Trajectory Tracking of a Two-Wheeled Mobile Robot Using Backstepping and Nonlinear PID Controller

This study aims to solve the issues of nonlinearity, non-integrity constraints, under-actuated systems in mobile robots. The wheeled robot is selected as the research object, and a kinematic and dynamic control model based on Internet of Things (IoT) and neural network is proposed. With the help of IoT sensors, the proposed model can realize effective control of the mobile robot under the premise of ensuring safety using the model tracking scheme and the radial basis function adaptive control algorithm. The results show that the robot can be controlled effectively to break the speed and acceleration constraints using the strategy based on the model predictive control, thus realizing smooth movement under the premise of safety. The self-adapting algorithm based on the IoT and neural network shows notable advantages in parameter uncertainty and roller skidding well. The proposed model algorithm shows a fast convergence rate of about 2 s, which has effectively improved performances in trajectory tracking and robustness of the wheeled mobile robot, and can solve the difficulties of wheeled mobile robots in practical applications, showing reliable reference value for algorithm research in this field.

In this paper, two knowledge based controllers are proposed to overcome the difficulties of a computed torque nonlinear controller (NC) in perfect trajectory tracking of nonholonomic wheeled mobile robots (WMRs). First, the effects of different dynamic models developed in angular andCartesian coordinate systems are fully examined on the persistent excitation condition and consequently on the trajectory tracking performance of WMRs. Using the dynamic model coordinated in theCartesian frame as the base of theNCresults in perfect compensation of large position off‐tracks and unbiased estimation of the plant's unknown parameters. However, using theWMR's dynamic model with rotation angles of driving wheels as the base of nonlinear and fuzzy controllers leads to accurate orientation tracking. Through replacing the proportional and differential terms of theNCby fuzzy functions, a fuzzy nonlinear controller (FNC) is generated. Due to the complicated dynamics of the WMR in which the center of mass does not coincide with the center of rotation, the expert knowledge of fuzzy controllers is extracted considering the rotation angles and rates of driving wheels as input variables. Fuzzy tuning of theNCresults in a superior tracking performance against measurement noises, though the control torques are decreased and smoothed significantly. Second, a complete fuzzy controller (FC) is generated to make perfect tracking of theWMR's position and orientation. The local stability analysis of fuzzy controllers is examined considering the corresponding analytical structures as nonlinear controllers. The superior performances of the proposed fuzzy controllers compared to those of theNCs are evaluated through simulations.

This paper present an optimal Fractional Order PID (FOPID) controller based on Particle Swarm Optimization (PSO) for controlling the trajectory tracking of Wheeled Mobile Robot(WMR).The issue of trajectory tracking with given a desired reference velocity is minimized to get the distance and deviation angle equal to zero, to realize the objective of trajectory tracking a two FOPID controllers are used for velocity control and azimuth control to implement the trajectory tracking control. A path planning and path tracking methodologies are used to give different desired tracking trajectories. PSO algorithm is using to find the optimal parameters of FOPID controllers. The kinematic and dynamic models of wheeled mobile robot for desired trajectory tracking with PSO algorithm are simulated in Simulink-Matlab. Simulation results show that the optimal FOPID controllers are more effective and has better dynamic performance than the conventional methods.

Due to the omnidirectional mobile robot's maneuverability, stability and its relatively simple control, it is used in wide range of applications. The aim of this paper is to develop a sliding mode controller that enables a three wheeled omnidirectional mobile robot to perform trajectory tracking tasks based on the robot's kinematic model. The performance of the sliding mode controller is illustrated by way of some simulation scenarios. The paper also provides a simulation software package, which is designed to allow users to investigate the trajectory tracking control problem for an omnidirectional mobile robot without the need to go through the cumbersome process of kinematic modelling and the sliding mode control design.

Several research studies are conducted based on the control of wheeled mobile robots. Nonholonomy constraints associated with wheeled mobile robots have encouraged the development of highly nonlinear control techniques. Nonholonomic wheeled mobile robot systems might be exposed to numerous payloads as per the application requirements. This can affect statically or dynamically the complete system mass, inertia, the location of the center of mass, and additional hardware constraints. Due to the nonholonomic and motion limited properties of wheeled mobile robots, the precision of trajectory tracking control is poor. The nonholonomic wheeled mobile robot tracking system is therefore being explored. The kinematic model and sliding mode control model are analyzed, and the trajectory tracking control of the robot is carried out using an enhanced variable structure based on sliding mode. The shear and sliding mode controls are designed, and the control stability is reviewed to control the trajectory of a nonholonomic wheeled mobile robot. The simulation outcomes show that the projected trajectory track control technique is able to improve the mobile robot’s control, the error of a pose is small, and the linear velocity and angular speed can be controlled. Take the linear and angular velocity as the predicted trajectory.

