Trajectory Tracking Problem Research Articles

Barrier Function-based adaptive fast non-singular terminal sliding mode tracking control for marine vessels

In this paper, finite-time trajectory tracking problem of the marine vessels (MVs) disturbed by highly coupled nonlinearities and unknown ocean current is solved by developing a barrier function-based adaptive fast non-singular terminal sliding mode control (BFAFNTSMC) method. Salient features are as follows: (1) The defined fast non-singular terminal sliding mode manifold (FNTSM) which introduces the finite-time ocean current observer (OCO) is proposed to guarantee the finite-time sliding motion for mismatched disturbance attenuation. (2) By devising a novel log-type barrier function adaptive sliding mode reaching law (BFARL) based on single switching logic, the synovial variable will converge to and maintain in a predefined neighborhood of zero in a finite time, without overestimating the control gain. (3) Finite-time convergence of trajectory tracking errors to the predefined neighborhood of zero can be guaranteed, independently of the boundaries of the lumped nonlinearities. The proposed method exhibits the satisfied properties of tracking performance as well as chattering alleviation. Simulation results and comparisons are further presented to illustrate remarkable effectiveness of the proposed approach.

Command filter-based adaptive fuzzy integral backstepping control for quadrotor UAV with input saturation

This paper presents an adaptive fuzzy integral backstepping control strategy combined with command filter to solve trajectory tracking problem of quadrotor unmanned aerial vehicle (UAV). By using Fuzzy logic system to approximate uncertain disturbance. The tracking error integral term is introduced to reduce the steady-state tracking error. The backstepping approach is combined with the command filter to solve the “computational explosion” problem, and the error compensation mechanism is introduced to reduce the influence of filtering error. The hyperbolic tangent function is used to solve the problem of input saturation. By choosing the appropriate Lyapunov function to calculate the adaptive law for tuning the adjustable parameters of the fuzzy logic system. Morever, the stability of the controller is analyzed by using Lyapunov stability theory. Numerical simulation results are provided to illustrate the effectiveness and superiority of the proposed control method.

Fuzzy PID Control of the Three-Degree-of-Freedom Parallel Mechanism Based on Genetic Algorithm

It is necessary to upgrade and transform the sorting equipment in the industrial production line. In order to improve production efficiency and reduce labor intensity, a high-speed lightweight parallel mechanism control system for the high-speed sorting and packaging of light items was studied. A fuzzy PID controller based on genetic algorithm (GA) optimization is proposed according to the nonlinear and strong coupling characteristics of the parallel mechanism (PM) control system. The inverse kinematic analysis was conducted to map the workspace trajectory tracking problem to the joint space. It was transformed into the trajectory planning and solving problems in the joint space. The motion trajectory was obtained utilizing quintic polynomial interpolation. Finally, the servo control system model was established, and the PID control parameters were optimized and self-tuned by the GA. They were applied to the fuzzy PID controller for simulation experiments. The simulation results showed that the GA-optimized fuzzy PID control system compared with the fuzzy PID control system had a 23.39% shorter rise time, 22.32% less regulation time, and 7.18% less steady-state error. The control system had a good dynamic and steady-state performance.

Adaptive Chattering-Free PID Sliding Mode Control for Tracking Problem of Uncertain Dynamical Systems

Aiming at the trajectory tracking problem with unknown uncertainties, a novel controller composed of proportional-integral-differential sliding mode surface (PIDSM) and variable gain hyperbolic reaching law is proposed. A PID-type sliding mode surface with an inverse hyperbolic integral terminal sliding mode term is proposed, which has the advantages of global convergence of integral sliding mode (ISM) and finite time convergence of terminal sliding mode (TSM), and the control effect is significantly improved. Then, a variable gain hyperbolic approach law is proposed to solve the sliding mode approaching velocity problem. The variable gain term can guarantee different approaching velocities at different distances from the sliding mode surface, and the chattering problem is eliminated by using a hyperbolic function instead of the switching function. The redesign of the sliding mode surface and the reaching law ensures the robustness and tracking accuracy of the uncertain system. Adaptive estimation can compensate for uncertain disturbance terms in nonlinear systems, and the combination with sliding mode control further improves the tracking accuracy and robustness of the system. Finally, the Lyapunov stability principle is used for stability analysis, and the simulation study verifies that the proposed control scheme has the advantages of fast response, strong robustness, and high tracking accuracy.

