Three-dimensional Trajectory Tracking Research Articles

Design and Real-Time Implementation of a Cascaded Model Predictive Control Architecture for Unmanned Aerial Vehicles

Modeling and control are challenging in unmanned aerial vehicles, especially in quadrotors where there exists high coupling between the position and the orientation dynamics. In simulations, conventional control strategies such as the use of a proportional–integral–derivative (PID) controller under different configurations are typically employed due to their simplicity and ease of design. However, linear assumptions have to be made, which turns into poor performance for practical applications on unmanned aerial vehicles (UAVs). This paper designs and implements a hierarchical cascaded model predictive control (MPC) for three-dimensional trajectory tracking using a quadrotor platform. The overall system consists of two stages: the mission server and the commander stabilizer. Different from existing works, the heavy computational burden is managed by decomposing the overall MPC strategy into two different schemes. The first scheme controls the translational displacements while the second scheme regulates the rotational movements of the quadrotor. For validation, the performance of the proposed controller is compared against that of a proportional–integral–velocity (PIV) controller taken from the literature. Here, real-world experiments for tracking helicoidal and lemniscate trajectories are implemented, while for regulation, an extreme wind disturbance is applied. The experimental results show that the proposed controller outperforms the PIV controller, presenting less signal effort fluctuations, especially in terms of rejecting external wind disturbances.

Three-Dimensional Path Tracking of Over-Actuated AUVs Based on MPC and Variable Universe S-Plane Algorithms

Autonomous Underwater Vehicles (AUVs) are widely used for the inspection of seabed pipelines. To address the issues of low trajectory tracking accuracy in AUV inspection processes due to uncertain ocean current disturbances, this paper designs a new dual-loop controller based on Model Predictive Control (MPC) and Variable Universe S-plane algorithms (S-VUD FLC, where VUD represents Variable Universe Discourse and FLC represents Fuzzy Logic Control) to achieve three-dimensional (3-D) trajectory tracking of an over-actuated AUV under uncertain ocean current disturbances. This paper uses MPC as the outer-loop position controller and S-VUD FLC as the inner-loop speed controller. The outer-loop controller generates desired speed instructions that are passed to the inner-loop speed controller, while the inner-loop speed controller generates control input and uses a direct logic thrust distribution method that approaches optimal energy consumption to distribute the thrust generated by the propellers to the over-actuated AUV, achieving closed-loop tracking of the entire trajectory. When designing the outer-loop MPC controller, the actual control input constraints of the system are considered, and control increments are introduced to reduce control model errors and the impact of uncertain external disturbances on the actual AUV model parameters. When designing the inner-loop S-VUD FLC, the strong robustness of the variable universe fuzzy controller and the easy construction characteristics of the S-plane algorithm are combined, and integral action is introduced to improve the system’s tracking accuracy. The stability of the outer loop controller is proven by the Lyapunov method, and the stability of the inner loop controller is verified by simulation. Finally, simulations show that the over-actuated AUV has fast tracking processes and high tracking result accuracy under uncertain ocean current disturbances, demonstrating the effectiveness of the designed dual-loop controller.

Robust adaptive three-dimensional trajectory tracking control for unmanned underwater vehicles with disturbances and uncertain dynamics

Aiming at the three-dimensional (3-D) trajectory tracking problem of UUV with uncertain dynamics in an unknown and bounded external disturbance environment, a new dual closed-loop controller based on nonlinear model predictive control (NMPC) and adaptive integral sliding mode control (AISMC) is designed. The outer-loop NMPC controller designed based on position and attitude tracking errors generates a virtual desired velocity command and transmits it to the inner-loop controller. The inner-loop adaptive integral sliding mode controller based on speed tracking error design combines adaptive radial basis (RBF) neural network controller and disturbance observer to approximate the uncertainty of system model parameters and environmental disturbances, and then generates the actual control input to the UUV system. Different from other cascaded control systems, the designed controller combines the advantages of display processing constraints of MPC and robustness of SMC, which can improve the robustness of the control system, it effectively considers the actual constraints of the system input and state, and avoids the saturation of the actuator. In addition, the stability of the closed-loop system with and without disturbances is proved respectively based on the Lyapunov method. Finally, simulation results verify the effectiveness of the proposed controller: Under the perturbation of 10% model parameters, the UUV can accurately track the desired trajectory.

