Trajectory Tracking Method Research Articles

Distributed observer-based formation trajectory tracking method of leader-following multi-AUV system

Aiming at the trajectory tracking issues of the multi-AUV system in the marine environment, a double-layer distributed control strategy is adopted to improve the convergence performance and deal with the time-delay interference, which contains an upper distributed observer and a lower consensus controller, without adopting any global measurement. First, the mathematical model of AUV is converted into a standard double integrator dynamic model by means of the feedback linearization. Then, fully considering two cases with or without delay, the convergence conditions and the upper limit of time-delay for the multi-AUV system are obtained through the eigenvalue analysis method of the characteristic equation. Finally, some comparative simulations are designed to confirm the effectiveness and the robustness of the proposed method.

Adaptive saturated tracking control for solid launch vehicles in ascending based on differential inclusion stabilization

The large-range uncertainties of specific impulse, mass flow per second, aerodynamic coefficients and atmospheric density during rapid turning in solid launch vehicles (SLVs) ascending leads to the deviation of the actual trajectory from the reference one. One of the traditional trajectory tracking methods is to observe the uncertainties by Extended State Observer (ESO) and then modify the control commands. However, ESO cannot accurately estimate the uncertainties when the uncertainty ranges are large, which reduces the guidance accuracy. This paper introduces differential inclusion (DI) and designs a controller to solve the large-range parameter uncertainties problem. When above uncertainties have large ranges, it can be combined with the ascent dynamic equation and described as a DI system in the mathematical form of a set. If the DI system is stabilized, all the subsets are stabilized. Different from the traditional controllers, the parameters of the designed controller are calculated by the uncertain boundaries. Therefore, the controller can solve the problem of large-range parameter uncertainties of in ascending. Firstly, the ascent deviation system is obtained by linearization along the reference trajectory. The trajectory tracking system with engine parameters and aerodynamic uncertainties is described as an ascent DI system with respect to state deviation, which is called DI system. A DI adaptive saturation tracking controller (DIAST) is proposed to stabilize the DI system. Secondly, an improved barrier Lyapunov function (named time-varying tangent-log barrier Lyapunov function) is proposed to constrain the state deviations. Compared with traditional barrier Lyapunov function, it can dynamically adjust the boundary of deviation convergence, which improve the convergence rate and accuracy of altitude, velocity and LTIA deviation. In addition, the correction amplitudes of angle of attack (AOA) and angle of sideslip (AOS) need to be limited in order to guarantee that the overload constraint is not violated during actual flight. In this paper, a fixed time adaptive saturation compensation auxiliary system is designed to shorten the saturation time and accelerate the convergence rate, which eliminates the adverse effects caused by the saturation. Finally, it is proved that the state deviations are ultimately uniformly bounded under the action of DIAST controller. Simulation results show that the DI ascent tracking system is stabilized within the given uncertainty boundary values. The feasible bounds of uncertainty is broadened compared with Integrated Guidance and Control algorithm. Compared with Robust Gain-Scheduling Control method, the robustness to the engine parameters are greatly improved and the control variable is smoother.

A Test Method for Obstacle-Avoidance Performance of Unmanned Surface Vehicles Based on Mobile-Buoy–Shore Multisource-Sensing-Data Fusion

