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.

Adaptive state-constrained/model-free iterative sliding mode control for aerial robot trajectory tracking

This paper develops a novel hierarchical control strategy for improving the trajectory tracking capability of aerial robots under parameter uncertainties.The hierarchical control strategy is composed of an adaptive sliding mode controller and a model-free iterative sliding mode controller(MFISMC).A position controller is designed based on adaptive sliding mode control(SMC)to safely drive the aerial robot and ensure fast state convergence under external disturbances.Additionally,the MFISMC acts as an attitude controller to estimate the unmodeled dynamics without detailed knowledge of aerial robots.Then,the adaption laws are derived with the Lyapunov theory to guarantee the asymptotic tracking of the system state.Finally,to demonstrate the performance and robustness of the proposed control strategy,numerical simulations are carried out,which are also compared with other conventional strategies,such as proportional-integralderivative(PID),backstepping(BS),and SMC.The simulation results indicate that the proposed hierarchical control strategy can fulfill zero steady-state error and achieve faster convergence compared with conventional strategies.

Adaptive Robust Control with Leakage-Type Control Law for Trajectory Tracking of Exoskeleton Robots

This paper investigates the trajectory following problem of exoskeleton robots with numerous constraints. However, as a typical nonlinear system with variability and parameter uncertainty, it is difficult to accurately achieve the trajectory tracking control for exoskeletons. In this paper, we present a robust control of trajectory tracking control based on servo constraints. Firstly, we consider the uncertainties (e.g., modelling errors, initial condition deviations, structural vibrations, and other unknown external disturbances) in the exoskeleton system, which are time-varying and bounded. Secondly, we establish the dynamic model and formulate a close-loop connection between the dynamic model and the real world. Then, the trajectory tracking issue is regarded as a servo constraint problem, and an adaptive robust control with leakage-type adaptive law is proposed with the guaranteed Lyapunov stability. Finally, we conduct numerical simulations to verify the performance of the proposed controller.

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.

An adaptive switching control approach for trajectory tracking of robotic manipulators

In order to design a suitable controller which can achieve accurate trajectory tracking and a good control performance, and guarantee the stability and robustness of a robot system due to external disturbances error and internal parameter variations, an adaptive switching control strategy is proposed. The proposed scheme is designed under the condition of bounded distances and consists of an adaptive switching law and a PD controller. Based on the Lyapunov stability theory, it is proved that the proposed scheme can guarantee the tracking performance of the robotic manipulator and is adapted to varying unknown loads. Simulations are carded out on a two-link robotic manipulator, which illustrate the feasibility and validity of the proposed control scheme and the robustness for variational payloads.

Adaptive saturated tracking control for solid launch vehicles in ascending based on differential inclusion stabilization

The large-range uncertainties of specific impulse,mass flow per second,aerodynamic coefficients and atmospheric density during rapid turning in solid launch vehicles(SLVs) ascending leads to the deviation of the actual trajectory from the reference one.One of the traditional trajectory tracking methods is to observe the uncertainties by Extended State Observer(ESO) and then modify the control commands.However,ESO cannot accurately estimate the uncertainties when the uncertainty ranges are large,which reduces the guidance accuracy.This paper introduces differential inclusion(DI) and designs a controller to solve the large-range parameter uncertainties problem.When above uncertainties have large ranges,it can be combined with the ascent dynamic equation and described as a DI system in the mathematical form of a set.If the DI system is stabilized,all the subsets are stabilized.Different from the traditional controllers,the parameters of the designed controller are calculated by the uncertain boundaries.Therefore,the controller can solve the problem of large-range parameter uncertainties of in ascending.Firstly,the ascent deviation system is obtained by linearization along the reference trajectory.The trajectory tracking system with engine parameters and aerodynamic uncertainties is described as an ascent DI system with respect to state deviation,which is called DI system.A DI adaptive saturation tracking controller(DIAST) is proposed to stabilize the DI system.Secondly,an improved barrier Lyapunov function(named time-varying tangent-log barrier Lyapunov function) is proposed to constrain the state deviations.Compared with traditional barrier Lyapunov function,it can dynamically adjust the boundary of deviation convergence,which improve the convergence rate and accuracy of altitude,velocity and LTIA deviation.In addition,the correction amplitudes of angle of attack(AOA) and angle of sideslip(AOS) need to be limited in order to guarantee that the overload constraint is not violated during actual flight.In this paper,a fixed time adaptive saturation compensation auxiliary system is designed to shorten the saturation time and accelerate the convergence rate,which eliminates the adverse effects caused by the saturation.Finally,it is proved that the state deviations are ultimately uniformly bounded under the action of DIAST controller.Simulation results show that the DI ascent tracking system is stabilized within the given uncertainty boundary values.The feasible bounds of uncertainty is broadened compared with Integrated Guidance and Control algorithm.Compared with Robust Gain-Scheduling Control method,the robustness to the engine parameters are greatly improved and the control variable is smoother.

