Optimal Trajectory Tracking Research Articles

Optimized trajectory tracking control with disturbance resistance for wheeled mobile robot

When unavoidable disturbances exist in practical applications, the unicycle wheeled mobile robot (WMR) with non-holonomic constraint is challenging to be accurately controlled in finite time. An optimized dual closed-loop strategy is proposed in this paper to solve the trajectory tracking control problem of the unicycle WMR. The control strategy with fast time convergence and anti-disturbance properties consists of kinematic and dynamics controllers and an optimization algorithm. The kinematic controller is designed with an improved backstepping method to eliminate the non-holonomic constraints. The robust sliding mode control (SMC) method with fixed-time convergence is used to construct the dynamics controller. The optimization algorithm enhances the performance of the strategy and achieves accurate control. The global convergence and robustness of the strategy are theoretically demonstrated. The effectiveness of the strategy is verified by comparison in simulations.

A lie group PMP approach for optimal stabilization and tracking control of autonomous underwater vehicles

AbstractIn this research, we explore a finite horizon optimal stabilization and tracking control scheme for the dynamical model of a 6‐DOF Autonomous Underwater Vehicle (AUV). Dynamical equations of the AUV are represented in a Lie group () framework, encompassing both translational and rotational motions. Utilizing a left Lie group action on , we define error function for velocities via a right transport map to effectively address optimal trajectory tracking. The optimal control objective is formulated as a trade‐off problem, aiming to minimize both errors and control effort simultaneously. Left action on yields the left trivialized Hamiltonian function from which the concomitant state and costate dynamical equations are derived using Pontryagin's Minimum Principle (PMP). Consequently, the resulting two‐point boundary value problem is solved to obtain optimal trajectories. We demonstrate the optimality of the resulting solution obtained from the derived control law. For ensuring boundedness in the presence of small disturbances, this study incorporates the effects of internal parametric uncertainties associated with added mass and inertia components, along with the influence of external disturbances induced by ocean currents. Through simulation validations, we confirm the alignment of our results with the theoretical developments, demonstrating that the proposed control law effectively mitigates both parametric uncertainties and ocean current disturbances.

Lifelong reinforcement learning tracking control of nonlinear strict-feedback systems using multilayer neural networks with constraints

This paper presents a novel safe integral reinforcement learning (IRL)-based optimal trajectory tracking scheme for nonlinear systems with uncertain dynamics that is subject to constraints. We leverage multilayer neural networks (MNNs) for actor-critic MNNs along with an NN identifier in the backstepping process for minimizing a discounted value function. A time-varying barrier Lyapunov function (TVBLF) is utilized for handling constraints and to provide safety assurances. Online weight update laws for the actor and critic MNNs are derived that are driven by Bellman error and control input error. We introduce an online lifelong learning (LL) method in the critic NN, utilizing the Bellman error in MNNs to address catastrophic forgetting. The method’s effectiveness is demonstrated through simulations on mobile robot multitask tracking. The paper concludes with a stability analysis of the closed-loop system.

Optimal trajectory tracking of uncertain nonlinear continuous-time strict-feedback systems with dynamic constraints

A novel method for optimal trajectory tracking of uncertain nonlinear systems by using adaptive dynamic programming (ADP)-based integral reinforcement learning (IRL) and neural networks (NNs) is proposed. The method utilises an actor-critic framework with optimal backstepping to minimise a discounted value function and uses a single-layer NN identifier for estimating the unknown dynamics. For safety assurance, a time-varying barrier Lyapunov function (TVBLF) is used in the control design to handle the constraints. A novel weight-tuning law by using the control input error, integral Bellman error, and the NN identifier is used for the actor-critic framework. A novel lifelong learning (LL)-based method for critic NN is utilised in an optimal framework by incorporating the Bellman error to mitigate catastrophic forgetting in multitasking scenarios. Stability analysis using Lyapunov stability theory is obtained for the overall closed-loop system. Simulations of leader-follower mobile robot formation control show a 25% reduction in the cost in multitasking scenarios.

Optimal trajectory tracking for uncertain linear discrete‐time systems using time‐varying Q‐learning

SummaryThis article introduces a novel optimal trajectory tracking control scheme designed for uncertain linear discrete‐time (DT) systems. In contrast to traditional tracking control methods, our approach removes the requirement for the reference trajectory to align with the generator dynamics of an autonomous dynamical system. Moreover, it does not demand the complete desired trajectory to be known in advance, whether through the generator model or any other means. Instead, our approach can dynamically incorporate segments (finite horizons) of reference trajectories and autonomously learn an optimal control policy to track them in real time. To achieve this, we address the tracking problem by learning a time‐varying ‐function through state feedback. This ‐function is then utilized to calculate the optimal feedback gain and explicitly time‐varying feedforward control input, all without the need for prior knowledge of the system dynamics or having the complete reference trajectory in advance. Additionally, we introduce an adaptive observer to extend the applicability of the tracking control scheme to situations where full state measurements are unavailable. We rigorously establish the closed‐loop stability of our optimal adaptive control approach, both with and without the adaptive observer, employing Lyapunov theory. Moreover, we characterize the optimality of the controller with respect to the finite horizon length of the known components of the desired trajectory. To further enhance the controller's adaptability and effectiveness in multitask environments, we employ the Efficient Lifelong Learning Algorithm, which leverages a shared knowledge base within the recursive least squares algorithm for multitask ‐learning. The efficacy of our approach is substantiated through a comprehensive set of simulation results by using a power system example.

