Trajectory Tracking Design Research Articles

Quantum Control Design by Lyapunov Trajectory Tracking and Optimal Control

In this paper, we investigate a Lyapunov trajectory tracking design method that incorporates a Schrödinger equation with a dipole subterm and polarizability. Our findings suggest that the proposed control law can overcome the limitations of certain existing control laws that do not converge. By integrating a quadratic performance index, we introduce an optimal control law, which we subsequently analyze for stability and optimality. We also simulate the spin-1/2 particle system to illustrate our results. These findings are further validated through numerical illustrations involving a 3D, 5D system, and a spin-1/2 particle system.

Adaptive super-twisted sliding mode trajectory tracking control for quadrotor UAV with prescribed performance based on finite-time disturbance observer

This study proposes a finite-time disturbed observer-based prescribed performance adaptive super-twisted sliding mode trajectory tracking control scheme for quadrotor UAV. Based on the super-twisted sliding mode algorithm, adaptive control, finite-time theory, and prescribed performance control, this scheme aims to achieve stable tracking of a quadrotor UAV along a defined trajectory. This is achieved even when faced with challenges such as modeling uncertainty, external uncertainty, and complex interference environments. Firstly, the coupling between the channels and the disturbance effects are unified as the aggregate disturbance. To address the issue of the adverse impact of aggregate disturbance on system performance, a new finite-time disturbance observer is developed to estimate the overall disturbance. The observer can effectively eliminate the negative effects of the aggregate disturbance without considering the disturbed boundary conditions during the design process. Secondly, the disturbance estimation information and the adaptive super-twisted algorithm are used to construct the adaptive super-twisted sliding mode controllers for the position and attitude loops, respectively. Then, a prescribed performance control is designed to predefined the time for the position loop to effectively suppress the deleterious effects of interference. This ensures that the position system can quickly meet the prescribed tracking requirements. Finally, the stability of the designed trajectory tracking control system is demonstrated using the Lyapunov theorem. Numerical simulation results verify the effectiveness and superiority of the proposed controller.

A GOA-Based Fault-Tolerant Trajectory Tracking Control for an Underwater Vehicle of Multi-Thruster System Without Actuator Saturation

This paper proposes an intelligent fault-tolerant control (FTC) strategy to tackle the trajectory tracking problem of an underwater vehicle (UV) under thruster damage (power loss) cases and meanwhile resolve the actuator saturation brought by the vehicle’s physical constraints. In the proposed control strategy, the trajectory tracking component is formed by a refined backstepping algorithm that controls the velocity variation and a sliding mode control deducts the torque/force outputs; the fault-tolerant component is established based on a Grasshopper Optimization Algorithm (GOA), which provides fast convergence speed as well as satisfactory accuracy of deducting optimized reallocation of the thruster forces to compensate for the power loss in different fault cases. Simulations with or without environmental perturbations under different fault cases and comparisons to other traditional FTCs are presented, thus verifying the effectiveness and robustness of the proposed GOA-based fault-tolerant trajectory tracking design. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the actuator saturation problem that exists in the trajectory tracking of an underwater vehicle (UV) when encountering power loss of the thruster system. The fault-tolerance trajectory tracking performance is affected by physical constraints of the vehicle when using the traditional methods as they may deduct excessive kinematic/dynamic requirements during the control process, thus inducing the deviation of the tracking trajectory. Therefore, the refined backstepping as well as the grasshopper optimization (GOA) are combined to eliminate the excess, where the refined backstepping is used to alleviate the speed jumps (kinematic outputs) and the GOA is to control the propulsion forces (dynamic outputs) when facing thruster fault cases. This innovates the industrial practitioners that the control design of the vehicle can be improved to avoid the tracking deviation brought by unsatisfied driving commands under fault cases through embedding optimization algorithms. Moreover, for the specific type of UV studied in this paper used for dam detection, simulations regarding practical dam detection such as the 3D polygonal line trajectory tracking and the frequently occurring UV single-fault cases are chosen, which can serve as references for practitioners working in the related field. In the future, underwater experiments of the UV will be investigated, with more effects of the practical environment involved.

