Trajectory planning and tracking control of lumped LTI systems

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.

<div class="section abstract"><div class="htmlview paragraph">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.</div></div>

Arm robot manipulator heavily applied in industries ranging from welding, pick-and-place, assembly, packaging, labeling, etc. Trajectory planning and tracking is the fundamental design of an arm robot manipulator. The trajectory is set and determined to satisfy a certain criterion effectively and optimally. Optimization of robot trajectory is necessary to ensure the good quality product and to save energy, and this optimization can be provided by the right modeling and design. This paper presents a review study of arm-robot manipulator design and control for trajectory tracking by investigating the modeling of an arm robot manipulator starting from kinematics, dynamics and the application of the more advanced methods. The idea of this paper comes from the popularity of inverse kinematics among students.

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.

This paper focuses on the trajectory planning and tracking control problems of multi-unmanned aerial vehicle (UAV) systems in complex environments. It combines the improved A* algorithm with the robust control method to achieve efficient trajectory planning and precise tracking control of multi-UAV systems. First, the improved A* algorithm is utilized to plan the trajectories of UAVs. Then, the trajectory expressions in analytical form are obtained through the UAV trajectory plotting algorithm. Next, a robust control method with uncertainties based on the Udwadia–Kalaba (UK) theory is proposed. Through the stability analysis of the Lyapunov function, the uniform boundedness and uniform ultimate boundedness of the system states are proven. Finally, simulation experiments on multi-UAV systems are carried out to verify the effectiveness of the proposed methods. The experimental results show that the trajectories planned based on the improved A* algorithm can achieve collision avoidance between UAVs. Meanwhile, the trajectory tracking error based on the proposed control method is superior to that of the traditional sliding mode control.

Time-optimal trajectory planning for unmanned ships along a specified path based on the phase plane

To solve the safety problems caused by the restriction of interaction space and the singular configuration of rehabilitation robot in terminal traction upper limb rehabilitation training, a trajectory planning and tracking control scheme for rehabilitation training is proposed. The human-robot safe interaction space was obtained based on kinematics modeling and rehabilitation theory, and the training trajectory was planned based on the occupational therapy in rehabilitation medicine. The singular configuration of the rehabilitation robot in the interaction space was avoided by exponential adaptive damped least square method. Then, a nonlinear controller for the upper limb rehabilitation robot was designed based on the backstepping control method. Radial basis function neural network was used to approximate the robot model information online to achieve model-free control. The stability of the controller was proved by Lyapunov stability theory. Experimental results demonstrate the effectiveness and superiority of the proposed singular avoidance control scheme.

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.

The centroid of the whole vehicle moves when the automatic guided vehicle (AGV) loads and unloads goods between stations in the intelligent factory, which reduces the trajectory tracking accuracy. To this end, the dynamics and kinematics models of a four-wheel steering AGV were established, and the Lyapunov direct method was used to construct a trajectory tracking controller with global asymptotic stability in this study. Based on the adaptive learning factor and inertia weight, an adaptive particle swarm optimization algorithm was designed to optimize the control parameters of the controller, and an adaptive global asymptotic tracking control (AGATC) controller was proposed. Under simulated working condition of moving centroid, the AGATC controller was compared with adaptive model predictive control (AMPC) controller, and the trajectory tracking simulation was carried out. The results show that the position deviation of the AGATC controller was 23.97% lower than that of the AMPC controller, and the trajectory tracking control accuracy is higher under the condition of moving centroid. Moreover, a prototype of AGV was developed, and the trajectory tracking control verification experiment was carried out. The results show that the error between simulation and experiment was less than 9.03%, which proves the authenticity and effectiveness of the AGATC controller. This study provides theoretical and experimental basis for intelligent factory to realize precision and intelligent handling technology.

The stratospheric airship is a low‐speed aircraft capable of remaining in near space for extended periods. It can transport payloads to perform various tasks, including intelligence gathering, reconnaissance, and surveillance. Trajectory tracking control is a critical technology that enables the airship to execute its missions, such as relocating flight sites and maintaining station‐keeping. Focusing on the large error in three‐dimensional trajectory decoupling control of stratospheric airship, a three‐dimensional trajectory direct tracking control method based on reinforcement learning was researched. According to the discrete state and action space, a Markov decision process model for the three‐dimensional trajectory tracking control problem was established. The Boltzmann random distribution of reward value and probability of wind direction angle were taken as the action selection criteria of the Q ‐learning algorithm, the cerebellar model articulation controller (CMAC) neural network was constructed for the discrete action value, and the optimal action sequence was fast obtained. Taking the cube and spherical discrete state distribution as an example, the trajectory tracking control method was validated through simulation. Simulation results show that, by properly setting the action range of actuators including fans, valves, and thrust vectors and refining state action value distribution, the proposed three‐dimensional trajectory control method has high tracking accuracy, the horizontal error is in a 10‐m level, the altitude error can achieve meter level, and the tracking trajectory is smooth and has well engineering realizability.

