Reservoir computing-driven inverse dynamics for autonomous vehicle trajectory tracking control.

Machine-learning based approaches for self-tuning trajectory tracking controllers under terrain changes in repetitive tasks

The trajectory tracking control of spacecraft with model uncertainty in autonomous rendezvous mission is studied. A nonlinear relative pose motion model is employed, where the position motion is described in the line-of-sight coordinate system. The relative rotation is described by modified Rodriguez parameters. The polynomial reference trajectory is used to define the trajectory tracking error, and the fractional power method of linear sliding mode is used to design an adaptive fixed-time trajectory tracking controller. This paper combines trajectory planning with fractional power feedback to guarentee the convergence of tracking error at a preset fixed time, while parametric uncertainties and disturbances are suppressed by variable structure control with boundary layer technology. With the Lyapunov function, it is strictly testified that the closed-system is stable, which states clearly that both the trajectory tracking error and the adaptive parameters can reach zero in a preset fixed time. Finally, by making use of the numerical simulation, it is obviously testified the availability of the controller proposed in the paper.KeywordsSpacecraft controlTrajectory tracking controlTrajectory planningFixed-time controlAdaptive controlStability

This paper proposes a fixed-time prescribed performance control technique to address the challenge of precise trajectory tracking control for unmanned surface vessels (USVs) in the presence of external time-varying disturbances and input saturation. To begin with, a fixed-time disturbance observer is created to handle the time-varying external interference. The observer can accurately estimate and compensate for the disturbance in a fixed time, which effectively improves the robustness of the system. Furthermore, to guarantee both the transient and steady-state response of the system, we employed a specific control technology that ensures the trajectory tracking error remains within a preset bounded range. Then, combined with the fixed-time disturbance observer, the command filter, the prescribed performance control technology, and the fixed-time stability theory, a fixed-time trajectory tracking control law is designed to make the trajectory tracking error of the system converge in a fixed time. Finally, an experiment was designed to validate the suggested control scheme. The results show that under the same conditions, compared with the nonlinear controller and the finite-time controller, the absolute error tracking index of this paper is the lowest, which means that the presented control scheme has higher accuracy.

This paper explores lane changing trajectory planning and tracking control for intelligent vehicle on curved road. A novel arcs trajectory is planned for the desired lane changing trajectory. A kinematic controller and a dynamics controller are designed to implement the trajectory tracking control. Firstly, the kinematic model and dynamics model of intelligent vehicle with non-holonomic constraint are established. Secondly, two constraints of lane changing on curved road in practice (LCCP) are proposed. Thirdly, two arcs with same curvature are constructed for the desired lane changing trajectory. According to the geometrical characteristics of arcs trajectory, equations of desired state can be calculated. Finally, the backstepping method is employed to design a kinematic trajectory tracking controller. Then the sliding-mode dynamics controller is designed to ensure that the motion of the intelligent vehicle can follow the desired velocity generated by kinematic controller. The stability of control system is proved by Lyapunov theory. Computer simulation demonstrates that the desired arcs trajectory and state curves with B-spline optimization can meet the requirements of LCCP constraints and the proposed control schemes can make tracking errors to converge uniformly.

Autonomous underwater vehicles (AUVs) have been widely used to perform underwater tasks. Due to the environmental disturbances, underactuated problems, system constraints, and system coupling, AUV trajectory tracking control is challenging. Thus, further investigation of dynamic characteristics and trajectory tracking control methods of the AUV motion system will be of great importance to improve underwater task performance. An AUV controller must be able to cope with various challenges with the underwater vehicle, adaptively update the reference model, and overcome unexpected deviations. In order to identify modeling strategies and the best control practices, this paper presents an overview of the main factors of control-oriented models and control strategies for AUVs. In modeling, two fields are considered: (i) models that come from simplifications of Fossen’s equations; and (ii) system identification models. For each category, a brief description of the control-oriented modeling strategies is given. In the control field, three relevant aspects are considered: (i) significance of AUV trajectory tracking control, (ii) control strategies; and (iii) control performance. For each aspect, the most important features are explained. Furthermore, in the aspect of control strategies, mathematical modeling study and physical experiment study are introduced in detail. Finally, with the aim of establishing the acceptability of the reported modeling and control techniques, as well as challenges that remain open, a discussion and a case study are presented. The literature review shows the development of new control-oriented models, the research in the estimation of unknown inputs, and the development of more innovative control strategies for AUV trajectory tracking systems are still open problems that must be addressed in the short term.

