Trajectory Tracking Control Algorithm Research Articles

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.

Trajectory Tracking Control of Intelligent X-by-Wire Vehicles

Vehicle intelligence is an effective way to improve driving safety and comfort and reduce traffic accidents. The trajectory tracking control of unmanned vehicles is the core module of intelligent vehicles. As a redundant system, the X-by-wire electric vehicle has the advantage that the turning angles and driving torque of the four wheels can be precisely controlled and it has a higher degree of controllability and flexibility. In this paper, a trajectory tracking control algorithm based on a hierarchical control architecture is designed based on x-by-wire vehicles. The hierarchical control algorithm architecture includes the trajectory tracking layer, tire force distribution layer, and actuator control layer. The trajectory tracking layer uses the longitudinal force, lateral force, and yaw moment as the control variables; the model predictive control algorithm controls the vehicle to follow the desired trajectory. The tire force distribution layer is solved by transforming the tire force distribution problem into a quadratic programming problem with constraints. Based on the expected resultant force and resultant moment, the longitudinal force and lateral force of each tire in the vehicle coordinate system are obtained. The actuator control layer converts the coordinate system to obtain the longitudinal force and lateral force in the tire coordinate system, which uses the arctangent function tire model to solve the desired tire slip angle, and then obtains the vehicle steer angle and driving torque. To verify the effectiveness of the trajectory tracking control algorithm of the hierarchical control architecture, the proposed trajectory tracking control algorithm is simulated and verified through the variable speed double line change condition and the low road friction coefficient double line change condition. The simulation results show that the control algorithm proposed in this paper has the accuracy to follow the desired trajectory.Definition:

Wall-Climbing Mobile Robot for Inspecting DEMO Vacuum Vessel

The vacuum vessel (VV) inside and outside inspection of the Demonstration Fusion Power Plant (DEMO) is very difficult due to various constraints, such as non-magnet effect material requirements, constrained space, and neutrons on its surfaces. We propose a design method for wall-climbing mobile robots (WMR) based on the vortex principle and investigate key technologies to meet VV inspection requirements. We developed a kinematic model based on the robot’s motion control requirements and a trajectory tracking control algorithm according to the tractrix principle, enabling the robot to follow the path for autonomous inspection. The impeller is designed based on the vortex principle. The aerodynamic characteristics and structural strength of the impeller were also analysed and optimised. A sliding-mode robust pressure control system was designed for the robot’s negative pressure adsorption, and its effectiveness was verified by simulation. Finally, an initial test prototype verified the structural design and vortex adsorption performance. We also addressed the potential applications of the WMR in DEMO and other fusion reactors.

Autonomous vehicle trajectory tracking lateral control based on the terminal sliding mode control with radial basis function neural network and fuzzy logic algorithm

Abstract. This paper will study a trajectory tracking control algorithm for electric vehicles based on a terminal sliding mode controller. First, a 3 degrees of freedom nonlinear vehicle model and a controller-oriented 2 degrees of freedom vehicle model are established. The preview time is adaptively adjusted based on the preview model. Then, the vehicle trajectory tracking controller, which uses the terminal sliding mode algorithm, is designed. The radial basis function (RBF) neural network algorithm is used to approximate the system variable parameters in the control model online. At the same time, fuzzy logic is used to control the gain parameters of the controller to reduce the chattering of the control system. Finally, the designed controller is verified by simulation. The maximum deviation of path tracking under different speeds is 0.6 m, and the target path can also be well followed under different road friction coefficients. The simulation results show that the controller designed in this paper can effectively carry out the vehicle trajectory tracking and lateral control and reduce the chattering to a certain extent.

Adaptive output feedback super twisting algorithm for trajectory tracking control of USVs with saturated constraints

This article investigates the trajectory tracking control of fully actuated unmanned surface vehicles (USVs) in the presence of lumped system uncertainty and input saturation. To address this problem, an output feedback scheme, which combines the saturated adaptive super twisting algorithm and non-singular fast terminal sliding mode (SASTA-NFTSM) technique, is proposed. First, the velocities and lumped system uncertainty including external disturbances and model uncertainties, are estimated by a finite-time extended state observer (FTESO), simultaneously in finite time. Second, to deal with the saturation constraints on actuators, a novel sliding mode reaching law scheme, namely SASTA, that consists of an anti-windup compensator and a super twisting algorithm based on switching logic adaptive gains is proposed. Finally, the trajectory tracking control of USVs is solved with the non-trivial combination of SASTA and NFTSM. The chattering phenomenon can be effectively attenuated by virtue of the continuous control laws compared with the traditional NFTSM control (NFTSMC) approaches. The tracking errors are guaranteed to converge to zero in finite time. Comparative simulation results demonstrate the effectiveness and advantage of the proposed scheme.

