Nonlinear Trajectory Tracking Research Articles

Indirect adaptive control of nonlinear system via dynamic multilayer neural networks with multi‐time scales

SummaryThis paper deals with adaptive nonlinear identification and trajectory tracking problem via dynamic multilayer neural network with different time scales. By means of a Lyapunov‐like analysis, we determine stability conditions for the on‐line identification. Then, a sliding mode controller is designed for trajectory tracking with consideration of the modeling error and disturbance. The main contributions of the paper lie in the following aspects. First, we extend our prior identification results of single‐layer dynamic neural networks with multi‐time scales to those of multilayer case. Second, the e‐modification in standard use in adaptive control is introduced in the on‐line update laws to guarantee bounded weights and bounded identification errors. Third, the potential singularity problem in controller design is solved by using new update laws for the NN weights so that the control signal is guaranteed bounded. The stability of proposed controller is proved by using Lyapunov function. Simulation results demonstrate the effectiveness of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.

Design of a Nonlinear PID Neural Trajectory Tracking Controller for Mobile Robot based on Optimization Algorithm

Design of a Nonlinear PID Neural Trajectory Tracking Controller for Mobile Robot based on Optimization Algorithm

Nonlinear feedback control and trajectory tracking of vehicle

This paper mainly studies nonlinear feedback control applied to the nonlinear vehicle dynamics with varying velocity. The main objective of this study is the stabilisation of longitudinal, lateral and yaw angular vehicle velocities. To this end, a nonlinear vehicle model is developed which takes both the lateral and longitudinal vehicle dynamics into account. Based on this model, a method to build a nonlinear state feedback control is first designed by which the complexity of system structure can be simplified. The obtained system is then synthesised by the combined Lyapunov–LaSalle method. The simulation results show that the proposed control can improve stability and comfort of vehicle driving. Moreover, this paper presents a lemma which ensures the trajectory tracking and path-following problem for vehicle. It can also be exploited simultaneously to solve both the tracking and path-following control problems of the vehicle ride and driving stability. We also show how the results of the lemma can be applied to solve the path-following problem, in which the vehicle converges and follows a designed path. The effectiveness of the proposed lemma for trajectory tracking is clearly demonstrated by simulation results.

Nonlinear systems identification and control via dynamic multitime scales neural networks.

This paper deals with the adaptive nonlinear identification and trajectory tracking via dynamic multilayer neural network (NN) with different timescales. Two NN identifiers are proposed for nonlinear systems identification via dynamic NNs with different timescales including both fast and slow phenomenon. The first NN identifier uses the output signals from the actual system for the system identification. In the second NN identifier, all the output signals from nonlinear system are replaced with the state variables of the NNs. The online identification algorithms for both NN identifier parameters are proposed using Lyapunov function and singularly perturbed techniques. With the identified NN models, two indirect adaptive NN controllers for the nonlinear systems containing slow and fast dynamic processes are developed. For both developed adaptive NN controllers, the trajectory errors are analyzed and the stability of the systems is proved. Simulation results show that the controller based on the second identifier has better performance than that of the first identifier.

A PRACTICAL TRAJECTORY TRACKING APPROACH FOR AUTONOMOUS MOBILE ROBOTS: NONLINEAR ADAPTIVE H2 DESIGN

A nonlinear adaptive trajectory tracking design for autonomous mobile robot and its practical implementation are presented in this paper. This approach can be applied to generate trajectory tracking control commands for autonomous mobile robot tracking predefined trajectories. The design objective is to specify one nonlinear controller with a parameter adaptive law that satisfies the adaptive H2 optimal performance. In general, it is hard to obtain the closed-form solution from this nonlinear trajectory tracking problem. Fortunately, based on the property of the trajectory tracking error dynamic system of the autonomous mobile robot, one closed-form solution to this problem can be obtained with a very simple form for the preceding control design.

A nonlinear trajectory tracking controller for mobile robots with velocity limitation via fuzzy gains

This paper proposes a fuzzy controller for trajectory tracking with unicycle-like mobile robots. Such controller uses two Takagi–Sugeno (TS) fuzzy blocks to generate its gains. The controller is able to limit the velocity and control signals of the robot, and to reduce the errors arising from its dynamics as well. The stability of the developed controller is proven, using the theory of Lyapunov. Experimental results show that the use of the proposed controller is attractive in comparison with the use of a controller with fixed saturation function.