Asymmetric integral barrier Lyapunov function-based dynamic surface control of a state-constrained morphing waverider with anti-saturation compensator

To satisfy wide-speed and long-range mission requirements, morphing aircraft can maintain optimal flight performance by changing their configuration during flight. As an advanced morphing aircraft, a cross-domain morphing waverider can change its wing geometry to maintain a high lift-to-drag ratio across the subsonic, transonic, and supersonic to hypersonic speed ranges. During the highly dynamic morphing process, the trajectory tracking problem of the morphing waverider is characterized by strong coupling, time-varying characteristics, parameter uncertainties, input saturation, and asymmetric state constraints. To address these problems, this paper proposes an asymmetric integral barrier Lyapunov function (AIBLF) based dynamic surface controller consisting of two loops, based on the six-degrees-of-freedom partial decoupled control-oriented model of a symmetric-sweep-wing morphing waverider. Specifically, a virtual control signal of three-axis angular rates is provided by the AIBLF-based flight controller to satisfy the predefined asymmetric constraints of the angle of attack, sideslip angle, and bank angle, combined with a disturbance observer to approximate the disturbances of multiple parameter uncertainties. Subsequently, the desired virtual control signal consisting of three-axis angular rates is derived by passing the above virtual control signal through a nonlinear adaptive filter to avoid the problem of complexity explosion. The control command is generated by the dynamic surface controller and a finite-time anti-saturation compensator to overcome input saturation. Additionally, a nonlinear disturbance observer is applied to estimate the lumped disturbance to realize feedforward compensation. According to the stability analysis, all signals in the closed-loop system are uniformly ultimately bounded while the states remain in the constraint sets. Finally, the performance of the proposed controller is evaluated through extensive and comparative numerical simulations under multiple disturbances. The proposed controller has a small tracking error and high convergence speed and can prevent states from exceeding the given bounds.

Tracking Control of Autonomous Car with Attention to Obstacle Using Model Predictive Control

Previous research of MPC for path tracking and obstacle avoidance showed the car was able to evade obstacles while tracking the path but ineffectively and path tracking tests show an oscillating movement of the car. The research was done by varying cost function weights and the car was assumed to have a constant velocity. The best performance was obtained when the error weight is greater than the input weight. This research aims to use MPC for trajectory tracking and obstacle avoidance by using Linear Time Variant MPC (LTV MPC), where the trajectory tracking problem is defined by using a time-varying reference. MPC parameter is varied to find the best performing design. In the obstacle avoidance system, obstacle detection is done by measuring the distance between the instant car position and the obstacle position. While an obstacle is detected, a new lateral position constraint is calculated. Trajectory tracking tests are done using 2 types of tracks, sine wave, and lane changing. Obstacle avoidance tests are done using 1 obstacle and 2 obstacles. Results are evaluated using RMSE of car position, cost function, and the nearest distance between car and obstacle. Results show that MPC was able to evade obstacles while tracking the time-varying reference with 0.4 s delay. However, some variations were not able to meet the safe zone constraints for obstacle avoidance.

Finite-time robust control of robotic manipulator with input deadzone and time-varying disturbance compensation

In this paper, the problem of trajectory tracking for robotic manipulator with input deadzone and time-varying disturbances is investigated using a continuous non-singular terminal sliding mode control (SMC). The robotic manipulator plays a vital role in industrial as well as many other applications. However, it faces numerous problems for accurate and fast trajectory tracking response in the presence of unknown uncertainties and external disturbances, that always have adverse affects on system closed-loop performance. This paper proposes a valid control design scheme to address the aforementioned practical issue. First, a non-singular terminal sliding mode surface is designed. Then, a robust control law is developed to guarantee the finite-time converges of system states to the origin. In addition, the sign function is substituted by saturation function, which can effectively reduce the chattering driven by the high-frequency switching item in the traditional SMC method. Moreover, the Lyapunov stability criterion is used to prove the stability of the closed-loop system. The efficiency of the designed control scheme is validated with numerical simulations.