Trajectory tracking control of wheeled mobile robot based on improved LSTM-DDPG algorithm

This paper proposed a deep deterministic policy gradient (DDPG) algorithm based on the clipped double Q-learning method and long short-term memory (LSTM) neural network for the trajectory tracking control of wheeled mobile robots (WMR). Firstly, aiming at solving the problem of overestimating state-action value in the DDPG algorithm, a double critic network is introduced to approximate the value function, and the minimum value will be taken to calculate the target value of actor network update, avoiding the algorithm falling into local optimal. Then, to overcome the difficulty caused by partial observability in reinforcement learning control, the historical states information will be used to generate the current action by an actor, which adopts an LSTM neural network processing the temporal relations in those historical states. Finally, the reinforcement learning agent based on the improved LSTM-DDPG algorithm is designed as the kinematic controller of WMR and provides reference values for the dynamic controller (two independent PI controllers). Simulation results verify the effectiveness of this control scheme based on the proposed algorithm for WMR trajectory tracking control, even in the presence of external disturbances and model parameter uncertainties.

A State-Compensated Deep Deterministic Policy Gradient Algorithm for UAV Trajectory Tracking

The unmanned aerial vehicle (UAV) trajectory tracking control algorithm based on deep reinforcement learning is generally inefficient for training in an unknown environment, and the convergence is unstable. Aiming at this situation, a Markov decision process (MDP) model for UAV trajectory tracking is established, and a state-compensated deep deterministic policy gradient (CDDPG) algorithm is proposed. An additional neural network (C-Net) whose input is compensation state and output is compensation action is added to the network model of a deep deterministic policy gradient (DDPG) algorithm to assist in network exploration training. It combined the action output of the DDPG network with compensated output of the C-Net as the output action to interact with the environment, enabling the UAV to rapidly track dynamic targets in the most accurate continuous and smooth way possible. In addition, random noise is added on the basis of the generated behavior to realize a certain range of exploration and make the action value estimation more accurate. The OpenAI Gym tool is used to verify the proposed method, and the simulation results show that: (1) The proposed method can significantly improve the training efficiency by adding a compensation network and effectively improve the accuracy and convergence stability; (2) Under the same computer configuration, the computational cost of the proposed algorithm is basically the same as that of the QAC algorithm (Actor-critic algorithm based on behavioral value Q) and the DDPG algorithm; (3) During the training process, with the same tracking accuracy, the learning efficiency is about 70% higher than that of QAC and DDPG; (4) During the simulation tracking experiment, under the same training time, the tracking error of the proposed method after stabilization is about 50% lower than that of QAC and DDPG.

Control Algorithm for Trajectory Tracking of an Underactuated USV under Multiple Constraints

A trajectory tracking control method based on the cascade of optimal guidance and adaptive control laws was proposed for trajectory tracking of an unmanned surface vehicle under multiple motion constraints including an ocean current disturbance environment. Considering the velocity and acceleration constraints, angular velocity, and angular acceleration constraints in guidance law design, motion planning was conducted with three degrees of freedom using a motion model and predictive control, while optimal guidance law was designed through a rolling optimization strategy to stabilize the position error under multiple constraints. Moreover, the stability of the guidance law was proven. In control law design, an adaptive observer was introduced to estimate and compensate for ocean current disturbance, which affected the precision of control. The course and velocity control laws were designed with the adaptive sliding mode control technology to stabilize the course angle and longitudinal velocity errors; the stability of these control laws was further proven. Based on the system design, the stability of the entire closed-loop control system was proven with the cascade system and Lyapunov theory. Theoretical analysis and simulation experiments demonstrated the effectiveness and advancement of the proposed algorithm.