T-S Fuzzy Model and Optimal Reaching Law-Based Sliding Mode Control for Nonlinear Trajectory Tracking

A novel sliding mode controller based on Takagi and Sugeno (T-S) fuzzy system model and optimal reaching law is presented to design the output tracking controller for the nonlinear system. The T-S fuzzy logic theory is used to build a global fuzzy state-space linear model, the sliding surface is defined by using pole assignment method, and the optimal switch control law which can drive the state variables to the sliding surface as soon as possible is designed under the condition of minimizing the defined cost function. The gains of optimal switch control law designed by using fuzzy logic algorithm alleviate the chattering phenomenon. Lyapunov equation is applied to prove the stability of controlled system. The simulation results show that the proposed approach can achieve nonlinear trajectory tracking with better performance and less chattering problem.

Trajectory linearization control for a miniature unmanned helicopter

Trajectory linearization control (TLC) approach is applied to design a nonlinear trajectory tracking controller for a miniature unmanned helicopter. The controller is based on nonlinear model derived from Newton-Euler equations, with collective and cyclic pitches being regarded as actual controls. Via model simplifications, the nonlinear helicopter model can be transformed into a cascaded form including four subsystems. Corresponding with the simplified cascaded structure, the proposed controller is constructed by synthesizing TLC designs for subsystems. Each of them includes designs of a pseudo-inversion and an error regulator. A summarized TLC algorithm for the unmanned helicopter is listed briefly after the detailed controller design process. Simulation results are provided to demonstrate performances of the closed-loop system.

A Novel Nonlinear Control Law with Trajectory Tracking Capability for Nonholonomic Mobile Robots: Closed-Form Solution Design

A novel nonlinear robust trajectory tracking control law for nonholonomic mobile robot is presented in this paper. This approach can be applied to generate trajectory tracking control commands on nonholonomic mobile robot movement. The design objective is to specify one nonlinear robust control law that satisfies the H2 performance, for the nonlinear trajectory tracking control of nonholonomic mobile robot. In general, it is hard to obtain the closed-form solution from this nonlinear trajectory-tracking problem. Fortunately, because of the skew symmetric property of the trajectory tracking system of the nonholonomic mobile robot and adequate choice of state variable transformation, the H2 trajectory-tracking problems can be reduced to solving one nonlinear time varying Riccati-like equations. Furthermore, one closed-form solution to this nonlinear time varying Riccati-like equation can be obtained with very simple forms for the preceding control design. Finally, there are two practical testing conditions: circular and square like reference trajectories are used for performance verifications.

An Adaptive Nonlinear Trajectory Tracking Design for Mobile Robots and it’s Practical Implementation

An adaptive nonlinear trajectory tracking design for mobile robot and its practical implementation are presented in this paper. The design objective is to specify one nonlinear controller with a parameter adaptive law that satisfies the adaptive H2 optimal performance. In general, it is hard to obtain the closed-form solution from this nonlinear trajectory-tracking problem. Fortunately, based on the property of the trajectory tracking system of the nonholonomic mobile robot, the adaptive H2 trajectory tracking problems can be reduced to solving one nonlinear time varying Riccati-like equations. Furthermore, one closed-form solution to this nonlinear time varying Riccati-like equation can be obtained with very simple forms for the preceding control design. Finally, there are two practical testing conditions: circular and S type reference trajectories are used for performance verification.

An Approximate Backstepping Based Trajectory Tracking Control of a Gun Launched Micro Aerial Vehicle in Crosswind

This paper considers the question of obtaining a nonlinear trajectory tracking control law for a comprehensive design of a Gun Launched Micro Aerial Vehicle (GLMAV) despite unknown aerodynamic effo...

Nonlinear trajectory tracking control of a new autonomous underwater vehicle in complex sea conditions

