Image based visual servoing for robot positioning tasks

Visual servoing has become a popular paradigm for the control of complex robotic systems: this sensor based approach exploits the image informations provided by one ore more cameras in a feedback control loop to drive the system to the desired configuration. Here authors will refers to a monocular system where the camera is mounted on the end effector of a 6-DOF manipulator. Among different Visual Servoing approaches Image Based Visual Servoing (IBVS) has been the most investigated in the literature because of its nice properties of robustness with respect to both robot modeling and camera calibration errors: in IBVS the control loop is in fact directly closed in the image; moreover IBVS doesn’t require the knowledge of the target/scene model (model-free approach). Despite its advantages IBVS may be affected by singularity and local minima problems of the control law: these drawbacks arise especially when the initial and the goal camera images respectively corresponding to the actual and desired system configurations are very different (i.e for large system displacements). To overcome these problems an image path planning can be exploited to ensure system convergence. In this paper author presents an off-line image path planning that can be used to execute system positioning task also in presence of large camera displacements: planning trajectories has been developed such as to make the robot end effector move on a 3D helix, connecting the initial and the desired arm configuration, by generating feasible robot twist-screws and keeping the target in the image field of view. During control execution also 3D target informations are retrieved through an adaptive estimation law. Both simulations and experimental results show the feasibility of the proposed approach.     

Global motion analysis of energy-based control for 3-link planar robot with a single actuator at the first joint

This paper studies nonlinear control of a 3-link planar robot moving in the vertical plane with only the first joint being actuated while the two other revolute joints are passive (called the APP robot below). A nonlinear energy-based controller is proposed, whose objective is to drive the APP robot into an invariant set where the first link is in the upright position and the total mechanical energy converges to its value at the upright equilibrium point (all three links are in the upright position). By presenting and using a new property of the motion of the APP robot, without any condition on its mechanical parameters, this paper proves that if the control gains are larger than specific lower bounds, then only a measure-zero set of initial conditions converges to three strictly unstable equilibrium points instead of converging to the invariant set. This paper presents numerical results for a physical 3-link planar robot to validate the obtained theoretical results and to demonstrate a switch–and–stabilize maneuver in which the energy-based controller is switched to a linear state feedback controller that stabilizes the APP robot at its upright equilibrium point.     

Effects of rotary inertia on sub- and super-critical free vibration of an axially moving beam

The most important issue in the vibration study of an engineering system is dynamics modeling. Axially moving continua is often discussed without the inertia produced by the rotation of the continua section. The main goal of this paper is to discover the effects of rotary inertia on the free vibration characteristics of an axially moving beam in the sub-critical and super-critical regime. Specifically, an integro-partial-differential nonlinear equation is modeled for the transverse vibration of the moving beam based on the generalized Hamilton principle. Then the effects of rotary inertia on the natural frequencies, the critical speed, post-buckling vibration frequencies are presented. Two kinds of boundary conditions are also compared. In super-critical speed range, the straight configuration of the axially moving beam loses its stability. The buckling configurations are derived from the corresponding nonlinear static equilibrium equation. Then the natural frequencies of the post-buckling vibration of the super-critical moving beam are calculated by using local linearization theory. By comparing the critical speed and the vibration frequencies in the sub-critical and super-critical regime, the effects of the inertia moment due to beam section rotation are investigated. Several interesting phenomena are disclosed. For examples, without rotary inertia, the study overestimates the stability of the axially moving beam. Moreover, the relative differences between the super-critical fundamental frequencies of the two theories may increase with an increasing beam length.     

FUNDAMENTAL FREQUENCY MAXIMIZATION DESIGN FOR CONTINUOUS FIBER-REINFORCED COMPOSITE STRUCTURES 1)

与传统的金属材料相比, 纤维增强复合材料在强度、刚度、抗断裂等诸多方面具备更优良的性能, 目前纤维增强复合材料已在汽车、航空航天等工业领域得到了广泛应用. 本文提出一种求解连续纤维增强复合材料结构无阻尼自由振动下的基频最大化问题的拓扑优化方法. 为了实现结构拓扑构型与纤维角度的同步优化, 建立了以准许的材料用量体积分数为约束、以结构的一阶特征值为目标函数的动力学拓扑优化模型, 该模型包括表征结构拓扑构型的密度设计变量和表征纤维方向的角度设计变量. 详细推导了特征值目标函数关于密度设计变量和角度设计变量的解析灵敏度列式, 并采用移动渐进线方法 (method of moving asymptotes, MMA) 进行了优化求解; 最后通过3个数值算例验证本文方法的有效性, 其中包括一个以刚度最大化为目标的静力学优化算例, 和两个以一阶特征值为目标的动力学优化算例. 结果表明, 所提方法优化迭代过程稳健, 收敛快, 能够在实现结构拓扑构型与纤维角度的一体化优化的同时, 有效提高结构的频率.     