Trajectory tracking is a problem of emphasis for the mobile robot. In this study, a coordinate transformation method was used to build a kinematic model of the wheeled mobile robot. A traditional proportional-integral-derivative control method was researched and improved by combining it with a neural network. A neural network proportional-integral-derivative trajectory tracking control method was thus designed, and a simulation experiment was performed using Simulink. The results show that in circular trajectory tracking control, the maximum errors of the X axis, Y axis, and θ were approximately 2.1 m, 2.3 m, and 0.4 rad, respectively, and that the system remained stable after running for 10 s. In straight-line trajectory tracking control, the maximum errors of the X axis, Y axis, and θ were approximately −0.8 m, 1.3 m, and 0.3 rad, respectively, and the system remained stable after running for 8 s. The error was relatively small, and the effect of trajectory tracking control was good. The studied method had good performance in terms of wheeled mobile robot trajectory tracking control and is worthy of further promotion and application.

In this paper, a trajectory tracking control for a non-holonomic differential wheeled mobile robot (WMR) system is presented. A big number of investigations have been used the kinematic model of mobile robot which is a nonlinear model in nature, thus a hard task to control it. This work focuses on the design of fuzzy PID controller tuned with a firefly optimization algorithm for the kinematic model of mobile robot. The firefly optimization algorithm has been used to find the best values of controller's parameters. The aim of this controller is trying to force the mobile robot tracking a pre-defined continuous path with the least possible value of error. Matlab Simulation results show that a good performance and robustness of the controller. This is confirmed by the value of minimized tracking error and the smooth velocity especially concerning presence of external disturbance or change in initial position of mobile robot.

Wheeled mobile robot (WMR) is usually applicable for executing an operational task around complicated environment; skidding and slipping phenomena unavoidably appear during the motion, which thus can compromise the accomplishment of the task. This paper investigates the trajectory tracking control problem of WMRs via disturbance rejection in the presence of wheel skidding and slipping phenomena. The kinematic and dynamic models with the perturbed nonholonomic constraints are established. The trajectory tracking control scheme at the dynamic level is designed so that the mobile robot system can track the virtual velocity asymptotically, and counteract the perturbation caused by the unknown skidding and slipping of wheels. Both simulation and experimental works are conducted, and the results prove the performance of the proposed control scheme is effective in terms of tracking precision and disturbance attenuation.

This work focuses on the trajectory tracking control of Wheeled Mobile Robots (WMRs) through neural networks and feedback control techniques. We employ different neural network architectures to analyze the environment, divide the road into segments, and generate reference trajectories for the WMR. For control purposes, we consider the nonlinear kinematic model of the WMR considering the nonholonomic constraints. Then, this kinematic model is fully linearized through a dynamic controller, which accomplishes the trajectory tracking objective. The reference trajectory procedure and control scheme combination are used to attain the desired trajectory tracking objective. To this end, we utilize a numerical simulator for a scale vehicle, namely the Autominy car. Numerical simulations using Matlab and the Robotic Operative System (ROS) demonstrate the performance of the proposed control methodology.

This manuscript presents a universal control law for a class of complex dynamic systems, such as mobile robots. The trajectory tracking problem is among the major problems in the field of robotics. The proposed universal control law solves the trajectory tracking problem of mobile robots. Despite a large body of research on developing robot's control laws conducted in the literature, the dynamic effects of robots are often not taken into consideration while deriving control laws that define their trajectories. In most cases, the robot's trajectory tracking and/or stabilization problems are addressed based on its kinematic model due to simplicity. Therefore, the need for a universal control law based on the robot's dynamic and/or kinematic model is significant. Even though the feedback control theory is well-established in the field of robotics, the control laws for dynamic systems are typically more complex than system models themselves. Furthermore, control laws are required to be adapted depending on models of different mobile robot systems. Here, the development of universal control law is underscored, i.e., the paper is aimed at developing universal dynamic tracking control law that solves the trajectory tracking problem of a class of mobile robots. The controller is tested through a set of computer simulations using a differential drive mobile robot operating in an indoor planar environment.

This paper presents a novel approach to address the challenges associated with the trajectory tracking control of wheeled mobile robots (WMRs). The proposed control approach is based on an indirect adaptive control PID using a neural network and discrete extended Kalman filter (IAPIDNN-DEKF). The proposed IAPIDNN-DEKF scheme uses the NN to identify the system Jacobian, which is used for tuning the PID gains using the stochastic gradient descent algorithm (SGD). The DEKF is proposed for state estimation (localization), and the NN adaptation improves the tracking error performance. By augmenting the state vector, the NN captures higher-order dynamics, enabling more accurate estimations, which improves trajectory tracking. Simulation studies in which a WMR is used in different scenarios are conducted to evaluate the effectiveness of the IAPIDNN-DEKF control. In order to demonstrate the effectiveness of the IAPIDNN-DEKF control, its performance is compared with direct adaptive NN (DA-NN) control, backstepping control (BSC) and an adaptive PID. On lemniscate, IAPIDNN-DEKF achieves RMSE values of 0.078769, 0.12086 and 0.1672. On sinusoidal trajectories, the method yields RMSE values of 0.01233, 0.015138 and 0.088707, and on sinusoidal with perturbation, RMSE values are 0.021495, 0.016504 and 0.090142 in x, y and θ, respectively. These results demonstrate the superior performance of IAPIDNN-DEKF for achieving accurate control and state estimation. The proposed IAPIDNN-DEKF offers advantages in terms of accurate estimation, adaptability to dynamic environments and computational efficiency. This research contributes to the advancement of robust control techniques for WMRs and showcases the potential of IAPIDNN-DEKF to enhance trajectory tracking and state estimation capabilities in real-world applications.