Autonomous underwater vehicles (AUVs) navigating in complex sea conditions usually require a strong control system to keep the fastness and stability. The nonlinear trajectory tracking control system of a new AUV in complex sea conditions was presented. According to the theory of submarines, the six-DOF kinematic and dynamic models were decomposed into two mutually non-coupled vertical and horizontal plane subsystems. Then, different sliding mode control algorithms were used to study the trajectory tracking control. Because the yaw angle and yaw angle rate rather than the displacement of the new AUV can be measured directly on the horizontal plane, the sliding mode control algorithm combining cross track error method and line of sight method was used to fulfill its high-precision trajectory tracking control in the complex sea conditions. As the vertical displacement of the new AUV can be measured, in order to achieve the tracking of time-varying depth signal, a stable sliding mode controller was designed based on the single-input multi-state system, which took into account the characteristic of the hydroplane and the amplitude and rate constraints of the hydroplane angle. Moreover, the application of dynamic boundary layer can improve the robustness and control accuracy of the system. The computational results show that the designed sliding mode control systems of the horizontal and vertical planes can ensure the trajectory tracking performance and accuracy of the new AUV in complex sea conditions. The impacts of currents and waves on the sliding mode controller of the new AUV were analyzed qualitatively and quantitatively by comparing the trajectory tracking performance of the new AUV in different sea conditions, which provides an effective theoretical guidance and technical support for the control system design of the new AUV in real complex environment.

Alternative trajectory-tracking control approach for marine surface vessels with experimental verification

SUMMARYExperiments with a nonlinear trajectory-tracking controller for marine unmanned surface vessels are reported. The tracking controller is designed using a nonlinear robust model-based sliding mode approach. The marine vehicles can track arbitrary desired trajectories that are defined in Cartesian coordinate as continuous functions of time. The planar dynamic model used for the controller design consists of 3 degrees of freedom (DOFs) of surge, sway, and yaw. The vessel only has two actuators, so the vessel is underactuated. Therefore, only two outputs, which are functions of the 3-DOF, can be controlled. The Cartesian position of a control point on the vessel is defined as the output. The orientation dynamics is not directly controlled. It has been previously shown that the orientation dynamics, as the internal dynamics of this underactuated system, is stable. The result of field experiments show the effectiveness of tracking control laws in the presence of parameter uncertainty and disturbance. The experiments were performed in a large outdoor pond using a small test boat. This paper reports the first theoretical development and experimental verification of the proposed model-based nonlinear trajectory-tracking controller.

Improved nonlinear trajectory tracking using RBFNN for a robotic helicopter

AbstractThis paper presents a backstepping control method using radial‐basis‐function neural network (RBFNN) for improving trajectory tracking performance of a robotic helicopter. Many well‐known nonlinear controllers for robotic helicopters have been constructed based on the approximate dynamic model in which the coupling effect is neglected; their qualitative behavior must be further analyzed to ensure that the unmodeled dynamics do not destroy the stability of the closed‐loop system. In order to improve the controller design process, the proposed controller is developed based on the complete dynamic model of robotic helicopters by using an RBFNN function approximation to the neglected dynamic uncertainties, and then proving that all the trajectory tracking error variables are globally ultimately bounded and converge to a neighborhood of the origin. The merits of the proposal controller are exemplified by four numerical simulations, showing that the proposed controller outperforms a well‐known controller in (J. Robust Nonlinear Control 2004; 14(12):1035–1059). Copyright © 2009 John Wiley & Sons, Ltd.

무인항공기의 Leader-Follower 편대비행을 위한 수정된 비선형 유도법칙

A formation flight guidance logic that enables the leader-follower station keeping between two UAVs is presented in this paper. The logic is motivated by the investigation of the relation between the proportional navigation and the nonlinear trajectory tracking guidance law, The simplicity of the presented method provides computational efficiency and allows easy implementation. An excellent performance of the proposed logic is demonstrated via various numerical simulations for multiple UAVs environment.