A high-performance neural network vehicle dynamics model for trajectory tracking control

Traditional models of vehicle dynamics engineered from physical principles are usually simplified and assumed, resulting in the model cannot accurately reflect the actual dynamic characteristics of the vehicle under some working conditions, affecting the control accuracy and even safety. In view of this, inspired by the single-track model, this paper uses the data-driven methods to establish a new high-performance time-delay feedback neural network vehicle dynamics model. The feedback connection of a network can describe complex dynamics. The multi-time-step input of the state and control can include highly nonlinear and strong coupling characteristics of a vehicle. The test results of modeling accuracy show that the proposed model can achieve higher vehicle dynamics prediction accuracy than nonlinear vehicle model. Different from the traditional vehicle dynamics model, the proposed model has long-term memory cells, which can implicitly predict coefficient of friction and can be applied to different road conditions. Then, the trajectory tracking control algorithm is designed based on the proposed vehicle model. According to the steady-state steering assumption, the feedforward front wheel steering angle is calculated, and the steady-state sideslip angle is integrated into the steering feedback according to the reference path to realize the reference trajectory tracking control. Finally, Simulink/CarSim is used to conduct the simulation analysis under the double lane change conditions to evaluate the proposed control algorithm. The analysis results show that the control algorithm based on the proposed model can achieve an accurate tracking control effect of a vehicle at medium and high speeds, providing high-accuracy track tracking and good lateral stability of intelligent vehicles.

Fast finite-time tracking control for a 3-DOF cable-driven parallel robot by adding a power integrator✰

Cable-driven parallel robots (CDPRs) usually suffer from kinematic and dynamic uncertainties, which makes it difficult for traditional trajectory tracking control algorithms to achieve high precision, fast response time, and robustness. In this study, we present a novel fast finite-time tracking control (FFTTC) algorithm which solves this problem to a large extent. Specifically, we firstly used a function of exponential errors with fractional power combined with API technique, to deal with the key difficulty of the convergence rate degradation which exists in traditional finite-time tracking control (TFTTC) when system states are far from the equilibrium point. Simultaneously, the API technique was used to avoid the problem of the explosion of complexity. To facilitate algorithm evaluation, the finite-time stability of the close system consisting of the proposed FFTTC algorithm and the CDPRs was proved mathematically and the settling time was estimated correspondingly. The trajectory tracking experiments were performed on a 3-DOF CDPR driven by 4 cables. Simulation and experimental results show that the proposed FFTTC algorithm can cope with external disturbances, variable load, and inaccurate model parameters. The comparison experiment indicates that the proposed FFTTC algorithm is superior to the model predictive control and TFTTC algorithms in precision, response speed and robustness.

On Active Vibration Absorption in Motion Control of a Quadrotor UAV

Conventional dynamic vibration absorbers are physical control devices designed to be coupled to flexible mechanical structures to be protected against undesirable forced vibrations. In this article, an approach to extend the capabilities of forced vibration suppression of the dynamic vibration absorbers into desired motion trajectory tracking control algorithms for a four-rotor unmanned aerial vehicle (UAV) is introduced. Nevertheless, additional physical control devices for mechanical vibration absorption are unnecessary in the proposed motion profile reference tracking control design perspective. A new dynamic control design approach for efficient tracking of desired motion profiles as well as for simultaneous active harmonic vibration absorption for a quadrotor helicopter is then proposed. In contrast to other control design methods, the presented motion tracking control scheme is based on the synthesis of multiple virtual (nonphysical) dynamic vibration absorbers. The mathematical structure of these physical mechanical devices, known as dynamic vibration absorbers, is properly exploited and extended for control synthesis for underactuated multiple-input multiple-output four-rotor nonlinear aerial dynamic systems. In this fashion, additional capabilities of active suppression of vibrating forces and torques can be achieved in specified motion directions on four-rotor helicopters. Moreover, since the dynamic vibration absorbers are designed to be virtual, these can be directly tuned for diverse operating conditions. In the present study, it is thus demonstrated that the mathematical structure of physical mechanical vibration absorbers can be extended for the design of active vibration control schemes for desired motion trajectory tracking tasks on four-rotor aerial vehicles subjected to adverse harmonic disturbances. The effectiveness of the presented novel design perspective of virtual dynamic vibration absorption schemes is proved by analytical and numerical results. Several operating case studies to stress the advantages to extend the undesirable vibration attenuation capabilities of the dynamic vibration absorbers into trajectory tracking control algorithms for nonlinear four-rotor helicopter systems are presented.

Tracking Control of Mobile Robots based on Rhombic Input Constraints

This paper focuses on the trajectory tracking control algorithm for Differential Wheeled Mobile Robots (DWMRs) based on rhombic input constraints. The kinematics and dynamics model of DWMRs are established, and vector analysis method is used to design the controller when the linear velocity and angular velocity of DWMRs were not mutually independently. Through the simulation of tracking 8-shaped curve, a good control performance is obtained.

