Achieve Trajectory Tracking Research Articles

Parallel-filter observer control with CCD measurements for space optical communication equipment on a moving platform

This paper reports a parallel-filter observer methodology to stabilize the line-of-sight (LOS) for space optical communication missions, which breaks the bandwidth limitation for achieving trajectory tracking on a moving platform with charge-coupled device (CCD) measurements. An equivalent high-order parallel-filter compensator is introduced to reduce the output of the controller, resulting in a stabilized high-bandwidth observer. The parallel-filter observer effectively mitigates the stability degradation associated with a single high-bandwidth filter. Furthermore, a high-bandwidth rate loop is conducive to ensuring the stability of the tracking gimbal in inertial space. The proposed approach directly uses and processes tracking errors to achieve LOS stabilization rather than relying on detailed knowledge of target dynamics to evaluate and compensate for target trajectory. Therefore, it is simple and applicable to provide excellent tracking performance for engineering applications with limited measurement bandwidth. Simulation and experimental results demonstrate the effectiveness of the proposed method for improving LOS stabilization in a tracking system with carrier disturbance and target motion.

Nonlinear Optimal and Multi-Loop Flatness-Basedcontrol of Omnidirectional 3-Wheel Mobile Robots

In this article, the control problem for omnidirectional 3-wheel autonomous mobile robots is solved with the use of (i) a nonlinear optimal control method (ii) a flatness-based control approach which is implemented in successive loops. To apply method (i) that is nonlinear optimal control, the dynamic model of the omnidirectional 3-wheel autonomous mobile robots undergoes approximate linearization at each sampling instant with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrix. The linearization point is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. To compute the feedback gains of the optimal controller an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The global stability properties of the nonlinear optimal control method are proven through Lyapunov analysis. To implement control method (ii), that is flatness-based control in successive loops, the state-space model of the omnidirectional 3-wheel autonomous mobile robot is separated into chained subsystems, which are connected in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input-output linearized flat systems. The state variables of the preceding (i-th) subsystem become virtual control inputs for the subsequent (i+1-th) subsystem. In turn, exogenous control inputs are applied to the last subsystem. The whole control method is implemented in successive loops and its global stability properties are also proven through Lyapunov stability analysis. The proposed method achieves trajectory tracking and autonomous navigation for the omnidirectional 3-wheel autonomous mobile robots without the need of diffeomorphisms and complicated state-space model transformations.

Research on lie group dynamics modeling and trajectory-tracking optimal control of intelligent ground vehicle

Abstract Aiming at the multi-objective integrated coordination problem of trajectory tracking control accuracy and vehicle stability, a Lie-group-based dynamics modeling and trajectory-tracking optimal control method of intelligent ground vehicle is proposed in this paper. Based on the theory of Lie group and Lie algebra, the kinematic relationship of intelligent ground vehicle was established, and the integral variational dynamic equation expression was established using the variational method and Lagrange principle. A vehicle performance index function that balances energy optimization and efficiency optimization was established by combining the two-degree-of-freedom dynamic equation and stability constraints of intelligent ground vehicle. On this basis, an optimal control method for trajectory tracking of intelligent ground vehicle is proposed based on Legendre interpolation polynomial discretization method and Gauss pseudospectral method. The comparative results show that the proposed optimal control method can balance vehicle motion control accuracy, real-time performance, and optimization solution efficiency, thereby ensuring the lateral stability control effect of vehicle while achieving trajectory tracking accuracy.

YoMo: Yoshimura Continuum Manipulator for MR Environment.

Origami robots have garnered attention due to their versatile deformation and potential applications, particularly for medical applications. In this article, we propose a Yoshimura continuum manipulator (YoMo) that can achieve accurate control of the tip position for the magnetic resonance (MR) environment. The YoMo made of a single piece of paper is cable-actuated to generate the bending and shortening deformation. The paper-based YoMo attached to an arc frame can readily function under different orientations in the MR environment. The design and fabrication of YoMo were formulated according to the Yoshimura folding pattern. The kinematics model based on constant curvature assumption was derived as a benchmark method to predict the tip position of the YoMo. The Koopman operator theory was applied to describe the relationship between the tip position and the length change under different orientations. The linear quadratic regulator integrated into the Koopman-based model (K-LQR) was adopted to achieve the trajectory tracking. Comprehensive experiments were carried out to examine the proposed YoMo, its modeling and control methods. The performance of the YoMo including stiffness and workspace was characterized via a customized test setup. The Koopman-based method demonstrates the superiority over the constant curvature-based model to predict the tip position. The K-LQR control method was examined with different trajectories, and the impact of the orientation, speed, and different trajectories were taken into consideration. The results demonstrate the YoMo is capable of achieving trajectory tracking with satisfied accuracy, indicating its potential for medical applications in the MR environment.