Trajectory Tracking Design for Unmanned Surface Vessels: Robust Control Approach

We propose a robust nonlinear trajectory tracking design by integrating a nonlinear model transformation, robust disturbance eliminator, and trajectory generator for unmanned surface vessels influenced by modeling uncertainties and ocean environmental disturbances. We designed this nonlinear control law to help control unmanned surface vessels following any designated sail trajectory constructed by the trajectory generator. With cubic spline interpolation, this trajectory generator can generate arbitrary smooth trajectories. Simulation results show that the proposed nonlinear robust control law has precise trajectory tracking performance and a robustness property for unmanned surface vessels under harsh ocean environmental disturbances and modeling uncertainties.

Neuro-Optimal Trajectory Tracking With Value Iteration of Discrete-Time Nonlinear Dynamics.

In this article, a novel neuro-optimal tracking control approach is developed toward discrete-time nonlinear systems. By constructing a new augmented plant, the optimal trajectory tracking design is transformed into an optimal regulation problem. For discrete-time nonlinear dynamics, the steady control input corresponding to the reference trajectory is given. Then, the value-iteration-based tracking control algorithm is provided and the convergence of the value function sequence is established. Therein, the approximation error between the iterative value function and the optimal cost is estimated. The uniformly ultimately bounded stability of the closed-loop system is also discussed in detail. Moreover, the iterative heuristic dynamic programming (HDP) algorithm is implemented by involving the critic and action components, where some new updating rules of the action network are provided. Finally, two examples are used to demonstrate the optimality of the present controller as well as the effectiveness of the proposed method.

Adaptive NN state error PCH trajectory tracking control for unmanned surface vessel with uncertainties and input saturation

AbstractA novel robust state error port controlled Hamiltonian (PCH) trajectory tracking controller of an unmanned surface vessel (USV) subject to time‐varying disturbances, dynamic uncertainties and control input saturation is presented. The proposed control scheme combines the advantages of the high robustness and energy minimization of the state error PCH approach and the approximation capability of adaptive radial basis function neural networks (RBFNNs). Adaptive RBFNNs are used to the time‐varying disturbances of the environment and unknown dynamics uncertainties of the USV model. The state error PCH control approach is designed such that the system can optimize energy consumption, and the state error PCH technique makes the designed trajectory tracking controller be easy to implement in practice. To handle the effect of the control input saturation, a Gaussian error function model is employed. It has been demonstrated that the proposed approach can maintain the USV's trajectory at the desired trajectory, while the closed‐loop control system can guarantee the uniformly ultimate boundedness. The energy consumption model of the USV is constructed to reveal to the energy consumption. Simulation results demonstrate the effectiveness of the proposed controller.

Trajectory tracking for agricultural tractor based on improved fuzzy sliding mode control.

Trajectory tracking is one of the key technologies for tractor automatic navigation. Its main purpose is to adjust the steering mechanism of the tractor to follow the planned trajectory. Thus, in this paper a trajectory tracking control system is designed for an agricultural tractor with the electric power steering mechanism. A DC brush motor is added on the steering column of the tractor and the hardware circuits for the steering controller are designed to control the front wheel angel. The three degrees of freedom model of the tractor is established, and a trajectory tracking control system is proposed including a fuzzy sliding mode controller and a steering angle tracking controller designed according to the internal mode control and minimized sensitivity theory. The effectiveness of the designed trajectory tracking control system is demonstrated by simulation analyses in reference to the planed trajectory.

Trajectory Tracking Design for a Swarm of Autonomous Mobile Robots: A Nonlinear Adaptive Optimal Approach

This research presents a nonlinear adaptive optimal control approach to the trajectory tracking problem of a swarm of autonomous mobile robots. Mathematically, finding an analytical adaptive control solution that meets the H2 performance index for the trajectory tracking problem when controlling a swarm of autonomous mobile robots is an almost impossible task, due to the great complexity and high dimensions of the dynamics. For deriving an analytical adaptive control law for this tracking problem, a particular formulation for the trajectory tracking error dynamics between a swarm of autonomous mobile robots and the desired trajectory is made via a filter link. Based on this prior analysis of the trajectory tracking error dynamics, a closed-form adaptive control law is analytically derived from a high-dimensional nonlinear partial differential equation, which is equivalent to solving the trajectory tracking problem of a swarm of autonomous mobile robots with respect to an H2 performance index. This delivered adaptive nonlinear control solution offers the advantages of a simple control structure and good energy-saving performance. From the trajectory tracking verification, this proposed control approach possesses satisfactory trajectory tracking performance for a swarm of autonomous mobile robots, even under the effects of huge modeling uncertainties.