Three-dimensional trajectory tracking guidance against near-space maneuvering targets with multiple constraints under wind field

This paper presents a three-dimensional disturbance observer-based adaptive tracking guidance scheme for the trajectory tracking problem of a missile intercepting a hypersonic vehicle with the wind field, autopilot lag dynamics, and input saturation. Unlike most of the existing missile trajectory tracking guidance systems without velocity controllability and external wind field model, the wind field model is added to the dynamic model, and the velocity control channel is introduced into the three-dimensional trajectory tracking guidance problem to prevent impractical scenarios and increase tracking precision. The proposed tracking guidance methodology incorporates the sliding mode and adaptive control techniques, in which the sliding mode motion is finite time stable independently of the tracking guidance system's initial conditions. Also, the super twisting switch control law is added to cope with the chattering problem. In this context, external uncertainty disturbances and unmeasured states are lumped into lump disturbance and estimated using the backpropagation neural network extended state observer. To this end, numerical simulations demonstrate the tracking to reach zero between 3 s and 5 s against various uncertainties in engineering practical, and position tracking errors are within 0.15 m, superior to the existing tracking guidance methods.

Optimal guidance law design for three-dimensional trajectory tracking of missiles based on fixed-gain disturbance observer

To address the trajectory tracking problem of missiles, an optimal disturbance rejection guidance law (ODRGL) in three dimensions is proposed under the premise of uncontrollable speed. Error models of the actual and the reference trajectory are built in channels of pitch and yaw, respectively. In the yaw channel, a modeling error is introduced as the model cannot be built directly. According to the separation theorem, the controller and the observer are designed respectively. A fixed-gain disturbance observer (FGDO) is proposed to estimate the disturbance such as wind disturbances and modeling errors, and the disturbance is compensated for feed-forward. The nominal error models of pitch and yaw channels are linearized by the differential geometric linearization theory, and then linear quadratic regulator (LQR) controllers are designed for the linearized models. The simulation results show that in the presence of wind disturbances and modeling errors, the optimal guidance law proposed in this paper can stabilize the original nonlinear system and ensure energy optimization.

A framework for simulating snow accumulation and ice accretion on high-speed trains

A simulation framework for three-dimensional particle trajectory tracking, snow accumulation and ice accretion modelling on solid bodies in high-speed air flow is presented. The framework, named HADICE, solves the aerodynamic flow field as Reynolds averaged Navier-Stokes (RANS), with optional hybrid RANS/LES capabilities for modelling complex turbulent flows. Particle trajectory tracking is performed in an Eulerian-Lagrangian approach and wall collision is modelled using a hard collision model with reflect condition and a momentum based trap condition. A novel accurate and robust iterative evaluation method for the local collection efficiency is proposed for arbitrary 3D geometry and flow. Ice accretion is modelled in a multi-step approach and iced geometry is updated through mesh deformation using a radial basis function (RBF) interpolation method. Snow accumulation and ice accretion predictions based on the framework are validated against climatic wind tunnel experimental measurements. A full 3D simulation is demonstrated for snow accumulation and ice accretion on a 1:8 scaled high-speed train model. Using the presented framework, snow accumulation and icing simulation for high-speed trains can be conducted in an accurate and efficient manner, which is of great importance for physical investigations and the design of anti-snow and ice protection systems.

