Adaptive Trajectory Tracking Control for Nonholonomic Wheeled Mobile Robots:A Barrier Function Sliding Mode Approach

The trajectory tracking control performance of nonholonomic wheeled mobile robots(NWMRs)is subject to nonholonomic constraints,system uncertainties,and external disturbances.This paper proposes a barrier function-based adaptive sliding mode control(BFASMC)method to provide high-precision,fast-response performance and robustness for NWMRs.Compared with the conventional adaptive sliding mode control,the proposed control strategy can guarantee that the sliding mode variables converge to a predefined neighborhood of origin with a predefined reaching time independent of the prior knowledge of the uncertainties and disturbances bounds.Another advantage of the proposed algorithm is that the control gains can be adaptively adjusted to follow the disturbances amplitudes thanks to the barrier function.The benefit is that the overestimation of control gain can be eliminated,resulting in chattering reduction.Moreover,a modified barrier function-like control gain is employed to prevent the input saturation problem due to the physical limit of the actuator.The stability analysis and comparative experiments demonstrate that the proposed BFASMC can ensure the prespecified convergence performance of the NWMR system output variables and strong robustness against uncertainties/disturbances.

Research of robust adaptive trajectory linearization control based on T-S fuzzy system

A robust adaptive trajectory linearization control （RATLC） algorithm for a class of nonlinear systems with uncertainty and disturbance based on the T-S fuzzy system is presented. The unknown disturbance and uncertainty are estimated by the T-S fuzzy system, and a robust adaptive control law is designed by the Lyapunov theory. Irrespective of whether the dimensions of the system and the rules of the fuzzy system are large or small, there is only one parameter adjusting on line. Uniformly ultimately boundedness of all signals of the composite closed-loop system are proved by theory analysis. Finally, a numerical example is studied based on the proposed method. The simulation results demonstrate the effectiveness and robustness of the control scheme.

Model-based trajectory tracking control for an electrohydraulic lifting system with valve compensation strategy

The natural frequency of the electrohydraulic system in mobile machinery is always very low,which brings difficulties to the controller design.To improve the tracking performance of the hydraulic system,mathematical modeling of the electrohydraulic lifting system and the rubber hose was accomplished according to an electrohydraulic lifting test rig built in the laboratory.Then,valve compensation strategy,including spool opening compensation (SOC) and dead zone compensation (DZC),was designed based on the flow-pressure characteristic of a closed-centered proportional valve.Comparative experiments on point-to-point trajectory tracking between a proportional controller with the proposed compensations and a traditional PI controller were conducted.Experiment results show that the maximal absolute values of the tracking error are reduced from 0.039 m to 0.019 m for the slow point-to-point motion trajectory and from 0.085 m to 0.054 m for the fast point-to-point motion trajectory with the proposed compensations.Moreover,tracking error of the proposed controller was analyzed and corresponding suggestions to reduce the tracking error were put forward.

A simple asymptotic trajectory control of full states of a unified chaotic system

A simple full-state asymptotic trajectory control （FSATC） scheme is proposed to asymptotically drive full states of a unified chaotic system （UCS） to arbitrary desired trajectories. The FSATC uses only information, i.e. one state of the UCS. A sinusoidal wave and two chaotic variables are taken as illustrative tracking trajectories to verify that using the proposed FSATC can make full UCS states track desired trajectories with high tracking accuracy in a finite time.

An observer based asymptotic trajectory control using a scalar state for chaotic systems

A state-observer based full-state asymptotic trajectory control （OFSTC） method requiring a scalar state is presented to asymptotically drive all the states of chaotic systems to arbitrary desired trajectories. It is no surprise that OFSTC can obtain good tracking performance as desired due to using a state-observer. Significantly OFSTC requires only a scalar state of chaotic systems. A sinusoidal wave and two chaotic variables were taken as illustrative tracking trajectories to validate that using OFSTC can make all the states of a unified chaotic system track the desired trajectories with high tracking accuracy and in a finite time. It is noted that this is the first time that the state-observer of chaotic systems is designed on the basis of Kharitonov＇s Theorem.

New trajectory linearization control for nonlinear systems undergoing harmonic disturbance

This paper presents a new trajectory linearization control scheme for a class of nonlinear systems subject to harmonic disturbance. It is supposed that the frequency of the disturbance is known, but the amplitude and the phase are unknown. A disturbance observer dynamics is constructed to estimate the harmonic disturbance, and then the estimation is used to implement a compensation control law to cancel the disturbance. By Lyapunov＇s direct method, a rigorous poof shows that the composite error of the closed-loop system can approach zero exponentially. Finally, the proposed method is illustrated by the application to control of an inverted pendulum. Compared with two existing methods, the proposed method demonstrates better performance in tracking error and response time.