Trajectory Tracking of Autonomous Vehicle with the Fusion of DYC and Longitudinal–Lateral Control

The current research of autonomous vehicle motion control mainly focuses on trajectory tracking and velocity tracking. However, numerous studies deal with trajectory tracking and velocity tracking separately, and the yaw stability is seldom considered during trajectory tracking. In this research, a combination of the longitudinal–lateral control method with the yaw stability in the trajectory tracking for autonomous vehicles is studied. Based on the vehicle dynamics, considering the longitudinal and lateral motion of the vehicle, the velocity tracking and trajectory tracking problems can be attributed to the longitudinal and lateral control. A sliding mode variable structure control method is used in the longitudinal control. The total driving force is obtained from the velocity error in order to carry out velocity tracking. A linear time-varying model predictive control method is used in the lateral control to predict the required front wheel angle for trajectory tracking. Furthermore, a combined control framework is established to control the longitudinal and lateral motions and improve the reliability of the longitudinal and lateral direction control. On this basis, the driving force of a tire is allocated reasonably by using the direct yaw moment control, which ensures good yaw stability of the vehicle when tracking the trajectory. Simulation results indicate that the proposed control strategy is good in tracking the reference velocity and trajectory and improves the performance of the stability of the vehicle.

Neural Network Based Robust Controller for Trajectory Tracking of Underwater Vehicles

A robust neural network controller （NNC） is presented for tracking control of underwater vehicles with uncertainties. The controller is obtained by using backstepping technique and Lyapunov function design in combination with neural network identification. Modeling errors and environmental disturbances are considered in the mathematical model. A twolayer neural network is introduced to compensate the modeling errors, while H∞ control strategy is used to achieve the L2-gain performance. The uniformly ultimately bounded （UUB） stabilities of tracking errors and NN weights are guaran- teed through the proposed controller. An on-line NN weights tuning algorithm is also propesed. Good performances of the tracking control system are illustrated bv the results of numerical simulations.

Optimal Control of a Mackerel-Mimicking Robot for Energy Efficient Trajectory Tracking

A robotic fish, BASEMACK1, is designed and fabricated by mimicking the shape of a live mackerel. Three DC servo-motors are serially linked together and actuated to mimic the mackerel＇s Carangiform motion. Hydrodynamic characteristics of a fish-mimetic test model are experimentally identified and utilized in order to numerically simulate fish swimming. The discrete set of kinematic and dynamic parameters are obtained by considering required horizontal and lateral forces and minimum energy consumption. Using the optimized parameter set, optimal control of the robot is studied.

Comparative Study of Trajectory Tracking Control for Automated Vehicles via Model Predictive Control and Robust H-infinity State Feedback Control

A comparative study of model predictive control(MPC)schemes and robust Hstate feedback control(RSC)method for trajectory tracking is proposed in this paper.The main objective of this paper is to compare MPC and RSC controllers’performance in tracking predefined trajectory under different scenarios.MPC controller is designed based on the simple longitudinal-yaw-lateral motions of a single-track vehicle with a linear tire,which is an approximation of the more realistic model of a vehicle with double-track motion with a non-linear tire mode.RSC is designed on the basis of the same method as adopted for the MPC controller to achieve a fair comparison.Then,three test cases are built in CarSim-Simulink joint platform.Specifically,the verification test is used to test the tracking accuracy of MPC and RSC controller under well road conditions.Besides,the double lane change test with low road adhesion is designed to find the maximum velocity that both controllers can carry out while guaranteeing stability.Furthermore,an extreme curve test is built where the road adhesion changes suddenly,in order to test the performance of both controllers under extreme conditions.Finally,the advantages and disadvantages of MPC and RSC under different scenarios are also discussed.