Finite-time optimal control for a class of nonlinear systems with performance constraints via critic-only ADP: Theory and experiments

This paper addresses the optimal control problem within the framework of adaptive dynamic programming (ADP) for a class of nonlinear systems subjected to performance constraints. A new finite-time optimal control scheme is developed to stabilize the system by using the critic-only neural network ADP method. Compared with the existing ADP-based optimal control methods with uniformly ultimately bounded stability, the provided control scheme ensures that the controlled system's state and neural network weight estimation error are finite-time stable. It can ensure optimality, prescribed performance, and finite-time stability of the closed-loop control system simultaneously through an integration of ADP, the prescribed performance control technique, and Lyapunov theory. The designed adaptive neural network weight update law can relax the persisting excitation condition. The proposed control scheme is implemented on a robotic experiment platform to achieve trajectory tracking and verify its effectiveness.

Coordinated strategy for path tracking and dynamic stability considering extreme obstacle avoidance in distributed drive electric vehicles

PurposeThis research aims to investigate the trajectory tracking problem for a four-wheel independent drive autonomous vehicle (4WID) and propose an integrated, coordinated control strategy to address the mutual interference between trajectory tracking and stability control in extreme cases.Design/methodology/approachThe authors establish an adaptive preview model that modifies the preview distance based on vehicle speed. They utilize a three-degrees-of-freedom vehicle model and employ model predictive control to calculate the necessary front wheel angle for trajectory tracking. In terms of longitudinal control, a longitudinal coordinated control mechanism is established to achieve the two conflicting objectives of trajectory tracking accuracy and dynamic stability through early deceleration. A stability controller based on sliding mode control (SMC) is designed, considering tire constraints and tracking the optimal yaw angle and sideslip angle. Furthermore, a lateral coordinated control strategy is developed, considering the weight coefficient of stability control, and the yaw moment is calculated and distributed based on the vehicle torque requirements.FindingsThe proposed integrated, coordinated control strategy successfully addresses the mutual interference between trajectory tracking and stability control in extreme cases for the 4WID vehicle. The strategy achieves trajectory tracking accuracy, dynamic stability and reduced energy consumption while taking into account tire constraints.Originality/valueWe have proposed a cooperative control strategy for the trajectory tracking problem of autonomous driving vehicles. This strategy is different from previous methods in that we have taken into account the integrated dynamic control in both longitudinal and lateral directions, balancing the conflicting control requirements and reducing energy consumption, improving trajectory tracking accuracy and vehicle dynamic stability. We have verified the feasibility of this strategy through joint simulation under different driving conditions.

Adaptive trajectory tracking control of robotic manipulators based on integral sliding mode

AbstractThis paper proposes an adaptive control scheme with finite‐time convergent property based on integral sliding mode to achieve trajectory tracking control of rigid robotic manipulators. The novel adaptive gain can be adjusted automatically with the system disturbance, as long as the disturbance and its derivative are bounded without requiring more information. Therefore, the control chattering effect can be mitigated obviously. The global robustness of system is guaranteed by Lyapunov stability analysis. Finally, the simulation of a two‐link manipulator is given to show that the desired trajectory tracking performance is obtained with the proposed adaptive sliding mode approach.

Recurrent neural network for trajectory tracking control of manipulator with unknown mass matrix.

Real-world robotic operations often face uncertainties that can impede accurate control of manipulators. This study proposes a recurrent neural network (RNN) combining kinematic and dynamic models to address this issue. Assuming an unknown mass matrix, the proposed method enables effective trajectory tracking for manipulators. In detail, a kinematic controller is designed to determine the desired joint acceleration for a given task with error feedback. Subsequently, integrated with the kinematics controller, the RNN is proposed to combine the robot's dynamic model and a mass matrix estimator. This integration allows the manipulator system to handle uncertainties and synchronously achieve trajectory tracking effectively. Theoretical analysis demonstrates the learning and control capabilities of the RNN. Simulative experiments conducted on a Franka Emika Panda manipulator, and comparisons validate the effectiveness and superiority of the proposed method.