A unified solution to swing-up control for n-link planar robot with single passive joint based on virtual composite links and passivity

This paper concerns the swing-up control of an n-link revolute planar robot with any one of the joints being passive. The goal is to design and analyze a swing-up controller that can bring the robot into any arbitrarily small neighborhood of the upright equilibrium point, at which all the links are in the upright position. We present a unified solution based on the notion of virtual composite link (VCL), which is a virtual link made up of one or more active links. By using the angles of two series of VCLs separated by the passive joint and using the total mechanical energy of the robot, we design a swing-up controller and analyze the global motion of the robot under the controller. The main new results of this paper are: (1) we obtain a lower bound for each control gain related to the angle of each VCL such that the closed-loop system has only one undesired equilibrium point in addition to the upright equilibrium point, and we present an original proof of the conditions on the control gains for a class of n-link underactuation-degree-one planar robots with an active first joint; (2) we provide a bigger control gain region for achieving the control objective than those of previous results on three- and n-link robots with a passive first joint; (3) we validate the theoretical results via numerical simulations on a 4-link robot with the passive joint in each of the four positions. This paper gains an insight into the passivity-based control of underactuated multiple-DOF systems.     

连续纤维增强复合材料结构基频最大化设计

与传统的金属材料相比, 纤维增强复合材料在强度、刚度、抗断裂等诸多方面具备更优良的性能, 目前纤维增强复合材料已在汽车、航空航天等工业领域得到了广泛应用. 本文提出一种求解连续纤维增强复合材料结构无阻尼自由振动下的基频最大化问题的拓扑优化方法. 为了实现结构拓扑构型与纤维角度的同步优化, 建立了以准许的材料用量体积分数为约束、以结构的一阶特征值为目标函数的动力学拓扑优化模型, 该模型包括表征结构拓扑构型的密度设计变量和表征纤维方向的角度设计变量. 详细推导了特征值目标函数关于密度设计变量和角度设计变量的解析灵敏度列式, 并采用移动渐进线方法 (method of moving asymptotes, MMA) 进行了优化求解; 最后通过3个数值算例验证本文方法的有效性, 其中包括一个以刚度最大化为目标的静力学优化算例, 和两个以一阶特征值为目标的动力学优化算例. 结果表明, 所提方法优化迭代过程稳健, 收敛快, 能够在实现结构拓扑构型与纤维角度的一体化优化的同时, 有效提高结构的频率.      

非自旋航天器混沌姿态运动及其参数开闭环控制

研究万有引力场中受大气阻力且存在结构内阻尼的非自旋航天器在椭圆轨道上平面天平动的混沌及其参数开闭环控制问题．在建立数学模型的基础上确定出现混沌的必要条件并数值验证混沌的存在性，提出非线性振动系统混沌运动的参数开闭环控制并应用于控制航天器的混沌姿态运动．     

一类新型仿生起竖结构设计及其动力学分析

由于生物能够通过丰富的运动形式完成特定的任务, 仿生设计方法受到了学者们的广泛关注. 蚯蚓在各种环境中具有出色的移动能力和适应性, 受此启发, 仿蠕虫机器人被提出并应用在搜救、医疗等领域. 然而现有的仿蠕虫机器人一般通过体节的轴向变形实现直线运动, 无法实现类似蛇类生物的起竖功能. 为了解决现有的仿蠕虫机器人无法起竖的问题, 本文提出了一种具有非线性多稳态性质的仿生柔性关节, 并在此基础上构建了多节仿生起竖结构以实现类似尺蠖、蛇等生物的起竖功能. 首先, 本文提出了一种仿生起竖关节模型, 推导了多节仿生起竖结构的总势能表达式, 从而建立了多节仿生起竖结构的动力学模型; 随后, 基于多节仿生起竖结构总势能的表达式和多元函数极值原理, 提出了实现需求起竖构型的结构参数设计准则, 利用动力学模型验证了结构参数设计准则的有效性, 并研究了需求构型的触发条件; 最后, 针对不同起竖节数的设计需求, 设计了相应节数的仿生起竖结构. 研究结果表明, 结构参数设计准则能够使得多节仿生起竖结构达到需求的仿生起竖构型, 并在需求构型处保持稳定平衡; 此外, 定义了初始激励与起竖构型的比例系数单调性变量, 并基于仿生起竖结构不同稳态的吸引盆揭示了上述变量构成的构型触发准则, 这为仿生起竖结构的构型切换提供了理论依据. 本文提出的仿生起竖结构对仿蠕虫机器人的功能拓展具有参考价值和指导意义, 也是对仿生设计理论的进一步完善.      

