Effect of the deformation in the inertia forces on the inverse dynamics of planar flexible mechanical systems

The inverse dynamics problem for articulated structural systems such as robotic manipulators is the problem of the determination of the joint actuator forces and motor torques such that the system components follow specified motion trajectories. In many of the previous investigations, the open loop control law was established using an inverse dynamics procedure in which the centrifugal and Coriolis inertia forces are linearized such that these forces in the flexible model are the same as those in the rigid body model. In some other investigations, the effect of the nonlinear centrifugal and Coriolis forces is neglected in the analysis and control system design of articulated structural systems. It is the objective of this investigation to study the effect of the linearization of the centrifugal and Coriolis forces on the nonlinear dynamics of constrained flexible mechanical systems. The virtual work of the inertia forces is used to define the complete nonlinear centrifugal and Coriolis force model. This nonlinear model that depends on the rate of the finite rotation and the elastic deformation of the deformable bodies is used to obtain the solution of the inverse dynamics problem, thus defining the joint torques that produce the desired motion trajectories. The effect of the linearization of the mass matrix as well as the centrifugal and Coriolis forces on the obtained feedforward control law is examined numerically. The results presented in this investigation are obtained using a slider crank mechanism with a flexible connecting rod.     

Impedance control of robots using voltage control strategy

Impedance control provides a unified solution for the position and force control of robot manipulators. The dynamic behavior of a robotic system in response to environment is prescribed by an impedance model formed as Thevenin model. This model is certain and linear while the robot manipulator is highly nonlinear, coupled, and uncertain. Therefore, impedance control must overcome nonlinearity, coupling, and uncertainty to convert the robotic system to the impedance model. To overcome these problems, this paper presents a novel impedance control for electrically driven robots, which is free from the manipulator dynamics. The novelty of this paper is the use of voltage control strategy to develop the impedance control. Compared with the commonly used impedance control, which is based on the torque control strategy, it is computationally simpler, more efficient, and robust. The mathematical verification and simulation results show the effectiveness of the control method.     

Nonlinear robust and optimal control of robot manipulators

In this paper, we propose a new optimal control method for robust control of nonlinear robot manipulators. Many industrial robot systems are required to perform relatively large angular movement with sufficient accuracy. In real circumstances, highly nonlinear manipulator dynamics and uncertainties such as unknown load placed on the manipulator, external disturbance, and joint friction make the precise control of manipulators a very challenging task. The main contribution of this work is to develop a new robust control strategy to accomplish the precise control of robot manipulators under load uncertainty using a nonlinear optimal control formulation and solution. This methodology is based on the underlying relation between the robust stability and performance optimality. A class of robust control problems can be transformed to an equivalent optimal control problem by incorporating the uncertainty bounds into the cost functional. The θ-D optimal control approach is utilized to find an approximate closed-form feedback solution to the resultant nonlinear optimal control problem via a perturbation process. Numerical simulations show that the proposed robust controller is able to control the robot manipulator precisely under large load variations.     

Decentralized direct adaptive fuzzy control of robots using voltage control strategy

Decentralized control is the most favorite control of robot manipulators due to computational simplicity and ease of implementation. Beside that, adaptive fuzzy control efficiently controls uncertain nonlinear systems. These motivate us to design a decentralized fuzzy controller. However, there are some challenging problems to guarantee stability. The state-space model of the robotic system including the robot manipulator and motors is in a noncompanion form, multivariable, highly nonlinear, and heavily coupled with a variable input gain matrix. For this purpose, adaptive fuzzy control may use all variable states. As a result, it suffers from computational burden. To overcome the problems, we present a novel decentralized Direct Adaptive Fuzzy Control (DAFC) of electrically driven robot manipulators using the voltage control strategy. The proposed DAFC is simple, in a decentralized structure with high-accuracy response, robust tracking performance, and guaranteed stability. Instead of all state variables, only the tracking error of every joint and its derivative are given as the inputs of the controller. The proposed DAFC is simulated on a SCARA robot driven by permanent magnet dc motors. Simulation results verify superiority of the decentralized DAFC to a decentralized PD-fuzzy controller.     