Sideslip angle estimation based active disturbance rejection 3D trajectory tracking control for powered parafoil system and hardware-in-the-loop simulation verification

The powered parafoil system is a cutting-edge flight vehicle that features a thrust mechanism with a propeller and an airdrop parafoil, providing outstanding benefits like extended flight endurance and elevated load-bearing capacity. However, the powered parafoil is a highly intricate and nonlinear system that relies on two actuators, steering gear, and thrust. Due to its underactuated and coupled characteristics, it presents significant challenges for three-dimensional (3D) trajectory tracking control. To address these issues, including the lack of convergence in lateral tracking error with existing trajectory tracking methods, this paper proposes a novel guidance system that provides both the guided yaw angle and forward velocity, where a reduced-order extended state observer (ESO) is utilized to estimate the sideslip angle. The input-to-state stable (ISS) theory proves the convergence of the guidance system. Furthermore, two linear active disturbance rejection controllers (LADRCs) are employed to decouple the horizontal and vertical control systems and facilitate tracking the horizontal trajectory and altitude. The proposed method is demonstrated through hardware-in-the-loop (HIL) trajectory tracking simulations on 3D straight lines and circular trajectories. Additionally, Monte Carlo simulations validate the robustness of the proposed control system.

Robust adaptive three-dimensional trajectory tracking control scheme design for small fixed-wing UAVs

This paper aims to tackle the three-dimensional trajectory tracking problems of small fixed-wing unmanned aerial vehicles subject to nonlinearities, uncertainties and wind disturbances via adaptive techniques. The control objective is to efficiently control the thrust and the deflections of control surfaces to ensure the unmanned aerial vehicle arrives at a specified location within a given time frame. However, achieving this goal for small fixed-wing unmanned aerial vehicles can be challenging because the precise dynamic model and several parameters are not accessible, making most existing control strategies unworkable. Motivated by these facts, based on feedback linearization techniques, we derive linear models with equivalent disturbances to describe the translational dynamics without requiring precise aerodynamic force model information. To deal with the dilemmas where the norm bounds of equivalent disturbances depend on control inputs, system states, and unknown disturbances, a novel robust adaptive control strategy is designed for position control. Based on the assumption of two-time separation, the control scheme incorporates two parts, namely, a position controller containing the horizontal-plane and altitude parts and a robust filter-based attitude regulator. Also, to prevent chattering issues, we design a practical and robust adaptive position controller under which the tracking error is ultimately bounded The overall closed-loop stability is theoretically investigated based on the Lyapunov arguments. Hardware-in-loop simulation experiments are performed to testify our developed control scheme.

Three-Dimensional Prescribed Performance Tracking Control of UUV via PMPC and RBFNN-FTTSMC

To address the search-and-docking problem in multi-stage prescribed performance switching (MPPS) scenarios, this paper presents a novel compound control method for three-dimensional (3D) underwater trajectory tracking control of unmanned underwater vehicles (UUVs) subjected to unknown disturbances. The proposed control framework can be divided into two parts: kinematics control and dynamics control. In the kinematics control loop, a novel parallel model predictive control (PMPC) law is proposed, which is composed of a soft-constrained model predictive controller (SMPC) and hard-constrained model predictive controller (HMPC), and utilizes a weight allocator to enable switching between soft and hard constraints based on task goals, thus achieving global optimal control in MPPS scenarios. In the dynamics control loop, a finite-time terminal sliding mode control (FTTSMC) method combining a finite-time radial basis function neural network adaptive disturbance observer (RBFNN-FTTSMC) is proposed to achieve disturbance estimation and fast convergence of velocity tracking errors. The simulation results demonstrate that the proposed PMPC-FTTSMC approach achieved an average improvement of 33% and 80% in the number of iterations compared with MPC with sliding mode control (MPC-SMC) and traditional MPC methods, respectively. Furthermore, the approach improved the speed of response by 35% and 44%, respectively, while accurately achieving disturbance observation and enhancing the system robustness.

