Trajectory Linearization Control Research Articles

Enhanced composite nonlinear extended state observer based on trajectory linearization control in presence of external and internal disturbance

Enhanced composite nonlinear extended state observer based on trajectory linearization control in presence of external and internal disturbance

Expandable Fully Actuated Aerial Vehicle Assembly: Geometric Control Adapted from an Existing Flight Controller and Real-World Prototype Implementation

An assembly composed of multiple aerial vehicles can realize omnidirectional motion with six degrees of freedom. Such an assembly has a heavier payload capacity and better fault tolerance compared with a single aircraft. Thus, such assemblies have the potential to become an ideal platform for manipulation. This paper investigates the controller design and prototype implementation for an expandable aerial vehicle assembly (AVA). The proposed AVA is composed of multiple sub-aircraft connected together via spherical joints at their center of mass. Each sub-aircraft can rotate around the spherical joint. The system dynamics of such an AVA can be separated into a slowly varying system and a fast varying system. The design criteria for a controller for this type of AVA was analyzed based on the similarity between the slowly varying system and a fully actuated rigid aircraft. This can reduce the design procedure for the controller and increase the expandability of the AVA. The stability criteria were carefully analyzed by considering the tracking error of each sub-aircraft. As an example, the controller of the AVA was designed using trajectory linearization control on the manifold, since the configuration space of the aircraft is a non-Euclidean space. A prototype composed of three quadrotors was implemented. The real-time expandable communication protocol among the different sub-aircraft was designed based on the CAN bus. Furthermore, the software and the hardware of the real-world prototype were developed. Both simulation and real-world tests were conducted, which validated the feasibility of the control design and the software implementation for an expandable assembly containing multiple aerial vehicles.

Spacecraft attitude control: Application of fine trajectory linearization control

One of the simplest and most popular methods to design a model-based controller for a nonlinear dynamic system is to apply linear control theories to the linearized model of the nonlinear system. For linearization, first-order Taylor series expansion is a straightforward and widely used method. Although the related linearization method is fairly simple, unfortunately, it causes an error in the linearized model, especially in highly nonlinear systems. Different strategies have been proposed to increase the robustness of linearization-based control methods against the linearization error. All of the methods somehow look at the linearization error as uncertainty or disturbance, which has to be rejected. Generally speaking, the lack of the linearization technique reduces the quality of control. One area in which quality and simplicity of control can be necessary is spacecraft attitude control. For the purpose of spacecraft attitude control, this paper improves a well-known trajectory linearization control (TLC) method as a simple and practical nonlinear trajectory tracking control method using an error-less, fine linearization technique. The modified TLC is then used to develop a control law for spacecraft attitude control with only three tunable control parameters and an approximation of the spacecraft inertia matrix. Finally, due to the elimination of uncertainty caused by the linearization error, in a simple way, the novel attitude controller leads to better performance in comparison with the traditional method. The superiority of the new approach is illustrated in numerical simulations.

Path Following Control Strategy for Underactuated Unmanned Surface Vehicle Subject to Multiple Constraints

AbstractThis paper is concerned with the path following control for an underactuated unmanned surface vehicle (USV) subject to modeling error and input saturation under time‐varying external disturbances. In this note, a novel trajectory linearization control (TLC) method is first introduced in the design of path following controller for an unmanned surface vessel. Adaptive line‐of‐sight (LOS) algorithm is used in the navigation strategy, which not only solves the sideslip angle problem caused by external disturbances but also optimizes the convergence speed. The neural network minimum learning parameter (MLP) method is used to compensate for modeling errors and external disturbances. Compared with multi‐layer neural networks, MLP solves the problem of ‘dimension disaster’. Meanwhile, in order to increase the robustness of the system, adaptive technology is employed to compensate for the compensation error of MLP. In addition, an auxiliary dynamic system is introduced into the controller design to address potential input saturation issue. Considering the above practical conditions, it is more convenient for the engineering implementation of the proposed control path following the control system. Using Lyapunov stability analysis theory, it is proven that all error signals in the system are uniformly ultimately bounded. Finally, two simulation experiments are presented to demonstrate the feasibility of the proposed control strategy. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Modeling and control of a hexacopter with a passive manipulator for aerial manipulation

In this paper, a multi-propeller aerial robot with a passive manipulator for aerial manipulation is presented. In order to deal with the collision, external disturbance, changing inertia, and underactuated characteristic during the aerial manipulation, an adaptive trajectory linearization control (ATLC) scheme is presented to stabilize the multi-propeller aerial robot during the whole process. The ATLC controller is developed based on trajectory linearization control (TLC) method and model reference adaptive control (MRAC) method. The stability of the proposed system is analyzed by common Lyapunov function. Numerical simulations are carried out to compare the ATLC with TLC controller facing collision, external disturbance and changing inertia during an aerial manipulation. Experimental results prove that the developed robot can achieve aerial manipulation in the outdoor environment.

