Residual learning–based model predictive control for mobile robot trajectory tracking

The article studies the trajectory tracking control problem of underactuated marine vehicles via the nonlinear model predictive control (NMPC) strategy, where practical control and state constraints present. It is a well-known challenging issue that the conventional NMPC is not applicable for underactuated marine vehicles, due to the fact that there does not exist a local static continuous state-feedback controller to stabilize the underactuated dynamics. To resolve this issue, this article proposes to construct an auxiliary time-varying tracking controller to aid terminal constraint design in the NMPC framework, where the time-varying tracking controller borrows the ideas from Lyapunov's direct method and backstepping approach. Based on this, a novel NMPC algorithm is designed to ensure trajectory tracking control of underactuated marine vehicles. Furthermore, a systematic parameter design approach is developed. Under the designed parameters, we show that the tracking error system is input-to-state stable (ISS). Finally, the effectiveness of the designed algorithm is verified by thorough simulation and hardware experiments.

In this paper, a nonlinear model predictive control (NMPC) scheme for path tracking of autonomous vehicles using discrete previewed points in the inertial coordinate is presented. The control objective is to improve the tracking accuracy under small lateral acceleration in the scenario of low speed and narrow space. The path tracking problem is formulated as a nonlinear model predictive control model, in which the vertical distance between the vehicle position and the tangent of previewed point is adopted to evaluate the tracking error. The discrete previewed points are generated from the path points independently, which does not rely on the approximate path functions. The iterative initial values of the optimization model are appropriately selected by combining with the Stanley method to accelerate optimization computations. A simulation comparison between the proposed NMPC controller and a linear model predictive control (LMPC) controller is conducted through Carsim-Matlab/Simulink co-simulations. Simulation results show that the proposed controller exhibits better tracking accuracy than the LMPC controller under small lateral acceleration, especially when the path curvature is large and continuously changing.

In this article, we present a quasi-infinite horizon nonlinear model predictive control (MPC) scheme for tracking of generic reference trajectories. This scheme is applicable to nonlinear systems, which are locally incrementally stabilizable. For such systems, we provide a reference generic offline procedure to compute an incrementally stabilizing feedback with a continuously parameterized quadratic quasi-infinite horizon terminal cost. As a result, we get a nonlinear reference tracking MPC scheme with a valid terminal cost for general reachable reference trajectories without increasing the online computational complexity. The practicality of this approach is demonstrated with a benchmark example.

Nonlinear Model Predictive Control of Electrical Submersible Pumps based on Echo State Networks

To improve the accuracy of tracking unmanned vehicles on known trajectories, two optimised model predictive control (MPC) trajectory tracking control systems are designed based on the adaptive compensation and robust control of a radial basis function (RBF) neural network. Based on the traditional MPC trajectory tracking controller and the local approximation characteristics of the RBF neural network, the proposed RBF compensation–MPC control system is designed to compensate for the inaccuracy in the MPC prediction model arising from modelling errors. The results show that this method can achieve a root mean square error of less than 0.3703 m for the lateral position. Subsequently, to suppress the error generated by the RBF neural network and reduce the degree of vehicle sideslip, the error is considered to be external interference, and the anti-interference characteristic of the RBF robust control is incorporated into the RBF robust-MPC control system. Following the re-optimisation of the RBF robust control, the root mean square error of the lateral position is set within 0.2352 m. The results of a MATLAB/Carsim joint simulation show that using the RBF robust control can improve the tracking accuracy of the traditional MPC controller compared with RBF compensation control, while simultaneously improving the driving stability of the vehicle.

The performance of the path tracking control system is poor when vehicles navigate under extreme conditions of high speed and large curvature due to the uncertainty of vehicle model parameters, modeling errors and disturbances. To address this issue, this paper introduces a Linear Model Predictive Controller (GP‐SOMPC) based on Gaussian Process (GP) and Snake Optimizer (SO) to achieve high‐performance trajectory tracking control under large curvatures through learning. This algorithm adopts a two‐degree‐of‐freedom vehicle dynamics model and models disturbances and unmodeled dynamics as Gaussian Processes (GP) using collected experimental data. Additionally, an Adaptive Weighting Coefficient Model Predictive Controller based on the Snake Optimizer (SO) method is presented to improve the poor adaptation of vehicle trajectory tracking accuracy according to reference path curvature under fixed weighting coefficients in traditional Model Predictive Control (MPC), which results in inadequate trajectory tracking precision. The simulation experiments have verified that the proposed GP‐SOMPC algorithm can enhance trajectory tracking precision under high‐speed, large curvature conditions and exhibits good adaptability to variations in path curvature.