INDI-based aggressive quadrotor flight control with position and attitude constraints

Recent studies have significantly contributed to the extensive use of quadrotors for delivery, mapping, and inspection. To further increase the versatility of quadrotors under confined environments, we focus on the precise trajectory tracking problem with position and attitude constraints. In tightly constrained scenarios, any slight error will infect flight security, especially in a large attitude maneuver. We utilize the incremental nonlinear dynamic inversion (INDI) method to precisely linearize the nonlinearities in the system and generalize it to the entire rotation space to reach a globally expressed control law. Meanwhile, the thrust alignment is introduced to improve the robustness against the mismatch between actuator dynamics and rotational dynamics, guaranteeing higher tracking accuracy. Improvements over a conventional geometry tracking controller are demonstrated in experiments where the quadrotor flies through an inclined narrow gap with orientation up to 90°. Flight tests also indicate the high disturbance rejection capabilities with the thrust alignment in gap traverse flight.

ANFIS-EKF-Based Single-Beacon Localization Algorithm for AUV

Singe-beacon localization technology can help Autonomous Underwater Vehicles (AUVs) to obtain precise positions by deploying only one beacon. It is considered as a promising way, benefiting from saving much time and labor compared with traditional Long-Baseline Localization (LBL). A typical single-beacon localization scheme contains two essential questions: the initial observability problem and long-endurance trajectory tracking problem. Aiming at these core problems, a comprehensive solution for single-beacon localization is described in this paper. An multi-hypothesis initial position discriminant method is proposed firstly, which helps to achieve accurate initial location based on observability analysis. Then, an Adaptive Network Fuzzy Inference System (ANFIS)-improved Extended Kalman Filter (EKF) method is proposed, in which single-beacon measuring information is fused with off-the-shelf sensors, including DVL, Compass, etc. ANFIS-EKF can help to improve trajectory tracking precisions by restraining the heavy loss of linearization in conventional EKF. Both simulation and field tests are conducted to verify the performance of the proposed algorithms.

Trajectory Tracking Design for a Swarm of Autonomous Mobile Robots: A Nonlinear Adaptive Optimal Approach

This research presents a nonlinear adaptive optimal control approach to the trajectory tracking problem of a swarm of autonomous mobile robots. Mathematically, finding an analytical adaptive control solution that meets the H2 performance index for the trajectory tracking problem when controlling a swarm of autonomous mobile robots is an almost impossible task, due to the great complexity and high dimensions of the dynamics. For deriving an analytical adaptive control law for this tracking problem, a particular formulation for the trajectory tracking error dynamics between a swarm of autonomous mobile robots and the desired trajectory is made via a filter link. Based on this prior analysis of the trajectory tracking error dynamics, a closed-form adaptive control law is analytically derived from a high-dimensional nonlinear partial differential equation, which is equivalent to solving the trajectory tracking problem of a swarm of autonomous mobile robots with respect to an H2 performance index. This delivered adaptive nonlinear control solution offers the advantages of a simple control structure and good energy-saving performance. From the trajectory tracking verification, this proposed control approach possesses satisfactory trajectory tracking performance for a swarm of autonomous mobile robots, even under the effects of huge modeling uncertainties.