Robust Path Following Control of Underactuated Unmanned Surface Vehicle With Disturbances and Input Saturation

This paper focuses on the accurate path following problem for an underactuated unmanned surface vehicle with uncertainties and environment disturbances. The proposed scheme can be divided into guidance loop and control loop: in the guidance loop, the proposed guidance law is utilized to calculate the desired yaw angle, as well as estimating unknown currents and sideslip angle simultaneously; in the control loop, a novel robust path following control law is developed by enhanced trajectory linearization control (TLC) technology, nonlinear tracking differentiator (NTD), sigmoid function based disturbance observer (SDO) and auxiliary dynamic system. The enhanced TLC is used as the main control framework to design the concise yaw rate and surge speed control laws, which makes the designed control law be simple and easy to implement in practice. SDO and auxiliary dynamic system are adopted to deal with unknown disturbances and input saturation, respectively. Meanwhile, NTD can provide an ideal differential and filtering effect. Theoretical analysis indicates that all the signals in the entire system are uniformly ultimately bounded. Finally, a comparative simulation substantiates the availability and superiority of the proposed scheme.

Trajectory linearization-based robust course keeping control of unmanned surface vehicle with disturbances and input saturation

This article addresses the problem of course keeping for unmanned surface vehicle (USV) subject to rudder servo characteristics, disturbances, uncertainties and rudder saturation. A double loop robust compound control strategy is developed by incorporating finite-time uncertainty observer (FUO) and auxiliary dynamic system into trajectory linearization control (TLC). TLC is an effective robust control technique with simple design structure, which is used in the course control experiment of USV for the first time. In each loop, the FUO and auxiliary system are designed to compensate unknown lumped disturbances and input saturation, respectively. A nonlinear tracking differentiator (NTD) is concurrently introduced to realize differentiation and filtering for the reference command. Strict stability analysis indicates that the entire system is uniformly ultimately bounded (UUB). Results from simulations and experiments are presented to validate the developed strategy.

Acceleration tracking control for a spinning glide guided projectile with multiple disturbances

A novel acceleration tracking controller is proposed in this paper, for a Spinning Glide Guided Projectile (SGGP) subject to cross-coupling dynamics, external disturbances, and parametric uncertainties. The cross-coupled dynamics for the SGGP are formulated with mismatched and matched uncertainties, and then divided into acceleration and angular rate subsystems via the hierarchical principle. By exploiting the structural property of the SGGP, model-assisted Extended State Observers (ESOs) are designed to estimate online the lumped disturbances in the acceleration and angular rate dynamics. To achieve a rapid response and a strong robustness, integral sliding mode control laws and sigmoid-function-based tracking differentiators are integrated into the ESO-based Trajectory Linearization Control (TLC) framework. It is proven that the acceleration tracking controller can guarantee the ultimate boundedness of the signals in the closed-loop system and make the tracking errors arbitrarily small. The superiority and effectiveness of the proposed control scheme in its decoupling ability, accurate acceleration tracking performance and anti-disturbance capability are validated through comparisons and extensive simulations.

Variable Bandwidth Adaptive Course Keeping Control Strategy for Unmanned Surface Vehicle

This paper proposes a new and original course keeping control strategy for an unmanned surface vehicle in the presence of modeling error, external disturbance and input saturation. The trajectory linearization control method is used as the basic algorithm to design the course keeping strategy, and the radial basis function neural network and disturbance observer are used to compensate modeling error and external disturbance respectively to enhance the robustness of the control system. Moreover, a robust term is used to compensate various compensation errors to further improve the robustness of the system. In addition, hyperbolic tangent function and Nussbaum function are hired to deal with the potential input saturation problem, and the neural shunting model is adopted to avoid the computational explosion caused by the derivation of virtual control law. Taking the above facts into account will help to further realize engineering practice. Finally, the control strategy proposed in this paper is compared with the classical proportional–integral–derivative control strategy. The simulation results show that the course control results of the proposed control strategy are more robust than proportional–integral–derivative control, regardless of whether the external disturbance is weak or strong.