Distributed implementation of nonlinear model predictive control for AUV trajectory tracking

This work presents the design and implementation of a data-driven Nonlinear Model Predictive Control (NMPC) framework for an Unmanned Aerial Vehicle (UAV) equipped with a 3-DOF robotic arm. Real-world datawas collected using the Matrice 100 platform and Dynamixel MX-28AR actuators to identify a high-dimensional linear model via Dynamic Mode Decomposition with Control (DMDc), capturing the interactions between the aerial vehicle and the manipulator across 21 state variables. This DMDc-based model is embedded within the NMPC formulation to predict system behavior over finite horizons. The UAV’s orientation is represented using quaternions, enabling continuous and singularity-free attitude control. Additionally, the redundancy of the UAV-manipulator system allows for the integration of secondary objectives into the cost function, supporting flexible task execution. To meet real-time requirements, the control problem is solved using the ACADOS solver. The resulting controller achieves high-precision tracking while managing internal constraints, demonstrating the potential of data-driven NMPC in aerial manipulation tasks.

The nonlinearities of the robotic manipulators and the uncertainties of their parameters represent big challenges against the controller design. Moreover, the tracking of regular and irregular trajectories with fewer overshoots, short settling time, and small steady-state error is the main target for the robotic response. The model predictive control (MPC) is an efficient controller to handle the performance requirements. However, the conventional MPC requires the linearization of the system model. The linearization of the model does not cover all dynamics of the robotic system. Thus, this paper introduces the nonlinear MPC (NLMPC) as a proper control method for the nonlinear systems instead of the conventional MPC. Specifically, this work proposes the use of NLMPC for controlling robotic manipulators. However, the NLMPC gains need proper tuning to attain good performance rather than the conventional methods. The neural network algorithm (NNA) considers a sufficient adaptive intelligent technique that can be utilized for this purpose. The restriction in a local optimum reveals the main issue versus artificial intelligence techniques. This paper suggests a new improvement to reinforce the exploration behavior of the NNA to overcome the local restriction issue. This modification is carried out by utilizing the polynomial mutation as an effective method to promise the exploration manner of the intelligence techniques. The proposed system can estimate all states from only the output to reduce the cost of the required sensors to measure all states. The results confirm the superiority of the proposed systems with the estimator with negligible change in the output response. The proposed modified NNA (MNNA) is evaluated with the main NNA, genetic algorithm-based PID control scheme, besides the cuckoo search algorithm-based PID control scheme from other works. The results confirm the robustness and effectiveness of the suggested MNNA-based NLMPC to track regular and irregular trajectories compared with other techniques.

In order to realize the trajectory tracking control of mobile robots, a global fast terminal sliding mode control method is proposed in the kinematic analysis. Based on the combination of the backstepping method and the thought of the fast terminal sliding mode control, the method is more superior than the backstepping design method on convergence time and convergence rate. The system state variables are designed based on based backstepping method, then, the controller is applied to mobile robot system by recursive structure of second order fast terminal sliding mode, the control law is designed by Lyapunov method. Finally, simulation results show the validity of the presented method.

A magnetic levitation system (Maglev) is a sensitive, multi-parameter, nonlinear, and unstable system that is utilized to levitate a ferromagnetic object in free space. Due to its vast applications, various research studies in the field of control strategy have become extremely important and challenging. This work proposes the design of a nonlinear model predictive (NMPC) control scheme for the object position control against the nonlinearities and uncertainties of a Maglev system. A novel bio-inspired Artificial Protozoa Optimization (APO) algorithm is used to fine-tune the NMPC parameters, which include best weighting matrices ( ), shorter prediction horizons ( ), and shorter time steps ( ) to minimize the objective cost function. The effective performance of the NMPC is verified using simulation-based results in MATLAB. The CasADi toolbox is utilized to solve nonlinear optimization problems and handle the nonlinearity of the Maglev system model. Simulations are implemented for three trajectories tracking (step, sine, and square) with 20% and without Maglev parameters perturbations. To prove the superiority of the proposed controller, comparisons are made with the conventional Linear Quadratic Regulator (LQR) and proportional-integral-derivative (PID) controllers. Two performance indices are introduced, Integral of Squared Error (ISE) and Integral of Absolute Error (IAE), to examine the tracking performances of the NMPC, LQR, and PID controller. The NMPC controller has shown more efficient performance and accurate results than other controllers. The contributions of this work include a new optimization technique of APO, a new engineering application of the APO integrated with NMPC to control a Maglev system, consideration of inherent nonlinearities and system constraints, and robustness improvement under perturbation.