The paper studies the trajectory tracking control problem of autonomous underwater vehicles (AUV) with practical constraints via economic model predictive control (EMPC) strategy. The cost function in EMPC is designed with two parts. One part is the trajectory tracking cost and the other part is the economic cost which is utilized to keep the AUV tracking within one side of the trajectory. We term this type of trajectory tracking as the unilateral trajectory tracking, which can be applied for hazardous area tracking and obstacle avoidance of AUVs. The effectiveness of the proposed approach is verified via thorough simulation studies.

This brief proposes a fractional-order <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ultra-local model</i> -based optimal model-free control (FO-OMFC) for trajectory tracking of 7-DOF iReHave upper-limb exoskeleton. This scheme is composed of fractional-order model-free controller (FO-MFC) and marine predators algorithm (MPA)-based parameter optimizer. Different from the existing model-free control, FO-MFC is designed based on a novel fractional-order <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ultra-local model</i> . Then, the FO-MFC incorporates fractional-order time-delay estimation (FOTDE) as well as fractional-order error convergence controller (FOECC). The referred FOTDE is used to eliminate the lumped disturbance of the controlled exoskeleton. And the FOECC guarantees the convergence of the exoskeleton’s trajectory tracking error. After that, the stability of closed-loop system is demonstrated by using Lyapunov theorem. Moreover, to obtain better control performance, the MPA is employed to search for optimal parameters of the FO-MFC. Finally, the co-simulation of iReHave exoskeleton based on SolidWorks and MATLAB is realized, and the results compared with other controllers and results under measurement noise are given to show the effectiveness and superiority of the proposed strategy.

&lt;div class="section abstract"&gt;&lt;div class="htmlview paragraph"&gt;Trajectory tracking control is a critical component of the autopilot system, essential for achieving high-performance autonomous driving. This paper presents the design of a stable, reliable, accurate, fast, and robust trajectory tracking controller. Specifically, a lateral and longitudinal trajectory tracking controller based on a linear parameter time-varying model predictive control (LPV-MPC) framework is designed. Firstly, a three-degree-of-freedom vehicle dynamics model and a tracking error model are established. Secondly, a multi-objective function and constraints considering tracking accuracy and lateral stability are formulated, and the quadratic programming (QP) method is employed to solve the optimization problem. Finally, PID speed tracking control is introduced in the longitudinal control scheme for comparison with the proposed MPC longitudinal speed control. A step velocity tracking test validates the effectiveness of the MPC speed tracking controller. In the lateral control scheme, double lane change and circumferential tests are designed to assess the comprehensive performance of the controller under medium-low adhesion road conditions. Additionally, the trajectory tracking performance of the proposed MPC controller is evaluated by comparing it with traditional Sliding Mode Control (SMC) and Linear Quadratic Regulator (LQR) trajectory tracking controllers. The simulation results indicate that the maximum heading error of the MPC controller is less than 0.09 rad, the heading error remains within 0.05 rad, and the front wheel angle stabilizes within 7.5 degrees under both operating conditions. Furthermore, the MPC controller ensures tracking accuracy and smoothness without any obvious jitter while minimizing control inputs to achieve optimal control, thereby significantly enhancing the accuracy and stability of the vehicle's trajectory tracking.&lt;/div&gt;&lt;/div&gt;

In this article, the problem of trajectory tracking control is studied for autonomous vehicle with consideration of the nonlinearity and coupling characteristics. To achieve accurately trajectory tracking in longitudinal and lateral motions simultaneously, a flatness disturbance-observer-based control scheme is developed to address the kinematic coupling issue of the vehicle, which can avoid extra modeling errors introduced by linearization. The main idea is that, derived from a suitable selection of flat outputs, the complex kinodynamic vehicle model is transformed into three fully-actuated subsystems with same structure, which will provide convenience for controller design. Then, in order to compensate the lumped disturbances caused by modeling and transformation, a disturbance-observer-based control strategy is designed via backstepping. Trajectory tracking control is accomplished through longitudinal, lateral and yaw motions simultaneously. The stability of the closed-loop dynamics is guaranteed in the framework of Lyapunov and input-to-state stability theories. Finally, the CarSim simulation tests demonstrate that the proposed integrated control method can successfully promote the trajectory tracking performance in different manoeuvres.

In this paper, we investigate the trajectory tracking control problem for autonomous underwater vehicles (AUVs) with time‐varying external disturbances of currents and waves in the sea. To solve the problem, a fixed‐time extended state observer (FTESO)‐based tracking controller is proposed. Firstly, by using the extended state observer, the FTESO is proposed for estimating the external disturbances and the velocities of the AUV within the fixed convergence time. Based on the FTESO, the fixed‐time controller is proposed for reducing the tracking errors and improving robustness performance. Theoretical analysis is given, which shows that the unknown external disturbances can be compensated and tracking error can converge to zero within the fixed time. Simulation results show that the proposed FTESO controller not only guarantees the fixed‐time convergence but also reduces the trajectory tracking errors of the AUV.