Predictor LOS-based trajectory linearization control for path following of underactuated unmanned surface vehicle with input saturation

This paper investigates a novel robust path following control scheme for unmanned surface vehicle (USV) with unknown dynamics, currents and actuator saturation. In the guidance loop, an improved predictor line-of-sight (PLOS) guidance law is presented, which is used in any parametric paths. In the control loop, we propose a yaw rate controller and a surge speed controller using trajectory linearization control (TLC) technology, finite-time nonlinear tracking differentiator (FTNTD), minimal learning parameter (MLP) technique and auxiliary system. The advantages of the developed scheme are that, first, the proposed PLOS provides the estimates of unknown sideslip angle and currents; second, the introduced TLC has a concise structure and strong robustness, and enhanced TLC only needs two parameters to be adjusted. A MLP technique is constructed to approximate lumped unknown dynamics, where the norm of all the weights is estimated instead of estimating each element to reduce computational burden. A FTNTD is concurrently used to achieve satisfactory differential and filter performance. Subsequently, a smooth auxiliary system is applied to handle input saturation constraint on actuator. Theoretical analysis illuminates that the system is semi-globally uniformly ultimately bounded (SGUBB). The effectiveness of the developed scheme is verified by simulation comparison and the error quantification performance.

A Time-Varying Lookahead Distance of ILOS Path Following for Unmanned Surface Vehicle

This paper is concerned with the path following control for an unmanned surface vessel subject to unknown dynamics and external disturbance. Firstly, an integral Line-of-Sight navigation strategy based on a fuzzy strategy to optimize lookahead distance to achieve faster convergence speed is proposed. Then a novel adaptive course control law based on trajectory linearization control technology is proposed, which is combined with the integral Line-of-Sight navigation strategy to form a complete unmanned surface vessel path following strategy. From the author's point of view, this is the first time that trajectory linearization control technology has been applied to the path following scheme by controlling the course. At the same time, in order to improve the robustness of the path following system, the unknown dynamics, external disturbance, and error in the system are compensated by neural network minimum learning parameter method with less computational complexity and a robust term, respectively. Furthermore, hyperbolic tangent function, Nussbaum function, and neural shunting model are introduced into the design of control law to solve the potential input saturation problem. Finally, the numerical simulation experiments of straight line and curve path following are given to prove the feasibility and universality of the whole set of path following scheme.

Trajectory Linearization-Based Adaptive PLOS Path Following Control for Unmanned Surface Vehicle with Unknown Dynamics and Rudder Saturation

This paper presents a novel robust control strategy for path following of an unmanned surface vehicle (USV) suffering from unknown dynamics and rudder saturation. The trajectory linearization control (TLC) method augmented by the neural network, linear extended state observer (LESO), and auxiliary system is used as the main control framework. The salient features of the presented strategy are as follows: in the guidance loop, a fuzzy predictor line-of-sight (FPLOS) guidance law is proposed to ensure that the USV effectively follows the given path, where the fuzzy method is introduced to adjust lookahead distance online, and thereby achieving convergence performance; in the control loop, we develop a practical robust path following controller based on enhanced TLC, in which the neural network and LESO are adopted to handle unmodeled dynamics and external disturbances, respectively. Meanwhile, a nonlinear tracking differentiator (NTD) is constructed to achieve satisfactory differential and filter performance. Then, the auxiliary system is incorporated into the controller design to handle rudder saturation. Using Lyapunov stability theory, the entire system is ensured to be uniformly ultimately bounded (UUB). Simulation comparisons illustrate the effectiveness and superiority of the proposed strategy.