Robust trajectory tracking control of underactuated unmanned surface vehicles with exponential stability: theory and experimental validation

PurposeTrajectory tracking is an important issue to underactuated unmanned surface vehicles (USVs). However, parametric uncertainties and environmental disturbances bring great challenges to the precise trajectory tracking control of USVs. This paper aims to propose a robust trajectory tracking control algorithm with exponential stability for underactuated USVs with parametric uncertainties and unknown environmental disturbances.Design/methodology/approachIn this method, the backstepping method and sliding mode control method are combined to ensure that the underactuated USV can track and maintain the desired trajectory. In addition, a modified switching-gain adaptation algorithm is adopted to enhance the robustness and reduce chattering. Besides, the global exponential stability of the closed-loop system is proved by Lyapunov’s direct method.FindingsThe proposed method in this paper offers a robust trajectory tracking solution to underactuated USVs and it is verified by simulations and experiments. Compared with the traditional proportion-integral-derivative method and several state-of-the-art algorithms, the proposed method has superior performance in simulation and experimental results.Originality/valueThis paper proposes a robust trajectory tracking control algorithm with exponential stability for underactuated USVs. The proposed method achieves exponential stability with better robustness and transient performance.

Design and Control of an Omnidirectional Mobile Wall-Climbing Robot

Omnidirectional mobile wall-climbing robots have better motion performance than traditional wall-climbing robots. However, there are still challenges in designing and controlling omnidirectional mobile wall-climbing robots, which can attach to non-ferromagnetic surfaces. In this paper, we design a novel wall-climbing robot, establish the robot’s dynamics model, and propose a nonlinear model predictive control (NMPC)-based trajectory tracking control algorithm. Compared against state-of-the-art, the contribution is threefold: First, the combination of three-wheeled omnidirectional locomotion and non-contact negative pressure air chamber adhesion achieves omnidirectional locomotion on non-ferromagnetic vertical surfaces. Second, the critical slip state has been employed as an acceleration constraint condition, which could improve the maximum linear acceleration and the angular acceleration by 164.71% and 22.07% on average, respectively. Last, an NMPC-based trajectory tracking control algorithm is proposed. According to the simulation experiment results, the tracking accuracy is higher than the traditional PID controller.

Development and Validation of Advanced Nonlinear Predictive Control Algorithms for Trajectory Tracking in Batch Polymerization

In this work, a computationally efficient nonlinear model-based control (NMBC) strategy is developed for a trajectory-tracking problem in an acrylamide polymerization batch reactor. The performance of NMBC is compared with that of nonlinear model predictive control (NMPC). To estimate the reaction states, a nonlinear state estimator, an unscented Kalman filter (UKF), is employed. Both algorithms are implemented experimentally to track a time-varying temperature profile for an acrylamide polymerization reaction in a lab-scale polymerization reactor. It is shown that in the presence of state estimators the NMBC performs significantly better than the NMPC algorithm in real time for the batch reactor control problem.

Tracking Control of Single-Axis Feed Drives Based on ADRC and Feedback Linearisation

The accuracy of manufacturing highly characterises the performance of industrial motion control. However, detrimental effects such as nonlinear coupling, model uncertainty and unknown external disturbances severely affect trajectory tracking performance. In this paper, we proposed an ADRC and feedback linearisation-based control algorithm for the high-precision trajectory tracking of feed drives. The controller was rigorously designed to ensure the convergence of observer states and tracking error. The applicability of the proposed approach was successfully demonstrated via high-fidelity simulation, and the numerical results based on different tracking methods were compared.

A Model Predictive Control with Preview-Follower Theory Algorithm for Trajectory Tracking Control in Autonomous Vehicles

Research on trajectory tracking is crucial for the development of autonomous vehicles. This paper presents a trajectory tracking scheme by utilizing model predictive control (MPC) and preview-follower theory (PFT), which includes a reference generation module and a MPC controller. The reference generation module could calculate reference lateral acceleration at the preview point by PFT to update state variables, and generate a reference yaw rate in each prediction point. Since the preview range is increased, PFT makes the calculation of yaw rate more accurate. Through physical constraints, the MPC controller can achieve the best tracking of the reference path. The MPC problem is formulated as a linear time-varying (LTV) MPC controller to achieve a predictive model from nonlinear vehicle dynamics to continuous online linearization. The MPC-PFT controller method performs well by increasing the effective length of the reference path. Compared with MPC and PFT controllers, the effectiveness and robustness of the proposed method are proved by simulations of two typical working conditions.