Separating Dissipative Pulses: The Exit Manifold

We prove that if a reaction-diffusion equation (in one space dimension) has asymptotically stable, exponentially localized traveling wave solutions then there are solutions of the system which are nearly the linear superposition of two such pulses moving in opposite directions away from one another. Moreover, such solutions are themselves asymptotically stable. This result is meant to complement analytic or numeric studies into interactions of such pulses over finite times which might result in the scenario treated here. Since the pulses are moving in opposite directions, it is not possible to put the problem into a moving reference frame which renders the linear problem autonomous. We overcome this difficulty by embedding the original system in a larger one wherein the linear part can be written as a time independent piece plus another piece which, even though it is non-autonomous and large, has certain properties which allow us to treat it as if it were a small perturbation.     

Hydrodynamic Interaction Between a Slightly Distorted Sphere and a Fixed Sphere

The planar motion of a slightly distorted sphere around a fixed sphere in an unbounded fluid is investigated by a perturbation approach. An approximate velocity potential is derived in terms of sets of singularities by using the successive potential method. In a relative coordinate system moving with the uniform stream, the kinetic energy of the fluid is expressed as a function of 15 added masses. Approximate analytical solutions of added masses in series form are obtained and applied to determine the trajectories of the slightly distorted sphere around a fixed sphere. The hydrodynamic interaction between two bodies is computed based on the dynamical equations of motion. It is found that the presence of a sphere generates an effect on the planar motion of the slightly distorted sphere and the initial configuration of the slightly distorted sphere has a decisive influence on the development of its subsequent rotational motion. Received 24 August 2000 and accepted 8 February 2001     

The shear flow behavior of LCPs based on a generalized Doi model with distortional elasticity

We consider the shear flow behavior of nematic LCPs, modeled via an extension of the Doi theory that incorporates the mean-field nematic potential due to Marrucci and Greco to account for distortional elasticity. Based upon the constitutive model that derives from this starting point, we utilize finite-element methods to investigate the LCP behavior in a planar shear flow. We assume that the LCP is pinned at the walls and is initially in its equilibrium configuration. The goal of our simulations is to explore the evolution of the LCP structure and the flow. Our results show that in-plane tumbling instabilities lead to a non-uniform orientation field, which, in turn, arrests tumbling. The resulting quasi-steady-state texture is characterized by a length scale that seems to be consistent with a Marrucci-like scaling. When we allow for out-of-plane tipping of the director, we predict an out-of-plane director instability, which is qualitatively consistent with what has been observed in experiments.     

Supercritical vibration of nonlinear coupled moving beams based on discrete Fourier transform

Natural frequencies of nonlinear coupled planar vibration are investigated for axially moving beams in the supercritical transport speed ranges. The straight equilibrium configuration bifurcates in multiple equilibrium positions in the supercritical regime. The finite difference scheme is developed to calculate the non-trivial static equilibrium. The equations are cast in the standard form of continuous gyroscopic systems via introducing a coordinate transform for non-trivial equilibrium configuration. Under fixed boundary conditions, time series are calculated via the finite difference method. Based on the time series, the natural frequencies of nonlinear planar vibration, which are determined via discrete Fourier transform (DFT), are compared with the results of the Galerkin method for the corresponding governing equations without nonlinear parts. The effects of material parameters and vibration amplitude on the natural frequencies are investigated through parametric studies. The model of coupled planar vibration can reduce to two nonlinear models of transverse vibration. For the transverse integro-partial-differential equation, the equilibrium solutions are performed analytically under the fixed boundary conditions. Numerical examples indicate that the integro-partial-differential equation yields natural frequencies closer to those of the coupled planar equation.     

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.     

振动驱动移动系统平面避障运动分析

近年来,工业机器人的应用领域日益广泛,可移动机器人的发展备受关注,为了在一些复杂环境中准确地完成作业,学者们提出并研究了振动驱动移动系统.本文研究了在各向异性黏性摩擦环境中一类有两个在平行轨道内做正弦运动的内部质量块的振动驱动移动系统的运动规律,提出了使系统完成包括避障等规定作业的驱动设计方法.首先利用第二类拉格朗日方程,建立了系统的动力学方程;然后,利用速度Verlet积分法分析了系统的运动规律,得到了内部驱动参数与系统运动轨迹、运动速度的关系;最后,结合振动驱动移动系统的运动规律,提出了使系统沿预设路径运动和实现避障运动的驱动设计方法.通过曲线离散得到了系统沿预设路径运动的移动轨迹,进而通过改变内部质量块的驱动参数,使系统沿预设路径运动.为了使移动系统在障碍物环境中达到目标位置,提出了结合栅格法,Floyd算法及最小顶点圆法的优化的路径规划计算方法,得到了振动驱动移动系统在障碍物环境中运动的最优路径,并通过改变内部质量块的驱动参数实现了移动系统的避障运动.     