Path Following of Underactuated Unmanned Surface Vehicle Based on Trajectory Linearization Control with Input Saturation and External Disturbances

This paper investigates the path following control problem for underactuated unmanned surface vehicle (USV) in the presence of unmodeled dynamics, external disturbances and input saturation. A novel adaptive robust path following control scheme is proposed by employing trajectory linearization control (TLC) technology and finite-time disturbance observer, which is composed of a concise yaw rate controller and a surge speed controller. The salient features of the proposed scheme include: a path following guidance law is designed to ensure USV effectively converging to and following the desired path; TLC is introduced into the field of USV motion control as new effective technique, and it is the first time used to design path following controller for underactuated USV; a finite-time nonlinear tracking differentiator is constructed not only to avoid the signal jump caused by derivation, but also to filter noise and high frequency interference. A finite-time disturbance observer (FDO) is devised to exactly observe the uncertain dynamics and unknown external disturbances, which improves the tracking accuracy and precise disturbance rejection of the proposed controller; then, an auxiliary dynamic system that is governed by smooth switching function is developed to compensate for the saturation constraint on actuator. Stability analysis verifies that all signals in the closed-loop system are uniformly ultimately bounded. Finally, simulation results and comparisons illustrate the superiority of the proposed control scheme.

Control Design for the Autonomous Horizontal Takeoff Phase of the Reusable Launch Vehicles

The control system design for the reusable launch vehicles (RLVs), especially in the autonomous horizontal takeoff phase, is a highly challenging task. Significant issues arise due to the high nonlinearity, large uncertainties of aerodynamic coefficients as well as strong coupling among axes of the airframe. This paper studies autonomous takeoff control problem of the RLVs by the means of trajectory linearization control (TLC) and model predictive control (MPC) theory. The six degree of freedom dynamic model is firstly established, and the flight strategy of takeoff and climb stage is provided through the characteristic analysis of RLVs. Furthermore, the guidance law for the climbing phase is proposed via the TLC method against the high nonlinearity, and a speed based gain-schedule strategy is given under the consideration of both aerodynamic force and friction force. In order to eliminate the ground effect interference, an improved model predictive control approach is presented by introducing the online parameter estimation of the ground effect interaction coefficient, and a coupled model predictive controller is designed by introducing the feedback of sideslip angle into the roll control channel to eliminate the coupling effect. Finally, the performance of the design method for autonomous takeoff control of RLVs is demonstrated through the comparison simulation analysis.

EXPERIMENTAL VERIFICATION STUDY ON TRAJECTORY TRACKING OF A NOVEL REHABILITATION EXOSKELETON SHOULDER JOINT

The trajectory linearization control (TLC) was applied to design an autonomous nonlinear trajectory tracking controller for a novel rehabilitation exoskeleton shoulder joint in this paper. TLC is a relatively new control method which was applied in aircraft and mobile robot, which had good performance on real-time trajectory tracking, anti-jamming and universality. As a new application in the exoskeleton shoulder joint controller design, the controller in this research contained two loops that separately based on the inverse kinematics and pseudo-inverse dynamics models of the exoskeleton shoulder. Two PI controllers as the error regulator can reduce the tracking error. The position and angular velocity error feedback were employed to constitute the closed-loops. Since the controller was based on model and linearization, it can adapt to both linear and nonlinear control processes. The simulation of three different trajectories for single degree of freedom movement of shoulder joint (shoulder flexion and extension, abduction and extension), and the movement of both the two degrees were given. The simulation results showed that the TLC controller can follow the exoskeleton shoulder trajectory steadily and accurately.

Robust path‐following control based on trajectory linearization control for unmanned surface vehicle with uncertainty of model and actuator saturation

AbstractThis article develops a novel path‐following control strategy for underactuated unmanned surface vehicle (USV) subject to unmodeled dynamics and unknown multiple disturbance. A practical robust path‐following controller is proposed using trajectory linearization control (TLC) technology, neural network, and auxiliary design system. First, the greatest advantage of this article is that the TLC technology is first introduced into the field of USV motion control, which provides a new direction for TLC technology research. Second, the underactuated model based on a transformation of the USV kinematics to Serret‐Frenet frame is simplified by introducing a nonlinear coordinate transformation. Meanwhile, to improve the robustness and reduce the computational complexity, radial basis function neural network is replaced by neural network with minimum learning parameter method to compensate for unmodeled dynamics and unknown multiple disturbance. In addition, an auxiliary dynamic system is used to reduce the risk of actuator saturation. The stability of the whole system was proved based on the Lyapunov criteria. Finally, the comparison results demonstrate the superior performance of the proposed approach. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Adaptive Course Control-Based Trajectory Linearization Control for Uncertain Unmanned Surface Vehicle Under Rudder Saturation

