFV) approach for the adaptive control of multivariable nonlinear systems is presented. With this method, the nonlinear plant is first linearized. The linearized bias and uncertainties as well as disturbances are assumed to be included in the model structure and their upper bound will be adaptively learned by the FBFV method. The output of the FBFV is used as the parameters of the robust controller in the sense that both the robustness and the asymptotic error convergence can be obtained for the multivariable nonlinear system. The effectiveness of the proposed analysis and design method is illustrated with a simulated example.

A decentralized learning control scheme for tracking control of robot manipulators is presented. In this scheme, each joint is considered as a subsystem and controlled independently. The interactions from other subsystems are treated as deterministic uncertainties. The desired trajectory and the output of each subsystem are reparametrized by Fourier series (FS). A learning controller designed in Fourier space regulates each harmonic component individually by forcing Fourier coefficients (FCs) of the actual output approach to the corresponding FCs of the desired trajectory which are known constants. Since the information of the system phase-delay is included in FCs, the time-delay of the system can be easily compensated. The learning controller only uses the input and output information of the subsystem, no a priori knowledge about the system models is required. The asymptotic convergence of the tracking is proved in the paper. The experimental results on a 3 DOF direct-drive robot show that convergence rate is faster compared with many other learning controllers and the performance of the closed-loop system is dramatically improved.

The problem of how to improve the transient performance of a single-link flexible robot arm rotating in a horizontal plane using FFT method is addressed in this paper. Lyapunov's direct method is used to prove the stability of the closed-loop system under the proposed control law. However, the performance of the system is limited by factors such as nonlinearity, lower resonate frequency and time-delay. In order to further improve the tracking performance, we proposed to use FFT to analyze the tracking error. Through the analysis we can obtain the information of the system in the frequency-domain. The information then is fed back to the system, so that the performance of the system can be enhanced. The experimental results of a single flexible arm are presented in this paper for illustration.

A model-free robust/adaptive decentralized controller for nonlinear uncertain robot manipulators is presented. The proposed controller consists of a PD controller, a robust/adaptive controller and dynamic compensator. The dynamic compensator is online up-dated based on the Taylor expansion in terms of the historical information of the individual local inputs to the system. The result obtained from the dynamic compensator is used to cancel the nonlinearity and uncertainties within the system to be controlled. The robust/adaptive controller is used to handle the effect of the residual dynamics, which is the difference of the dynamics of the system and the estimated one. The stability analysis of the closed-loop system is performed based on a modified version of Lyapunov's theory. Experimental results on the tracking control of a 3-DOF direct drive robot are presented for illustration.

An auto-focusing system that consists of a compact disk (CD) optical head and a piezoelectric translator (PZT) is developed for measuring the displacement or profile of a tested surface. The modified CD optical head provides the defocusing signal from the tested surface. The defocusing signal is then used to drive the PZT via a feedback controller. The focus spot of the optical head follows the displacement of the tested surface through the movement of the PZT. The displacement or the profile of the tested surface can be obtained through three ways with different accuracy: the integration of the focus error signal (FES), the curve of driving voltage to expansion distance of the PZT or a secondary sensing device of displacement. The resolution of the system can reach 10 nm and the accuracy is 0.05 /spl mu/m. Some design considerations such as the control algorithm of focus servo and error analysis of the system are addressed in this paper. The measurement system and the sensor based on the CD pickup can also be applied to position sensing for robot as well as the noncontact probe for localization.

A new control scheme is proposed for a class of nonlinear uncertain time-varying systems tracking control. The proposed controller combines advantages of both robust and adaptive control schemes. Unlike the traditional robust control scheme, the proposed controller does not require to know the structure of uncertainties, but can still ensure the asymptotic stability of the closed-loop system. Comparing with the traditional adaptive control scheme, this controller can deal with time-varying parameter uncertainties, and the uncertain parameters do not need to be a linear function of the states. The stability analysis of the closed-loop system is performed based on the newly developed theory presented in this paper. An experimental result on a positioning table is presented for illustration.

An approach is proposed to simultaneously control the contact forces exerted on a constraint surface and the position of the end-effector, both in the presence of frictional forces on the constraint surface. The approach, using a novel formulation of the dynamics model, is based on a linear state feedback. A feedforward and PI (proportional-integral) feedback control strategy is proposed along with a design procedure. Using the proposed control method the trajectory following problem is solved and the closed-loop system is shown to be asymptotically stable. Numerical examples of a two-link robot moving along a constraint surface are presented for illustration.>

Some aspects of automatic deburring by a robot are considered. The strategy proposed is based on constrained motion control, in which both force and position of the robot are simultaneously controlled. However, in practice, a robot may be in free unconstrained motion before it comes in contact with the environment. In order to control the deburring operation without switching controllers for the unconstrained and constrained motions respectively, an additional controller is proposed, and a control strategy is used so that these three controllers for the robot are automatically switched. This ensures that the robot is stable during the whole process of deburring. A numerical example of a deburring process with a two degrees-of-freedom robot is presented for illustration.>

The design of a robust nonlinear feedback controller is addressed for an N-degree-of-freedom robot with bounded uncertainty in the dynamic model's parameters. It is demonstrated that the proposed controller makes the robot system practically stable when both unknown payload variation and joint frictional force are taken into consideration. It is also shown that this controller can guarantee the practical stability of the robot system when a collision between the robot and its environmental occurs. Sufficient conditions for global practical stability are derived using Lyapunov's second method. A numerical simulation of a two-link robot manipulator with bounded parameter to illustrate the proposed control system.>