A Back-stepping Based Trajectory Tracking Controller for a Non-chained Nonholonomic Spherical Robot

Spherical robot has good static and dynamic stability, which provides it with strong viability in hostile environment, but the lack of effective control methods has hindered its application and development. This article deals with the dynamic trajectory tracking problem of the spherical robot BHQ-2 designed for unmanned environment exploration. The dynamic model of the spherical robot is established with a simplified Boltzmann-Hamel equation, based on which a trajectory tracking controller is designed by using the back-stepping method. The convergence of the controller is proved with the Lyapunov stability theory. Numerical simulations show that with the controller the robot can globally and asymptotically track desired trajectories, both linear and circular.

Quaternion-based Nonlinear Trajectory Tracking Control of a Quadrotor Unmanned Aerial Vehicle

At present, most controllers of quadrotor unmanned aerial vehicles（UAVs） use Euler angles to express attitude. These controllers suffer a singularity problem when the pitch angle is near 90°, which limits the maneuverability of the UAV. To overcome this problem, based on the quatemion attitude representation, a 6 degree of freedom（DOF） nonlinear controller of a quadrotor UAV is designed using the trajectory linearization control（TLC） method. The overall controller contains a position sub-controller and an attitude sub-controller. The two controllers regulate the translational and rotational motion of the UAV, respectively. The controller is improved by using the commanded value instead of the nominal value as the input of the inner control loop. The performance of controller is tested by simulation before and after the improvement, the results show that the improved controller is better. The proposed controller is also tested via numerical simulation and real flights and is compared with the traditional controller based on Euler angles. The test results confirm the feasibility and the robustness of the proposed nonlinear controller. The proposed controller can successfully solve the singularity problem that usually occurs in the current attitude control of UAV and it is easy to be realized.

Trajectory linearization control of an aerospace vehicle based on RBF neural network

An enhanced trajectory linearization control （TLC） structure based on radial basis function neural network （RBFNN） and its application on an aerospace vehicle （ASV） flight control system are presensted. The influence of unknown disturbances and uncertainties is reduced by RBFNN thanks to its approaching ability, and a robustifying itera is used to overcome the approximate error of RBFNN. The parameters adaptive adjusting laws are designed on the Lyapunov theory. The uniform ultimate boundedness of all signals of the composite closed-loop system is proved based on Lyapunov theory. Finally, the flight control system of an ASV is designed based on the proposed method. Simulation results demonstrate the effectiveness and robustness of the designed approach.

STUDY ON SENSOR-BASED CONTROL METHOD FOR HARMONIC DRIVE SYSTEM

A new type of robust traje ctory tracking control for harmonic using joint torque sensor and joint acceleration sensor information is concerned with.Joint torque sensor information is used to compensate the uncertainty of link and load parameters. Joint acceleration feedback control will enhace the robustness of the driving system, resist the dynamic uncertainties and disturbing torque acted on the joint axis within definite bandwidth, improve the joint tracking performance, and resist the vibration of the load side of the harmonic drive system. Experimental studies are carried out and comparison of several controllers , such as PD and sensor- based control, the experimental results clearly illustrate the effectiveness of the proposed methods.

Dynamic modelling and PFL-based trajectory tracking control for underactuated cable-driven truss-like manipulator

In recent years,an innovative underactuated robot was developed,named as underactuated cable-driven trusslike manipulator(UCTM),to be suitable in aerospace applications.However,there has been strong consensus that the stabilization of planar underactuated manipulators without gravity is a great challenge since the system includes a second order nonholonomic constraint and most classical control methods are not suitable for this kind of system.Furthermore,the complexity of the truss-like structure results in tremendous difficulty of computational complicacy and high nonlinearity during dynamic modelling in addition to controller design.It is paramount to solve these difficulties for UCTM's future applications.To solve the above difficulties,this paper presents a dynamic modelling method for UCTM and a trajectory tracking control method based on partial feedback linearization(PFL)that fulfills the control goal of moving UCTM from its original position to a desired position by tracking a given trajectory of the joint angles.To achieve this,a model equivalent method is proposed to make UCTM equivalent with a three-link manipulator in the sense of dynamic behavior.Then the Lagrangian equation combined with complex vector method is proposed in the dynamic modelling process of UCTM,which simplifies the derivation procedure.Based on the established dynamic model,a coordinate transformation method is proposed to transform the control force matrix into the conventional form of an underactuated system,so that the control force can be separated from the unactuated term.The PFL method in combination with the LQR control method is then proposed to realize the targets that the joint angles can track given desired trajectory.Simulation experiments are conducted to verify the correctness and effectiveness of the proposed methods.