A differential flatness theory approach to observer-based adaptive fuzzy control of MIMO nonlinear dynamical systems

The paper proposes a solution to the problem of observer-based adaptive fuzzy control for MIMO nonlinear dynamical systems (e.g. robotic manipulators). An adaptive fuzzy controller is designed for a class of nonlinear systems, under the constraint that only the system’s output is measured and that the system’s model is unknown. The control algorithm aims at satisfying the $H_\infty $ tracking performance criterion, which means that the influence of the modeling errors and the external disturbances on the tracking error is attenuated to an arbitrary desirable level. After transforming the MIMO system into the canonical form, the resulting control inputs are shown to contain nonlinear elements which depend on the system’s parameters. The nonlinear terms which appear in the control inputs are approximated with the use of neuro-fuzzy networks. Moreover, since only the system’s output is measurable the complete state vector has to be reconstructed with the use of a state observer. It is shown that a suitable learning law can be defined for the aforementioned neuro-fuzzy approximators so as to preserve the closed-loop system stability. With the use of Lyapunov stability analysis, it is proven that the proposed observer-based adaptive fuzzy control scheme results in $H_{\infty }$ tracking performance.     

Discrete adaptive fuzzy control for asymptotic tracking of robotic manipulators

This paper presents a novel discrete adaptive fuzzy controller for electrically driven robot manipulators. It addresses how to overcome the nonlinearity, uncertainties, discretizing error and approximation error of the fuzzy system for asymptotic tracking control of robotic manipulators. The proposed controller is model-free in the form of discrete Mamdani fuzzy controller. The parameters of fuzzy controller are adaptively tuned using an adaptive mechanism derived by stability analysis. A robust control term is used to compensate the approximation error of the fuzzy system for asymptotic tracking of a desired trajectory. The controller is robust against all uncertainties associated with the robot manipulator and actuators. It is easy to implement since it requires only the joint position feedback. Compared with fuzzy controllers which employ all states to guarantee stability, the proposed controller is very simpler. Stability analysis and simulation results show its efficiency in the tracking control.     

Orientation-error observer-based tracking control of nonholonomic mobile robots

In this paper, a novel trajectory tracking controller is proposed for mobile robots with unknown orientation angle by employing the orientation-error observer (OEO). In order to overcome the local stability resulted from linearization design methods, an asymptotically stable controller is designed using Lyapunov’s direct method. This method breaks down nonlinear systems into low-dimensional systems and simplifies the controller design using virtual auxiliary error function and partial Lyapunov functions. A state-feedback controller for the nonlinear error dynamics of the mobile robot is combined with an observer that estimates the orientation-error based on available trajectory information and measurement of the position coordinates. The stability of the system is easily proved via the Lyapunov theory. Abundant simulation and experiment results validate the effectiveness and superiority of the proposed control method.     

Multi-step transversal and tangential linearization methods applied to a class of nonlinear beam equations

A novel and continuously parameterized form of multi-step transversal linearization (MTrL) method is developed and numerically explored for solving nonlinear ordinary differential equations governing a class of boundary value problems (BVPs) of relevance in structural mechanics. A similar family of multi-step tangential linearization (MTnL) methods is also developed and applied to such BVP-s. Within the framework of MTrL and MTnL, a BVP is treated as a constrained dynamical system, i.e. a constrained initial value problem (IVP). While the MTrL requires the linearized solution manifold to transversally intersect the nonlinear solution manifold at a chosen set of points across the axis of the independent variable, the essential difference of the present MTrL method from its previous version [Roy, D., Kumar, R., 2005. A multistep transversal linearization (MTL) method in nonlinear structural dynamics. J. Sound Vib. 17, 829–852.] is that it has the flexibility of treating nonlinear damping and stiffness terms as time-variant damping and stiffness terms in the linearized system. The resulting time-variant linearized system is then solved using Magnus’ characterization [Magnus, W., 1954. On the exponential solution of differential equations for a linear operator. Commun. Pure Appl. Math., 7, 649–673.]. Towards numerical illustrations, response of a tip loaded cantilever beam (Elastica) is first obtained. Next, the response of a simply supported nonlinear Timoshenko beam is obtained using a variationally correct (VC) model for the beam [Marur, S., Prathap, G., 2005. Nonlinear beam vibration problems and simplification in finite element model. Comput. Mech. 35(5), 352–360.]. The new model does not involve any simplifications commonly employed in the finite element formulations in order to ease the computation of nonlinear stiffness terms from nonlinear strain energy terms. A comparison of results through MTrL and MTnL techniques consistently indicate a superior quality of approximations via the transversal linearization technique. While the usage of tangential system matrices is common in nonlinear finite element practices, it is demonstrated that the transversal version of linearization offers an easier and more general implementation, requires no computations of directional derivatives and leads to a consistently higher level of numerical accuracy. It is also observed that higher order versions of MTrL/MTnL with Lagrangian interpolations may not work satisfactorily and hence spline interpolations are suggested to overcome this problem.     

