Design Of Trajectory Tracking Controller Research Articles

Trajectory tracking controller design for wheeled Mobile robot with velocity and torque constraints

This article investigates the trajectory tracking control problem for wheeled mobile robot (WMR) subject to both velocity and torque constraints. Firstly, a more general model is established by considering the displacement between the centre of mass and the midpoint of the driving wheels of the WMR, based on which, a new bounded kinematic controller is proposed by combining the first-order filtering approach to keep the trajectory tracking error asymptotically stable. Then the dynamic controller is designed and the stability of the overall closed-loop system is proved by the Lyapunov stability theory and Barbalat's lemma. Some conditions are given to ensure that both the velocity constraints and torque constraints are satisfied. Finally, some numerical examples are given to show the effectiveness and advantages of the method proposed in this paper.

Trajectory Tracking Control Design for 4WS Vehicle Based on Particle Swarm Optimization and Phase Plane Analysis

With the rapid development of today’s society, the traffic environment has become more and more complex. As an essential part of intelligent vehicles, trajectory tracking has attracted significant attention for its stability and safety. It is prone to poor accuracy and instability in extreme working conditions like high speed. In this paper, a trajectory tracking control strategy to ensure lateral stability at a high speed and low attachment limit conditions is proposed for distributed drive vehicles. The model predictive controller (MPC) was used to control the front wheel angle, and the particle swarm optimization (PSO) algorithm was designed to optimize the MPC control parameters adaptively. The sliding mode controller controls the rear wheel angle, and the vehicle instability degree is judged by analyzing the β − β˙ phase plane. The controllers of different instability degrees are designed herein. Finally, a torque divider is designed to consider the actuation anti-slip. The designed controller is verified by Carsim and MATLAB-Simulink co-simulation. The results show that the trajectory tracking controller designed in this paper effectively improves the tracking accuracy under the premise of ensuring stability.

Disturbance Observer-Based Fixed-Time Tracking Control for a Tilt Trirotor Unmanned Aerial Vehicle

This paper proposed a new fixed-time trajectory tracking control strategy based on the disturbance observer (DOB) for a tilt trirotor unmanned aerial vehicle (TTUAV) which is subject to unknown external disturbances. To facilitate the TTUAV's trajectory tracking controller design, the dynamic model of the TTUAV is divided into two subsystems, the position subsystem (outer-loop) and the attitude subsystem (inner-loop). For the dynamics of the TTUAV's outer-loop, the unknown external disturbances consist of the unknown wind disturbances, the unknown aerodynamic frictions forces, the lateral force generated by the rear servo and the states coupling between the outer-loop and the inner-loop. Then, a nonlinear DOB is designed to estimate the unknown external disturbances, and a nonsingular terminal sliding-mode controller (NTSMC) is further developed to drive the TTUAV's position tracking errors to zero in a fixed time. For the dynamics of the TTUAV's inner-loop, the unknown external disturbances are mainly introduced by the aerodynamic frictions torques. Then, a modified sliding mode controller is designed to reject the unknown external disturbances, and to ensure that the attitude tracking errors converge to zero exponentially. In addition, a composite stability analysis based on Lyapunov stability theory is provided to guarantee the fixed-time convergence of the closed-loop dynamics of the TTUAV. Finally, the results of the real-time experiments are presented to verify the effectiveness of the proposed control strategy.

Nonsingular Hierarchical Approach for Trajectory Tracking Control of Miniature Helicopter with Model Uncertainties

Based on hierarchical inner-outer loop strategy, the tracking control for the helicopter system could be designed individually for the position loop and for the attitude loop, thus simplifying the underactuated control problem. However, due to the nonlinear coupling between the position dynamics and rotation dynamics, the performance of the position control is affected by attitude errors, especially when the attitude control can not tracks the reference attitude instantaneously. This work provides a hierarchical trajectory tracking control design for the helicopter with model uncertainties, ensuring the stability of the overall system considering the perturbation caused by attitude tracking errors and the nonlinear coupling. The attitude of the helicopter is descried by unit-quaternion, for which anti-unwinding control design is presented. Besides, the criteria for avoidance of singularity in generation of the reference attitude is derived. Simulation results demonstrate the effectiveness of the design.

Nonlinear Robust Adaptive Control of Universal Manipulators Based on Desired Trajectory

The introduction of a dynamic model in robot trajectory tracking control design can significantly improve its trajectory tracking accuracy, but there are many uncertainties in the robot dynamic model which can be dealt with through robust control and adaptive control. The prevailing robust control as well as adaptive control methods require real-time computation of robot dynamics, but the extreme complexity of the robot dynamics equations makes it difficult to apply these methods in real industrial systems. To this end, this article proposes a robust adaptive control method based on the desired trajectory, which uses the desired trajectory to compute most of the control terms offline, including the robot’s nominal dynamics and regression matrices, and substantially reduces the need for real-time computation of the feedback signals. The robust term modifies the perturbation of the inertial parameters of the links, the adaptive term learns the friction coefficients of the joints online, and an additional compensation term is designed to satisfy the Lyapunov stability condition of the system. Finally, taking a universal manipulator as the experimental platform, the control performances of different control methods are compared to show the feasibility of the controller and the effective reduction in real-time computational complexity.

