Trajectory Tracking Control Algorithm Research Articles

Self-triggered Fuzzy Trajectory Tracking Control for the Stratospheric Airship

A self-triggered trajectory tracking control algorithm, which considers unknown disturbance and actuator saturation, has been studied to address the energy and onboard equipment life limitation problems of stratospheric airships. The controller is based on a backstepping-sliding mode method, utilizing the fuzzy logic systems and auxiliary systems to handle unknown disturbance and actuator saturation, respectively. Based on the continuity of the control law, the self-triggered condition is designed whose paradigm is used to build the fuzzy logic systems. Compared with the existing stratospheric airships event-triggered controller, continuous state detection and calculation are avoided. It is proved that the tracking errors and the weight matrix errors of the fuzzy logic system are uniformly ultimately bounded both at the trigger moment and within the trigger interval. Additionally, Zeno behavior is avoided without imposing additional parameter restrictions. Simulation results demonstrate the effectiveness of the proposed algorithm. Based on execution frequency, the proposed algorithm can conserve 98.3% of resources compared to the traditional algorithm and 97.5% of resources compared to the event-triggered algorithm.

Model Simplification for Asymmetric Marine Vehicles in Horizontal Motion—Verification of Selected Tracking Control Algorithms

This paper addresses a trajectory tracking control algorithm for underactuated marine vehicles moving horizontally in which the current in the North–East–Down frame is constant. This algorithm is a modification of a control scheme based on the input-output feedback linearization method, for which the application condition was that the vehicle was symmetric with respect to the left and right sides. The proposed control scheme can be applied to a fully asymmetric model, and, therefore, the geometric center can be different from the center of mass in both the longitudinal and lateral directions. A velocity transformation to generalized vehicle equations of motion was used to develop a suitable controller. Theoretical considerations were supported by simulation tests performed for a model with 3 degrees of freedom, in which the performance of the proposed algorithm was compared with that of the original algorithm and the selected control scheme based on a combination of backstepping and integral sliding mode control approaches.

Compliant variable admittance adaptive fixed-time sliding mode control for trajectory tracking of robotic manipulators

Abstract This paper presents a compliant variable admittance adaptive fixed-time sliding mode control (SMC) algorithm for trajectory tracking of robotic manipulators. Specifically, a compliant variable admittance algorithm and an adaptive fixed-time SMC algorithm are combined to construct a double-loop control structure. In the outer loop, the variable admittance algorithm is developed to adjust admittance parameters during a collision to minimize the collision time, which gives the robot compliance property and reduce the rigid collision influence. Then, by employing the Lyapunov theory and the fixed-time stability theory, a new nonsingular sliding mode manifold is proposed and an adaptive fixed-time SMC algorithm is presented in the inner loop. More precisely, this approach enables rapid convergence, enhanced steady-state tracking precision, and a settling time that is independent of system initial states. As a result, the effectiveness and improved performance of the proposed algorithm are demonstrated through extensive simulations and experimental results.

Research on two stage obstacle-avoidance trajectory planning and trajectory tracking control in curves

The existing obstacle-avoidance trajectory planning and trajectory tracking control algorithms have limitations such as long-time consumption, high failure rate in dynamic traffic environments, and insufficient trajectory tracking accuracy in curved roads. Based on the above problems, this paper designs a two stage obstacle-avoidance trajectory planner based on nonlinear optimization theory. In first stage Part-NLP, only considering the safety obstacle avoidance, a point mass model and linearization constraints are established to quickly solve the initial trajectory. In the second stage Full-NLP, considering smooth soft constraints comprehensively, the initial trajectory is optimized by establishing driving corridors and a lightweight iterative framework. In control module, this paper selects a linear quadratic form lateral trajectory tracking controller, and the parameters were optimized through the carnivorous plant algorithm. The joint simulation results show that in dynamic traffic environment of curved roads, the two stage planner proposed can accurately plan safe and smooth obstacle avoidance trajectories, and there is a significant reduction in time consumption compared to traditional NLP algorithms. The control strategy can accurately track the planned trajectories, with lateral error controlled within plus or minus 0.1 m, heading error controlled within plus or minus 0.15 rad, speed tracking error controlled within plus or minus 0.15 m/s, and vehicle yaw angle error controlled within plus or minus 0.04 rad; the hardware-in-loop test results indicate that the controller can achieve real-time and accurate trajectory tracking.