In order to avoid the influence of the test system itself on the autonomous navigation and performance test accuracy of unmanned surface vehicles (USVs), a test method for the obstacle-avoidance performance of USVs based on mobile-buoy–shore multisource-sensing-data fusion is proposed. In this method, a mobile-buoy-integrated test system is designed (that is, the test instrument is installed on the mobile buoy). The buoy is both the carrier of the test instrument and the obstacle. The software and hardware functions of the test system are realized in modules, and the obstacle-avoidance monitoring function of the USV is realized by the trajectory-tracking method of buoy perception preprocessing and shore adaptive weighted fusion. Then, on the basis of the mobile-buoy–shore sensing-data-fusion method, performance tests and a quantitative evaluation of the obstacle perception, static-obstacle avoidance, and dynamic-obstacle avoidance of the USV were carried out. The results show that: (1) the tested USV can accurately identify the distance between buoys; (2) the three static-obstacle-avoidance performance scores of the single obstacle, continuous obstacle, and inflection-point obstacle are 74.81, 77.14, and 47.61, respectively, and the quantitative evaluation score of the static-obstacle-avoidance comprehensive performance is 66.4; (3) the obstacle-avoidance-performance scores of overtaking, encounter, and cross encounter are about 53.92, 36.51, and 6.48, respectively, and the quantitative evaluation score of the comprehensive performance of the dynamic-obstacle avoidance is 72.36. The above quantitative evaluation results show that the system can: participate in track intervention and obstacle-avoidance monitoring as an obstacle; give the static- and dynamic-obstacle-avoidance quantitative evaluation results in a predetermined way, which verifies the feasibility and effectiveness of the obstacle-avoidance-performance test system of the USV on the basis of mobile-buoy–shore multisource-sensing fusion; and be used for the testing and evaluation of the obstacle-avoidance performance of USVs.

Trajectory tracking for quadrotors: An optimization‐based planning followed by controlling approach

AbstractWe present an optimization‐based reference trajectory tracking method for quadrotor robots for slow‐speed maneuvers. The proposed method uses planning followed by the controlling paradigm. The basic concept of the proposed method is an analogy with linear quadratic Gaussian in which nonlinear model predictive control (NMPC) is employed for predicting optimal control policy in each iteration. Multiple‐shooting is suggested over direct‐collocation for imposing constraints when modeling the NMPC. Incremental Euclidean distance transformation map is constructed for obtaining the closest free distances relative to the predicted trajectory; these distances are considered obstacle constraints. The reference trajectory is generated ensuring dynamic feasibility. The objective is to minimize the error between the quadrotor's current pose and the desired reference trajectory pose in each iteration. Finally, we compared the proposed method with two other approaches and showed that the proposed method outperforms the said approaches in terms of reaching the goal without any collision. Additionally, we published a new data set that can be used for evaluating the performance of trajectory tracking algorithms.

A Finite-Time Trajectory-Tracking Method for State-Constrained Flexible Manipulators Based on Improved Back-Stepping Control

In order to solve the trajectory-tracking-control problem of the state-constrained flexible manipulator systems, a finite-time back-stepping control method based on command filtering is presented in this paper. Considering that the virtual signal requires integration in each step, which will lead to high computational complexity in the traditional back-stepping, the finite-time command filter is used to filter the virtual signal and to obtain the intermediate signal in finite time, to thus reduce the computational complexity. The compensation mechanism is used to eliminate the error generated by the command filter. Furthermore, the adaptive estimation method is introduced to approach the uncertainty of the state-constrained flexible manipulator system. Then, the Lyapunov function is used to prove that the tracking error of the system can be stabilized in a sufficiently small origin neighborhood within a finite time. The simulation of a single rod flexible manipulator system demonstrates the effect of the proposed approach.

An underwater moving dipole tracking method of artificial lateral line based on intelligent optimization and recursive filter

Inspired by the lateral line system of fish, an artificial lateral line system is proposed for underwater target detection. The dipole is treated as a standard and simplified target. In previous studies, most researchers focused on the dipole at a fixed position and the trajectory tracking of a moving dipole was barely considered. In this paper, a new trajectory tracking method for a moving dipole is proposed. First, based on the instant pressure amplitude and loss function, the dipole trajectory is tracked by particle swarm optimization (PSO). Then, the PSO-tracked trajectory is optimized by using recursive filters such as a Kalman filter (KF) and a particle filter (PF) to reduce the tracking error. The experiment result showed that when the trajectory of the dipole was rectangular, the target tracking accuracy of PSO was competitive compared with the Gauss–Newton method. The mean error distance (MED) of PSO was 12.51 mm. The PF showed better optimization performance than the KF in this study, and the corresponding MED of the PF was 7.064 mm. The main factor that caused tracking errors was pressure mismatch. In the simulation, when pressure mismatch was not considered, the performance of the proposed dipole tracking method was highly improved.

