Value iteration based approximate dynamic programming for mobile robot trajectory tracking with persistent inputs

Many researchers have become interested in wheeled mobile robot (WMR) trajectory tracking control in recent years. This is due to the increased application of mobile robots in the industry, the military, the home, and public service. Classically, the movement of WMR is controlled depending on its kinematic model. However, in real-time applications, both the dynamic and kinematic models of robots and external disturbance and uncertainty affect system performance. This paper proposes backstepping combined with a Nonlinear Proportional-Integral-Derivative (NPID) controller to control a two-wheeled mobile robot (TWMR). The kinematic and dynamic models of the WMR are derived. The dynamic modeling is derived using a Lagrangian approach, and stability of the system is achieved using the Lyapunov method. The controller gains are optimized using the Genetic Algorithm optimization technique. The proposed algorithms’ performance is tested using Matlab software. The simulation result shows that the proposed method achieved preferable reference trajectory tracking with a minimum tracking error. The proposed controller outperforms the GA-based backstepping plus PID controller in terms of root-mean-square (RMS) of trajectory tracking error (47.36% in a linear and 60.32% in a nonlinear case). In addition, it shows good unknown disturbance rejection and initial point change in all scenarios.

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.

This study deals with a nonlinear constrained control system for the trajectory tracking of wheeled mobile robots (WMR) with constraints. To this aim, a new constrained controller is developed for WMR based on a predictive approach with input limitations for trajectory tracking. The proposed method leads to an optimization problem that is solved by the Karush Kuhn Tucker conditions (KKT) which employ a continuous nonlinear model of WMR. Finally, the performance of the proposed control method is evaluated by realistic motion models within a virtual robot experimentation platform (V-Rep). The results indicate that the proposed control method not only decreases the trajectory tracking error in the presence of input constraints but also it is suitable for online implementation compared with conventional nonlinear model predictive control (NMPC).

To solve the trajectory tracking of service robots in autonomous navigation, a novel self-tuning proportional–integral–derivative controller identified by a radial basis function neural network (radial basis function proportional–integral–derivative controller) is presented. The error regarding the lateral distance and directional deviation angle of the service robot is taken as the control deviation in the radial basis function proportional–integral–derivative controller. During the trajectory tracking, the proportional–integral–derivative parameters of the proposed controller can be adaptively adjusted online by using a radial basis function identification network. To keep the tracking effect of the service robot from being influenced by the initial values (i.e. the initial proportional–integral–derivative parameters and their learning rates) of the radial basis function proportional–integral–derivative controller, a chaos small-world algorithm is introduced to optimize them. The simulation results of the trajectory tracking show that the proposed controller can realize online adjustment of proportional–integral–derivative parameters according to actual conditions of service robots and is characterized by strong noise and disturbance suppression capability. The optimization of the radial basis function network controller based on chaos small-world algorithm can further improve the trajectory tracking precision. Additionally, experiments in the indoor environment further support the validity of the proposed radial basis function proportional–integral–derivative controller for trajectory tracking of service robots.

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.

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.

A trajectory tracking design for wheeled mobile robots is presented in this article. The design objective is to develop one nonlinear robust control law for the trajectory tracking problem of wheeled mobile robots in the presence of modeling uncertainties. The main contribution of this investigation is as follows. Under the effects of modeling uncertainties, an effective control design which can quickly converge tracking errors between the controlled wheeled mobile robot and the desired trajectory is derived mathematically. Generally, it is difficult to develop a nonlinear robust control design for the trajectory tracking problem of wheeled mobile robots due to the complexity and nonlinearity of the wheeled mobile robots’ dynamics. Fortunately, based on a series analysis for the tracking error dynamics of the controlled wheeled mobile robot, one promising solution is obtained. For verifying the trajectory tracking performance of this proposed method, two scenarios are utilized in the simulations and the practical tests.

In this paper, a double closed-loop backstepping controller is designed for 3D trajectory tracking of a turtle-inspired amphibious spherical robot suffering from problems that include model uncertainties, environmental disturbances, and unmeasured velocity. The proposed controller scheme tackles three primary challenges: the differentiation explosion of the traditional backstepping method, unmeasured velocity, and the consideration of lumped disturbances. Beginning with an outer-loop backstepping controller, a virtual feedback variable is constructed to simplify the design of the backstepping controller. Meanwhile, to avoid the problem of differentiation explosion, tracking differentiators (TDs) are utilized to estimate the differentiation of the desired velocity in an inner-loop backstepping controller. Moreover, there are some uncertainty disturbances in the task of tracking the trajectory of a turtle-inspired amphibious spherical robot (TASR), such as the parameters of the hydrodynamic model and environmental disturbances. A linear extended state observer (LESO) is designed to estimate and compensate for the lumped disturbances. Furthermore, as the velocity states of the TASR are unmeasured, the LESO is also utilized to estimate the velocity states in surge, yaw, and heave degrees. Therefore, the TASR only needs to supply its position and orientation information for the trajectory tracking task. Note that this paper details both the design process of the proposed controller and a rigorous theoretical analysis. In addition, numerical simulations are conducted, and the results demonstrate the feasibility and superiority of the proposed method.