Fuzzy Adaptive Whale Optimization Control Algorithm for Trajectory Tracking of a Cable-Driven Parallel Robot

Fuzzy Adaptive Whale Optimization Control Algorithm for Trajectory Tracking of a Cable-Driven Parallel Robot

Trajectory Tracking Control Algorithm of Two-wheel Rutting Model

In the development of unmanned two-wheeled self-balancing vehicle, it is very important to consider the trajectory tracking of unmanned two-wheeled self-balancing vehicle. In order to study the track tracking problem of unmanned two-wheeled self-balancing vehicle, the kinematic model of unmanned two-wheeled vehicle and the relation between its roll Angle and the kinematic model were established. The simulation platform is built to realize the unmanned two-wheeled vehicle and realize the circular track tracking at 5m/s, and the tracking performance of the track tracking controller under the circular track is verified.

Fast Trajectory Tracking Control Algorithm for Autonomous Vehicles Based on the Alternating Direction Multiplier Method (ADMM) to the Receding Optimization of Model Predictive Control (MPC).

In order to improve the real-time performance of the trajectory tracking of autonomous vehicles, this paper applies the alternating direction multiplier method (ADMM) to the receding optimization of model predictive control (MPC), which improves the computational speed of the algorithm. Based on the vehicle dynamics model, the output equation of the autonomous vehicle trajectory tracking control system is constructed, and the auxiliary variable and the dual variable are introduced. The quadratic programming problem transformed from the MPC and the vehicle dynamics constraints are rewritten into the solution of the ADMM form, and a decreasing penalty factor is used during the solution process. The simulation verification is carried out through the joint simulation platform of Simulink and Carsim. The results show that, compared with the active set method (ASM) and the interior point method (IPM), the algorithm proposed in this paper can not only improve the accuracy of trajectory tracking, but also exhibits good real-time performance in different prediction time domains and control time domains. When the prediction time domain increases, the calculation time shows no significant difference. This verifies the effectiveness of the ADMM in improving the real-time performance of MPC.

Trajectory tracking control of unmanned marine vehicles with thruster faults based on broad learning system

The presence of unknown nonlinearities in the model of unmanned marine vehicles is inevitable. This paper proposes a new trajectory tracking control algorithm for nonlinear unmanned marine vehicles with model uncertainty, ocean disturbances and thruster faults. Broad learning system is first employed to approximate the nonlinear functions of the model, and an adaptive mechanism is used to estimate the unknown bounds of disturbances and thruster faults. And sliding mode controller is designed for unmanned marine vehicles with unknown nonlinearity and thruster faults to ensure the asymptotic stability of the tracking trajectory error system. It should be mentioned that the proposed approximator based on broad learning system can reduce the calculation time and decrease the estimation error arbitrarily. Finally, simulation studies have verified the effectiveness of the proposed control scheme.

A Self-Adaptive Double Q-Backstepping Trajectory Tracking Control Approach Based on Reinforcement Learning for Mobile Robots

When a mobile robot inspects tasks with complex requirements indoors, the traditional backstepping method cannot guarantee the accuracy of the trajectory, leading to problems such as the instrument not being inside the image and focus failure when the robot grabs the image with high zoom. In order to solve this problem, this paper proposes an adaptive backstepping method based on double Q-learning for tracking and controlling the trajectory of mobile robots. We design the incremental model-free algorithm of Double-Q learning, which can quickly learn to rectify the trajectory tracking controller gain online. For the controller gain rectification problem in non-uniform state space exploration, we propose an incremental active learning exploration algorithm that incorporates memory playback as well as experience playback mechanisms to achieve online fast learning and controller gain rectification for agents. To verify the feasibility of the algorithm, we perform algorithm verification on different types of trajectories in Gazebo and physical platforms. The results show that the adaptive trajectory tracking control algorithm can be used to rectify the mobile robot trajectory tracking controller’s gain. Compared with the Backstepping-Fractional-Older PID controller and Fuzzy-Backstepping controller, Double Q-backstepping has better robustness, generalization, real-time, and stronger anti-disturbance capability.

Research on Coupled Control Algorithm for Trajectory Tracking of Rear-Wheel Distributed Drive Vehicles

Research on Coupled Control Algorithm for Trajectory Tracking of Rear-Wheel Distributed Drive Vehicles

Collision-Free Model Predictive Trajectory Tracking Control for UAVs in Obstacle Environment

In this paper, we propose a collision-free model predictive trajectory tracking control algorithm for unmanned aerial vehicles (UAVs) in environments with both static obstacles and dynamic obstacles. Collision avoidance is ensured by obtaining outer polyhedral approximations of each interval of the dynamic obstacles trajectories based on MINVO basis, and then optimizing a plane to separate the polyhedra and the trajectory of the UAV. By incorporating the resulting computationally efficient collisionfree constraints and divers physical constraints, a model predictive control (MPC) optimization problem is formulated with a tailored terminal constraint set, which can be solved by a standard nonlinear programming solver. Moreover, the control theoretic properties are established, including recursive feasibility, the guarantee of collision avoidance, as well as closed-loop stability. Finally, the efficacy of the proposed algorithm is successfully evaluated by a simulation in a multi-obstacle environment.

