Feedback linearization control of flexible joint robots

In this paper, the control of a two link, flexible joint manipulator is examined. Among external forces, an exogenous constraint force acting on the end-effector is included. The manipulator dynamics are described by:

. On the assumption that f(x), g(x) and J^T f_e(x) are smooth vector fields, it is shown that the inner loop control u is of the form:

u=1/dT_n,g(v−dT_n,(ƒ(x)+J^Tƒ_e(x)))

where u is an outer loop control signal and y = T(x) is a diffleomorphism that transform (a) into linear system. As the position control scheme is adopted, the value of the contact force is not controlled.

The results for the inner loop control are substantiated by simulation of a two-link robot model. The robustness of the control method is examined and a Lyapunov-based control correction, similar to that of the free motion case, is implemented. Results are obtained for parametric errors of up to 50%. In the simulation, the manipulator is required to follow a specified joint trajectory such that the end-effector traces a sinusoidal path along a constraint surface. The results obtained illustrate the tracking of the link reference trajectory and indicate that the inner loop corrections are valid.     

Adaptive neural network output feedback control for flexible multi-link robotic manipulators

In this paper, a novel approach for adaptive control of flexible multi-link robots in the joint space is presented. The approach is valid for a class of highly uncertain systems with arbitrary but bounded dimension. The problem of trajectory tracking is solved through developing a stable inversion for robot dynamics using only joint angles measurement; then a linear dynamic compensator is utilised to stabilise the tracking error for the nominal system. Furthermore, a high gain observer is designed to provide an estimate for error dynamics. A linear in parameter neural network based adaptive signal is used to approximate and eliminate the effect of uncertainties due to link flexibilities and vibration modes on tracking performance, where the adaptation rule for the neural network weights is derived based on Lyapunov function. The stability and the ultimate boundedness of the error signals and closed-loop system is demonstrated through the Lyapunov stability theory. Computer simulations of the proposed robust controller are carried to validate on a two-link flexible planar manipulator.     

Predictive control based on neural network models with I/O feedback linearization

This paper presents an approach for the constrained non-linear predictive control problem based on the input-output feedback linearization (IOFL) of a general non-linear system modelled by a discrete-time affine neural network model. Using the resulting linear system in the formulation of the original non-linear predictive control problem enables to restate the optimization problem as the minimization of a quadratic function, which solution can be found using reliable and fast quadratic programming (QP) routines. However, the presence of a non-linear feedback linearizing controller maps the original linear input constraints onto non-linear and state dependent constraints on the controller output, which invalidates a direct application of QP routines. In order to cope with this problem and still be able to use QP routines, an approximate method is proposed which simultaneously guarantees a feasible solution without constraints violation over the complete prediction horizon within a finite number of steps, while allowing only for a small performance degradation.     

Control of flexible joint robots via external linearization approach

Based on the feedback linearization structure algorithm of differential geometric nonlinear control theory, an external linearization approach to the control of multilink flexible joint robots is considered in this article. The resulting externally linearized and input-output decoupled closed-loop system contains a linear subsystem and a nonlinear subsystem. The linear part describing the rigid motor motions is suitable for the design of nominal trajectory following control. However, the nonlinear joint deformation subsystem will cause perturbations in the nominal trajectory. To actively damp out the elastic vibrations and to render the complete closed-loop system robust to uncertainty in system parameters, a combined LQR stabilizer and servocompensator is used as the internal stabilization and error correcting control. The tracking errors of the end effector caused by the quasi-static joint deflections due to gravity can be compensated for by taking into account the nominal deflections in the trajectory planning and LQ regulation. A three-link PUMA type arm is tested via simulation.     

基于神经网络的非线性系统轨迹线性化自适应容错控制

针对一类仿射非线性系统,首先采用轨迹线性化方法将其等价表示为线性时变系统;然后利用神经网络构建伪逆模型以及动态故障模型：最后基于模型参数变化,应用李亚普诺夫稳定性理论构建标称系统控制器及故障补偿控制律,从而实现系统故障下的稳定有界容错控制．仿真结果表明了所提出算法的有效性．     

Adaptive feedback linearization control of chaotic systems via recurrent high-order neural networks