Robust nonlinear model predictive control of a bionic underwater robot with external disturbances

Aimed at the trajectory tracking control problem of bionic underwater robots, this paper designs a novel two-dimensional trajectory tracking method based on robust nonlinear model predictive control (RNMPC) and a central pattern generator (CPG) for use in the trajectory tracking of a bionic underwater robot with an external disturbance. First, the overall mathematical model of the robot is established, a robust nonlinear model predictive controller based on a tube for trajectory tracking is designed, and then the stability of the controller is proved by the Lyapunov stability analysis method. Second, a transformation function is designed to combine the CPG motion controller at the bottom layer and the RNMPC trajectory tracking controller at the upper layer in order to establish an RNMPC-CPG controller, which improves the coordination and smoothness of the motion of the bionic robot in the trajectory tracking process. Finally, a simulation experiment is designed to verify the tracking performance of the bionic underwater robot with external disturbances. The simulation results demonstrate the effectiveness of the controller.

A New Trajectory Tracking Control Method for Fully Electrically Driven Quadruped Robot

To improve the accuracy of tracking the trunk center-of-mass (CoM) trajectory and foot-end trajectory in a fully electrically driven quadruped robot, an efficient and practical new trajectory tracking control method is designed. The proposed trajectory tracking method is mainly divided into trunk balance controller (TBC) and swing leg controller (SLC). In TBC, a quadruped robot dynamics model is developed to find the optimal foot-end force that follows the trunk CoM trajectory based on the model predictive control (MPC) principle. In SLC, the Bessel curve is planned as the desired trajectory at the foot-end, while the desired trajectory is tracked by a virtual spring-damping element driving the foot-end, meanwhile, the radial basis function neural network (RBFNN) is applied for supervisory control to improve the control performance for the system. The experimental results show that the control method can modify the robot’s foot-end trajectory tracking effect, so that the stability error can be eliminated and the robustness of the controller can be improved, meanwhile, the linear and circular trajectory for CoM can be tracked accurately and quickly.

Trajectory tracking of in-wheel motor electric vehicles based on preview time adaptive and torque difference control

In order to improve the accuracy of trajectory tracking of in-wheel motor electric vehicles, a preview time adaptive trajectory tracking method based on iterative algorithm and fuzzy control is proposed. Firstly, based on the vehicle’s three-degree-of-freedom model, the vehicle is controlled to track trajectory based on model predictive control (MPC). The preview step size and sampling period of MPC are adjusted by iterative function and fuzzy controller, respectively. Then, In order to optimize MPC active steering control, a differential torque controller is established to realize the trajectory tracking control of differential torque steering. Finally, Carsim/Simulink co-simulation analysis and real vehicle verification are done. The simulation results show that the controller can complete the trajectory tracking control of the in-wheel motor intelligent vehicle, and the stability and steering performance are good. The controller has good robustness and adaptability according to road adhesion conditions and vehicle speed changes. At the same time, the trajectory tracking accuracy of the MPC controller is better than sliding mode variable structure control (SMC). The real vehicle verification results show that when the real vehicle tracking under different speeds, the adaptive preview time controller designed in this paper has good trajectory tracking performance and stability.

Workspace, stiffness analysis and design optimization of coupled active-passive multilink cable-driven space robots for on-orbit services