Optimal robust voltage control of electrically driven robot manipulators

This paper develops a novel robust optimal voltage control of electrically driven robot manipulators. The whole robotic system including the robot manipulator and motors is considered in the control problem. Particle Swarm Optimization (PSO) is used to optimize the control design parameters, thus the performance of control system is highly improved. Beside this, we use Voltage Control Strategy (VCS) which is more robust, faster, less coupled, and less computational compared with the common strategy called as Torque Control Strategy (TCS). To state these advantages, it is reasoning that the TCS is dependent on the manipulator dynamics whereas the VCS can be free from it. The robust optimal voltage control is verified by convergence analysis. A comparative study between the VCS and the TCS confirms superiority of the VCS to the TCS. Simulation results present effectiveness of the proposed methods applied on a spherical robot manipulator driven by permanent magnet dc motors.     

Adaptive nonlinear model predictive control design of a flexible-link manipulator with uncertain parameters

This paper presents a novel adaptive nonlinear model predictive control design for trajectory tracking of flexible-link manipulators consisting of feedback lineariza-tion, linear model predictive control, and unscented Kalman filtering. Reducing the nonlinear system to a linear system by feedback linearization simplifies the optimization prob-lem of the model predictive controller significantly, which, however, is no longer linear in the presence of parame-ter uncertainties and can potentially lead to an undesired dynamical behaviour. An unscented Kalman filter is used to approximate the dynamics of the prediction model by an online parameter estimation, which leads to an adaptation of the optimization problem in each time step and thus to a better prediction and an improved input action. Finally, a detailed fuzzy-arithmetic analysis is performed in order to quantify the effect of the uncertainties on the control structure and to derive robustness assessments. The control structure is applied to a serial manipulator with two flexible links containing uncertain model parameters and acting in three-dimensional space.     

Approximate continuous fixed-time terminal sliding mode control with prescribed performance for uncertain robotic manipulators

This paper studies an approximate continuous fixed-time terminal sliding mode control (CFTSMC) with prescribed performance for uncertain robotic manipulators. A transformation concerning tracking error using a fixed-time prescribed performance function is proposed to guarantee the transient and steady-state performance of trajectory tracking control for uncertain robotic manipulators within fixed time. Utilizing the transformed error, a smooth fixed-time sliding mode surface is designed. Then, based on the proposed sliding mode surface, an approximate CFTSMC scheme is presented to achieve inherent chattering-free control for uncertain robotic manipulators. According to the Lyapunov stability theory, it is proved that the position tracking error can be bounded in the prescribed performance boundaries and globally converges to a defined small region within fixed time and then approaches exponentially to the origin. Several numerical simulation results demonstrate the effectiveness and superiority of the proposed control strategy for uncertain robotic manipulators.

     

EXACT LINEARIZATION BASED MULTIPLE-SUBSPACE ITERATIVE RESOLUTION TO AFFINE NONLINEAR CONTROL SYSTEM

To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structural mechanics and optimal control, multiple-substructure method was inducted to solve the optimal control problem which was linearized. And finally the solution to the original nonlinear system was found. Compared with the classical linearizational method of Taylor expansion, this one diminishes the abuse of error expansion with the enlargement of used region.     

Robust trajectory tracking control for a laboratory helicopter

This paper presents a robust nonlinear control strategy to deal with the trajectory tracking control problem for a laboratory helicopter. The helicopter model is considered as a nominal one with uncertainties such as unmodeled nonlinear dynamics, parametric uncertainties, and external disturbances. The proposed control approach incorporates the feedback linearization technique (FLT) and the signal compensation technique. The FLT is first applied to achieve the linearization of the nominal nonlinear model for reducing the conservation of the robust compensator design. A nominal controller based on the linear quadratic regulation method is designed for the linearized nominal system, whereas a robust compensator is introduced to restrain the influences of the uncertainties. It is shown that the trajectory tracking errors of the closed-loop system are ultimately bounded, and the boundaries can be specified by choosing the controller parameters. Simulation and experimental results on the lab helicopter verify the effectiveness of the proposed method.     