Geometrically exact planar beams with initial pre-stress and large curvature: Static configurations,natural frequencies,and mode shapes

Within this paper, an analytical formulation is provided and used to determine the natural frequencies and mode shapes of a planar beam with initial pre-stress and large variable curvature. The static configuration, mode shapes, and natural frequencies of the pre-stressed beam are obtained by using geometrically exact, Euler–Bernoulli beam theory. The beam is assumed to be not shear deformable and inextensible because of its slenderness and uniform, closed cross-section, as well as the boundary conditions under consideration. The static configuration and the modal information are validated with experimental data and compared to results obtained from nonlinear finite-element analysis software. In addition to the modal analysis about general static configurations, special consideration is given to an initially straight beam that is deformed into semi-circular and circular static configurations. For these special circular cases, the partial differential equation of motion is reduced to a sixth-order differential equation with constant coefficients, and solutions of this system are examined. This work can serve as a basis for studying slender structures with large curvatures.     

A proposed hybrid neural network for position control of a walking robot

The use of a proposed recurrent neural network control system to control a four-legged walking robot is presented in this paper. The control system consists of a neural controller, a standard PD controller, and the walking robot. The robot is a planar four-legged walking robot. The proposed Neural Network (NN) is employed as an inverse controller of the robot. The NN has three layers, which are input, hybrid hidden and output layers. In addition to feedforward connections from the input layer to the hidden layer and from the hidden layer to the output layer, there is also a feedback connection from the output layer to the hidden layer and from the hidden layer to itself. The reason to use a hybrid layer is that the robot’s dynamics consists of linear and nonlinear parts. The results show that the neural-network controller can efficiently control the prescribed positions of the stance and swing legs during the double stance phase of the gait cycle after sufficient training periods. The goal of the use of this proposed neural network is to increase the robustness of the control of the dynamic walking gait of this robot in the case of external disturbances. Also, the PD controller alone and Computed Torque Method (CTM) control system are used to control the walking robot’s position for comparison.     

Synthesizing Controls for an Uncertain System with a Conditionally Invariant Set

Controls are synthesized for a nonlinear uncertain system with two moving sets. These sets are conditionally invariant and uniformly asymptotically stable with respect to the solutions of a controlled uncertain system     

Adaptive robust maneuvering control for nonlinear systems via dynamic surface technique

In this paper, the adaptive robust controller based on dynamic surface technique is investigated for the maneuvering problem of uncertain nonlinear systems with external disturbances. As preliminary, the definition of semi-globally uniformly practically asymptotically stable and its Lyapunov criterion are presented. The static part of controller with smooth robust compensator and adaptive law is designed to achieve the geometric task of maneuverability, and the dynamic control is proposed to reach the speed task by filtered-gradient update law. Moreover, utilizing first-order filter, the problem of “dimensional explosion” is avoided in controller design. Simulation is conducted for three-mecanum-wheeled mobile robot actuated by DC motors to illustrate the effectiveness of the control strategy.

     

Boundary-layer corrections for stress and strain fields in randomly heterogeneous materials

Boundary-layer effects on the effective response of fibre-reinforced media are analysed. The distribution of the fibres is assumed random. A methodology is presented for obtaining non-local effective constitutive operators in the vicinity of a boundary. These relate ensemble averaged stress to ensemble averaged strain. Operators are also developed which re-construct the local fields from their ensemble averages. These require information on the local configuration of the medium. Complete information is likely not to be available, but averages of these operators conditional upon any given local information generate corresponding conditional averages of the fields. Explicit implementation is performed within the framework of an approximation of Hashin-Shtrikman type. Two types of geometry are considered in examples: a half-space and a crack in an infinite heterogeneous medium. These are representative, asymptotically, of the field in the vicinity of any smooth boundary, and in the vicinity of a crack tip, respectively. Results have been obtained for the case of anti-plane deformation, realized by the imposition of either Dirichlet or Neumann conditions on the boundary; those for the Neumann condition are presented and discussed explicitly. The stresses in both fibre and matrix adjacent to a crack tip are shown to differ substantially from the values that would be predicted by ordinary homogenization.     

基于摇臂——转向架结构月球车的越障能力判断准则

对轮式移动系统进行越障分析时,常以垂直越障作为评价标准.但是,月球车在凹凸不平的月面上行驶时,垂直越障模型不具有一般性.为此,本文对基于摇臂-转向架结构月球车在任意路面的越障进行了研究.一般情况下,由于任意路面越障模型相对复杂,可以建立的独立平衡方程数目少于未知变量数,因此无法得到越障能力与路面参数的函数关系式.针对上述问题,文中将最大有效牵引力假设引入越障模型中,得到了一种任意路面越障能力的判断准则.通过算例分析,表明了所提方法的有效性.