Event-trigger NMPC for 3-D trajectory tracking of UUV with external disturbances

In this paper, a novel Three-Dimensional (3-D) trajectory tracking method based on Event-triggered Nonlinear Model Predictive Control (ENMPC) is designed for an Underwater Unmanned Vehicle (UUV) with external disturbances. Firstly, the 5-Degrees of Freedom (5-DoF) model of UUV is represented by both kinematics and dynamics. After that, a Nonlinear Model Predictive Control (NMPC) algorithm is designed for the 3-D trajectory tracking of UUV, and the feasibility of the control method and the stability of the closed-loop system are proved, which are further verified by simulation experiments. Then, an event-triggered mechanism is introduced on the basis of NMPC algorithm, which reduces the amount of calculation iterations without affecting the 3-D trajectory tracking performance. Finally, the simulation results verify the feasibility and effectiveness of the proposed algorithm. Compared with the Traditional Model Predictive Control (TMPC) and NMPC algorithm, the ENMPC strategy can effectively reduce the amount of calculation iterations and improve the tracking efficiency.

Three-Dimensional Trajectory Tracking of AUV Based on Nonsingular Terminal Sliding Mode and Active Disturbance Rejection Decoupling Control

This paper presents a nonsingular terminal sliding mode and active disturbance rejection decoupling control (NTSM-ADRDC) scheme for the three-dimensional (3D) trajectory tracking of autonomous underwater vehicles (AUV). Firstly, the AUV model is decoupled into five independent single input–single output (SISO) channels using ADRDC technology. Secondly, the NTSM-ADRDC controller is designed. The linear extended state observer (LESO) is used to observe the AUV state variables, and estimate the total disturbance of the system. In addition, to improve the system error convergence rate, the combination of exponential reaching rate and NTSM constitutes a nonlinear states error feedback control law for the controller. Finally, the stability of the proposed control law is proved using the Lyapunov theory. The simulation results demonstrate the effectiveness and robustness of the designed NTSM-ADRDC trajectory tracking approach.

Adaptive fixed-time backstepping control for three-dimensional trajectory tracking of underactuated autonomous underwater vehicles

An adaptive fixed-time backstepping control is proposed to achieve the three-dimensional trajectory tracking control of an underactuated autonomous underwater vehicle (AUV) in the presence of model uncertainty and external disturbances. In this paper, the dynamics of the AUV in terms of five degrees of freedom (DOFs) are discussed. Considering it is an underactuated AUV, a virtual velocity guidance law is derived using the backstepping method. For velocity convergence, an adaptive fixed-time control is derived without model parameters, with adaptive adjusting law tackling system unknows. Theoretical analyses demonstrate that the tracking error converges to a small bounded field within a fixed time in the proposed control scheme. The effectiveness and superiority of the proposed method are verified by simulation results.

Self-Scheduled LPV Control of Asymmetric Variable-Span Morphing UAV

In this study, a novel framework for the flight control of a morphing unmanned aerial vehicle (UAV) based on linear parameter-varying (LPV) methods is proposed. A high-fidelity nonlinear model and LPV model of an asymmetric variable-span morphing UAV were obtained using the NASA generic transport model. The left and right wing span variation ratios were decomposed into symmetric and asymmetric morphing parameters, which were then used as the scheduling parameter and the control input, respectively. LPV-based control augmentation systems were designed to track the normal acceleration, angle of sideslip, and roll rate commands. The span morphing strategy was investigated considering the effects of morphing on various factors to aid the intended maneuver. Autopilots were designed using LPV methods to track commands for airspeed, altitude, angle of sideslip, and roll angle. A nonlinear guidance law was coupled with the autopilots for three-dimensional trajectory tracking. A numerical simulation was performed to demonstrate the effectiveness of the proposed scheme.

Adaptive optimal 3D nonlinear compound line-of-sight trajectory tracking control for over-actuated AUVs in attitude space

This paper is concentrated on three-dimensional (3D) trajectory tracking control for over-actuated autonomous underwater vehicles (AUVs) in attitude space. In order to design the guidance, navigation, and control system for this problem, a nonlinear compound line-of-sight (NCLOS) guidance law is introduced to stabilize the position errors. Considering the nonlinear relationship between hydrodynamic angle and orientation angle, the kinematic controller is designed based on the NCLOS guidance law to converge the attitude errors, especially in roll degree of freedom. Due to the perturbation of parameters and uncertain interferences, a dynamic controller is proposed based on fast terminal sliding mode control and adaptive anti-interference law to ensure the finite-time stability for the filtering errors of virtual velocity by backstepping technology. Also, the global stability of the whole system is verified. After that, a damped BFGS sequential quadratic programming algorithm is introduced to solve the multi-objectives and multi-constraints optimization problem for the rudder control allocation in attitude space. Finally, the numerical simulations are conducted with validity and adaptability performances in 3D trajectory tracking control for over-actuated AUVs.

