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 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.

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.

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.

Adaptive Trajectory Tracking Control of Wheeled Mobile Robots with Nonholonomic Constraint

A mobile robot is one of the well-known nonholonomic systems. In this paper, a new adaptive tracking controller for the kinematic model of a nonholonomic mobile robot with unknown parameters is proposed. Stability of the rule is proved through the use of a Liapunov function. The artificial electrostatic field cooperates with error posture in steering in the controller. At last, this method is implemented on the simulations and the wheeled mobile robot. Results show the effectiveness of the controllers.

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.

Parameter Identification and Application of Slippage Kinematics for Tracked Mobile Robots

A new parameter identification method is proposed to solve the slippage problem when tracked mobile robots execute turning motions.Such motion is divided into two states in this paper:pivot turning and coupled turning between angular velocity and linear velocity.In the processing of pivot turning,the slippage parameters could be obtained by measuring the end point in a square path.In the process of coupled turning,the slippage parameters could be calculated by measuring the perimeter of a circular path and the linear distance between the start and end points.The identification results showed that slippage parameters were affected by velocity.Therefore,a fuzzy rule base was established with the basis on the identification data,and a fuzzy controller was applied to motion control and dead reckoning.This method effectively compensated for errors resulting in unequal tension between the left and right tracks,structural dimensions and slippage.The results demonstrated that the accuracy of robot positioning and control could be substantially improved on a rigid floor.

Adaptive trajectory tracking control of two-wheeled self-balance robot

Wheeled mobile robot is one of the well-known nonholonomic systems. A two-wheeled sell-balance robot is taken as the research objective. This paper carried out a detailed force analysis of the robot and established a non-linear dynamics model. An adaptive tracking controller for the kinematic model of a nonhotonomic mobile robot with unknown parameters is also proposed. Using control Lyapunov function （CLF）, the controller＇s global asymptotic stability has been proven. The adaptive trajectory tracking controller decreases the disturbance in the course of tracking control and enhances the real-time control characteristics. The simulation result indicated that the wheeled mobile robot tracking can be effectively controlled.

Seam-tracking based on dynamic trajectory planning for a mobile welding robot

A new seam-tracking method based on dynamic trajectory planning for a mobile welding robot is proposed in order to improve the response lag of the mobile robot and the high frequency oscillation in seam-tracking.By using a front-placed laser-based vision sensor to dynamically extract the location of the weld seam in front of torch,the trend and direction of the weld line is roughly obtained.The robot system autonomously and dynamically performs trajectory planning based on the isometric approximation model.Arc sensor technology is applied to detect the offset during welding process in real time.The dynamic compensation of the weld path is done in combination with the control of the mobile robot and the executive body installed on it.Simulated and experimental results demonstrate that the method effectively increases the stability of welding speed and smoothness of the weld track,and hence the weld formation in curves and corners is improved.

Autonomous trajectory tracking control method for an agricultural robotic vehicle

To address the nonlinearities and external disturbances in unstructured and complex agricultural environments,this paper investigates an autonomous trajectory tracking control method for agricultural ground vehicles.Firstly,this paper presents the design and implementation of a lightweight,modular two-wheeled differential drive vehicle equipped with two drive wheels and two caster wheels.The vehicle comprises drive wheel modules,passive wheel modules,battery modules,a vehicle frame,a sensor system,and a control system.Secondly,a novel robust trajectory tracking method was proposed,utilizing an improved pure pursuit algorithm.Additionally,an Online Particle Swarm Optimization Continuously Tuned PID(OPSO-CTPID)controller was introduced to dynamically search for optimal control gains for the PID controller.Simulation results demonstrate the superiority of the improved pure pursuit algorithm and the OPSO-CTPID control strategy.To validate the performance,the vehicle was integrated with a seeding and fertilizing machine to realize autonomous wheat seeding in an agricultural environment.Experimental outcomes reveal that the vehicle of this study completed a seeding operation exceeding 1 km in distance.The proposed method can robustly and smoothly track the desired trajectory with an accuracy of less than 10 cm for the root mean square error(RMSE)of the curve and straight lines,given a suitable set of parameters,meeting the requirements of agricultural applications.The findings of this study hold significant reference value for subsequent research on trajectory tracking algorithms for ground-based agricultural robots.