This paper presents a trajectory tracking control scheme for a three wheeled mobile robot using sliding mode control method system. The indoor mobile robot system is subject to parameter perturbation and external interference during trajectory tracking control, and the problem of slow tracking speed and large tracking error will occur. In order to improve the tracking precision, a sliding mode control algorithm based on new approach law is proposed. Firstly, the motion control model of mobile robot is established, and a sliding mode trajectory tracking controller is designed. Then adopting MATLAB to track the linear and circular trajectories, the tracking error converges to zero around 3s. Experimental results show that sliding mode control method effectively reduces sliding mode control input chattering, and the convergence speed and tracking accuracy improve. Finally, the effectiveness of the control method is thus verified in practice.

This paper explores lane changing trajectory planning and tracking control for intelligent vehicle on curved road. A novel arcs trajectory is planned for the desired lane changing trajectory. A kinematic controller and a dynamics controller are designed to implement the trajectory tracking control. Firstly, the kinematic model and dynamics model of intelligent vehicle with non-holonomic constraint are established. Secondly, two constraints of lane changing on curved road in practice (LCCP) are proposed. Thirdly, two arcs with same curvature are constructed for the desired lane changing trajectory. According to the geometrical characteristics of arcs trajectory, equations of desired state can be calculated. Finally, the backstepping method is employed to design a kinematic trajectory tracking controller. Then the sliding-mode dynamics controller is designed to ensure that the motion of the intelligent vehicle can follow the desired velocity generated by kinematic controller. The stability of control system is proved by Lyapunov theory. Computer simulation demonstrates that the desired arcs trajectory and state curves with B-spline optimization can meet the requirements of LCCP constraints and the proposed control schemes can make tracking errors to converge uniformly.

Compared to four-wheel independent drive and steering (4WID4WIS) mobile robots, three-wheel independent drive and steering (3WID3WIS) mobile robots are more cost-effective due to their lower cost, lighter weight, and better handling performance, even though their acceleration performance is reduced. This paper proposes a dynamic model predictive control (DMPC) controller for trajectory tracking of 3WID3WIS mobile robots to simplify the computational complexity and improve the accuracy of traditional model predictive control (MPC). The A* algorithm with a non-point mass model is used for path planning, enabling the robot to navigate quickly in narrow and constrained environments. Firstly, the kinematic model of the 3WID3WIS mobile robot is established. Then, based on this model, a DMPC trajectory tracking controller with dynamic effects is developed. By replacing MPC with DMPC, the computational complexity of MPC is reduced. During each control period, the prediction horizon is dynamically adjusted based on changes in trajectory curvature, establishing a functional relationship between trajectory curvature and prediction horizon. Subsequently, a comparative study between the proposed controller and the traditional MPC controller is conducted. Finally, the new controller is applied to address the trajectory tracking problem of the 3WID3WIS mobile robot. The experimental results show that DMPC improves the lateral trajectory tracking accuracy by 62.94% and the heading angle tracking accuracy by 34.81% compared to MPC.

Trajectory tracking control is indispensable for a wheeled mobile robot to achieve successful navigation. The classical tracking control systems that are used in wheeled mobile robots do not compensate for the parameter uncertainties and external disturbances. For control strategy, this paper presents a novel hybrid approach, combining a neural network-based kinematic controller and a model reference adaptive control. The controller parameters are adaptively determined online using neural networks. The adaptively tuned kinematic controller ensures a fast convergence to the desired trajectory. The model reference adaptive controller retains the desired tracking performance when parameter and model uncertainties occur. The Lyapunov stability method is used to obtain the adaptive gains which guarantee the asymptotic stability of the error dynamics, where the error is the difference between the outputs of the reference model and the actual plant. The performance of the proposed controller is compared with that of the PID controller, kinematic controller, and adaptive dynamic controller using different performance analysis indices such as integral absolute error, integral squared error, and mean absolute error. Simulation studies demonstrate that the proposed controller achieves high tracking accuracy and fast convergence as compared to the PID, kinematic, and adaptive dynamic controllers considering parameter uncertainties and slip disturbances. The outcomes of the simulation studies also illustrate that the proposed controller achieves the best transient performance. Experiments using real-world tests based on a two-wheeled differential drive robot architecture have elucidated the feasibility of the developed controller regarding tracking accuracy, total control effort, and robustness against uncertainties.