Optimal iterative feedforward parameter tuning for varying trajectory under actuator constraints

AbstractThis paper presents a feedforward control algorithm that combines the benefits of optimal iterative learning control (OILC) and model‐based feedforward control (MFC) using iterative feedforward tuning and input shaping filter (IFT‐ISF) for industrial motion systems. OILC effectively compensates for tracking errors in repeating tasks under actuator constraints. However, its performance deteriorates when the trajectory changes. In contrast, MFC can achieve high performance for varying trajectory tracking tasks, but its performance may degrade for constrained systems if the control force exceeds the actuator saturation boundary. The proposed algorithm aims to overcome these limitations to achieve optimal trajectory tracking performance for varying trajectories under actuator constraints. Simulation and experimental results demonstrate that the proposed algorithm achieves optimal tracking performance while complying with the actuator constraints. The algorithm provides a data‐driven approach without requiring the tedious process of model identification. By combining the benefits of OILC and IFT‐ISF, the proposed algorithm can achieve high‐performance trajectory tracking for both repeating and varying tasks under actuator constraints, making it suitable for industrial motion systems.

Optimal trajectory tracking of tractor-trailer wheeled platforms taken into account wheel dynamics

Tractor-trailer wheeled platforms are recognized as articulated robotic systems which consist of a frontrunner active mobile platform (known as tractor) that pulls one or more passive platforms (known as trailers). Regarding to their novel features such as maximum load carrying capacity and minimum energy consumption, this category of mobile platforms is widely employed for conveying purposes and transportation. The presented article deals with path tracking optimization of the tractor-trailer platform using the indirect method of the optimal control. First, nonlinear motion relations of the modular platform are obtained considering kinematic constraints and inertia characteristics of the wheels. Then, the obtained dynamic equations are considered as constraints of the optimal problem, and as a result an appropriate objective criterion is determined for the optimal trajectory tracking. In the following, a proper solution for the optimal problem is developed and accordingly some simulations are presented. In view of the wheels dynamics, the obtained results reveal competency and applicability of the proposed procedure for the optimal tracking of the tractor-trailer wheeled mobile platforms.

Multilayer adaptive critic design with digital twin for data-driven optimal tracking control and industrial applications

In this paper, an optimal trajectory tracking control problem for general nonlinear systems is investigated. An adaptive critic control method with the digital twin (DT) theory is developed. Divergent from the existing tracking control methods, the advantages of adaptive dynamic programming (ADP) and the theory of DT are combined in this paper, and the novel multilayer artificial system structure is constructed. The action-critic structure is employed by each artificial system to obtain an approximate optimal control policy. The model network (MN) is built by using the actual input and output data sets of the controlled system, which means the dependence on the dynamics of the system is overcame. Then, the weights of the trained action network (AN) and MN are passed to the real system to realize the optimal tracking control. The feasibility of the algorithm is proved by theoretical analysis. Finally, the algorithm is applied to a simple nonlinear torsional pendulum system and an industrial wastewater treatment system (WWTS), and the effectiveness of the algorithm is verified. The algorithm effectively realizes the tracking control of nonlinear systems.

Continual online learning-based optimal tracking control of nonlinear strict-feedback systems: application to unmanned aerial vehicles

A novel optimal trajectory tracking scheme is introduced for nonlinear continuous-time systems in strict feedback form with uncertain dynamics by using neural networks (NNs). The method employs an actor-critic-based NN backstepping technique for minimizing a discounted value function along with an identifier to approximate unknown system dynamics that are expressed in augmented form. Novel online weight update laws for the actor and critic NNs are derived by using both the NN identifier and Hamilton-Jacobi-Bellman residual error. A new continual lifelong learning technique utilizing the Fisher Information Matrix via Hamilton-Jacobi-Bellman residual error is introduced to obtain the significance of weights in an online mode to overcome the issue of catastrophic forgetting for NNs, and closed-loop stability is analyzed and demonstrated. The effectiveness of the proposed method is shown in simulation by contrasting the proposed with a recent method from the literature on an underactuated unmanned aerial vehicle, covering both its translational and attitude dynamics.