The use of space robots (SRs) for on-orbit services (OOSs) has been a hot research topic in recent years. However, the space unstructured environment (i.e.: confined spaces, multiple obstacles, and strong radiation interference) has greatly restricted the application of SRs. The coupled active-passive multilink cable-driven space robot (CAP-MCDSR) has the characteristics of slim body, flexible movement, and electromechanical separation, which is very suitable for extreme space environments. However, the dynamic and stiffness modeling of CAP-MCDSRs is challenging, due to the complex coupling among the active cables, passive cables, joints, and the end-effector. To deal with these problems, this paper proposes a workspace, stiffness analysis and design optimization method for such type of MCDSRs. Firstly, the multi-coupling kinematics relationships among the joint, cables and the end-effector are established. Based on hybrid series-parallel characteristics, the improved coupled active–passive (CAP) dynamic equation is derived. Then, the maximum workspace, the maximum stiffness, and the minimum cable tension are resolved, among them, the overall stiffness is the superposition of the stiffness produced by the active and the passive cable. Furthermore, the workspace, the stiffness, and the cable tension are analyzed by using the nonlinear optimization method (NOPM). Finally, an 8-DOF CAP-MCDSR experiment system is built to verify the proposed modeling and trajectory tracking methods. The proposed modeling and analysis results are very useful for practical space applications, such as designing a new CAP-MCDSR, or utilizing an existing CAP-MCDSR system.

Trajectory tracking method of natural gas, district heating and power systems

The accurate state trajectory is essential for the optimal control of natural gas, district heating and power systems. However, the measurements experience random errors and bad data inevitably, which may cause undesirable control strategies. Aiming at this problem, a state trajectory tracking method of natural gas, district heating and power systems is proposed. The physical model of natural gas, district heating and power systems coupled by combined heating and power units and gas turbine units is established based on partial differential equations and Holt’s exponential smoothing techniques. To enhance the tracking accuracy, the predicted states by the physical model and measurements are combined by Kalman filter technologies, and a novel tracking method of natural gas, district heating and power systems is proposed. The method is applied on natural gas, district heating and power systems with a 14-pipe heating system, 30-node gas system and IEEE 39-bus system coupled by two combined heating and power units and gas turbine units. The total variances and filter coefficients are used to evaluate the tracking performance. The results indicate that filter coefficients are less than 1, meaning the method has the ability to enhance the tracking accuracy compared with the measurements.

A robust adaptive-fuzzy-proportional-derivative controller for a rehabilitation lower limb exoskeleton

Achieving high performance controller for multi-joints actuators on rehabilitation lower limb exoskeleton (RLLE) is difficult due to its non-linear characteristics. The controller performance with less tracking error is a key challenge in their controller. Therefore, this paper presents a new particle swarm optimization based initialization of model reference adaptive for fuzzy logic proportional derivative controller (Adaptive-FLC-PD), used in RLLE for passive mode rehabilitation exercise. The RLLE modelling, which integrates a lower-limb exoskeleton coupled with a direct current motor as joint actuator and a patient leg model, was simulated in MATLAB. The lower-limb exoskeleton motion is realised via a trajectory tracking method that imitates a therapist-administered manual activity during passively rehabilitation exercise. An Adaptive-FLC-PD was designed to control the direct current motor and drive the hip and the knee of the lower-limb exoskeleton. The stability analysis of Adaptive-FLC-PD has been shown by the applied Lyapunov function. The performance of the Adaptive-FLC-PD was compared with the fuzzy logic controller (FLC) and FLC-proportional derivative (FLC-PD) algorithms. The numerical analysis ascertained the performance of the Adaptive-FLC-PD in designing, tuning and simulating control system of RLLE.

Segmented guidance law for single moving mass controlled reentry vehicle with multiple constraints

This paper addresses the problem of low guidance accuracy when the traditional guidance method is adopted on the single moving mass controlled reentry vehicle (SMMCRV) with multiple constraints. More specifically, the range and the velocity cannot be controlled accurately by the single bank angle. To solve the aforementioned problems, the segmented guidance law is employed for the reentry phase to achieve the goal of considerable range adjustment and meeting multiple constraints, which consists of the reference trajectory planning & tracking method and the modified rolling guidance law, making full use of the range adjustment capability of the high-altitude phase and the deceleration capacity of the low-altitude phase. For the high-altitude phase, it is difficult to guarantee the precise control of the velocity and range with the bank angle. Therefore, the varying-weight trajectory planning method and adaptive trajectory tracking method considering the combination between tracking errors are employed. In addition, to decrease the influence caused by the lateral motion and the multiple changing rolling direction, the lateral logic and improved B-spline fitting method are also proposed. For the low-altitude phase, the lateral deviation is counteracted by the high speed rotation. Considering the influence on the stability of the SMMCRV caused by the too high rotation, the nonlinear error angle command is designed and the finite-time guidance law is proposed to obtain the high guidance accuracy. Compared with the traditional method, lower terminal velocity dispersion, higher terminal accuracy and lower rotation speed can be obtained, which can be also demonstrated by the numerical simulation.