A Survey of Intelligent Driving Vehicle Trajectory Tracking Based on Vehicle Dynamics

<div>Trajectory tracking control, as one of the core technologies of intelligent driving vehicles, determines the driving performance and safety of intelligent driving vehicles and has received extensive attention and research. In recent years, most of the research results of trajectory tracking control are only applicable to conventional working conditions; however, the actual operating conditions of intelligent driving vehicles are complex and variable, so the research of trajectory tracking control algorithm should be extended to the high-speed low-adhesion coefficient, large curvature, variable curvature, and other compound limit working conditions. This requires more consideration of the vehicle dynamics in the controller design. In this article, a comprehensive review of trajectory tracking control under extreme operating conditions is conducted from three levels: vehicle dynamics model, vehicle speed tracking (longitudinal motion control), and path tracking (transverse motion control), and the existing research results are analyzed and summarized to obtain the research trends and pain points and difficulties in each field. On this basis, the future outlook of trajectory tracking control is proposed, which is expected to provide some help and inspiration to the research workers in this field.</div>

Coupled lateral and longitudinal trajectory tracking control with a modified vehicle kinematics model for autonomous vehicles

Abstract The paper proposes a coupled lateral and longitudinal trajectory tracking control algorithm based on model predictive control (MPC) to enhance the precision and stability of trajectory tracking of autonomous vehicles. The coupled MPC controller is developed based on a modified vehicle kinematics model, which simultaneously takes the steering angle and the longitudinal speed as control variables. The modified vehicle model and the coupled MPC controller are verified by CarSim and MATLAB/Simulink co-simulation experiments. Simulation results demonstrate that, at the cost of 12 percent increase in average computational time, the proposed coupled MPC controller leads to an approximate 48 percent reduction in tracking error compared to the benchmarking coupled lateral and longitudinal MPC controller based on the classic kinematics model.

Adaptive Control Algorithm for Trajectory Tracking of Underactuated Unmanned Surface Vehicle (UUSV)

The ability to track the trajectory or path on the sea surface remains a key measurement in the control system of an unmanned surface vehicle (USV). In this research, the designed algorithm defines the path and minimizes the disturbances to zero. Underactuated USVs are ships or boats, which operate on the water surface without a crew and the underactuated system has low actuators than its degree of freedom (DOF). The adaptive control strategy is applied to the unbounded system as the ocean due to its high performance, while the robust control system attains high performance in the bounded system. To consider the trajectory tracking of UUSV and provide an optimal control strategy for a ship in the presence of external disturbances, the study presents a controller-based on model reference adaptive control with an integrator (MRACI), which guarantees the stability of a closed-loop system. The vehicle experiences variations in the system response due to external disturbance. This abovementioned scheme reduces the variations to nearly equal to zero making the vehicle stable. First, use computer-based simulation to verify the proposed controller under two different scenarios. Then, simulation results show that the designed scheme lowers the errors and performs well.

Intelligent electric vehicle trajectory tracking control algorithm based on weight coefficient adaptive optimal control

The track tracking effect of intelligent vehicle directly affects the safety of vehicle and passengers. In the process of intelligent vehicle track tracking, the track tracking accuracy is related to many factors such as track curvature, road friction coefficient, and longitudinal speed change. In this paper, a new lateral and longitudinal coupling control algorithm is proposed. Based on the vehicle dynamics model and the optimal control theory, combined with the fuzzy control theory, the Fuzzy Linear Quadratic Regulator (FLQR) lateral optimal controller is designed, and feed-forward control and predictive controller are added. According to the real-time tracking lateral error and fuzzy control algorithm fed back by the system, the weight coefficient of the lateral displacement deviation in the cost function is dynamically adjusted; considering the coupling effect of lateral and longitudinal controllers of vehicle trajectory tracking control, a model predictive control (MPC) longitudinal speed controller is designed based on MPC theory, considering acceleration constraint and acceleration variation constraint, and taking lateral stability as evaluation index. A joint simulation platform is built based on CarSim and Simulink. The simulation results show that the designed lateral and longitudinal coupling controller of FLQR + MPC has better track tracking accuracy and can improve the driving stability of the vehicle; finally, the tracking effect of the designed algorithm is verified by real vehicle experiments. The maximum error of the designed controller algorithm in real vehicle tracking is 0.56 m, and the tracking effect is good.