Dynamics Modeling and Robust Trajectory Tracking Control for a Class of Hybrid Humanoid Arm Based on Neural Network

In order to solve the problem of trajectory tracking for a class of novel serial-parallel hybrid humanoid arm（HHA）, which has parameters uncertainty, frictions, disturbance, abrasion and pulse forces derived from motors, a multistep dynamics modeling strategy is proposed and a robust controller based on neural network（NN）-adaptive algorithm is designed. At the first step of dynamics modeling, the dynamics model of the reduced HHA is established by Lagrange method. At the second step of dynamics modeling, the parameter uncertain part resulting mainly from the idealization of the HHA is learned by adaptive algorithm. In the trajectory tracking controller, the radial basis function（RBF） NN, whose optimal weights are learned online by adaptive algorithm, is used to learn the upper limit function of the total uncertainties including frictions, disturbances, abrasion and pulse forces. To a great extent, the conservatism of this robust trajectory tracking controller is reduced, and by this controller the HHA can impersonate mostly human actions. The proof and simulation results testify the validity of the adaptive strategy for parameter learning and the neural network-adaptive strategy for the trajectory tracking control.

Trajectory tracking control for underactuated unmanned surface vehicles with dynamic uncertainties

The trajectory tracking control problem for underactuated unmanned surface vehicles(USV) was addressed, and the control system took account of the uncertain influences induced by model perturbation, external disturbance, etc. By introducing the reference, trajectory was generated by a virtual USV, and the error equation of trajectory tracking for USV was obtained, which transformed the tracking problem of underactuated USV into the stabilization problem of the trajectory tracking error equation. A backstepping adaptive sliding mode controller was proposed based on backstepping technology and method of dynamic slide model control. By means of theoretical analysis, it is proved that the proposed controller ensures that the solutions of closed loop system have the ultimate boundedness property. Simulation results are presented to illustrate the effectiveness of the proposed controller.

Nonlinear trajectory tracking control of a new autonomous underwater vehicle in complex sea conditions

Autonomous underwater vehicles (AUVs) navigating in complex sea conditions usually require a strong control system to keep the fastness and stability. The nonlinear trajectory tracking control system of a new AUV in complex sea conditions was presented. According to the theory of submarines,the six-DOF kinematic and dynamic models were decomposed into two mutually non-coupled vertical and horizontal plane subsystems. Then,different sliding mode control algorithms were used to study the trajectory tracking control. Because the yaw angle and yaw angle rate rather than the displacement of the new AUV can be measured directly on the horizontal plane,the sliding mode control algorithm combining cross track error method and line of sight method was used to fulfill its high-precision trajectory tracking control in the complex sea conditions. As the vertical displacement of the new AUV can be measured,in order to achieve the tracking of time-varying depth signal,a stable sliding mode controller was designed based on the single-input multi-state system,which took into account the characteristic of the hydroplane and the amplitude and rate constraints of the hydroplane angle. Moreover,the application of dynamic boundary layer can improve the robustness and control accuracy of the system. The computational results show that the designed sliding mode control systems of the horizontal and vertical planes can ensure the trajectory tracking performance and accuracy of the new AUV in complex sea conditions. The impacts of currents and waves on the sliding mode controller of the new AUV were analyzed qualitatively and quantitatively by comparing the trajectory tracking performance of the new AUV in different sea conditions,which provides an effective theoretical guidance and technical support for the control system design of the new AUV in real complex environment.

