Feedback linearization of the nonlinear model of a small-scale helicopter

In order to design a nonlinear controller for small-scale autonomous helicopters, the dynamic characteristics of a model helicopter are investigated, and an integrated nonlinear model of a small-scale helicopter for hovering control is presented. It is proved that the nonlinear system of the small-scale helicopter can be transformed to a linear system using the dynamic feedback linearization technique. Finally, simulations are carried out to validate the nonlinear controller.     

Closed-form inverse kinematic solution for fluoroscopic C-arms

This paper presents a closed-form solution to the inverse kinematic problem for general fluoroscopic C-arms. The resulting algorithm determines the necessary joint parameters for imaging a given point of interest p→ from a given direction z→. The existence and uniqueness of the solution is proven for all p→ and z→. The inverse kinematics lays the basis for a completely robotized C-arm. The paper describes some applications for such an automatized device and presents the first results.     

An inverse kinematic solution for kinematically redundant robot manipulators

An inverse kinematic analysis addresses the problem of computing the sequence of joint motion from the Cartesian motion of an interested member, most often the end effector. Although the rates and accelerations are related linearly through the Jacobian, the positions go through a highly nonlinear transformation from one space to another. Hence, the closed-form solution has been obtained only for rather simple manipulator configurations where joints intersect or where consecutive axes are parallel or perpendicular. For the case of redundant manipulators, the number of joint variables generally exceeds that of the constraints, so that in this case the problem is further complicated due to an infinite number of solutions. Previous approaches have been directed to minimize a criterion function, taking into account additional constraints, which often implies a time-consuming optimization process. In this article, a different approach is taken to these problems. A Newton-Raphson numerical procedure has been developed based on a composite Jacobian which now includes rows for all members under constraint. This procedure may be applied to solve the inverse kinematic problem for a manipulator of any mechanical configuration without having to derive beforehand a closed-form solution. The technique is applicable to redundant manipulators since additional constraints on other members as well as on the end effector may be imposed. Finally, this approach has been applied to a seven degree-of-freedom manipulator, and its ability to avoid obstacles is demonstrated.     

Analytical solution to inverse kinematic problem for 6-DOF robot-manipulator

Analytical solution to inverse kinematic problem for 6-DOF (Degree Of Freedom) robot-manipulators is considered. Well-known approaches to solving the problem involve geometrical and numerical methods. In this paper we discuss the solution technique based on deriving the system of nonlinear equations and solving it in the general view.     

Error-back-propagation solution to the inverse kinematic problem of redundant manipulators

In this paper, the inverse kinematics problem of the generalized n-degrees-of-freedom robot is solved using the error-back-propagation algorithm. The efficiency of the proposed solution has been mewed for redundant manipulators using 5000 randomly chosen Cartesian coordinates within the robot's workspace. Comparison with two other methods, the well-known pseudoinverse method and a technique based on genetic algorithms, shows that the accuracy of the present method is substantially better.     

Nonlinear system identification of a small-scale unmanned helicopter

This paper presents a comprehensive method for identifying the nonlinear model of a small-scale unmanned helicopter. The model structure is obtained by first principles derivation, and the model parameters are determined by direct measurement and system identification. A new adaptive genetic algorithm is proposed to identify the parameters that cannot be directly measured. To simplify the identification process, the overall system is divided into two subsystems for identification: the heave–yaw dynamics and the lateral–longitudinal dynamics. On the basis of the input–output data collected from actual flight experiments, these two subsystems are identified using the proposed algorithm. The effectiveness of the identified model is verified by comparing the response of the simulation model with the actual response during the flight experiments. Results show that the identified model can accurately predict the response of the small-scale helicopter. Furthermore, the identified model is used for the design of an attitude controller. The experiment results show that the identified model is suitable for controller design.     

一种新的六自由度机械臂运动学反解方法研究

针对运用解析法对机械臂进行运动学反解仅适用于具有特定结构机械臂的不足,提出能量优化的遗传算法进行机械臂运动学反解的方法。为便于能量的量化计算,在进行机械臂运动学分析的基础上,建立四连杆简化模型。采用实数编码方式,以机械臂各关节角上下限为依据,建立与之相对应的染色体。以机械臂各连杆势能变化及机械臂末端与期望值之差作为适应度函数,评估个体的适应度。通过概率的方法实现选择、交叉和变异操作。实验结果证明了该方法的正确性。     

Trajectory planning and trajectory tracking for a small-scale helicopter in autorotation

The design of a high-performance guidance and control system for a small-scale helicopterUnmanned Aerial Vehicle (UAV), with an engine OFF flight condition (i.e. autorotation), is known to be a challenging task. It is the purpose of this paper to present a Trajectory Planning (TP) and Trajectory Tracking (TT) system, having onlinecomputational tractability. The presented Flight Control System (FCS) is anchored within the aggregated paradigms of differential flatness based optimal planning, and robust control based tracking. In particular the first real-time feasible, model-based TP and model-based TT, for a small-scale helicopter in autorotation is being demonstrated using a high-fidelity, high-order, nonlinear helicopter simulation.     