Fixed-Time Sliding Mode-Based Active Disturbance Rejection Tracking Control Method for Robot Manipulators

This work investigates the issue of a hybrid trajectory tracking control algorithm (HTCA) for robot manipulators (RMs) with uncertain dynamics and the effect of external disturbances. Following are some proposals for achieving the control target. Firstly, to achieve the active disturbance rejection, we propose a uniform second-order sliding mode disturbance observer (USOSMDO) to obtain directly the lumped uncertainties without their prior upper-bound information. Secondly, a fixed-time singularity-free terminal sliding surface (FxSTSS) is proposed to obtain a fixed-time convergence of the tracking control error (TCE) without the singularity in the control input. Then, using information on the proposed USOSMDO, our HTCA is formed based on the FxSTSS and the fixed-time power rate reaching law (FxPRRL). The control proposal not only stabilizes with the global fixed-time convergence but also attains high tracking accuracy. In addition, the chattering problem also is handled almost completely. Finally, numerical simulations verify the effectiveness and advantages of applying the proposed HTCA to a FARA robot.

Nonlinear Path Generation and Tracking Control Design for a Mobile Robot*

This paper proposes trajectory generation and tracking control methods for a differential drive wheel mobile robot. The reference trajectory is generated as a polynomial function in time variable while the tracking control algorithm is constructed using Lyapunov's stability criteria. Experimental results are reported to show the good performance of the proposed trajectory generation and tracking control algorithms.

Research on a New Rehabilitation Robot for Balance Disorders.

The treatment of patients with balance disorders is an urgent problem to be solved by the medical community. The causes of balance disorders are diverse. An aging population, traffic accidents, stroke, genetic diseases and so on are all possible factors. It has brought great pain and inconvenience to patients and their families. At present, there are two main types of assisted rehabilitation training robots for patients with balance disorders: exoskeleton robots and end robots. The exoskeleton robot is generally installed on the outside of the patient's body to follow their movement, which can support the weight of the body and provide power support to help the patient train and recover lower limb ability. The use of end robots is usually to secure the patient's foot to the motion platform and control the pedal to drive the lower limbs to conduct gait training. Such passive training is more suitable for patients with severe disorders. The patient has low awareness of active participation. This paper focuses on research on end rehabilitation training robots for balance disorders. In this paper, a robotic system for rehabilitation training of patients with balance disorders is invented. The robot body is a 9 degree of freedom (DOF) redundant series-parallel hybrid motion platform. Two sets of motion platforms with symmetrical mirror images are used together to simulate different motion modes of the human body and drive the human body to move. Each set of motion platforms is composed of a 6-DOF vestibular parallel device and a 3-DOF proprioception parallel device. It has the advantages of DOF decoupling and fast response, proposing a new structural form for the design of proprioceptive and vestibular simulation platforms. The robot's functional level can be divided into a vestibular sense module and a proprioception module according to the structure. The two modules can work independently to achieve different functions or work together to achieve complex motion and multisensory fusion. This robot is a redundant mechanism device with 9 DOFs. Through a reasonable distribution of DOF and motion, the robot's working space can be increased, and the robot's flexibility and motion performance can be improved. In this paper, a trajectory tracking control algorithm for vestibular and proprioceptive simulation is proposed, which can provide unlimited body sense training for patients within the robot's limited motion range.

Analyses of autonomous underwater vehicle trajectory tracking control algorithms

Analyses of autonomous underwater vehicle trajectory tracking control algorithms

Event-triggered sliding mode trajectory tracking control for underactuated unmanned surface vessel

This article considers the trajectory tracking control for underactuated unmanned surface vessel and actuator loss caused by frequent updating of the controller. An event-triggered sliding mode trajectory tracking control algorithm is proposed for the problems. A sliding mode tracking controller is designed by the integral sliding surface at the beginning to guarantee global asymptotic tracking of the desired trajectory. Based on the tracking controller, the event-triggered condition is designed in the channel of the controller to actuator, which effectively reduces the update frequency of the controller. Theoretical analysis proves that the states of underactuated unmanned surface vessel are uniformly stable, while the Zeno behavior is prevented. The results of the numerical simulation are presented to demonstrate the effectiveness of the proposed algorithm.