Multi-target trajectory tracking in multi-frame video images of basketball sports based on deep learning

INTRODUCTION: There is occlusion interference in the multi-target visual tracking process of basketball video images, which leads to poor accuracy of multi-target trajectory tracking. This paper studies the multi-target trajectory tracking method in multi-frame video images of basketball sports based on deep learning. OBJECTIVES: Aiming at the problem of target occlusion in the tracking process and the problem of trajectory tracking anomaly caused by target occlusion, a modified algorithm is proposed. METHODS: The method is divided into two parts: detection and tracking. In the detection part, the YOLOv3 algorithm in deep learning technology is used to detect each target in the video, and the original YOLOv3 backbone network Darknet-53 is replaced by the lightweight backbone network MobileNetV2 to extract the target features. RESULTS: Based on the target detection results, the Kalman filter is used to predict the next position and bounding box size of the target to obtain the target trajectory prediction results according to the current target position, then a hierarchical data association algorithm is designed, and multi-target tracking of the same category is completed based on the target appearance feature similarity and feature similarity. CONCLUSION: The experimental results show that the method can accurately detect the targets in multi-frame video images in basketball sports and obtain high-precision target trajectory tracking results.

Dynamic Modeling and Backstepping Control of a Wheeled Mobile Robot With Skidding and Slipping effects

The development of a tracking control using a backstepping method for a wheeled mobile robot under the effect of skidding and slipping is presented in this paper. The dynamic model of a differential drive mobile robot with skidding and slipping effects is used to solve the trajectory tracking problem. The proposed control scheme is based on a backstepping strategy and under the assumption of knowledge of the disturbance. Simulations results are showed, to prove the effectiveness of the proposed method together with a comparison with similar strategies already presented in the literature.

Modified computed torque control for trajectory tracking of a 8 DOF mobile manipulator robot

In this paper, a nonlinear controller based on a computed torque control scheme is proposed for solving the trajectory tracking problem of a 8 DOF mobile manipulator robot, considering a (2,0) type differential mobile robot that satisfy its nonholonomic constraint. A stability analisys using Lyapunov method is presented; semiglobal, uniformly ultimately bounded (UUB) stability is proved. Numeric simulation with a circular parametric trajectory using KUKA youBot model is shown. Results show an effective convergence and good control performance.

Model predictive control using LPV approach for trajectory tracking of quadrotor UAV with external disturbances

PurposeThe rotorcraft technology is very interesting area since last few decades due to variety of applications. One of the rotorcrafts is the quadrotor unmanned aerial vehicle (QUAV), which contains four rotors mounted on an airframe with an onboard controller. The QUAV is a highly nonlinear system and underactuated. Its controller design is very challenging task, and the need of controller is to make it autonomous based on mission planning. The purpose of this study is to design a controller for quadrotor UAV for attitude stabilization and trajectory tracking problem in presence of external environmental disturbances such as wind gust.Design/methodology/approachTo address this problem, the model predictive control has been designed for attitude control and feedback linearization control for the position control using the linear parameter varying (LPV) approach. The trajectory tracking problem has been addressed using the circular trajectory and helical trajectory.FindingsThe simulation results show the efficient performance with good trajectory tracking even in presence of external disturbances in both the scenarios considered, one for circular trajectory tracking and other for helical trajectory tracking.Originality/valueThe novelty of the work came from using the LPV approach in controller design, which increases the robustness of the controller in presence of external disturbances.

Fuzzy variable impedance-based adaptive neural network control in physical human–robot interaction

This article focus on the problems of trajectory tracking and motion constraint for physical human–robot interaction, and a compliant adaptive control method is proposed for stable and safe physical human–robot interaction during the interaction. First, a fuzzy variable impedance control strategy is given to make the robot to use suitable impedance parameters in different motion states, which can improve positioning accuracy and reduce the interaction force. Second, by transforming the safety interaction constraint into output constraint, a tan-type barrier Lyapunov function is presented to guarantee the safety of human partner in physical human–robot interaction. Third, an adaptive neural network is employed to design the adaptive controller to handle with the dynamic uncertainties and improve the robustness of the system. Finally, simulation results of a 2-degree-of-freedom manipulator are presented to show the effectiveness of the proposed method.