In this paper, an adaptive neural network (NN) trajectory tracking control scheme is developed for underactuated autonomous underwater vehicles (AUVs) subject to unknown dynamic parameters and unknown disturbances. A novel additional control based on Nussbaum function is proposed to handle the underactuation problem of AUVs. The radial basis function NNs with minimal learning parameter (MLP) are employed to online approximate the compounded uncertain item due to unknown dynamic parameters and unknown disturbances. On the basics of the above, an adaptive NN trajectory tracking control law is proposed using command filtered vector-backstepping design tool. As a result, the computational burden of the developed trajectory tracking control scheme is significantly reduced, Theoretical analysis indicates that the proposed control law can force the AUV track the desired trajectory and guarantee that all signals in the trajectory tracking closed-loop control system are bounded. Simulation results on an AUV verify the effectiveness of our developed control scheme.

This paper presents the design of two predefined-time active fault-tolerant controllers for the trajectory tracking of autonomous underwater vehicles (AUVs) which can address actuator faults without causing actuator saturation. The first controller offers improved steady-state trajectory tracking precision, while the second ensures a nonsingular property. Firstly, a predefined-time sliding mode controller is formulated based on a predefined-time disturbance observer by integrating a novel predefined-time auxiliary system to prevent the control input from exceeding the actuator’s physical limitations. Subsequently, a non-singular backstepping controller is introduced to circumvent potential singularities in the sliding mode controller, guaranteeing that the trajectory tracking error is uniformly ultimately bounded (UUB) within the predefined time. Additionally, theoretical analysis and simulation results are presented to illustrate the advantages of the proposed method.

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.

In most extant flight trajectory tracking control schemes, such as sliding mode control, gain parameter selection is time-consuming owing to the lack of explicit methods or rationales for the selection. Therefore, we herein propose a simple and efficient parameter selection method for sliding mode control. To demonstrate the effectiveness of the proposed method, we designed several types of trajectory tracking control laws for a rotorcraft. We derived the relation between gain parameters and desired damping ratio/desired natural frequency by utilizing modal analysis to transform trajectory tracking error as a second order system with respect to position and heading angle. Thus, we rationally determined gain parameters based on the expected system response, which corresponded to the classical response expected in a second order system. After implementing our method to the trajectory tracking control law for a Bo-105 rotorcraft in simulations, we determined that tracking performances can be upgraded or degraded based on damping ratio and natural frequency. In our controller design, as the desired damping ratio increased, although no significant differences exist at high damping ratio, undesired oscillatory responses disappeared. Further, the effects of variation in desired natural frequencies are not as significantly evident as those due to variation in damping ratio. However, the effects of desired natural frequency can be observed in the heading angle of the current trajectory tracking control design; as the natural frequency increased, the tracking accuracy increased. Therefore, the proposed method can serve as a guideline for tuning many parameters involved in the design of an advanced control law.KeywordsRotorcraftTrajectory tracking controlSliding mode controlGain selection

Multi-robot collaboration and marine robotics constitute key research directions in intelligent autonomous systems. In this context, multi-ROV cooperative operations are increasingly deployed for sunken ship search missions. A central technical challenge in such applications is to ensure efficient, non-redundant coverage while maintaining accurate formation tracking. This scenario confronts two principal difficulties. First, overlapping operational regions among multiple ROVs tend to produce both redundant coverage and search blind zones. Second, trajectory tracking accuracy is significantly degraded by the combined effects of hydrodynamic disturbances and inherent actuator constraints in ROVs. To address these challenges, an improved dynamic window approach (DWA), incorporating a search distance penalty mechanism, is proposed for multi-ROV trajectory planning. Concurrently, a cascaded tracking control architecture is constructed, wherein a model predictive kinematic controller generates constrained velocity references, while an adaptive sliding mode dynamic controller augmented with an extended state observer provides robust disturbance rejection. Collaborative search is conducted using a three-ROV leader–follower formation. Simulation results indicate that regional search coverage is effectively improved and areas of repeated detection are significantly reduced by the proposed planning algorithm. Real-time trajectory tracking is achieved by the designed controller under two typical extreme strong disturbance conditions, namely, time-varying disturbances and abrupt disturbances, on the premise of satisfying thruster thrust constraints. The proposed scheme enables all three ROVs to successfully complete the tracking task under time-varying disturbances while reducing the frequency of thrust saturation events by up to seven times. In contrast, under the conventional MPC–ASMC controller, one ROV deviates from the formation and fails to complete the tracking task. Under abrupt disturbances, the proposed approach reduces the trajectory tracking error by up to six times and decreases the frequency of thrust saturation events by up to four times.