TRAJECTORY GENERATION AND CONTROL FOR NON-CIRCULAR CNC TURNING

A trajectory generation method which is based on NURBS interpolation is studied to improve the fitting accuracy and smoothness of non-circular cross section and obtain higher accuracy of the final non-circular profile control. After using the NURBS, the most optimized and smooth trajectory for the linear actuator can be obtained. For the purpose of machining the non-circular cross section by CNC turning, the fast response linear actuator has been used. The control algorithm which is compound control of proportional-integral-differential （PID） and iterative learning control has been developed for non-circular profile generation. By using the NURBS interpolation and the compound control of PID and iterative learning control, the final motion accuracy of linear actuator has been improved, therefore, the machining accuracy of the non-circular turning can be improved.

Trajectory Control of Scale-Free Dynamical Networks with Exogenous Disturbances

In this paper, the trajectory control of multi-agent dynamical systems with exogenous disturbances is studied. Suppose multiple agents composing of a scale-free network topology, the performance of rejecting disturbances for the low degree node and high degree node is analyzed. Firstly, the consensus of multi-agent systems without disturbances is studied by designing a pinning control strategy on a part of agents, where this pinning control can bring multiple agents＇ states to an expected consensus track. Then, the influence of the disturbances is considered by developing disturbance observers, and disturbance observers based control （DOBC） are developed for disturbances generated by an exogenous system to estimate the disturbances. Asymptotical consensus of the multi-agent systems with disturbances under the composite controller can be achieved for scale-free network topology. Finally, by analyzing examples of multi-agent systems with scale-free network topology and exogenous disturbances, the verities of the results are proved. Under the DOBC with the designed parameters, the trajectory convergence of multi-agent systems is researched by pinning two class of the nodes. We have found that it has more stronger robustness to exogenous disturbances for the high degree node pinned than that of the low degree node pinned.

Adaptive trajectory linearization control for hypersonic reentry vehicle

This paper presents an improved design for the hypersonic reentry vehicle(HRV) by the trajectory linearization control(TLC) technology for the design of HRV. The physics-based model fails to take into account the external disturbance in the flight envelope in which the stability and control derivatives prove to be nonlinear and time-varying, which is likely in turn to increase the difficulty in keeping the stability of the attitude control system. Therefore, it is of great significance to modulate the unsteady and nonlinear characteristic features of the system parameters so as to overcome the disadvantages of the conventional TLC technology that can only be valid and efficient in the cases when there may exist any minor uncertainties. It is just for this kind of necessity that we have developed a fuzzy-neural disturbance observer(FNDO) based on the B-spline to estimate such uncertainties and disturbances concerned by establishing a new dynamic system. The simulation results gained by using the aforementioned technology and the observer show that it is just due to the innovation of the adaptive trajectory linearization control(ATLC) system. Significant improvement has been realized in the performance and the robustness of the system in addition to its fault tolerance.

Trajectory tracking control of characteristic model for nonplanar hex-rotor UAV

The nonplanar hex-rotor unmanned aerial vehicle(UAV)has much higher driving property,greater payload capacity and damage tolerance than quad-rotor UAV.It is difficult to design a highperformance controller of easy engineering implementation for strongly coupled nonlinear hex-rotorUAV system.In response to this practical problem,an adaptive trajectory tracking control based oncharacteristic model for nonplanar hex-rotor is studied.Firstly,the dynamic model for the hex-rotorUAV is devised.Secondly,according to dynamic characteristics,environmental characteristics andcontrol performance requirements,the characteristic model of the hex-rotor UAV is constructed.Then,based on the characteristic model,a golden section adaptive controller is designed to realizetrajectory tracking.Furthermore,the stability analysis of the closed loop hex-rotor system is given.Finally,the validity of the proposed trajectory tracking control method adopted in the nonplanar hex-rotor UAV is demonstrated via numerical simulations and hex-rotor prototype experiments.

Trajectory tracking control based on linear active disturbance rejection controller for 6-DOF robot manipulator

The trajectory tracking control for a 6-DOF robot manipulator with multiple inputs and outputs,non-linearity and strong coupling is studied.Firstly,a dynamical model for the 6-DOF robot manipulator is designed.From the view point of practical engineering,considering the model uncertainties and external disturbances,the robot manipulator is divided into 6 independent joint subsystems,and a linear active disturbance rejection controller(LADRC)is developed to track trajectory for each subsystem respectively.LADRC has few parameters that are easy to be adjusted in engineering.Linear expansion state observer(LESO)as the uncertainty observer is able to estimate the general uncertainties effectively.Eventually,the validity and robustness of the proposed method adopted in 6-DOF robot manipulator are demonstrated via numerical simulations and 6-DOF robot manipulator experiments,which is of practical value in engineering application.