Trajectory-tracking control of an underactuated unmanned surface vehicle based on quasi-infinite horizon model predictive control algorithm

The method of a designed trajectory tracking for an underactuated unmanned surface vehicle (USV) in the presence of ocean disturbances is addressed in this paper; the differential flatness theory is applied to get the reference inputs and speed states at the reference position trajectory. Second, a transition process is arranged for the reference trajectory to reduce the overshoot of the actuator, which caused by the large deviation in the initial tracking. Third, the nonlinear disturbance observer is designed to obtain the estimated values of unknown disturbances in the ocean. Then, a controller-based model predictive control (MPC) and terminal cost function is designed for the nominal system. The inherent robustness of the controller and estimates of the observer are used to resist and compensate disturbances. Finally, the simulation experiments of linear trajectory and sinusoidal trajectories are carried out to prove the effectiveness and reliability of the control algorithm designed.

Control Allocation Design for Torpedo-Like Underwater Vehicles with Multiple Actuators

For solving the transformation problem between the desired nonlinear control laws and installed actuators’ input commands of torpedo-like underwater vehicles, one closed-form control allocation method is proposed in this article. The goal of this study is to optimally distribute the desired nonlinear control law to each single actuator installed on the torpedo-like underwater vehicle. The first step of this proposed control allocation method is to arrange the required types, numbers, and positions of the installed actuators and then build up the thrust configuration matrix for the developed torpedo-like underwater vehicle. In this step, the desired nonlinear control law can be optimally distributed to output commands of installed actuators based on the optimization method. Next, through collecting the input and output data of each installed actuator by practical experiments, the mathematical transformation of input and output commands of each installed actuator can be found. For verifying performance of this proposed control allocation method, simulations with the robust trajectory tracking design of a torpedo-like underwater vehicle with four fins, four rudders, and one thruster are executed in this investigation.

Energy Saving Control Approach for Trajectory Tracking of Autonomous Mobile Robots

This research presents an adaptive energy-saving H2 closed-form control approach to solve the nonlinear trajectory tracking problem of autonomous mobile robots (AMRs). The main contributions of this proposed design are as follows: closed-form approach, simple structure of the control law, easy implementation, and energy savings through trajectory tracking design of the controlled AMRs. It is difficult to mathematically obtained this adaptive H2 closed-form solution of AMRs. Therefore, through a series of mathematical analyses of the trajectory tracking error dynamics of the controlled AMRs, the trajectory tracking problem of AMRs can be transformed directly into a solvable problem, and an adaptive nonlinear optimal controller, which has an extremely simple form and energy-saving properties, can be found. Finally, two test trajectories, namely circular and S-shaped reference trajectories, are adopted to verify the control performance of the proposed adaptive H2 closed-form control approach with respect to an investigated H2 closed-form control design.

Micrometer Level Control Design of Piezoelectric Actuators: Fuzzy Approach

In this investigation, a fuzzy-based micrometer level control design with a guaranteed trajectory tracking performance for piezoelectric actuators which naturally have hysteresis effects is proposed. Nominal dynamics of the controlled piezoelectric actuators are described by adopting Takagi and Sugeno fuzzy models initially. Via interpolating Takagi and Sugeno local fuzzy model, a robust fuzzy-based controller is developed to eliminate hysteresis, modeling uncertainties and external disturbances. Meanwhile, the tracking error is expected to be reduced as small as possible with respect to all bounded desired trajectories. This proposed fuzzy-based controller has an easy to implement control structure. The trajectory tracking design problem of piezoelectric actuators of this study is transferred to a linear matrix inequality problem, and based on the convex optimization technique, the solution of the trajectory tracking design problem of piezoelectric actuators can be solved efficiently. From the simulation results, it is obvious that this proposed fuzzy-based control design possesses robustness property and can converge tracking errors to zero in micrometer level.