Optimization-based adaptive trajectory tracking controller design of self-balanced vehicle with asymptotic prescribed performance

To handle with the nonlinear external disturbances and unmodeled dynamics of self-balanced vehicle (SBV), a novel adaptive trajectory tracking controller based on asymptotic prescribed performance is proposed. First, a velocity planner based on kinematic is constructed to control the velocity signal to improve the motion stability of SBV. Second, the prescribed performance function (PPF) is designed to prescribe transient-state and steady-state performances (TSP). Afterwards, an optimization-based predictive control (OPC) is proposed for accurate trajectory tracking of SBV. Furthermore, a modified radial basis function neural network (RBFNN) approximator is developed to compensate the unmodeled dynamics and the nonlinear external disturbances of the SBV. The overall system stability is proved with the help of Lyapunov theorem. Finally, the tracking performance and anti-interference robustness of the proposed control method are verified by comparative numerical simulations.

Advanced robust control design and experimental verification for trajectory tracking of model-based uncertain collaborative robots

At the core of this research is the pursuit of enhancing the trajectory tracking performance of six-degree-of-freedom collaborative robots, with a particular focus on addressing the challenges posed by uncertainties in real-world applications. One of the primary issues encountered with existing methods is the susceptibility of trajectory tracking to uncertainties, which can significantly hinder the performance of robotic systems. To address these challenges, we propose an advanced control method, known as the model-based proportional-derivative controller, or MPDP controller for short, which represents an innovative fusion of model-based PD control principles with a robust control algorithm. This amalgamation is driven by the need to mitigate the impact of uncertainties and external disturbances on trajectory tracking. A comprehensive assessment grounded in Lyapunov theory has been undertaken to validate the effectiveness of our approach. The analysis has firmly established that our method ensures not only the ultimate boundedness but also the uniform boundedness of the robotic system, which is critical for its operational stability. Both experimental and simulation studies have been meticulously conducted to benchmark the performance of the MPDP controller against the conventional proportional-integral-derivative controller, which serves as a widely adopted baseline in the field. The results unequivocally demonstrate the superiority of the MPDP controller across multiple dimensions. It exhibits exceptional robustness, resulting in a smaller steady-state tracking error, a critical advantage when addressing inherent uncertainties and external disturbances that can perturb the robot system. This translates to a more stable trajectory tracking performance. Furthermore, the MPDP controller empowers the robot with the capability to precisely follow predefined trajectories, thus ensuring high-precision and reliable execution of tasks. This feature significantly contributes to an overall enhancement of system performance and productivity.

Robust proportional control for trajectory tracking using parameter and perturbation adaptive estimators

The principal contribution of this paper is the feedback design of an output trajectory tracking controller applied to a certain class of mechanical systems. The controller does not need velocity measurements for its implementation and achieves the trajectory tracking control aim. We propose adaptive estimators to determine the plant parameters and constant external perturbations. When the plant is affected by time-variant external perturbations, an observer filter that can be implemented to recover an estimation of the time-variant perturbations can replace the adaptive estimator. The closed-loop stability is analysed throughout Lyapunov tools. We illustrate the performance of the proposed control structure via numerical simulations and experiments, the numerical simulations are carried out for a pendulum coupled to a DC motor and the experiments are accomplished for a mass-spring-damper system.

Robust trajectory tracking control design for the robotic arm with uncertainty and experimental validation

The robotic arm is a complicated system with multiple inputs and outputs, strong coupling, containing uncertainties and nonlinearities. This study proposes a new practical robust control method based on the dynamics model and tracking error, including a model- and error-based proportional-differential feedback term and an error-based robust term. Specifically, the dynamics of the system are modeled using the Lagrangian method. Uncertainties are presumed to be time-varying but limited. Based on the Lyapunov method, the proposed controller has theoretically demonstrated the controlled system with uniform boundedness (UB) and uniform ultimate boundedness (UUB). Furthermore, the radius of the ultimately bounded hypersphere is arbitrarily small based on selecting appropriate design parameters. Based on the two-degree-of-freedom (2-DOF) planar robotic arm experimental platform, the self-developed rapid controller prototype CSPACE-RT is intended to eliminate tedious programming or debugging, significantly simplifying the experimental process. Finally, numerical simulation and experiment results verified the excellent control performance of the suggested controller.