Robust Approximate Optimal Trajectory Tracking Control for Quadrotors

This paper uses the adaptive dynamic programming (ADP) method to achieve optimal trajectory tracking control for quadrotors. Relying on an established mathematical model of a quadrotor, the approximate optimal trajectory tracking control, which consists of the steady-state control input and the approximate optimal feedback control input, is designed for a nominal system. Considering the compound disturbances in position and attitude dynamic models, disturbance observers are introduced. The estimated values are used to design robust compensation inputs to suppress the effect of the compound disturbances for good trajectory tracking performance. Theoretically, the Lyapunov theorem demonstrates the stability of a closed-loop system. The robustness and effectiveness of the proposed controller are confirmed by the simulation results.

Fuzzy Optimal Fault-Tolerant Trajectory Tracking Control of Underactuated AUVs With Prescribed Performance in 3-D Space

Fuzzy Optimal Fault-Tolerant Trajectory Tracking Control of Underactuated AUVs With Prescribed Performance in 3-D Space

Lifelong Learning-Based Optimal Trajectory Tracking Control of Constrained Nonlinear Affine Systems Using Deep Neural Networks.

This article presents a novel lifelong integral reinforcement learning (LIRL)-based optimal trajectory tracking scheme using the multilayer (MNN) or deep neural network (Deep NN) for the uncertain nonlinear continuous-time (CT) affine systems subject to state constraints. A critic MNN, which approximates the value function, and a second NN identifier are together used to generate the optimal control policies. The weights of the critic MNN are tuned online using a novel singular value decomposition (SVD)-based method, which can be extended to MNN with the N-hidden layers. Moreover, an online lifelong learning (LL) scheme is incorporated with the critic MNN to mitigate the problem of catastrophic forgetting in the multitasking systems. Additionally, the proposed optimal framework addresses state constraints by utilizing a time-varying barrier function (TVBF). The uniform ultimate boundedness (UUB) of the overall closed-loop system is shown using the Lyapunov stability analysis. A two-link robotic manipulator that compares to recent literature shows a 47% total cost reduction, demonstrating the effectiveness of the proposed method.

Synchronous Position-Attitude Loop Regulation-Based Distributed Optimal Trajectory Tracking Control for Multi-UAVs Formation With External Disturbances

Synchronous Position-Attitude Loop Regulation-Based Distributed Optimal Trajectory Tracking Control for Multi-UAVs Formation With External Disturbances

T-type multilevel inverter-fed interior PM machine drives based on the voltage regulation feedback and the model predictive control

The tracking of optimal current trajectories in an interior permanent magnet (IPM) synchronous machine is traditionally realized by a complex online tracking, inaccurate analytical equations, or tiresome offline calibration methods. This paper proposes a modified hybrid feed-forward/feedback flux-weakening algorithm for IPM synchronous machines. In this paper, the utilized power converter is a standard T-type multilevel inverter, and hence, the voltage and current harmonics contents of the conventional two-level inverter are improved. The control algorithm utilizes the optimal current profile for maximum torque per ampere (MTPA) operation and a voltage regulation (VR) feedback control for efficient flux-weakening operation. For infinite-speed IPM machine drives, the d-q current components are limited to follow the maximum torque per voltage (MTPV) trajectory. A low-complexity model predictive control (MPC) is employed to minimize the conflict that arises from using cascaded PI control loops for current and speed control. The performance of the drive is investigated based on the Prius 2004 IPM parameters. Extensive simulation scenarios were performed using the MATLAB/SIMULINK which validates the effectiveness of the proposed algorithm. Real-time simulations based on the dSPACE DS 1103 platform are conducted to confirm the system validity for real hardware implementation. The proposed IPM drive system proves simple structure, fast response, and low harmonic contents.

Optimized Trajectory Tracking for Robot Manipulators with Uncertain Dynamics: A Composite Position Predictive Control Approach

This study addresses the trajectory tracking control challenges of robot manipulators with uncertain dynamics. The aim is to achieve precise and smooth trajectory regulation through a novel composite position predictive control (PPC) scheme that integrates motion profile and disturbance preview techniques. First, we perform offline dynamics identification and feedforward compensation alongside a pre-defined motion profile. To handle the disturbances arising from uncertain dynamics, a super-twisting disturbance observer is designed, resulting in a dynamically compensated prediction model. Furthermore, the receding optimization operations for PPC are executed by solving an optimal solution associated with a joint angle tracking error. The combination of feedforward and feedback control improves the robot manipulator’s absolute positioning accuracy as opposed to the conventional model predictive control method, especially when dealing with uncertain dynamics. The effectiveness of the proposed control method is confirmed through trajectory tracking experiments conducted on a six-degree-of-freedom robot platform with varying end-effector loads. The experimental results demonstrate that the proposed PPC method enhances tracking accuracy by approximately 45% and 25% when compared to the traditional inverse dynamic control (IDC) and the robust IDC approaches, respectively.