Trajectory tracking and speed control for intelligent vehicles are put forward higher requirements on accuracy by the high traffic density scenario. A standard Model Predictive Control (MPC) algorithm focuses on the trajectory tracking but ignores the speed control. This paper proposes a simultaneous trajectory tracking and speed control algorithm based on MPC approach to address fine control in both space and time dimensions for intelligent vehicles. A threefold cost function including lateral and longitudinal speed as well as comfort has been proposed to improve the control algorithm. The simulations and comparisons demonstrate that the proposed method has a better tracking and speed control performance than the existing method.

Trajectory tracking is a problem of emphasis for the mobile robot. In this study, a coordinate transformation method was used to build a kinematic model of the wheeled mobile robot. A traditional proportional-integral-derivative control method was researched and improved by combining it with a neural network. A neural network proportional-integral-derivative trajectory tracking control method was thus designed, and a simulation experiment was performed using Simulink. The results show that in circular trajectory tracking control, the maximum errors of the X axis, Y axis, and θ were approximately 2.1 m, 2.3 m, and 0.4 rad, respectively, and that the system remained stable after running for 10 s. In straight-line trajectory tracking control, the maximum errors of the X axis, Y axis, and θ were approximately −0.8 m, 1.3 m, and 0.3 rad, respectively, and the system remained stable after running for 8 s. The error was relatively small, and the effect of trajectory tracking control was good. The studied method had good performance in terms of wheeled mobile robot trajectory tracking control and is worthy of further promotion and application.

To improve the stability and accuracy of quintic polynomial trajectory tracking, an MPC (model predictive control) and fuzzy PID (proportional‐integral‐difference)‐ based control method are proposed. A lateral tracking controller is designed by using MPC with rule‐based horizon parameters. The lateral tracking controller controls the steering angle to reduce the lateral tracking errors. A longitudinal tracking controller is designed by using a fuzzy PID. The longitudinal controller controls the motor torque and brake pressure referring to a throttle/brake calibration table to reduce the longitudinal tracking errors. By combining the two controllers, we achieve satisfactory trajectory tracking control. Relative vehicle trajectory tracking simulation is carried out under common scenarios of quintic polynomial trajectory in the Simulink/Carsim platform. The result shows that the strategy can avoid excessive trajectory tracking errors which ensures a better performance for trajectory tracking with high safety, stability, and adaptability.

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 this thesis, we design and develop controllers for trajectory planning and trajectory tracking to tackle autonomous high-speed overtaking for the next generation of autonomous vehicles. Both the controllers are developed for a JLR Range Rover Sport that is capable of autonomous driving functionalities. To assist with controller development, a high-fidelity vehicle model previously developed in IPG Carmaker is utilised that contains all the multi-body interactions and non-linear tyre characteristics. Trajectory Planning Autonomous high-speed driving is a safety-critical task and it is imperative that the planned trajectory of the vehicle can ensure safety (collision-avoidance) while computing smooth and feasible trajectories. We propose a trajectory planning framework that utilises information of the traffic vehicles to identify safe driving zones on the road using potential field functions and a robust model predictive controller for generating feasible trajectories that ensure the vehicle remains within the safe zones while performing the overtaking manoeuvre. The closed-loop performance of this controller is validated in a high-fidelity co-simulation environment. Trajectory Tracking The trajectory tracking controller is designed to ensure that the vehicle tracks the trajectory as closely as possible and preserves the lateral-yaw stability at all times. In this thesis, an Enhanced Model Reference Adaptive Control algorithm is used to design a generic lateral tracking controller for an autonomous vehicle. The control algorithm is applied to a vehicle path tracking problem and its tracking performance is investigated when subjected to external disturbances such as crosswind, road surface changes, modelling errors, and parameter miss-matches in a high-fidelity co-simulation environment. Combined Planning & Control Finally, the design of a combined motion planning & control scheme is carried out. The lateral tracking controller is augmented to include the dynamics of the steering actuator system and the updated tracking controller is combined with the RMPC based sophisticated path-planning framework to present a hierarchical closed-loop control architecture for autonomous overtaking. This architecture is implemented on the IPG CarMaker/Simulink environment and validated with different overtaking manoeuvring scenarios.