Adaptive sliding mode control for quadrotor transport systems with uncertain parameters and disturbances

SummaryQuadrotor transportation systems have been widely utilized in both commercial and civilian fields. However, challenges arise due to the variable payload mass and unpredictable wind disturbances during cargo transport, potentially leading to excessive payload swinging and system instability. To tackle this issue, this article proposes an adaptive sliding mode control approach that concurrently achieves trajectory tracking for the quadrotor and mitigates payload swinging. In the outer loop subsystem, the quadrotor dynamics model is partitioned into two components that is, actuated and underactuated components. Sliding surfaces are designed based on this divided system model, and two adaptive laws are designed to compensate for payload mass uncertainty and unknown wind disturbances. The system's asymptotic stability is assured through the application of the Lyapunov theorem. In the inner loop subsystem, a disturbance rejection controller is formulated. Comparative simulation results conclusively demonstrate the outstanding performance of the proposed method in terms of trajectory tracking and robustness.

Enhanced three-dimensional trajectory tracking control for AUVs in variable operating conditions using FMPC-FTTSMC

In addressing the variable operating conditions encountered in complex underwater tasks, an enhanced three-dimensional tracking control method is proposed for autonomous underwater vehicle (AUV) based on fuzzy model predictive control-finite time terminal sliding mode control (FMPC-FTTSMC). Firstly, to enhance adaptability to tasks and environments, fuzzy model predictive control method is designed to achieve precise three-dimensional trajectory tracking. Additionally, a fuzzy weight allocator is employed to enable AUV to autonomously adjust optimization strategies based on real-time states such as task type, speed, and distance from the seabed, thus better coping with changing conditions and improving the universality of the control method. Secondly, a dynamic controller is designed using the finite-time terminal sliding mode control method, combined with a finite-time radial basis function neural network (FTRBFNN) disturbance observer to accurately estimate disturbances. Finally, simulation results demonstrate that the proposed method effectively reduces optimization solving time compared to traditional model predictive control, achieves trajectory tracking control under various conditions, meets preset state constraints, and demonstrates excellent tracking accuracy and robustness.

Design and motion control of a tendon-driven continuum robot for aerospace applications

Continuum robots are flexible and compliant. Compared to the case in conventional articulated manipulators, the driving unit can be placed outside the workspace of the robot, so that the motion orientation has a relatively complete linear configuration flow, which can be applied to a special environment with narrow and multiple obstacles such as aerospace. This study presents the development process of a tendon-driven continuum robot (TCR) with a high length-diameter ratio. The skeleton structure which imitates a snake is composed of continuous joints in series. The driving device is operated by using a tendon-driven method, which reduces the complexity of the driving box and control system significantly. The diameter of the robot is designed to be 5 mm, which enables it to work in a narrow and slender space with certain flexibility. Subsequently, a kinematic model of the robot is established. The mode function backbone method is applied to realize TCR trajectory planning. An idea of segmented solving is adopted to achieve trajectory tracking control of the continuum robot. Finally, a prototype of the continuum robot is produced, and the rationality of the robot design and the effectiveness of the motion control method are verified through trajectory simulations and experiments. The robot can perform inspection tasks within a narrow gap of 20 mm with good environmental adaptability.

Trajectory Tracking Control of Unmanned Underwater Vehicle Based on Projected Perpendicular Guidance Method with Disturbance Observer

Unmanned underwater vehicles (UUVs) possess impressive maneuverability and versatility, but controlling them during trajectory tracking can be challenging due to their susceptibility to external disturbances and perturbations in their model parameters. Additionally, the UUV has four degrees of freedom underwater, but only three control inputs, making it a typical underactuated system. To address these issues, this paper introduces a novel optimize sliding mode control (OPSMC) algorithm grounded in projected perpendicular guidance (PPG). The PPG algorithm transforms the three-degree-of-freedom path trajectory control into two-degree-of-freedom heading tracking control and surge velocity tracking control by designing virtual posture angles. Optimized sliding mode control, based on sliding mode control, improves control precision and reduces control input chattering by constructing optimization functions for control inputs. During trajectory tracking, UUVs are susceptible to external environmental disturbances and perturbations in system model parameters. Disturbance observers are employed to estimate these disturbances and perturbations. Finally, MATLAB/Simulink is used for numerical simulation experiments. The simulation results demonstrate that the PPG algorithm effectively enables underactuated UUVs to achieve trajectory tracking control. The designed optimized sliding mode controller and disturbance observer enhance the control precision and robustness of the system.