This paper highlights, neural network (NN) based adaptive control using backstepping control technique is proposed for robot manipulator trajectory tracking. Firstly, the vector of current is considered as the control variable for robot manipulator mechanical subsystem by using the adaptive update algorithm of NN and an enclosed control input for the desired vector of current is constructed. So that, the goal of trajectory tracking of robot manipulator is achieved. Secondly, the voltage commands are constructed in order to control the joint currents to follow the anticipated value by using the NN controller in order to manipulate the dynamics of DC motor. Simplicity of control law is achieved by using proposed control technique along with low computational cost. In addition, robot manipulator and its actuator dynamics does not require the mathematical representation of model. The weight values of NN's and robotic manipulator parameters are adaptively updated. The efficiency and usefulness of proposed scheme on 2-DOF robot manipulator is analyzed by using the running mean error. The results depicts that the proposed model out perform than the conventional PD controller in terms of enhanced robotic manipulator trajectory tracking.

This paper addresses the challenge of bidirectional trajectory tracking, for the first time in literature, in wheeled mobile robots (WMRs) powered by renewable energy by thoroughly considering all involved subsystems. A comprehensive robust multilevel average controller is developed, utilizing the mathematical models of the WMR's mechanical structure, actuators, and power stage. At the mechanical-level, a kinematic control is implemented to ensure precise trajectory tracking. The actuator-level control incorporates two controllers based on differential flatness theory, managing the dynamic behavior of the actuators to achieve smooth and efficient motion. Finally, the power-stage-level employs two additional controllers, also based on flatness theory, dedicated to the power stage subsystem. The effectiveness of the proposed robust controller is experimentally validated using: A differential WMR prototype and a BK Precision PVS60085MR for replicating the characteristics of a commercial photovoltaic (PV) panel. System integration is facilitated by the DS1104 control board and implemented using MATLAB/Simulink software for real-time operation. The experimental results demonstrate the multilevel average controller's robustness and reliability, highlighting its capacity to maintain precise bidirectional trajectory tracking even in the presence of sudden changes in system parameters. • Bidirectional trajectory tracking in solar WMRs, considering all subsystems. • Use of full-bridge Buck inverters in the power stage to drive the actuator subsystem. • Validation on a WMR using Bézier polynomial-based bidirectional trajectories. • Experimental verification of the controller under disturbances in WMR's parameters. • Controller evaluation against a three-level strategy reported in the literature.

A torque controller based on adaptive robust control is proposed for trajectory tracking of nonholonomic wheeled mobile robot with kinematic and dynamic uncertainties. In this controller, the parametric uncertainties are estimated by the adaptive control, and the non-parametric uncertainties are compensated by the adaptive robust control. The operation efficiency of the system is improved by distinguishing the differences between parametric and non-parametric uncertainties. Furthermore, the transient performance of adaptive control is optimized by the adaptive robust control and the measurements of uncertainties bounds are avoided, this strengthened the applicability of the controller. The uniformly ultimately bounded of closed-loop control system is proved by the Lyapunov theory. Simulations show that the adversely impacts of complex system uncertainties can be eliminated effectively and the high-precision trajectory tracking is guaranteed.

In this study, model predictive control with softening constraints is applied to a non‐holonomic wheeled mobile robot for trajectory tracking in the presence of external disturbances. In order to improve real‐time robustness of the wheeled mobile robot, a linearised tracking error model is used to predict system behaviours. The proposed control scheme contains a feedforward controller and a feedback controller, in which both control constraints and control increment constraints are considered to achieve trajectory tracking smoothly. Finally, numerical simulations demonstrate the performances of the control scheme.

A novel control approach is proposed for trajectory tracking of a wheeled mobile robot with unknown longitudinal and lateral slipping. A kinematic model of a tracked wheeled mobile robot (WMR) is established in this paper, in which both longitudinal and lateral slipping is considered and processed as three time-varying parameters. The Unscented Kalman Filter (UKF) with the low pass filter is then introduced for real-time estimation of the slipping parameters online. Considering the practical physical constrains, a stable tracking control law for this robot system is proposed by the backstepping method. Asymptotic stability is guaranteed by Lyapunov theory. Simulation results show the effectiveness and robustness of the proposed method.

To achieve high-precision trajectory tracking for robotic manipulators subject to unknown nonlinearities and external disturbances, a backstepping sliding mode control strategy incorporating a dual-path extreme learning machine (DP-ELM) and a disturbance observer is proposed. The DP-ELM approximates the system’s unknown nonlinearities via two parallel paths: a main path driven by joint angle errors to capture dominant nonlinearities, and an auxiliary path utilizing angular velocity errors to compensate for unmodeled high-frequency residuals. To enhance approximation capability and computational efficiency, a multi-scale feature extraction mechanism and a Top-K dynamic sparse activation strategy are integrated into the network. Furthermore, an exponentially convergent disturbance observer is designed to estimate external disturbances online. Both numerical simulations in Simulink and experiments on a physical platform of a 3-degree-of-freedom (3-DOF) robotic manipulator demonstrate that the proposed scheme yields superior tracking accuracy, rapid convergence, and strong robustness against disturbances compared to existing methods.