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.

Position Errors and Interference Prediction-Based Trajectory Tracking for Snake Robots

This work presents a trajectory tracking control method for snake robots.This method eliminates the influence of time-varying interferences on the body and reduces the offset error of a robot with a predetermined trajectory.The optimized line-of-sight(LOS)guidance strategy drives the robot’s steering angle to maintain its anti-sideslip ability by predicting position errors and interferences.Then,the predictions of system parameters and viscous friction coefficients can compensate for the joint torque control input.The compensation is adopted to enhance the compatibility of a robot within ever-changing environments.Simulation and experimental outcomes show that our work can decrease the fluctuation peak of the tracking errors,reduce adjustment time,and improve accuracy.

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.

Modeling and Trajectory Tracking Control for Flapping-Wing Micro Aerial Vehicles

This paper studies the trajectory tracking problem of flapping-wing micro aerial vehicles(FWMAVs)in the longitudinal plane.First of all,the kinematics and dynamics of the FWMAV are established,wherein the aerodynamic force and torque generated by flapping wings and the tail wing are explicitly formulated with respect to the flapping frequency of the wings and the degree of tail wing inclination.To achieve autonomous tracking,an adaptive control scheme is proposed under the hierarchical framework.Specifically,a bounded position controller with hyperbolic tangent functions is designed to produce the desired aerodynamic force,and a pitch command is extracted from the designed position controller.Next,an adaptive attitude controller is designed to track the extracted pitch command,where a radial basis function neural network is introduced to approximate the unknown aerodynamic perturbation torque.Finally,the flapping frequency of the wings and the degree of tail wing inclination are calculated from the designed position and attitude controllers,respectively.In terms of Lyapunov's direct method,it is shown that the tracking errors are bounded and ultimately converge to a small neighborhood around the origin.Simulations are carried out to verify the effectiveness of the proposed control scheme.

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.

Adaptive Trajectory Tracking Control for a Nonholonomic Mobile Robot

As one of the core issues of the mobile robot motion control, trajectory tracking has received extensive attention. At present, the solution of the problem only takes kinematic or dynamic model into account separately, so that the presented strategy is difficult to realize satisfactory tracking quality in practical application. Considering the unknown parameters of two models, this paper presents an adaptive controller for solving the trajectory tracking problem of a mobile robot. Firstly, an adaptive kinematic controller utilized to generate the command of velocity is designed based on Backstepping method. Then, in order to make the real velocity of mobile robot reach the desired velocity asymptotically, a dynamic adaptive controller is proposed adopting reference model and Lyapunov stability theory. Finally, through simulating typical trajectories including circular trajectory, fold line and parabola trajectory in normal and perturbed cases, the results illustrate that the control scheme can solve the tracking problem effectively. The proposed control law, which can tune the kinematic and dynamic model parameters online and overcome external disturbances, provides a novel method for improving trajectory tracking performance of the mobile robot.

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.

Stabilization and trajectory tracking of autonomous airship's planar motion

The stabilization and trajectory tracking problems of autonomous airship＇s planar motion are studied. By defining novel configuration error and velocity error, the dynamics of error systems are derived. By applying Lyapunov stability method, the state feedback control laws are designed and the close-loop error systems are proved to be uniformly asymptotically stable by Matrosov theorem. In particular, the controller does not need knowledge on system parameters in the case of set-point stabilization, which makes the controller robust with respect to parameter uncertainty. Numerical simulations illustrate the effectiveness of the controller designed.

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.

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.

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.

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.

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.

Trajectory tracking and obstacle avoidance method for robots based on fast terminal sliding mode

For accurate trajectory tracking and obstacle avoidance in finite time of a nonholonomic mobile robot,a trajectory tracking controller based on global fast terminal sliding mode method is proposed,which has the advantages of chattering-free and adjustable convergence time.First of all,the kinematics model of the robot is established in mobile carrier coordinates.Secondly,the global structure including terminal attractor and exponential convergence of the fast terminal sliding mode trajectory tracking controller is proved by Lyapunov stability theory,ensuring that the trajectory and heading angle tracking error converges to a smaller zero range in finite time.Finally,the artificial potential field obstacle avoidance method is introduced to make the robot not only track the reference trajectory strictly,but also avoid the obstacles.The simulation results show that the proposed method can achieve a stable tracking control in finite time for a given reference trajectory.

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.

A Stable Analytical Solution Method for Car-Like Robot Trajectory Tracking and Optimization

In this paper, the car-like robot kinematic model trajectory tracking and control problem is revisited by exploring an optimal analytical solution which guarantees the global exponential stability of the tracking error. The problem is formulated in the form of tracking error optimization in which the quadratic errors of the position, velocity, and acceleration are minimized subject to the rear-wheel car-like robot kinematic model. The input-output linearization technique is employed to transform the nonlinear problem into a linear formulation. By using the variational approach, the analytical solution is obtained, which is guaranteed to be globally exponentially stable and is also appropriate for real-time applications. The simulation results demonstrate the validity of the proposed mechanism in generating an optimal trajectory and control inputs by evaluating the proposed method in an eight-shape tracking scenario.

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.