Robots and automated systems are increasingly being introduced to unknown and dynamic environments where they are required to handle disturbances, unmodeled dynamics, and parametric uncertainties. Robust and adaptive control strategies are required to achieve high performance in these dynamic environments. In this paper, we propose a novel adaptive model predictive controller that combines model predictive control (MPC) with an underlying $\mathcal{L}_{1}$ adaptive controller to improve trajectory tracking of a system subject to unknown and changing disturbances. The $\mathcal{L}_{1}$ adaptive controller forces the system to behave in a predefined way, as specified by a reference model. A higher-level model predictive controller then uses this reference model to calculate the optimal reference input based on a cost function, while taking into account input and state constraints. We focus on the experimental validation of the proposed approach and demonstrate its effectiveness in experiments on a quadrotor. We show that the proposed approach has a lower trajectory tracking error compared to non-predictive, adaptive approaches and a predictive, nonadaptive approach, even when external wind disturbances are applied.

HighlightsWhat are the main findings?In response to the limited existing research on high-speed autonomous driving under low-adhesion, slippery road conditions, a novel MPC-PID fused trajectory tracking control algorithm is proposed. This approach significantly enhances tracking accuracy and vehicle stability under such complex scenarios.Joint simulation results demonstrate that the proposed method improves trajectory tracking accuracy by at least 22.2%, while comfort, fuel economy, and safety are improved by 9.4%, 19.8%, and 5.3%, respectively.What is the implication of the main finding?This work provides theoretical support and simulation validation for high-speed trajectory tracking control under low-adhesion conditions, offering high engineering applicability and practical significance.The proposed approach facilitates real-time, precise, and robust autonomous driving in dynamically complex environments, promoting the deployment of high-performance control strategies in real-world applications.Autonomous vehicle trajectory tracking control is one of the hot topics in the autonomous driving field. One of the most widely used control methods is MPC (Model Predictive Control). As the control system generally becomes more nonlinear and complex, more nonlinear system factors are added to the MPC method. However, tracking accuracy and the amount of calculation needed are both dependent on a lot of contradictions for NMPC (Nonlinear Model Predictive Control). This research proposes a control algorithm for MPC-fused PID (Proportional-Integral-Derivative) control that ensures tracking accuracy under different high-speed driving conditions on wet and slippery road surfaces. The objective of the algorithm is twofold: first, to enhance trajectory tracking accuracy, and second, to ensure real-time control and optimize the vehicle’s comfort, economy, and safety indexes. The results of the joint simulation in Carsim/MATLAB Simulink show that trajectory tracking accuracy is improved by at least 22.2% under high-speed driving conditions of a vehicle on a wet and slippery road. At the same time, the comfort, economy, and safety of the vehicle are improved by at least 9.4%, 19.8%, and 5.3%, respectively.

A hierarchical control architecture, divided into upper and lower control levels, for the trajectory tracking control of mobile robots is proposed in this paper. The objective of the upper control level is to navigate the mobile robot on the desired trajectories by means of the kinematic model. A control law based on backstepping techniques is synthesized to make the posture error asymptotically stable. On the lower control level, the dynamic model of the robot is adopted from practical viewpoint. In order to guarantee the global asymptotic stability and demanded performance, a time-varying adaptive tracking control is designed such that the generalized velocities can converge to the upper control level's inputs. A hybrid controller is developed to incorporate the kinematic controller into the dynamic controller to deal with uncertain dynamic parameters of the mobile robot. Simulation results are utilized to illustrate the effectiveness of the proposed control algorithm.

A novel model predictive control- (MPC-) based trajectory tracking controller for mobile robot is proposed using the event-triggering mechanism, and the aim is to solve the problem that the MPC optimization problem requires a large amount of online computation and communication resources. This method includes two different event-triggering strategies, namely, the event-triggering based on threshold curve and the event-triggering based on threshold band. The selection of the triggering threshold is achieved by applying the statistical method to the historical data of the trajectory tracking of the mobile robot under the classic MPC method. Simulation and experimental tests illustrate that the proposed approach is able to significantly reduce the computation and communication burdens without affecting the control performance. Furthermore, the experimental results show that compared with the classic MPC-based tracking method, the proposed two event-triggering strategies can reduce 28.1% and 75.7% of the computation load and 0.886 s and 2.385 s communication time.