Nonlinear dynamic modeling and control of a small-scale helicopter

A test bench for experimental testing of the attitude control of a small-scale helicopter is constructed. A nonlinear model with 10 states is developed for this experimental setup. The unknown model parameters are estimated using the extended Kalman filter with flight test data of the helicopter operating on the test bench. In this work, it is proved that the nonlinear helicopter dynamic model may be globally feedback linearized using the dynamic feedback linearization technique. In order to satisfy multiple closed-loop performance specifications simultaneously, a controller is proposed by applying the Convex Integrated Design (CID) method to the feedback linearized model. Finally, the controller is tested in simulation demonstrating the closed-loop performance of the proposed controller.     

小型无人直升机的数学建模与仿真

小型无人直升机是一个复杂的非线性系统.为了真正实现小型无人直升机的自主飞行,须对其进行精确的数学建模.本文以Raptor90小型无人直升机为研究平台,综合考虑了直升机在不同飞行模态下的飞行特性,利用基于叶素理论的积分算法,对直升机进行非线性建模,并对所建模型进行数值仿真.仿真结果表明,所建模型能够较好的反应直升机的动态响应特性,所建模型具有较高精度,可基于此模型进行飞行控制器的设计.     

Nonlinear robust control of a small-scale helicopter on a test bench

A nonlinear robust controller design procedure is presented, which is designed to simultaneously satisfy multiple conflicting closed-loop performance specifications. Significantly, a robust performance specification for the experimental system, developed for studying the attitude control of a small-scale helicopter in our previous work, is discussed quantitatively. The robust performance specifications and nominal multiple closed-loop performance specifications are conflicting. Use of the Convex Integrated Design (CID) method can provide, where feasible, a single closed-loop controller which satisfies a set of multiple conflicting performance specifications. However, the resultant controller has a complex form. Here, the standard CID method is extended to a more general control system framework to solve the conflicting simultaneous performance design problem. When compared with the standard CID design, the extended CID design procedure generates a relatively simple closed-loop controller. Finally, the synthesised controller is tested in simulation and is validated with an experimental small-scale test helicopter, demonstrating the performance of the proposed controller.     

Robust nonlinear motion control of a helicopter

We consider the problem of controlling the vertical motion of a nonlinear model of a helicopter, while stabilizing the lateral and horizontal position and maintaining a constant attitude. The reference to be tracked is given by a sum of a constant and a fixed number of sinusoidal signals, and it is assumed not to be available to the controller. This represents a possible situation in which the controller is required to synchronize the vehicle motion with that of an oscillating platform, such as the deck of a ship in high seas. We design a nonlinear controller which combines recent results on nonlinear adaptive output regulations and robust stabilization of systems in feedforward form by means of saturated controls. Simulation results show the effectiveness of the method and its ability to cope with uncertainties on the plant and actuator model.     

小型无人直升机的姿态与高度自适应反步控制

针对小型无人直升机的姿态与高度控制问题, 本文提出了一种基于反步法的自适应控制策略. 具体而言, 首先对小型无人直升机的运动学模型进行了等效变换, 使系统中未知参数满足线性参数化条件, 然后应用反步法设计了包含主旋翼挥舞模型的姿态与高度自适应控制器, 并借助Lyapunov方法和芭芭拉定理对闭环系统的稳定性进行了严格的数学分析. 最后, 对该控制器的性能进行了仿真验证, 结果表明在直升机质量和惯性矩阵存在不确定性(未知)的情况下, 该控制算法依然能够取得良好的控制效果.     

Efficient solution of nonlinear,underdetermined inverse problems with a generalized PDE model

Several parameter estimation problems (or “inverse” problems) such as those that occur in hydrology and geophysics are solved using partial differential equation (PDE)-based models of the physical system in question. Likewise, these problems are usually underdetermined due to the lack of enough data to constrain a unique solution. In this paper, we present a framework for the solution of underdetermined inverse problems using COMSOL Multiphysics (formerly FEMLAB) that is applicable to a broad range of physical systems governed by PDEs. We present a general adjoint state formulation which may be used in this framework and allows for faster calculation of sensitivity matrices in a variety of commonly encountered underdetermined problems. The aim of this approach is to provide a platform for the solution of inverse problems that is efficient, flexible, and not restricted to one particular scientific application.We present an example application of this framework on a synthetic underdetermined inverse problem in aquifer characterization, and present numerical results on the accuracy and efficiency of this method. Our results indicate that our COMSOL-based routines provide an accurate, flexible, and scalable method for the solution of PDE-based inverse problems.     