Research on dynamic landing guidance algorithm for the maritime quadrotor

The dynamic landing guidance of the marine quadrotor is composed of trajectory guidance and landing guidance, which can't be completed by the traditional land-based landing guidance method. In addition, complex sea environment will increase the difficulty in dynamic landing guidance such as enhancing the position deviation, which will make the quadrotor unable to land accurately. To address the large trajectory tracking error when the quadrotor is flying, an adaptive step-based line-of-sight (LOS) guidance algorithm is adopted in this work to achieve dynamic three-dimensional (3D) trajectory tracking. The algorithm can not only track the trajectory of the quadrotor in a 3D space based on the position information of the wave glider, but also dynamically adjust the tracking angle and orientation in real time based on the distance and orientation information to improve the tracking accuracy. To address the low accuracy in dynamic positioning of the quadrotor while landing on the wave glider floating body, a visual landing guidance method with fused electromagnetic compensation is used. It can improve accuracy in the dynamic landing guidance of the April Tag visual reference system and reduce the interference from shaking of the wave glider floating body on landing positioning guidance of the quadrotor. The simulation results verify that the proposed algorithm can effectively reduce the trajectory tracking error of the quadrotor and accelerate trajectory convergence. The sea trial experiments prove that the trajectory tracking and landing guidance algorithm adopted in this work can well guide the quadrotor in dynamic and accurate landing on the wave glider floating body, and shorten the time.

FPGA-based Control Design and Implementation of DELTA robots Using Horizontal-Axial Pneumatic Actuators

This study researched, analyzed, and applied a field-programmable gate array (FPGA) to develop a control system for the DELTA robot with three pneumatic actuation subsystems. To achieve positioning accuracy, a dual-feedback control framework is first applied to control the position of a rodless pneumatic actuator. The inner pressure difference between the actuator and cylinder was used as feedback signals. Then, the derived dynamic model is included in the control strategy to conduct decoupling and system linearization on the nonlinear parallel manipulator using inverse dynamic control. Additionally, to realize the operation of the integrated control system under the FPGA environment, a multilayered neural network framework is designed to learn the inverse dynamic control behaviors. The motion control experiments involving single- and three-axis translational parallel manipulators revealed that the established FPGA-based control system exhibits high precision over the reachable workspace regarding the DELTA robot's three-dimensional trajectory tracking control.

A double-loop control framework for AUV trajectory tracking under model parameters uncertainties and time-varying currents

Three-dimensional (3D) trajectory tracking of the underactuated autonomous underwater vehicle (AUV) is a challenging task due to the coupled nonlinear system dynamics, imprecise model parameters and time-varying currents. First, a double-loop framework incorporating the backstepping strategy is developed to decouple the tracking error for position into tracking error for controllable orientation. Second, three adaptive robust control (ARC) strategies are generated using desired compensation ARC, indirect ARC and direct/indirect ARC as controllers in the framework, respectively. Among these three strategies, two parameter adaptation laws are used to deal with the uncertainty of the model parameters, based on desired regressor and physical model, respectively. In addition, the three control strategies under this framework also show strong robustness to unknown time-varying ocean currents. Finally, the stability analysis and numerical simulation are presented. Under the numerical simulation of imprecise model parameters and unknown ocean currents, the transient and stable tracking performance of the three proposed control strategies is demonstrated.