Frequency‐trajectory‐oriented control strategy for primary frequency regulation of wind farms

AbstractWith the rapid increase of wind power penetration, the frequency indicators of power system, encompassing frequency deviation and rate of change of frequency (RoCoF), are prone to exceed the pertinent relay thresholds, thus leading to serious power outages. Wind farms can participate in primary frequency regulation (PFR) to alleviate the above problem. However, wind farms reserve capacity (WFRC) presented by overspeed control and pitch angle control is the important factor for frequency safety especially when large disturbance occurs, and it varies obviously in different conditions. Thus, WFRC should be utilized optimally to avoid insufficient or excessive response of wind farms in PFR. To overcome the challenge, this paper proposes frequency‐trajectory‐oriented control (FTOC) for wind farms based on a two‐fold optimization framework, seeking to obtain the best frequency control performances in PFR through realizing the optimal compromise between frequency results and the consumption of WFRC. First, when the frequency indicators deviate significantly from the normal values, the optimal frequency trajectory is planned periodically according to the local standards and operation conditions, thereby minimizing the total consumption of WFRC on the premise of frequency safety. Second, based on model predictive control and a real‐time power system parameters estimator, the total reference power of wind farms, which helps the frequency track the latest planned trajectory, is optimally distributed among wind generators according to their reserve capacity. In this case, through the optimal frequency trajectory planning and tracking, the new method in this paper not only effectively prevents the frequency results from exceeding the local standards under diverse conditions, but also finds the optimal balance among frequency indicators safety, frequency trajectory smoothness, and the reserve capacity consumption of wind power generators. Finally, the simulation results prove the effectiveness and advancement of FTOC.

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.

Human-in-the-loop distributed cooperative tracking control with applications to autonomous ground vehicles: A data-driven mixed iteration approach

This paper proposes a data-driven learning algorithm for the human-in-the-loop cooperative tracking control of multi-agent systems with completely unknown dynamics. The core role of the human is to supervise a team of agents via sending a control command to only the leader vehicle, where the leader is a non-autonomous agent that has a nonzero but bounded control input receiving the control command from the human operator. To effectively reduce communication frequency among vehicles, a distributed observer only using the relative input–output information is projected to approximate the relative state information of agents. Then, taking the transient state into account instead of the steady-state, a value iteration (VI) algorithm is proposed to solve the optimal output trajectory tracking control without an initial stabilizing control policy but sacrificing the convergence rate. Under the VI algorithm, a mixed iteration (MI) algorithm by making the full advantages of both VI and the traditional policy iteration algorithms is developed, which not only guarantees the convergence rate but also removes the requirement of an initial stabilizing control policy. Finally, a practical multi-robot network is provided to verify and compare the advantages of the proposed theoretical algorithm.

Event-triggered adaptive dynamic programming for optimal tracking control of unmanned surface vessel with input constraints

In this paper, an event-triggered control mechanism scheme based on dynamic surface control and adaptive dynamic programming (DSC-ETCADP) is proposed for optimal trajectory tracking of the unmanned surface vessel (USV) with input constraints. First, the control structure is designed using dynamic surface control (DSC) as feedforward control and adaptive dynamic programming as feedback control, which not only ensures the tracking of reference trajectory but also improves the control accuracy. Second, due to the data-driven nature of adaptive dynamic programming (ADP) and the ability to adjust parameters online, it can be solved by USV with unknown disturbance. Third, the event-triggered mechanism can save computation and reduce the number of executions of the controller, in addition to avoiding Zeno behavior. Finally, according to the Lyapunov stability theory, all signals in the closed-loop system are globally uniformly and ultimately bounded (UUB). The DSC-ETCADP scheme is compared with DSC method. Simulation results demonstrate the effectiveness of the proposed method.

Autonomous Trajectory Tracking Integrated Control of Unmanned Surface Vessel

Trajectory tracking control of unmanned surface vessels (USVs) has become a popular topic. Regarding the problem of ship collision avoidance encountered in trajectory tracking, more attention needs to be paid to the algorithm application, namely the characteristics of flexibility and accessibility. Thus, a fusion framework of field theoretical planning and a model predictive control (MPC) algorithm is proposed in this paper to obtain a realizable collision-free tracking trajectory, where the trajectory smoothness and collision avoidance constraints under a complex environment need to be considered. Through the designed fast matching (FM) method based on the electric field model, the algorithm gains the direction trend of collision avoidance planning and then combines it with a flexible distance to reconstruct the architecture of the MPC and constraint system, generating the optimal trajectory tracking controller. The new algorithm was tested and validated for several situations, and it can potentially be developed to advance collision-free trajectory tracking navigation in multivessel situations.