In the realm of nonlinear control, feedback linearization via differential geometric techniques has been a concept of paramount importance. However, the applicability of this approach is quite limited, in the sense that a detailed knowledge of the system nonlinearities is required. In practice, most physical chaotic systems have inherent unknown nonlinearities, making real-time control of such chaotic systems still a very challenging area of research. In this paper, we propose using the recurrent high-order neural network for both identifying and controlling unknown chaotic systems, in which the feedback linearization technique is used in an adaptive manner. The global uniform boundedness of parameter estimation errors and the asymptotic stability of tracking errors are proved by the Lyapunov stability theory and the LaSalle-Yoshizawa theorem. In a systematic way, this method enables stabilization of chaotic motion to either a steady state or a desired trajectory. The effectiveness of the proposed adaptive control method is illustrated with computer simulations of a complex chaotic system.     

Adaptive actuator compensation control with feedback linearization

An adaptive inverse controller is developed for feedback linearizable nonlinear systems with nonsmooth actuator nonlinearities. The use of an actuator nonlinearity inverse and a feedback linearizing controller leads to an error equation suitable for deriving an adaptive update law for the inverse parameters. Closed-loop signal boundedness is proved analytically, and system performance improvement is shown by simulation results. Such adaptive control schemes are also developed for multivariable nonlinear systems with actuator nonlinearities. For nonlinear systems that do not possess a relative degree, dynamic extension is employed to realize adaptive inverse compensation designs for actuator nonlinearities. These adaptive designs ensure closed-loop stability in the presence of uncertain actuator nonlinearities     

Robust dynamic surface control of flexible joint robots using recurrent neural networks

A robust neuro-adaptive controller for uncertain flexible joint robots is presented. This control scheme integrates H-infinity disturbance attenuation design and recurrent neural network adaptive control technique into the dynamic surface control framework. Two recurrent neural networks are used to adaptively learn the uncertain functions in a flexible joint robot. Then, the effects of approximation error and filter error on the tracking performance are attenuated to a prescribed level by the embedded H-infinity controller, so that the desired H-infinity tracking performance can be achieved. Finally, simulation results verify the effectiveness of the proposed control scheme.     

基于MGPI模型的SMA柔性驱动自适应NN控制

形状记忆合金(SMA)作为一类仿人肌肉驱动的智能柔性驱动材料,在机器人及高端制造等领域逐步得到应用,但由于SMA的热力学效应,造成输入输出之间存在强饱和回滞非线性,从而影响了驱动性能.此外在引入负载后, SMA柔性驱动部件输出性能表现出更为复杂的驱动特性.因此,如何有效抑制带载条件下SMA柔性驱动部件强饱和非线性影响,成为提升驱动性能的关键.针对此问题,本文重点研究带载条件下SMA柔性驱动部件的建模及驱动控制算法.针对SMA驱动部件中的强饱和非线性特性,本文提出一类修正(MGPI)回滞模型来进行表征.通过设定线性输入形状函数,不仅有效解析表征SMA驱动部件中的饱和回滞非线性,并且便于控制器设计.基于MGPI模型,考虑柔性驱动部件的动态特性,本文提出了带载条件下的SMA柔性驱动部件的自适应神经网络控制算法,实现考虑内部非线性和外部干扰条件下的驱动精度有效提升,并保证全局稳定性.     

Neural Network Based Feedback Linearization Control of an Unmanned Aerial Vehicle

This paper presents a flight control design for an unmanned aerial vehicle (UAV) using a nonlinear autoregressive moving average (NARMA-L2) neural network based feedback linearization and output redefinition technique.The UAV investigated is non- minimum phase.The output redefinition technique is used in such a way that the resulting system to be inverted is a minimum phase system.The NARMA-L2 neural network is trained off-line for forward dynamics of the UAV model with redefined output and is then inverted to force the real output to approximately track a command input.Simulation results show that the proposed approaches have good performance.     

A globally stable state feedback controller for flexible joint robots

The paper addresses the problem of controlling the joints of a flexible joint robot with a state feedback controller and proposes a gradual way of extending such a controller towards the complete decoupling of the robot dynamics. The global asymptotic stability for the state feedback controller with gravity compensation is proven, followed by some theoretical remarks on its passivity properties. By proper parameterization, the proposed controller structure can implement a position, a stiffness or a torque controller. Experimental results on the DLR lightweight robots validate the method.     