Event-Triggered Sliding Mode Control for Trajectory Tracking of Nonlinear Systems

In this paper, an event-triggered sliding mode control approach for trajectory tracking problem of nonlinear input affine system with disturbance has been proposed. A second order robotic manipulator system has been modeled into a general nonlinear input affine system. Initially, the global asymptotic stability is ensured with conventional periodic sampling approach for reference trajectory tracking. Then the proposed approach of event-triggered sliding mode control is discussed which guarantees semi-global uniform ultimate boundedness. The proposed control approach guarantees non-accumulation of control updates ensuring lower bounds on inter-event triggering instants avoiding Zeno behavior in presence of the disturbance. The system shows better performance in terms of reduced control updates, ensures system stability which further guarantees optimization of resource usage and cost. The simulation results are provided for validation of proposed methodology for tracking problem by a robotic manipulator. The number of aperiodic control updates is found to be approximately 44% and 61% in the presence of constant and time-varying disturbances respectively.

Trajectory tracking of powered parafoil based on characteristic model based all-coefficient adaptive control

One of the primary difficulties in using powered parafoil(PPF) systems is the lack of effective trajectory tracking controllers since the trajectory tracking control is the essential operation for PPF to accomplish autonomous tasks. The characteristic model(CM) based all-coefficient adaptive control(ACAC) designed for PPF systems in horizontal and vertical trajectory control is proposed. The method is easy to use and convenient to adjust and test. Just a few parameters are adapted during the control process. In application, vertical and horizontal CMs are designed and ACAC controllers are constructed to control vertical altitude and horizontal trajectory of PPF based on the proposed CMs, respectively. Result analysis of different simulations shows that the applied ACAC control method is effective for trajectory tracking of the PPF systems and the approach guarantees the transient performance of the PPF systems with better disturbance rejection ability.

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.

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.

Pressure observer based adaptive robust trajectory tracking control of a parallel manipulator driven by pneumatic muscles

This paper presents a pressure observer based adaptive robust controller (POARC) for posture trajectory tracking of a parallel manipulator driven by three pneumatic muscles without pressure sensors. Due to model errors of the static forces and friction forces of pneumatic muscles, simplified average flow rate characteristics of valves, unknown disturbances of entire system, and unmeasured pressures, there exist rather severe parametric uncertainties, nonlinear uncertainties and dynamic uncertainties in modeling of the parallel manipulator. A nonlinear pressure observer is constructed to estimate unknown pressures on the basis of a single-input-single-output (SISO) decoupling model that is simplified from the actual multiple-input-multiple-output (MIMO) coupling model of the parallel manipulator. Then, an adaptive robust controller integrated with the pressure observer is developed to accomplish high precision posture trajectory tracking of the parallel manipulator. The experimental results indicate that the system with the proposed POARC not only achieves good control accuracy and smooth movement but also maintains robustness to disturbances.

Control of trajectory tracking of two-wheeled differential spherical mobile robot

This paper presents a two-wheeled differential spherical mobile robot in view of the problems that the motion of spherical robot is difficult to control and the sensor is limited by the spherical shell.The robot is simple in structure,flexible in motion and easy to control.The kinematics and dynamics model of spherical mobile robot is established according to the structure of spherical mobile robot.On the basis of the adaptive neural sliding mode control,the trajectory tracking controller of the system is designed.During the simulation of the s-trajectory and circular trajectory tracking control of the spherical mobile robot,it is concluded that the spherical mobile robot is flexible in motion and easy to control.In addition,the simulation results show that the adaptive neural sliding mode control can effectively track the trajectory of the spherical robot.The adaptive control eliminates the influence of unknown parameters and disturbances,and avoids the jitter of left and right wheels during the torque output.

Trajectory tracking and formation control based on consensus in high-dimensional multi-agent systems

This paper discusses consensus problems for high-dimensional networked multi-agent systems with fixed topology. The communication topology of multi-agent systems is represented by a digraph. A new consensus protocol is proposed, and consensus convergence of multigent systems is analyzed based on the Lyapunov stability theory. The consensus problem can be formulated into solving a feasible problem with bilinear matrix inequality （BMI） constrains. Furthermore, the consensus protocol is extended to achieving tracking and formation control. By introducing the formation structure set, each agent can gain its individual desired trajectory. Finally, numerical simulations are provided to show the effectiveness of our strategies. The results show that agents from arbitrary initial states can asymptotically reach a consensus. In addition, agents with high-dimensional can track any target trajectory, and maintain desired formation during movement by selecting appropriate structure set.