Adaptive Learning with Large Variability of Teaching Signals for Neural Networks and Its Application to Motion Control of an Industrial Robot

Recently, various control methods represented by proportional-integral-derivative （PID） control are used for robotic control. To cope with the requirements for high response and precision, advanced feedforward controllers such as gravity compensator, Coriolis/centrifugal force compensator and friction compensators have been built in the controller. Generally, it causes heavy computational load when calculating the compensating value within a short sampling period. In this paper, integrated recurrent neural networks are applied as a feedforward controller for PUMA560 manipulator. The feedforward controller works instead of gravity and Coriolis/centrifugal force compensators. In the learning process of the neural network by using back propagation algorithm, the learning coefficient and gain of sigmoid function are tuned intuitively and empirically according to teaching signals. The tuning is complicated because it is being conducted by trial and error. Especially, when the scale of teaching signal is large, the problem becomes crucial. To cope with the problem which concerns the learning performance, a simple and adaptive learning technique for large scale teaching signals is proposed. The learning techniques and control effectiveness are evaluated through simulations using the dynamic model of PUMA560 manipulator.

An Integrated Hydrodynamics and Control Model of A Tethered Underwater Robot

An integrated hydrodynamics and control model to simulate tethered underwater robot system is proposed. The governing equation of the umbilical cable is based on a finite difference method, the hydrodynamic behaviors of the underwater robot are described by the six-degrees-of-freedom equations of motion for submarine simulations, and a controller based on the fuzzy sliding mode control(FSMC) algorithm is also incorporated. Fluid motion around the main body of moving robot with running control ducted propellers is governed by the Navier–Stokes equations and these nonlinear differential equations are solved numerically via computational fluid dynamics(CFD) technique. The hydrodynamics and control behaviors of the tethered underwater robot under certain designated trajectory and attitude control manipulation are then investigated based on the established hydrodynamics and control model. The results indicate that satisfactory control effect can be achieved and hydrodynamic behavior under the control operation can be observed with the model; much kinematic and dynamic information about tethered underwater robot system can be forecasted, including translational and angular motions of the robot, hydrodynamic loading on the robot, manipulation actions produced by the control propellers, the kinematic and dynamic behaviors of the umbilical cable. Since these hydrodynamic effects are fed into the proposed coupled model, the mutual hydrodynamic influences of different portions of the robot system as well as the hydrological factors of the undersea environment for the robot operation are incorporated in the model.

Integrated guidance and control design of the suicide UCAV for terminal attack

A novel integrated guidance and control (IGC) design method is proposed to solve problems of low control accuracy for a suicide unmanned combat aerial vehicle (UCAV) in the terminal attack stage. First of all, the IGC system model of the UCAV is built based on the three-channel independent design idea, which reduces the difficulties of designing the controller. Then, IGC control laws are designed using the trajectory linearization control (TLC). A nonlinear disturbance observer (NDO) is introduced to the IGC controller to reject various uncertainties, such as the aerodynamic parameter perturbation and the measurement error interference. The stability of the closed-loop system is proven by using the Lyapunov theorem. The performance of the proposed IGC design method is verified in a terminal attack mission of the suicide UCAV. Finally, simulation results demonstrate the superiority and effectiveness in the aspects of guidance accuracy and system robustness.

Achievement of chaotic synchronization trajectories of master-slave manipulators with feedback control strategy

This paper addresses a master-slave synchro- nization strategy for complex dynamic systems based on feedback control. This strategy is applied to 3-DOF pla- nar manipulators in order to obtain synchronization in such complicated as chaotic motions of end-effectors. A chaotic curve is selected from Duffing equation as the trajectory of master end-effector and a piecewise approximation method is proposed to accurately represent this chaotic trajectory of end-effectors. The dynamical equations of master-slave manipulators with synchronization controller are derived, and the Lyapunov stability theory is used to determine the stability of this controlled synchronization system. In numer- ical experiments, the synchronous motions of end-effectors as well as three joint angles and torques of master-slave manipulators are studied under the control of the proposed synchronization strategy. It is found that the positive gain matrix affects the implementation of synchronization con- trol strategy. This synchronization control strategy proves the synchronization＇s feasibility and controllability for com- plicated motions generated by master-slave manipulators.