고속 권상운동과 흔들림억제 궤적추종을 위한 천정주행 크레인의 퍼지 비선형 적응제어

천정주행 크레인의 고속 권상작업 및 흔들림 억제 궤적추종을 위한 비선형 적응제어 방법을 제시한다. 천정주행 크레인의 흔들림 운동은 트롤리의 가속도. 권상로프의 길이 및 권상속도와 강하게 결합되어 있다. 이는 비간섭 제어 기반의 흔들림 억제 궤적추종 제어법칙을 설계하는데 있어 장애요인으로 작용한다. 이러한 문제를 해결하기 위해, 트롤리의 가속도와 권상속도의 영향을 최소화하는 방법으로 불확실성이 존재하는 경우에도 흔들림 운동의 궁극적 균일 유계성을 보장하는 퍼지 비선형 적응형 흔들림 억제 궤적추종제어법칙을 제안한다. 특히, 제안한 방법은 파라미터 변화. 외란 등을 포함한 시스템 불확실성을 퍼지 불확실성 관측기를 이용하여 보상한다. 따라서, 퍼지관측기의 근사화 오차가 영으로 수렴할 때 추종오차 및 흔들림 각도의 궁극적 한계치는 영으로 감소한다. 끝으로 제안한 방법의 성능검증을 위한 모의실험 견과를 제시한다. Nonlinear adaptive control of overhead cranes is investigated for anti-sway trajectory tracking with high-speed hoisting motion. The sway dynamics of two dimensional underactuated overhead cranes is heavily coupled with the trolley acceleration, hoisting rope length, and the hoisting velocity which is an obstacle in the design of decoupling control based anti-sway trajectory tracking control law To cope with this obstacle. we propose a fuzzy nonlinear adaptive anti-sway trajectory tracking control law guaranteeing the uniform ultimate boundedness of the sway dynamics even in the presence of uncertainties in such a way that it cancels the effect of the trolley acceleration and hoisting velocity on the sway dynamics. In particular. system uncertainties, including system parameter uncertainty unmodelled dynamics, and external disturbances, are compensated in an adaptive manner by utilizing fuzzy uncertainty observers. Accordingly, the ultimate bound of the tracking errors and the sway angle decrease to zero when the fuzzy approximation errors decrease to zero. Finally, numerical simulations are performed to confirm the effectiveness of the proposed scheme.

Flatness‐Based Trajectory Tracking Control of an Underconstrained Cable Suspension Manipulator

AbstractCable suspension manipulators support a payload platform in space by several spatially arranged cables with computercontrolled winches. The winches are mounted either fixed or on movable trolleys. Compared to conventional cranes, it is possible to control not only the translational motion of the payload but also its orientation in order to perform, for example, assembly tasks. By this, cable suspension manipulators combine the ability of cranes to support heavy payloads in a large workspace with the dexterity of robot manipulators.The present contribution treats nonlinear trajectory tracking control of cable suspension manipulators that are kinematically undetermined and statically determined. In particular, the cable suspension manipulator Cablev [4] is considered that has been developed at University of Rostock (Fig. 1). Its payload platform is supported by three cables with winches mounted on trolleys that move themselves on a gantry. Thus, the payload platform may perform sway motions with three degrees of freedom while the cable lengths are kept fixed. Applications are, for example, precise handling and assembling large and heavy components on construction sites or on shipyards. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Trajectory Tracking for Unmanned Air Vehicles With Velocity and Heading Rate Constraints

This paper considers the problem of constrained nonlinear trajectory tracking control for unmanned air vehicles (UAVs). We assume that the UAV is equipped with longitudinal and lateral autopilots which reduces the 12-state model to a six-state model with altitude, heading, and velocity command inputs. One of the novel features of our approach is that we explicitly account for heading rate and velocity input constraints. For a UAV, the velocity is constrained to lie between two positive constants, and therefore presents particular challenges for the control design. We propose a control Lyapunov function (CLF) approach. We first introduce a CLF for the input constrained case, and then construct the set of all constrained inputs that are with respect to this CLF. The control input is then selected from this feasible set. The proposed approach is applied to a simulation scenario, where the UAV is assigned to transition through several targets in the presence of multiple dynamic threats.

Iterative learning neural network control for nonlinear system trajectory tracking

This paper presents a neural network control scheme for tracking a non-periodic trajectory with a finite time interval from the view point of the iterative learning control. A system with time-varying but iteration-invariant uncertainties can be controlled by this scheme. The controller consists of a series of local networks. Every point along the desired trajectory has its own one for approximating the nonlinearity in a neighborhood only. An iterative training law described by a positive definite discrete kernel is presented. The control scheme is applied to robot movement imitation by visual servo. Stability of the controller is ensured.

Adaptive Realization of Linear Closed-Loop Tracking Dynamics in the Presence of Large System Model Errors

A novel adaptive feedback control approach for nonlinear mechanical systems is presented. The approach applies to nonlinear trajectory tracking and has the remarkable property that the tracking error dynamics asymptotically approach a specified linear PID response for the case where the external disturbances are constant. The methodology applies to a large class of nonlinear mechanical systems, however, it is illustrated for the case of nonlinear rigid body maneuvers subject to actuator saturation constraints and large uncertainty of the system mass and inertia properties. While the system mass or inertias are not identified in this approach, the external disturbances are accurately estimated if they are constant or slowly varying with respect to the adaptation rate. A benefit of this method is that it requires no a priori knowledge of the unknown system parameters or bounds thereof.