Relay-Switching-Based Fixed-Time Tracking Controller for Nonholonomic State-Constrained Systems: Design and Experiment

Dear Editor, This paper investigates the fixed-time trajectory tracking controller design for nonholonomic chained systems with static state constraints. Firstly, a fixed-time tracking control law is given to carry out relay switching, which divides the controller development process into two stages. For the goal of designing fixed-time tracking controller in the second stage and avoiding the explosion of complexity, fixed-time filters are introduced. Under these preparations, a fixed-time tracking controller is elaborated by applying barrier-Lyapunov-function-based backstepping. In addition, a new tracking controller is also proposed to guarantee that the tracking error system is bounded before switching. It has been proved that the resulting closed-loop tracking error system states converge to a small neighborhood around zero within a fixed time and output states are kept in the predefined constrained regions.

Time-Varying Trajectory Tracking Controller Design for Cable-Suspended Planar Parallel Robots

Time-Varying Trajectory Tracking Controller Design for Cable-Suspended Planar Parallel Robots

Tridimensional vector path abstracting and trajectory tracking control on ramps of full self-driving vehicle

Under the constraints of time and the corresponding vehicle location, trajectory tracking control of full self-driving vehicles on ramps requires higher speed to overcome the increase in the driving distance caused by the road slope. Two-dimensional trajectory tracking methods are not applicable to roads with various gradients in reality. Here we discuss a series of studies on tridimensional vector path abstracting and trajectory tracking, collectively designing a network physical model with meaningful nodes for describing real roads and a trajectory tracking controller suitable for ramps. Almost all kinds of paths can be characterized by several simple polynomials, which are then used as the path demand in trajectory tracking control. A vehicle kinematics model considering its vertical location and slope angle attitude is formulated, based on which, model predictive control algorithm is used for the trajectory tracking controller design by regulating the vehicle speed and front wheel steering angle. The developed approach is downloaded into an intelligent control unit and tested in the real world by using a self-driving test vehicle to fully realize the practical application.

Modeling and Trajectory Tracking Control for a Multi-Section Continuum Manipulator

This paper presents a dynamic modeling and trajectory tracking control design for a hyper-redundant continuum manipulator (HRM), which is able to continuously bend along its length. The HRM has the advantages of high flexibility, large workspace, and low inertia, but also poses challenges of complex kinematics, and dynamic coupling. To address these challenges, the kinematics model was developed based on the piecewise constant curvature (PCC) assumption that captures the relationship between the cable lengths, joint angles, and end-effector pose. Inverse kinematics is presented geometrically by solving trigonometric equations. The dynamic model for the continuum robot (CR) is derived using the Euler–Lagrange representation, which incorporates the effects of gravity and elasticity. Accordingly, three control strategies are developed and applied to a two-section continuum robot, which are the inverse dynamic proportional integral derivative controller (PID), fuzzy logic controller (FLC), and sliding mode controller (SMC). We validate our proposed methods through simulations on various 3D trajectories, utilized MATLAB symbolic math toolbox in conjunction with Simulink simulation; demonstrate and evaluate different close-loop dynamic control responses for different scenarios. This simulation used in the creation of a unique animated simulation for a whole 3D continuum robot while tracking its desired trajectories. Finally, the simulation results demonstrate that our proposed methods can effectively control the HRM with high tracking performance, exhibiting enhanced responses in terms of settling time, rising time, and steady-state error. While the developed SMC outperforms Poth's PID and FLC in terms of robustness and settling time (51% and 10.3%), respectively.

Bond Graph-Based Modelling and Control of Electromagnetic Levitation System Using Firefly Optimization

This paper focuses on the modelling and control of an electromagnetic suspension using the bond graph tool. This technique combines graphical and relational aspects to establish connections between bond graph elements, particularly in deducing junction relationships and employing bicausal inversion for trajectory tracking controller design. To determine the controller parameters, we utilized a meta-heuristic method called Firefly for optimization, thus avoiding the need for trial and error. The simulation was conducted using 20-Sim software and a Matlab/Simulink script, which yielded improved results. This paper presents an initial contribution that demonstrates the integration of meta-heuristic optimization and the bond graph tool for parameter selection in 20-sim simulation software.