Robust Finite-Time Trajectory Tracking Control of Wheeled Mobile Robots with Parametric Uncertainties and Disturbances

In this paper, a robust finite-time tracking control scheme is proposed for wheeled mobile robots with parametric uncertainties and disturbances. To eliminate the effect of lumped uncertainties,a nonlinear extended state observer(NESO) is employed to estimate the unknown states as well as uncertainties, and the corresponding coefficients are tuned via pole placement technique. Based on the observation values, the finite-time sliding mode controller is presented to guarantee that both the sliding mode variables and tracking errors converge to zero within finite time. Simulation results are given to demonstrate the effectiveness of the proposed control method.

Kinematics-based four-state trajectory tracking control of a spherical mobile robot driven by a 2-DOF pendulum

Spherical mobile robot has compact structure, remarkable stability, and flexible motion,which make it have many advantages over traditional mobile robots when applied in those unmanned environments, such as outer planets. However, spherical mobile robot is a special highly under-actuated nonholonomic system, which cannot be transformed to the classic chained form. At present, there has not been a kinematics-based trajectory tracking controller which could track both the position states and the attitude states of a spherical mobile robot. In this paper, the four-state(two position states and two attitude states) trajectory tracking control of a type of spherical mobile robot driven by a 2-DOF pendulum was studied. A controller based on the shunting model of neurodynamics and the kinematic model was deduced, and its stability was demonstrated with Lyapunov’s direct method. The control priorities of the four states were allocated according to the magnification of each state tracking error in order to firstly ensure the correct tracking of the position states. The outputs(motor speeds) of the controller were regulated according to the maximum speeds and the maximum accelerations of the actuation motors in order to solve the speed jump problem caused by initial state errors, and continuous and bounded outputs were obtained. The effectiveness including the anti-interference ability of the proposed trajectory tracking controller was verified through MATLAB simulations.

Dynamic modeling and simulation for nonholonomic welding mobile robot

Based on the Newton-Euler method, the dynamic behaviors of the left and right driving wheels and the robot body for the welding mobile robot were derived. In order to realize the combination control of body turning and slider adjustment, the dynamic behaviors of sliders were also investigated. As a result, a systematic and complete dynamic model for the welding mobile robot was constructed. In order to verify the effectiveness of the above model, a sliding mode tracking control method was proposed and simulated, the lateral error stabilizes between -0.2 mm and ＋0.2 mm, and the total distance of travel for the slider is consistently within 4-2 ram. The simulation results verify the effectiveness of the established dynamic model and also show that the seam tracking controller based on the dynamic model has excellent performance in terms of stability and robustness. Furthermore, the model is found to be very suitable for practical applications of the welding mobile robot.

Data-driven iterative learning trajectory tracking control for wheeled mobile robot under constraint of velocity saturation

Considering the wheeled mobile robot(WMR)tracking problem with velocity saturation,we developed a data‐driven iterative learning double loop control method with constraints.First,the authors designed an outer loop controller to provide virtual velocity for the inner loop according to the position and pose tracking error of the WMR kinematic model.Second,the authors employed dynamic linearisation to transform the dynamic model into an online data‐driven model along the iterative domain.Based on the measured input and output data of the dynamic model,the authors identified the parameters of the inner loop controller.The authors considered the velocity saturation constraints;we adjusted the output velocity of the WMR online,providing effective solutions to the problem of velocity saltation and the saturation constraint in the tracking process.Notably,the inner loop controller only uses the output data and input of the dynamic model,which not only enables the reliable control of WMR trajectory tracking,but also avoids the influence of inaccurate model identification processes on the tracking performance.The authors analysed the algorithm's convergence in theory,and the results show that the tracking errors of position,angle and velocity can converge to zero in the iterative domain.Finally,the authors used a simulation to demonstrate the effectiveness of the algorithm.

Seam tracking control for mobile welding robot based on vision sensor

To solve the seam tracking problem of mobile welding robot,a new controller based on the dynamics of mobile welding robot was designed using the method of backstepping kinematics into dynamics.A self-turning fuzzy controller and a fuzzy-Gaussian neural network(FGNN) controller were designed to complete coordinately controlling of cross-slider and wheels.The fuzzy-neural control algorithm was described by applying the Gaussian function and back propagation(BP) learning rule was used to tune the membership function in real time by applying the FGNN controller.To make the tracking more quickly and smoothly,the neural network controller based on dynamic model was designed,which utilized self-learning and self-adaptive ability of the neural network to deal with the partial uncertainty and the disturbances of the parameters of the robot dynamic model and real-time compensate the dynamics coupling.The results show that the selected control input torques make the system globally and asymptotically stable based on the Lyapunov function selected out;the accuracy of the proposed controller tracing is within ±0.4 mm and can satisfy the requirements of practical welding project.