In the presence of the uncertain system dynamics, unknown time-varying disturbances and rudder saturation, this paper develops a novel robust adaptive course control scheme for unmanned surface vehicle (USV). Considering the characteristics of the rudder servo system, a double loop course controller of the practical and concise is proposed by the enhanced trajectory linearization control (TLC) technology. The key features of the developed controller are that, first, the neural networks are employed to online approximate unmodeled dynamics, and adaptive techniques are adopted to deal with completely unknown external disturbances; second, auxiliary systems that are governed by smooth switching functions, are developed in an unprecedented manner to compensate for the saturation constraints on actuators. The main innovation can be summarized as that the TLC technology is applied to the USV motion control field as a new control algorithm, and the enhanced technology based on traditional TLC not only reduces the number of adjustment parameters but also has simple structure and high robustness. Furthermore, a low frequency learning method improves the applicability of the algorithm. The stability analysis is established using the Lyapunov theory. Simulation results and comparison verify the effectiveness of the proposed strategy.

Robust Adaptive Trajectory Linearization Control for Tracking Control of Surface Vessels With Modeling Uncertainties Under Input Saturation

This paper develops a novel adaptive trajectory tracking control strategy to enhance the tracking performance for surface vessels with unmodeled dynamics and unknown time-varying disturbances. A high robustness and precision trajectory tracking controller is presented by using trajectory linearization control (TLC) technology, neural network, extended state observer (ESO), nonlinear tracking differentiator, and auxiliary dynamic system. First, the greatest advantage of this paper is that the TLC technology is first introduced into the field of surface vessels motion control, which provides a new direction for TLC technology research. Then, to further enhance the control performance and robustness of the system, the neural network with minimum learning parameter is used to replace the classical radial basis function neural network to approximate unmodeled dynamics, which can reduce the burden of computing. A novel reduced-order ESO is constructed to estimate unknown time-varying disturbances to achieve real-time compensation. Meanwhile, nonlinear tracking differentiator is employed to realize the derivative of virtual control command, as well as to provide command filtering. In addition, an auxiliary dynamic system is designed to reduce the risk of actuator saturation. The stability of the closed-loop system is guaranteed based on the Lyapunov criteria. Lastly, the comparison results demonstrate the superior performance of the proposed approach.

Adaptive course control based on trajectory linearization control for unmanned surface vehicle with unmodeled dynamics and input saturation

This paper presents a novel course control strategy for unmanned surface vehicles (USV) subject to unmodeled dynamics and time-varying external disturbance. A practical adaptive course controller is proposed by trajectory linearization control (TLC) technology, neural network minimum learning parameter method (MLP), disturbance observer (DOB) and auxiliary design system. MLP and DOB are introduced to compensate for unmodeled dynamics and time-varying external disturbance, respectively. In addition, auxiliary design system is hired to deal with input saturation issue. By Lyapunov stability theory, it is proved that all the error signals in the course control system are uniform ultimate bounded. The advantages of the developed control strategy are that first, from the author’s point of view, TLC technology is applied to the field of USV motion control for the first time, which opens a new research direction of this algorithm; second, MLP with a smaller computational burden is used to replace radial basis function (RBF) neural network, which is more convenient for engineering implementation; third, the proposed scheme has strong anti-interference ability, which can compensate for the inherent defect that the USV with a smaller volume is susceptible to external disturbance. Finally, numerical simulations prove the effectiveness and correctness of the proposed control strategy.

Trajectory linearization control on SO(3) with application to aerial manipulation

The dynamics of multi-DOF aerial manipulators is complex system evolving in non-Euclidean Lie group, making design and tuning of the control of such systems challenge. In this paper we consider the nonlinear geometric control for aerial manipulation system. The linearized tracking error kinematic equation of motion on SO(3) is obtained from the variation on SO(3). Based on the linearized tracking error kinematic equation of motion on SO(3), the trajectory linearization control for the kinematics on SO(3) is investigated. The decoupled dynamics of multi-DOF aerial manipulator enables us to apply the results of trajectory linearization control for the kinematics on SO(3). We then design the entire controller for aerial manipulation system by composing different trajectory linearization control loops. Such controller structure eases the controller implementation and tuning procedure. The stability of the proposed controlled system is analyzed using Lyapunov’s method. The proof is finished from inner loop to outer loop. It is proven that the closed loop shape system is exponentially stable. The attraction basin of the configuration error for the shape system can almost cover the whole SO(3)×Rn. The stability of the system considering the actuator dynamics and perturbations is also discussed in this paper. From the stability of the shape system, the stability of the entire system is proven. The stability analysis results are further verified through several numerical simulations.