Neural Network Trajectory Tracking Control on Electromagnetic Suspension Systems

A new adaptive-like neural control strategy for motion reference trajectory tracking for a nonlinear electromagnetic suspension dynamic system is introduced. Artificial neural networks, differential flatness and sliding modes are strategically integrated in the presented adaptive neural network control design approach. The robustness and efficiency of the magnetic suspension control system on desired smooth position reference profile tracking can be improved in this fashion. A single levitation control parameter is tuned on-line from a neural adaptive perspective by using information of the reference trajectory tracking error signal only. The sliding mode discontinuous control action is approximated by a neural network-based adaptive continuous control function. Control design is firstly developed from theoretical modelling of the nonlinear physical system. Next, dependency on theoretical modelling of the nonlinear dynamic system is substantially reduced by integrating B-spline neural networks and sliding modes in the electromagnetic levitation control technique. On-line accurate estimation of uncertainty, unmeasured external disturbances and uncertain nonlinearities are conveniently evaded. The effective performance of the robust trajectory tracking levitation control approach is depicted for multiple simulation operating scenarios. The capability of active disturbance suppression is furthermore evidenced. The presented B-spline neural network trajectory tracking control design approach based on sliding modes and differential flatness can be extended to other controllable complex uncertain nonlinear dynamic systems where internal and external disturbances represent a relevant issue. Computer simulations and analytical results demonstrate the effective performance of the new adaptive neural control method.

Design of autonomous vehicle trajectory tracking controller based on Neural Network Predictive Control

When the linear Model Predictive Control (MPC) algorithm is used for trajectory tracking control of autonomous vehicles in high-speed turning conditions, the tracking accuracy is usually decreased due to the low fidelity of the predictive model. To deal with this problem, a trajectory tracking controller based on Neural Network Predictive Control (NNPC) is designed in this paper. The data collected from driving simulation experiments is used for the Back Propagation Neural Network (BPNN) training process to obtain the vehicle state predictive models. To reduce the iteration times of the rolling optimization module of NNPC, Particle Swarm Optimization (PSO) with Fitness Allocating Inertia Weights (PSO-FAIW) algorithm is proposed, which can allocate inertia weights in light of the distance between each particle’s fitness and the best fitness of the swarm. Finally, the performance of the controller designed in this paper is verified based on MATLAB /Simulink. The simulation results demonstrate that the controller proposed in this paper can give consideration to tracking accuracy and real-time performance.

Formation Control for Leader–Follower Wheeled Mobile Robots Based on Embedded Control Technique

The formation control problem for leader–follower wheeled mobile robots (WMRs) is investigated in this article. A formation control strategy is proposed based on the embedded control technique. Different from the conventional design philosophy of designing the formation controller based on the formation tracking errors directly, the proposed strategy decomposes the formation control task into two subtasks. One is the virtual signal generator (i.e., virtual follower) design, and the other is the trajectory tracking controller design. The virtual signal generator is devised to act as a virtual follower such that it “achieves” the desired formation control goal, whose output is taken as the reference trajectory for the follower. To solve the subtask of trajectory tracking controller design, an unconstrained controller and a constrained controller with saturated velocities are designed, respectively. A rigorous stability analysis of the closed-loop system is given under these two kinds of controllers. Comparative simulations and experiments among the unconstrained controller with higher gains/lower gains and the constrained controller are given to illustrate the feasibility and effectiveness of the proposed formation control strategy.

Optimized Adaptive PID Controller Design for Trajectory Tracking of a Quadcopter

Optimized Adaptive PID Controller Design for Trajectory Tracking of a Quadcopter

Coupled trajectory optimization and tuning of tracking controllers for parafoil generator

ABSTRACT The high-altitude wind power generation (HAWPG) parafoil is an innovative generator with remarkable environmental benefits. Due to the unique trajectory shape, there is an inherent coupling between the pitch and yaw channels, which imposes severe difficulties in the trajectory optimization and tracking controller design. To deal with this intrinsic problem, the trajectory optimization and tracking of the HAWPG parafoil are provided in a comprehensive manner. By using the pseudospectral method (PSM), the parametric optimal trajectory, which has the maximum net power generation, can be obtained. To satisfactorily track this trajectory, well-tuned trajectory controllers are needed to ensure the desired generation performance for the strong coupling dynamics between the two channels. The deep deterministic policy gradient (DDPG) algorithm is applied to the joint tuning of two conventional PID controllers for strongly coupled nonlinear dynamics. A reasonable cost function is established in this process. The mappings between the errors and control gains for the two channels can then be obtained. The gain tuning results are interpretable and well match the empirical knowledge. The simulations are carried out and the comparisons are performed with regard to multiple uncertainties and perturbations. The effectiveness of the proposed method can be illustrated.

A feedback linearisation algorithm for single-track models with structural stability properties

To support the design of trajectory tracking controllers, by way of linear tools, for vehicles characterised by nonholonomic constraints, this paper proposes a feedback linearising law for single-track dynamic models. The main characteristics of this algorithm are its simplicity, its independence from any vehicle model parameter, apart from the position of the center of mass, and its robustness. A numerical bifurcation analysis demonstrates that, for physically meaningful values of the center of mass deviation, the equilibrium is structurally asymptotically stable. Experimental results, concerning the linearising law and its application as inner loop of a trajectory tracking controller, are also presented, confirming the efficacy of the proposal.