Multi-Objective Comprehensive Control of Trajectory Tracking for Four-In-Wheel-Motor Drive Electric Vehicle With Differential Steering

For 4MIDEV with differential steering, the trajectory tracking multi-objective control method is studied. The dynamics model of the four-in-wheel motor independent-drive vehicle (4MIDEV) is established comprehensively considering the differential steering dynamics characteristics, longitudinal dynamics characteristics, and lateral dynamics characteristics. Takagi Sugeno (T-S) fuzzy method is adopted to deal with the nonlinear and time-varying characteristics of the model parameters such as vehicle longitudinal speed and the front steering wheel angle. The trajectory tracking control targets are divided into the kinematic control target considering the trajectory tracking accuracy and the dynamics control target considering longitudinal speed tracking as well as lateral stability performance. The generalized $H_{2}$ norm and $H_{\infty }$ norm are selected to constrain the kinematic control target and the dynamics control target respectively. The generalized $H_{2}/H_{\infty }$ trajectory tracking controller is designed to improve the trajectory tracking accuracy and longitudinal speed tracking as well as lateral stability performance. The hardware in the loop test (HIL) verified that the designed trajectory tracking multi-objective controller can improve the comprehensive performance of vehicle and balance the trajectory tracking accuracy between the longitudinal and lateral dynamics performance.

Self-Learning Robust Control Synthesis and Trajectory Tracking of Uncertain Dynamics.

In this article, we investigate the self-learning robust control synthesis and tracking design of general uncertain dynamical systems. Based on the adaptive critic learning, the robust stabilization method is developed with the help of conducting problem transformation. In addition, by considering the optimal control solution with a discounted cost function, the established method is extended to address the robust trajectory tracking design problem. The Lyapunov stability analysis is also conducted for proving the robustness of the related control plants. Finally, the simulation verification with the three case studies is provided in terms of robust stabilization and trajectory tracking, respectively.

Control Design of a Swarm of Intelligent Robots: A Closed-Form H2 Nonlinear Control Approach

A closed-form H2 approach of a nonlinear trajectory tracking design and practical implementation of a swarm of wheeled mobile robots (WMRs) is presented in this paper. For the nonlinear trajectory tracking problem of a swarm of WMRs, the design purpose is to point out a closed-form H2 nonlinear control method that analytically fulfills the H2 control performance index. The key and primary contribution of this research is a closed-form solution with a simple control structure for the trajectory tracking design of a swarm of WMRs is an absolute achievement and practical implementation. Generally, it is challenging to solve and find out the closed-form solution for this nonlinear trajectory tracking problem of a swarm of WMRs. Fortunately, through a sequence of mathematical operations for the trajectory tracking error dynamics between the control of a swarm of WMRs and desired trajectories, this H2 trajectory tracking problem is equal to solve the nonlinear time-varying Riccati-like equation. Additionally, the closed-form solution of this nonlinear time-varying Riccati-like equation will be acquired with a straightforward form. Finally, for simulation-controlled performance of this H2 proposed method, two testing scenarios, circular and S type reference trajectories, were applied to performance verification.

Trajectory Tracking Control Algorithm for Autonomous Vehicle Considering Cornering Characteristics

Trajectory tracking control is a key technology in the research and development of autonomous vehicles. With the aim of addressing problems such as low control accuracy and poor real-time performance, which can occur easily when an autonomous vehicle avoids obstacles, this research focuses on the trajectory tracking control algorithm for autonomous vehicle considering cornering characteristics. First, the vehicle dynamics model and tire model are established through appropriate simplification. Then, based on the basic principle of model predictive control, a linear time-varying model predictive controller (LTV MPC) that considers the cornering characteristics is designed and optimized. Finally, using CarSim and MATLAB/Simulink software, a joint simulation model is established and the trajectory tracking performance of the controlled vehicle under different vehicle speeds and road adhesion conditions are tested through simulation experiments in combination with the double-shift line reference trajectory. The simulation results show the LTV MPC controller that considers cornering characteristics has good self-adaptability under complicated and severe working conditions, and no cases, such as car sideslip or track departure, were observed. Compared with other controllers and algorithms, the designed trajectory tracking controller has remarkable comprehensive performance, exhibits superior robustness and anti-interference ability, and significant improvements in the trajectory tracking control accuracy and real-time performance. The proposed control algorithm is of great importance in improving the tracking stability and driving safety of autonomous vehicles under complex extreme conditions and conducive to the further development and improvement of the technological level of intelligent vehicle driving assistance.