A unified solution scheme for inverse dynamics

In this paper, a completely new solution scheme for inverse dynamics, which can be commonly applied in different types of link systems such as open- or closed-loop mechanisms, or ones constituting rigid or flexible link members, is presented. The scheme is developed using the finite element method (FEM), which evaluates the entire system as a continuum with the equation of motion in Cartesian coordinates and in dimension of force. The inverse dynamics is calculated by using a matrix-form relation to the nodal forces obtained by the FEM. The matrix-form equations are divided individually into terms of force, transformation between coordinates and length, which makes the scheme potentially better in terms of applicability and expansibility. The scheme cannot only deal with open- and closed-loop link systems independently, but it can also deal seamlessly with those that gradually change their forms and dynamics. There is also no need to revise the basic numerical algorithm of the scheme, regardless of the stiffness of the constituting link member, i. e. rigid or flexible. The main objective of this paper is to present the extensive ability of the scheme as a unified scheme, by carrying out calculations on several types of rigid and flexible manipulators, along with an application to feed-forward control of a link mechanism which continuously changes its form from an open- to a closed-loop.     

Height and attitude active disturbance rejection controller design of a small-scale helicopter

Small-scale helicopters are very attractive because of their unique features.However,autonomous flight control for small-scale helicopters is still a challenging work because they are naturally unstable,strongly nonlinear,and sensitive to disturbances.In this paper,we focus on the design of a height and attitude active disturbance rejection controller(ADRC)for a small-scale helicopter constructed in our lab.Firstly,a comprehensive nonlinear model for the platform is presented,which is obtained through first principles modeling and system identification.The controller is designed using backstepping technique incorporated with extended state observer(ESO),which is used to estimate the unknown disturbances.Then,the estimate is introduced into the control law to compensate for the disturbances.The design specifications of military rotorcraft are introduced to guide the controller design to achieve specified control performance.Considering the physical limitations,reference models are designed to shape the desired control responses.At last,several flight simulations are carried out to validate the effectiveness and robustness of the proposed controller.The results show that the proposed controller works well and Level 1 performance can be achieved.     

Improved nonlinear trajectory tracking using RBFNN for a robotic helicopter

This 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.     

A weighted LS-SVM approach for the identification of a class of nonlinear inverse systems

In this paper, a weighted least square support vector machine algorithm for identification is proposed based on the T-S model. The method adopts fuzzy c-means clustering to identify the structure. Based on clustering, the original input/output space is divided into several subspaces and submodels are identified by least square support vector machine (LS-SVM). Then, a regression model is constructed by combining these submodels with a weighted mechanism. Furthermore we adopt the method to identify a class of inverse systems with immeasurable state variables. In the process of identification, an allied inverse system is constructed to obtain enough information for modeling. Simulation experiments show that the proposed method can identify the nonlinear allied inverse system effectively and provides satisfactory accuracy and good generalization. Supported by the National Natural Science Foundation of China (Grant No. 60874013) and the Doctoral Project of the Ministry of Education of China (Grant No. 20070286001)     

Electrostatic comb-drive actuators made of polyimide for actuating micromotion convert mechanisms

 For conventional micromachines, in particular, micromotion convert mechanisms, the output points of the mechanism can move horizontally when input points move in the same direction. Therefore, we have proposed a three-dimensional motion convert mechanism whose output points can move vertically when the input points move in the horizontal direction. This 2-degree-of-freedom (DOF) mechanism consists of electrostatic comb-drive actuators and a basic mechanism with large-deflective elastic hinges. In this study, the characteristics of comb-drive actuators are analyzed. The electrostatic comb-drive actuator which is made up of polyimide is fabricated by CVD, RIE, Wet etching, etc., technologies. The relationship between the input (voltage) and the output (displacement) of the drive has been analyzed both theoretically and experimentally. Received: 26 December 1998 / Accepted: 4 January 1999     

一类非线性直升机模型的滑模降阶控制器设计

针对带有交叉耦合的多输入CE150直升机模型,研究了一类多输入仿射非线性系统的控制设计问题,基于滑模变结构控制理论,采用了一种新的控制器设计方法:滑模降阶方法,即反复运用变结构控制理论,对一类高阶的仿射非线性系统,构造了合适的微分同胚变换函数,把初始高阶系统降至低阶系统,并构造了变结构控制律,再利用当前级和上一级控制输入的映射关系反推出初始系统的控制输入.通过CE150直升机模型仿真结果表明,该方法有效可行.