Real-time Non-linear Target Tracking Control of Wheeled Mobile Robots

A control strategy for real-time target tracking for wheeled mobile robots is presented.Using a modified Kalman filter for environment perception,a novel tracking control law derived from Lyapunov stability theory is introduced.Tuning of linear velocity and angular velocity with mechanical constraints is applied.The proposed control system can simultaneously solve the target trajectory prediction,real-time tracking,and posture regulation problems of a wheeled mobile robot.Experimental results illustrate the effectiveness of the proposed tracking control laws.

Precise trajectory tracking of mecanum-wheeled omnidirectional mobile robots via a novel fixed-time sliding mode control approach

This paper proposes a novel fixed-time sliding mode control approach for trajectory-tracking tasks of a mecanum-wheeled omnidirectional mobile robot.First,the idea of two-phase attractors is introduced into the domain of sliding mode control,and a new fixed-time sliding surface is proposed.Then,according to this sliding surface,a new type of nonsingular fast terminal sliding mode control algorithm is designed for the omnidirectional mobile robot,which can realize a fast fixed-time convergence property.The stability of the control system is proven scrupulously,and a guideline for control-parameter tuning is expounded.Finally,experiments are implemented to test the trajectory-tracking performance of the robot.Experimental results demonstrate the superiority of the proposed sliding surface and the corresponding control scheme in comparison with benchmark controllers.

Accurate parameter estimation of systematic odometry errors for two-wheel differential mobile robots

Odometry using incremental wheel encoder odometry suffers from the accumulation of kinematic sensors provides the relative robot pose estimation. However, the modeling errors of wheels as the robot＇s travel distance increases. Therefore, the systematic errors need to be calibrated. The University of Michigan Benchmark（UMBmark） method is a widely used calibration scheme of the systematic errors in two wheel differential mobile robots. In this paper, the accurate parameter estimation of systematic errors is proposed by extending the conventional method. The contributions of this paper can be summarized as two issues. The first contribution is to present new calibration equations that reduce the systematic odometry errors. The new equations were derived to overcome the limitation of conventional schemes. The second contribu tion is to propose the design guideline of the test track for calibration experiments. The calibration performance can be im proved by appropriate design of the test track. The simulations and experimental results show that the accurate parameter es timation can be implemented by the proposed method.

Smooth-optimal Adaptive Trajectory Tracking Using an Uncalibrated Fish-eye Camera

This paper presents a two-stage smooth-optimal trajectory tracking strategy.Different from existing methods,the optimal trajectory tracked point can be directly determined in an uncalibrated fish-eye image.In the first stage,an adaptive trajectory tracking controller is employed to drive the tracking error and the estimated error to an arbitrarily small neighborhood of zero.Afterwards,an online smooth-optimal trajectory tracking planner is proposed,which determines the tracked point that can be used to realize smooth motion control of the mobile robot.The tracked point in the uncalibrated image can be determined by minimizing a utility function that consists of both the velocity change and the sum of cross-track errors.The performance of our planner is compared with other tracked point determining methods in experiments by tracking a circular trajectory and an irregular trajectory.Experimental results show that our method has a good performance in both tracking accuracy and motion smoothness.

Adaptive tracking control for uncertain dynamic nonholonomic mobile robots based on visual servoing

The trajectory tracking control problem of dynamic nonholonomic wheeled mobile robots is considered via visual servoing feedback. A kinematic controller is firstly presented for the kinematic model, and then, an adaptive sliding mode controller is designed for the uncertain dynamic model in the presence of parametric uncertainties associated with the camera system. The proposed controller is robust not only to structured uncertainties such as mass variation but also to unstructured one such as disturbances. The asymptotic convergence of tracking errors to equilibrium point is rigorously proved by the Lyapunov method. Simulation results are provided to illustrate the performance of the control law.