Trajectory Tracking Based on Adaptive Sliding Mode Control for Agricultural Tractor

Trajectory tracking is one of the key technologies for high-precision agriculture and has been the research focus by a large number of academics. In order to design a simple trajectory tracking control scheme, an adaptive sliding mode control based on lateral deviation is proposed. To reduce the chattering phenomenon, an adjustable parameter associated with the sliding surface and system error is introduced, by which the forward gain value can be regulated with the state change. According to the established tractor model, the desired front wheel angle can be obtained as the output of the sliding mode controller. A modified Smith predictor structure based two degree of freedom control scheme is designed to follow the desired front wheel angle. The effectiveness of the designed trajectory tracking control system is demonstrated by simulations, especially the performance of preventing chattering phenomenon.

Fixed time terminal sliding mode trajectory tracking design for a class of nonlinear dynamical model of air cushion vehicle

This manuscript proposes a robust fixed time terminal sliding mode prototype for trajectory tracking of the nonlinear dynamics of an under-actuated air cushion vehicle. Nonlinearity, external disturbances, internal uncertainties and unmodeled dynamics are the main difficulties that an amphibious vehicle is faced with in its maneuver. The main contribution of the proposed methodology is to overcome these problems based on both the guaranteed stability in sense of Lyapunov and the fixed time tracking error even if the initial values are changed. Robustness against uncertainties and disturbances, fixed time convergence of tracking error to zero are other merits of the proposed approach. The simulation results demonstrate the effectiveness and superiority of suggested scheme.

Research on Maneuvering Trajectory Tracking Accuracy of Target Missile Based on Feedback Linearization

Aiming at the trajectory tracking accuracy of missile target, a trajectory tracking guidance law is designed based on feedback linearization theory and linear quadratic optimal control theory, and the tracking accuracy of the designed trajectory tracking guidance law under different maneuvering trajectories is tested. The motion equations of missiles are typical non-linear motion models, so feedback linearization is introduced as an exact linearization method, and the definition and necessary and sufficient conditions of feedback linearization theory are listed. Firstly, the non-linear equations of the longitudinal motion of target missile are established, and the feedback linearization method is used to linearize the non-linear model accurately. Then, the linearized model is designed by using the linear quadratic optimal control theory, and a target trajectory tracking guidance law is obtained. Finally, given gust disturbance and different maneuvering trajectories, the designed trajectory tracking guidance law is simulated, and the tracking accuracy of the guidance law is studied by changing the control coefficient. The results show that the trajectory tracking guidance law based on feedback linearization has excellent trajectory tracking ability, good tracking accuracy and strong anti-jamming ability under different maneuvering trajectories.

Trajectory Tracking Control of a Hydraulic System Using TSMCSPO based on Sliding Perturbation Observer

This paper proposes a new designed trajectory tracking method for a hydraulic manipulator, which is the terminal sliding mode control with sliding perturbation observer (TSMCSPO). The dynamics of the hydraulic system are complex and uncertain, it also generates a large reaction force when working as an excavator or a dismantling robot. In this paper, the new control law is designed to force the trajectory of the hydraulic system to follow the reference despite complex dynamics, modeling error, the huge reaction force, and dynamic uncertainties. The sliding perturbation observer (SPO) in TSMCSPO estimates all disturbances from the outside environment, dynamic uncertainties, and modeling errors in real time. We included a simulation and an experiment to verify the approach, and to demonstrate the performance compared with other controllers (SMCSPO, SMC, and TSMC). Stabilities of SPO and TSMCSPO were analyzed based on the Lyapunov stability theory.