Decoupled Planes’ Non-Singular Adaptive Integral Terminal Sliding Mode Trajectory Tracking Control for X-Rudder AUVs under Time-Varying Unknown Disturbances

This paper analyzes the trajectory tracking problem in decoupled planes for X-rudder AUVs under time-varying, unknown environmental interferences. The proposed scheme consists of the kinematic control law based on the compound line-of-sight guidance law and the dynamic control law based on a non-singular adaptive integral terminal sliding mode control (NAITSMC) to avoid the chattering problems, parameter perturbation, and time-varying disturbances. Meanwhile, we introduce a reduced-order extended state observer (RESO) to compensate for unknown ocean currents by the first-order Gauss–Markov process. We verify the whole system of the proposed scheme through global asymptotic stability, then present a set of numerical simulations revealing robustness and adaptability performances in decoupled planes.

Direction and Trajectory Tracking Control for Nonholonomic Spherical Robot by Combining Sliding Mode Controller and Model Prediction Controller

A spherical robot is a nonlinear, nonholonomic, and unstable system which increases the difficulty of the direction and trajectory tracking problem. In this study, we propose a new direction controller Hierarchical Terminal Sliding Mode Controller (HTSMC), an instruction planning controller called Model Prediction Control-based Planner (MPCBP), and a trajectory tracking framework named MPCBP-HTSMC-HSMC (MHH). The HTSMC is designed by integrating a fast terminal algorithm, a hierarchical method, the motion features of a spherical robot, and its dynamics. In addition, the new direction controller has an excellent control effect with a quick response speed and strong stability. MPCBP can obtain optimal commands that are then transmitted to the velocity and direction controller. Since the two torque controllers in MHH are all Lyapunov-based sliding mode controllers, the MHH framework may achieve optimal control performance while assuring stability. Finally, the two controllers eliminate the requirement for MPCBP's stability and dynamic constraints. Finally, hardware experiments demonstrate the efficacy of the HTSMC, MPCBP, and MHH.

Robust Trajectory Tracking Control for Uncertain 3-DOF Helicopters With Prescribed Performance

This article presents a robust control scheme for the trajectory tracking problem of a three-degree-of-freedom helicopter with prescribed transient and steady-state performance. The control design does not employ any information regarding the dynamics of the system. In addition, the transient and steady-state response of the system with respect to a given time-varying trajectory is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> and explicitly imposed by certain designer-specified performance functions and is fully decoupled from the control gain selection and the dynamic model parameters. Finally, both simulation and experimental results verify the theoretical findings.

Sliding-Mode Control of Full-State Constraint Nonlinear Systems: A Barrier Lyapunov Function Approach

This study presents the design of a robust control based on the sliding-mode theory to solve both; the stabilization and the trajectory tracking problems of nonlinear systems subjected to a class of full-state restrictions. The selected nonlinear system satisfies a standard Lagrangian structure affected by nonparametric uncertainties. A barrier Lyapunov function is used to ensure the state constraints by designing a time-varying gain, which guarantees the fulfillment of the predefined state constraints even under external perturbations. The proposed design methodology for the barrier sliding-mode control (BSMC) ensures the convergence of the sliding surface in finite time to the origin. Consequently, the asymptotic convergence of the states to the corresponding equilibrium point is achieved. The finite-time stability of the origin in the closed-loop system with the proposed controller has been demonstrated using the second Lyapunov stability method. The suggested controller was evaluated on a two-link robotic manipulator. Then, the obtained results showed better stabilization and tracking performances (while the restrictions are satisfied) than the traditional first-order sliding-mode or linear state feedback controllers.

A new geometric trajectory tracking controller for the unicycle mobile robot

This work proposes a geometric controller to solve the trajectory tracking problem for a differential drive mobile robot. The proposed control design exploits the properties of the mobile robot attitude configuration space and the cascade structure of the translational and rotational kinematic models. It is formally proven, through Lyapunov arguments, that the closed-loop error dynamics is almost globally asymptotically stable. Numerical simulation results illustrate the performance of the proposed control algorithm.