单足机器人周期跳跃控制的虚拟约束方法

 研究单足机器人周期跳跃控制问题．弹簧支撑倒立摆模型可以比较准确地描述动物的跳跃行为,但无控制的自然跳跃抗干扰能力较差,一般采用轨迹跟踪控制方法实现单足机器人周期跳跃．当系统存在比较大的误差时,传统的时间轨迹跟踪控制方法存在明显的不足．引入虚拟约束技术,采用基于空间路径跟踪的控制方法可以克服时间轨迹跟踪的不足．采用点足机器人模型,并通过控制腿伸缩的方式为系统提供动力,将跳跃过程分为地面摆动和腾空飞行两个阶段,并通过起飞和着陆两个事件完成两个阶段之间的转换,整个系统模型属于欠驱动非光滑动力学系统．根据简化的动力学方程获得系统的虚拟约束解析表达式,并采用部分反馈线性化方法结合PD 控制设计系统的控制律．分析了系统的混合零动力学方程,并证明了闭环系统的临界稳定性．仿真结果表明,提出的控制方法可以实现单足机器人的周期跳跃控制,并且对外部干扰具有较强的鲁棒性．     

变长度弹性伸缩腿双足机器人动力学与控制

研究了半被动双足机器人的平面稳定行走的控制问题．基于弹簧质点模型，采用拉格朗日方法分别得到双足机器人单支撑阶段与双支撑阶段的动力学方程，对机器人系统的动力学方程求得周期解．应用非线性系统状态反馈线性化理论，在双足机器人的单支撑阶段和双支撑阶段中，通过控制双足机器人的腿长度，实现稳定的周期行走．在理论分析的基础上，对控制算法进行了仿真与研究．结果表明：在周期行走过程中，文中采用的变长度控制算法可以使双足机器人克服外界的干扰，并具有较强的抗干扰性．     

Stability case study of the ACROBOTER underactuated service robot

The dynamics of classical robotic systems are usually described by ordinary differential equations via selecting a minimum set of independent generalized coordinates. However, different parameterizations and the use of a nonminimum set of (dependent) generalized coordinates can be advantageous in such cases when the modeled device contains closed kinematic loops and/or it has a complex structure. On one hand, the use of dependent coordinates, like natural coordinates, leads to a different mathematical representation where the equations of motion are given in the form of differential algebraic equations. On the other hand, the control design of underactuated robots usually relies on partial feedback linearization based techniques which are exclusively developed for systems modeled by independent coordinates. In this paper, we propose a different control algorithm formulated by using dependent coordinates. The applied computed torque controller is realized via introducing actuator constraints that complement the kinematic constraints which are used to describe the dynamics of the investigated service robotic system in relatively simple and compact form. The proposed controller is applied to the computed torque control of the planar model of the ACROBOTER service robot. The stability analysis of the digitally controlled underactuated service robot is provided as a real parameter case study for selecting the optimal control gains.     

A nonlinear high gain observer based input–output control of flexible link manipulator

The input–output control strategy needs all of the states feedback. However, in flexible link robot manipulators, measuring the time rate of elastic degrees of freedom is practically impossible. In this paper, a new nonlinear high gain observer has been developed to estimate the elastic degrees of freedom and their time derivatives. The control strategy is based on an output redefinition approach which stabilizes the zero dynamics of the manipulator. Finally, the results are presented by implementing the proposed observer and controller on a single link flexible manipulator. Numerical simulations will support the validity of our research results.     

平流层飞艇动力学与控制研究进展

本文简要介绍了飞艇的发展沿革和研究现状. 通过同传统的航空器、航天器、潜艇和低空飞艇进行比较, 阐述了平流层飞艇的飞行原理. 从基本运动模型和复杂受力情况的角度, 系统地讨论了飞艇动力学研究进展, 包括空气动力学研究、静力分析、热力学分析、柔性体动力学及流固耦合研究. 然后综述了飞艇控制方法研究进展, 包括小扰动线性化控制、输入输出反馈线性化控制、基于Lyapunov 非线性稳定性的控制及其他控制方法. 最后展望了在平流层飞艇动力学与控制领域需要从6 个方面加强研究.