Event Visualization and Trajectory Tracking of the Load Carried by Rotary Crane.

Tracking the trajectory of the load carried by the rotary crane is an important problem that allows reducing the possibility of its damage by hitting an obstacle in its working area. On the basis of the trajectory, it is also possible to determine an appropriate control system that would allow for the safe transport of the load. This work concerns research on the load motion carried by a rotary crane. For this purpose, the laboratory crane model was designed in Solidworks software, and numerical simulations were made using the Motion module. The developed laboratory model is a scaled equivalent of the real Liebherr LTM 1020 object. The crane control included two movements: changing the inclination angle of the crane’s boom and rotation of the jib with the platform. On the basis of the developed model, a test stand was built, which allowed for the verification of numerical results. Event visualization and trajectory tracking were made using a dynamic vision sensor (DVS) and the Tracker program. Based on the obtained experimental results, the developed numerical model was verified. The proposed trajectory tracking method can be used to develop a control system to prevent collisions during the crane’s duty cycle.

UAV-BS Formation Control Method Based on Loose Coupling Structure

We propose a novel formation control method considering the challenges of formation keeping, unmanned aerial vehicle (UAV) control, and position adjustment in UAV Base Station (UAV-BS) formation control scenarios. The method is based on a loose coupling structure inspired by the traditional virtual structure method. Firstly, a type of new formation is designed for UAV-BS group. When the UAV-BS group keep a stable network, the centers of all UAV-BS moving trajectory, e.g., circular, are treated as virtual points to form a rigid body. When the UAV-BS group transforms between different formations, the real positions of the UAV-BS group are used to form a rigid body. Secondly, we redesign a trajectory tracking method for UAV-BS to control the flight direction. A flight direction controller is designed for UAV-BS, based on nonlinear guidance logic. According to the empirical model of error feedback, an error corrector is designed to control the position error between the UAV-BS and the virtual point. Simulation results show that the proposed algorithm can satisfactorily complete the formation and control of UA-BS. Besides, the algorithm can reduce the difficulty of formation control of UAV-BS and the requirements of formation control for computing power and network communication.

Badminton players’ trajectory under numerical calculation method

Abstract The trajectory tracking of badminton players’ arm shots can be used effectively to enhance the player’s shot quality. To track the image trajectory of the batting arm, it is necessary to calculate the body posture ratio and tightness of the target area of the batting arm, to filter the background interference of the image segment of the batting and to complete the efficient tracking of the trajectory of the arm batting image. The traditional method combines the adaptive threshold segmentation method to extract the hitting arm target from the background, but ignores filtering out the background interference of the hitting image fragment. This paper proposes a trajectory tracking method based on the morphological operator of the batter image of the arm stroke. The method consists of (1) differentially calculating the image sequence of the hitting arm during two consecutive shots, (2) estimating the Gaussian model parameters of the differential image of the hitting arm during the hitting process, (3) extracting the outline of the moving target of the hitting arm during the hitting process and then calculating the body posture ratio of the hitting target area and compactness, (4) filtering the background interference of the shot image fragment, (6) constructing a global matching approximation function of the moving target and (7) finally determining the motion trajectory of the badminton arm of the batter. Simulation results show that the proposed method can effectively track the target of the hitting arm during the hitting process and generate a continuous trajectory of the hitting arm.