A T-S Fuzzy Quaternion-Value Neural Network-Based Data-Driven Generalized Predictive Control Scheme for Mecanum Mobile Robot

Four-mecanum-wheeled omnidirectional mobile robots (FMOMR) are widely used in many practical scenarios because of their high mobility and flexibility. However, the performance of trajectory tracking would be degenerated largely due to various reasons. To deal with this issue, this paper proposes a data-driven algorithm by using the T-S fuzzy quaternion-value neural network (TSFQVNN). TSFQVNN is tailored to obtain the controlled autoregressive integral moving average (CARIMA) model, and then the generalized predictive controller (GPC) is designed based on the CARIMA model. In this way, the spatial relationship between the three-dimensional pose coordinates can be preserved and training times can be reduced. Furthermore, the convergence of the proposed algorithm is verified by the Stone–Weierstrass theorem, and the convergence conditions of the algorithm are discussed. Finally, the proposed control scheme is applied to the three-dimensional (3D) trajectory tracking problem on the arc surface, and the simulation results prove the necessity and feasibility of the algorithm.

Three-Dimensional Trajectory Tracking for a Heterogeneous XAUV via Finite-Time Robust Nonlinear Control and Optimal Rudder Allocation

This paper proposes a novel three-dimensional trajectory tracking control methodology for a heterogeneous X-rudder autonomous underwater vehicle (XAUV) that can achieve finite-time convergence, complex actuator dynamics handling, and energy-efficient optimized rudder allocation. Under a compound robust control scheme, the trajectory tracking problem is decomposed into three sub-problems: kinematics control, dynamics control, and rudder allocation. For kinematics control, a novel finite-time line-of-sight (FTLOS) guidance law is proposed, which can achieve faster position and orientation tracking when compared with classical LOS guidance, and is rarely studied in the existing finite time control methods. In the dynamics control loop, global finite-time terminal sliding mode control (FTTSMC) laws are provided to solve the heading control, pitching control, and surge velocity tracking control problems, where finite-time convergence is achieved in both the approaching stage and sliding mode holding stage. The multi-source uncertainties with unknown upper bounds in both kinematics and dynamics loops are well treated by finite-time extended disturbance observers (FTEDOs), thus ensuring the system robustness. Moreover, the influence of complex actuator dynamics is fully considered by employing a RBFNN compensator to deal with the propeller saturation and proposing an energy-efficient optimal rudder allocator to tackle the multi-objective and multi-constraint heterogeneous X-rudder angle assignment problem. Finally, simulation verifications are carried out for two different scenarios, where Case 1 focuses on the adaptability of the algorithm to different conditions and Case 2 focuses on the superiority of the algorithm over three other commonly used algorithms. The comparative simulation results show that the proposed controller has good adaptability to different initial and disturbance conditions, and performs better than three other classical controllers, especially in convergence speed, tracking accuracy, stability, and energy consumption.

Pulsed power to control growth of silicon nanoparticles in low temperature flowing plasmas

Low-temperature plasmas have seen increasing use for synthesizing high-quality, mono-disperse nanoparticles (NPs). Recent work has highlighted that an important process in NP growth in plasmas is particle trapping—small, negatively charged nanoparticles become trapped by the positive electrostatic potential in the plasma, even if only momentarily charged. In this article, results are discussed from a computational investigation into how pulsing the power applied to an inductively coupled plasma (ICP) reactor may be used for controlling the size of NPs synthesized in the plasma. The model system is an ICP at 1 Torr to grow silicon NPs from an Ar/SiH4 gas mixture. This system was simulated using a two-dimensional plasma hydrodynamics model coupled to a three-dimensional kinetic NP growth and trajectory tracking model. The effects of pulse frequency and pulse duty cycle are discussed. We identified separate regimes of pulsing where particles become trapped for one pulsed cycle, a few cycles, and many cycles—each having noticeable effects on particle size distributions. For the same average power, pulsing can produce a stronger trapping potential for particles when compared to continuous wave power, potentially increasing particle mono-dispersity. Pulsing may also offer a larger degree of control over particle size for the same average power. Experimental confirmation of predicted trends is discussed.