Accelerated Gradient Approach For Deep Neural Network-Based Adaptive Control of Unknown Nonlinear Systems.

Recent connections in the adaptive control literature to continuous-time analogs of Nesterov's accelerated gradient method have led to the development of new real-time adaptation laws based on accelerated gradient methods. However, previous results assume that the system's uncertainties are linear-in-the-parameters (LIP). To compensate for non-LIP uncertainties, our preliminary results developed a neural network (NN)-based accelerated gradient adaptive controller to achieve trajectory tracking for nonlinear systems; however, the development and analysis only considered single-hidden-layer NNs. In this article, a generalized deep NN (DNN) architecture with an arbitrary number of hidden layers is considered, and a new DNN-based accelerated gradient adaptation scheme is developed to generate estimates of all the DNN weights in real-time. A nonsmooth Lyapunov-based analysis is used to guarantee the developed accelerated gradient-based DNN adaptation design achieves global asymptotic tracking error convergence for general nonlinear control affine systems subject to unknown (non-LIP) drift dynamics and exogenous disturbances. A comprehensive set of simulation studies are conducted on a two-state nonlinear system, a robotic manipulator, and a complex 20-D nonlinear system to demonstrate the improved performance of the developed method. Our simulation studies demonstrate enhanced tracking and function approximation performance from both DNN architectures and accelerated gradient adaptation.

Simplified Strategy for Trajectory Tracking Application of a Passive Suspension Rover-Type Mobile Robot

In the present work, based on an approximate modelling of a rover-type robot and a proportional control law, a simplified trajectory tracking strategy for a passive suspension rover-type mobile robot was developed. This strategy achieves trajectory tracking and the autonomous displacement of a rover, of which its configuration involves complex kinematics and dynamics. All these lineaments reduce the complexity of the analysis, the number of electronic components to implement, the computational requirements and the energy consumption. The robotic system used is based on the Shrimp rover, which is a robot with a passive suspension that is capable of carrying out displacements over rough terrain. The tests were performed using numerical simulations with different desired trajectories, and also using experimental tests using a passive suspension rover-type mobile robot.

Adaptive composite learning control of a flexible two‐link manipulator with unknown spatiotemporally varying disturbance

AbstractThis article presents a novel adaptive composite learning (ACL) control strategy combining reinforcement learning and a disturbance observer (DOB) to address vibration issues in a flexible two‐link manipulator (FTLM) system affected by unknown spatiotemporally varying disturbances. Based on the assumed mode method, the FTLM system is initially transformed into an ordinary differential equation model, while effectively capturing the elastic deformation and vibration characteristics of the flexible link. A composite learning controller, based on the actor‐critic algorithm and DOB, is then developed to achieve trajectory tracking and vibration suppression in the FTLM system. The DOB in the controller compensates for unknown disturbances resulting in reduced system error. It is noting that the proposed optimal control strategy is continuously gathering system experience and evaluating the current policy's effectiveness. The stability and robustness of the closed‐loop system incorporating the composite controller are analyzed using Lyapunov's direct method, and the semi‐global uniform ultimate boundedness of the tracking and vibration errors are also demonstrated. To validate the effectiveness and superiority of the proposed ACL controller, comparative simulations and experiments are conducted on the Quanser experimental platform.

Trajectory tracking of binocular vision system for picking robot based on fast non-singular terminal sliding mode control

This paper proposes a non-singular fast terminal sliding mode control method for a binocular active vision platform of a picking robot with unknown dynamics. The method uses radial basis function (RBF) neural networks to achieve trajectory tracking accuracy and enhance robustness against external interference. A non-singular fast terminal sliding mode controller is designed for the system’s convergence within a limited time. An adaptive neural network approximates the unknown nonlinear function of the dynamic model. Stability and finite-time convergence of the closed-loop system are established using Lyapunov theory. Experimental verification on the binocular vision platform demonstrates position and speed errors converging to the desired trajectory within 2 and 1 second, respectively. Moreover, when subjected to external interference, the position and velocity errors converge within 0.1 seconds. Simulation experiments confirm the method’s effectiveness in improving convergence speed, trajectory tracking accuracy, and robustness against external interference, while reducing system chattering.