Badminton players’ trajectory under numerical calculation method

Abstract The trajectory tracking of badminton players’ arm shots can be used effectively to enhance the player’s shot quality. To track the image trajectory of the batting arm, it is necessary to calculate the body posture ratio and tightness of the target area of the batting arm, to filter the background interference of the image segment of the batting and to complete the efficient tracking of the trajectory of the arm batting image. The traditional method combines the adaptive threshold segmentation method to extract the hitting arm target from the background, but ignores filtering out the background interference of the hitting image fragment. This paper proposes a trajectory tracking method based on the morphological operator of the batter image of the arm stroke. The method consists of (1) differentially calculating the image sequence of the hitting arm during two consecutive shots, (2) estimating the Gaussian model parameters of the differential image of the hitting arm during the hitting process, (3) extracting the outline of the moving target of the hitting arm during the hitting process and then calculating the body posture ratio of the hitting target area and compactness, (4) filtering the background interference of the shot image fragment, (6) constructing a global matching approximation function of the moving target and (7) finally determining the motion trajectory of the badminton arm of the batter. Simulation results show that the proposed method can effectively track the target of the hitting arm during the hitting process and generate a continuous trajectory of the hitting arm.

Reinforcement learning-based NMPC for tracking control of ASVs: Theory and experiments

We present a reinforcement learning-based (RL) model predictive control (MPC) method for trajectory tracking of surface vessels. The proposed method uses an MPC controller in order to perform both trajectory tracking and control allocation in real-time, while simultaneously learning to optimize the closed loop performance by using RL and system identification (SYSID) in order to tune the controller parameters. The efficiency of the method is evaluated by performing simulations on the unmanned surface vehicle (USV) ReVolt, as well as simulations and sea trials on the autonomous urban passengers ferry milliAmpere. Our results demonstrate that the proposed method is able to outperform other state of the art methods both in tracking performance, as well as energy efficiency.

Trajectory Tracking Method of Volleyball Player’s Arm Hitting Image Based on D-P Algorithm

Aiming at the problems of poor image tracking effect, low precision, and long time in the process of image tracking of volleyball player’s arm hitting, a volleyball player's arm hitting image tracking method based on D-P algorithm is proposed. This paper analyzes the basic concept, basic principle, and basic equation of D-P algorithm and collects the arm stroke trajectory image of volleyball players under the three-dimensional visual model. Using wavelet multiscale decomposition method, the arm stroke trajectory of volleyball players is filtered, and the edge contour feature points of the arm stroke image of volleyball players are extracted. Using the gray histogram feature extraction method, the gray information of volleyball player's arm hitting trajectory image is enhanced. Combined with pixel adaptive enhancement technology, the key action feature points of volleyball player's arm hitting image trajectory are located. Based on D-P algorithm, the volleyball player's arm hitting image trajectory is adjusted and modified to realize the correct tracking of volleyball player's arm hitting image trajectory. The experimental results show that the trajectory tracking effect of volleyball player's arm hitting image is better, which can effectively improve the tracking accuracy and shorten the tracking time.

Trajectory tracking of tail-sitter aircraft by ℓ1 adaptive fault tolerant control

This paper proposes an &#x2113;<inf>1</inf> adaptive fault tolerant control method for trajectory tracking of tail-sitter aircraft in the state of motor loss fault. The tail-sitter model considers the uncertainties produced by the features of nonlinearities and couplings which cause difficulties in control. An &#x2113;<inf>1</inf> adaptive controller is designed to reduce the position and attitude error when actuators have faults. A reference trajectory containing large maneuver flight transitions is designed, which makes it even harder for the &#x2113;<inf>1</inf> controller to track accurately. Compensators are designed to assist &#x2113;<inf>1</inf> adaptive controller tracking of the reference trajectory. The stability of the &#x2113;<inf>1</inf> adaptive controller including compensators is proved. Finally, the simulation results are used to analyse the effectiveness of the proposed controller. Compared to the H<inf>&#x221E;</inf> controller, the &#x2113;<inf>1</inf> adaptive controller with compensators has better performance in position control and attitude control under fault tolerance state even when the aircraft conducts large maneuver. Besides, as the &#x2113;<inf>1</inf> adaptive control method separates feedback control and adaptive law design, the response speed of the whole system is improved.