Adaptive neural network control of nonlinear systems by state andoutput feedback

This paper presents a novel control method for a general class of nonlinear systems using neural networks (NNs). Firstly, under the conditions of the system output and its time derivatives being available for feedback, an adaptive state feedback NN controller is developed. When only the output is measurable, by using a high-gain observer to estimate the derivatives of the system output, an adaptive output feedback NN controller is proposed. The closed-loop system is proven to be semi-globally uniformly ultimately bounded (SGUUB). In addition, if the approximation accuracy of the neural networks is high enough and the observer gain is chosen sufficiently large, an arbitrarily small tracking error can be achieved. Simulation results verify the effectiveness of the newly designed scheme and the theoretical discussions.     

Adaptive output feedback control for nonlinear time-delay systems using neural network

This paper extends the adaptive neural network （NN） control approaches to a class of unknown output feedback nonlinear time-delay systems. An adaptive output feedback NN tracking controller is designed by backstepping technique. NNs are used to approximate unknown functions dependent on time delay, Delay-dependent filters are introduced for state estimation. The domination method is used to deal with the smooth time-delay basis functions. The adaptive bounding technique is employed to estimate the upper bound of the NN approximation errors. Based on Lyapunov- Krasovskii functional, the semi-global uniform ultimate boundedness of all the signals in the closed-loop system is proved, The feasibility is investigated by two illustrative simulation examples.     

冗余度TT-VGT机器人的神经网络自适应控制

提出了采用神经网络进行模型参考自适应控制(MRAC)的方案,建立了自适应控制的状态模型,并推导出相应的自适应算法;最后对冗余度TT-VGT机器人自适应控制进行了仿真。     

基于脉冲推力的半被动双足机器人无模型神经网络控制

研究了半被动双足机器人的平面稳定行走控制问题。以最简行走模型为动力学模型,采用沿支撑腿方向的脚后跟脉冲推力作为行走动力源。考虑到系统模型的非线性特征,将基于三角函数扩展的函数链接型人工神经网络控制算法引入到机器人系统中,以产生系统所需的脉冲推力。并采用基于数据驱动的无模型同步扰动随机逼近算法对神经网络的权值进行更新。利用庞加莱映射方法分析了半被动双足机器人行走的稳定条件。在理论分析的基础上,对该算法进行了仿真研究。仿真结果表明：文中所提算法在收敛快速性上要优于迭代学习控制算法,可以实现双足机器人平面上的稳定周期行走。且雅可比矩阵的特征值均位于单位圆内,满足系统的稳定条件。     

A tracking controller for flexible joint robots using only linkposition feedback

A dynamic output feedback controller for flexible joint robots is presented which guarantees asymptotic tracking of a desired trajectory, starting from arbitrary initial conditions. The controller needs only the measurements of the positions of the links and the knowledge of an upper bound on the initial tracking error     

Adaptive neural network control based on neural observer for quadrotor unmanned aerial vehicle

This paper proposes an adaptive neural network control with neural state’s observer for quadrotor. The adaptive approach is used to solve the dynamics uncertainty problem of the controller. To perform the control, a Single Hidden Layer Neural Network (SHLNN) is used. Based on the structure of Sliding Mode Observer (SMO), a new neural observer is proposed to estimate the states. The aim of this work is to propose an observer insensitive to the measurement noise. The stability proof of global system is made by Lyapunov direct method. The adaptation laws of both artificial neural networks (ANNs) are derived from Lyapunov theory. The proposed controller is validated by simulation on the quadrotor under measurement noise conditions. A comparative study with SMO is made to highlight the performances of the proposed neural observer.     

Adaptive neural network output feedback control of stochastic nonlinear systems with dynamical uncertainties

In this paper, a robust adaptive neural network (NN) backstepping output feedback control approach is proposed for a class of uncertain stochastic nonlinear systems with unknown nonlinear functions, unmodeled dynamics, dynamical uncertainties and without requiring the measurements of the states. The NNs are used to approximate the unknown nonlinear functions, and a filter observer is designed for estimating the unmeasured states. To solve the problem of the dynamical uncertainties, the changing supply function is incorporated into the backstepping recursive design technique, and a new robust adaptive NN output feedback control approach is constructed. It is mathematically proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by choosing design parameters appropriately. The simulation example and comparison results further justify the effectiveness of the proposed approach.