Adaptive Neural Network Tracking Control of Robotic Manipulators Based on Disturbance Observer

This article presents an adaptive neural network (ANN) control scheme based on a disturbance observer that can achieve trajectory tracking control of robotic manipulators under external disturbances and dynamic model uncertainties. Firstly, an ANN controller based on full-state feedback is derived using the backstepping technique to achieve an online approximation of uncertainty. The integral sliding mode surface with a position error is introduced into the controller, which reduces the steady-state error of the system and enhances robustness. Then, a novel disturbance observer is designed to estimate both the approximation errors of the ANN and external disturbances, and to provide compensation for the controller, effectively suppressing the trajectory tracking errors caused by approximation errors and disturbances. Subsequently, the Lyapunov stability theory is utilized to demonstrate the stability of the developed control strategy and the boundedness of all closed-loop signals. Finally, numerical simulations are used to confirm the efficacy of the proposed control method.

Active disturbance rejection control of flexible industrial manipulator: A MIMO benchmark problem

Robotic manipulators are widely used in modern industry. In order for robot manipulators to achieve trajectory tracking control, the end-effectors must move precisely along the given trajectories. The nonlinearity, strong coupling, and uncertainty of the system make trajectory tracking very complicated and difficult. An approach for robust feedback control is presented in this paper as a solution to this problem. The design relies on active disturbance rejection control to estimate unknown disturbances affecting the plant. The controlled system is an uncertain two-link manipulator with elastic gear transmissions, described by nonlinear friction and elasticity. It is based on an industrial benchmark problem. The model has two significant uncertainties: parametric uncertainty as well as external disturbances that affect tools and motors. A simulation-based evaluation of the proposed control method and a comparison of its performance, considering specific robustness requirements and trajectory tracking, are presented. The comparison includes the baseline controller, the QFD (Quality Function Deployment) method, and PD-CNN (PD Control Compensation based on the Cascade Neural Network). Computer simulations of the proposed controller are carried out to validate the ABB (Asea Brown Boveri) industrial benchmark. The simulation results demonstrate superiority in meeting stability and target value requirements. The stability and ultimate boundedness of the tracking error of ADRC (Active Disturbance Rejection Control) are demonstrated.

Model-free low-power observer based robust trajectory tracking control of UAV quadrotor with unknown disturbances

PurposeThe purpose of this paper is to design an output-feedback algorithm based on low-power observer (LPO), robust chattering-free controller and nonlinear disturbance observer (DO) to achieve trajectory tracking of quadrotor in the Cartesian plane.Design/methodology/approachTo achieve trajectory tracking control, firstly the decoupled rotational and translational model of quadrotor are modified by introducing backstepped state-space variables. In the second step, robust integral sliding mode control is designed based on the proportional-integral-derivative (PID) technique. In the third step, a DO is constructed. In next step, the measurable outputs, i.e. rotational and translational state variables, are used to design the LPO. Finally, in the control algorithm all state variables and its rates are replaced with its estimates obtained using the state-observer.FindingsThe finding includes output-feedback control (OFC) algorithm designed by using a LPO. A modified backstepping model for rotational and rotational systems is developed prior to the design of integral sliding mode control based on PID technique. Unlike traditional high-gain observers (HGO), this paper used the LPO for state estimation of quadrotor systems to solve the problem of peaking phenomenon in HGO. Furthermore, a nonlinear DO is designed such that it attenuates disturbance with unknown magnitude and frequency. Moreover, a chattering reduction criterion has been introduced to solve the inherited chattering issue of controllers based on sliding mode technique.Practical implicationsThis paper presents input and output data-driven model-free control algorithm. That is, only input and output of the quadrotor model are required to achieve the trajectory tracking control. Therefore, for practical implementation, the number of on-board sensor is reduced.Originality/valueAlthough extensive research has been done for designing OFC algorithms for quadrotor, LPO has never been implemented for the rotational and translational state estimations of quadrotor. Furthermore, the mathematical model of rotational and translational systems is modified by using backstepped variables followed by the controller designed using PID and integral sliding mode control technique. Moreover, a DO is developed for attenuation of disturbance with unknown bound, magnitude and frequency.

Adaptive predictor-based control for a helicopter system with input delays: Design and experiments

In this paper, we consider a 2-degrees-of-freedom (DOF) helicopter system subject to long input delays and uncertain system parameters. To address the challenges including unknown system parameters and input delays in control design, we develop an adaptive predictor-feedback control law to achieve trajectory tracking. Stability of the closed-loop system is further established, where the tracking errors are shown to converge towards zero. Through simulation and experiments on the helicopter system, we illustrate that tracking of a desired trajectory is achieved with the proposed control scheme.