A simple and quick control strategy for a class of first-order nonholonomic manipulator

This paper presents a simple and quick control strategy for a class of first-order nonholonomic manipulator: planar n-link manipulator with a passive first joint (no gravity). The control target is driving its endpoint from any initial position to any target position. First, we reduce the planar n-link manipulator to a planar three-link one by maintaining the states (angles and angular velocities) of n-3 active links in the initial value all the time. That is, we only adjust the states of the remaining two active links in the whole control process, and these two adjusted active links are chosen to guarantee that the target position is in the reachable region of the planar n-link manipulator by using the enumeration method. Then, we divide the whole control process into two stages for the reduced planar three-link manipulator. In each stage, the manipulator becomes a planar two-link one by maintaining the states of one adjusted active link to be the constant value. The state constraint existing between the passive first link and the adjusted active link is obtained by using the integral characteristics of a planar two-link manipulator. Meantime, the geometric constraint between the position of the endpoint and angles of all joints is obtained based on the homogeneous coordinate transformation method. According to the above two kinds of constraint, the target angles of the two adjusted active links are calculated by employing the particle swarm optimization algorithm. When the two adjusted active links are controlled to their target angles in turn, the control target of the planar n-link manipulator is completed. Finally, simulation results demonstrate that the proposed control strategy is valid and rapid.     

Dynamic modeling and extended bifurcation analysis of flexible-link manipulator

Abstract

In this article, the nonlinear dynamic analysis of a flexible-link manipulator is presented. Especially, the possibility of chaos occurrence in the system dynamic model is investigated. Upon the occurrence of chaos, the system dynamical behavior becomes unpredictable which in turn brings about uncertainty and irregularity in the system motion. The importance of this investigation is pronounced in similar systems such as double pendulum and single-link flexible manipulator. What makes this study distinct from previous ones is the increase in the number of links as well as the changing the bifurcation parameters from system mechanical parameters to force and torque inputs. To this aim, the motion equations of the N-link robot, which are derived with the aid of the recursive Gibbs-Appell formulation and the assumed modes method, are used. In the end, the equations of motion are developed for a two-link flexible manipulator, and its nonlinear dynamical behavior is analyzed via numerical integration of discrete equations. The results are presented in the form of bifurcation diagrams (for variation of torque amplitude), time histories, phase-plane portraits, Poincaré sections, and fast Fourier transforms. The outcomes indicate that when there is no offset, the decrease in damping results in chaotic generalized modal coordinates. In addition, as the excitation frequency decreases from 2π to π, a limiting amplitude is created at 0.35 before which the behavior of generalized rigid and modal coordinates is different, while this behavior has more similarity after this point. An experimental setup is also used to check the torques as the system input.     

Forward position analysis of 6-3 Linapod parallel manipulators

In this study closed-form solutions to the forward kinematic problems are obtained for a particular type of six degree-of-freedom parallel manipulator called 6-3 Linapod. The 6-3 Linapod parallel manipulators have a 6-3 PSS (or PUS) structure, and forward kinematic solutions are obtained by using the solution procedure for 6-3 SPS (or UPS) manipulators. In this procedure, a 6-3 Linapod is first transformed into its equivalent mechanism, namely an inclined 3RS manipulator, and then the condition that the three spherical joints on the moving platform form an equilateral triangle leads us to obtain three polynomial equations in three unknowns. These equations are solved by using Sylvester dialytic elimination method. Each set of real roots corresponds to a particular configuration of the manipulator. Solutions so obtained are verified by performing inverse position analysis. A method to identify configurations containing crossed links is presented in this study, which is based on the interpretation of link crossing as intersection of a link with a triangle, whose vertices are positions of joints on the corresponding links.     

空间机械臂捕获卫星过程的碰撞动力学模拟及镇定运动的鲁棒控制

讨论了漂浮基空间机械臂捕获未知运动目标卫星的接触碰撞动力学建模和接触碰撞后系统镇定运动的控制问题。利用第二类拉格朗日方法和牛顿-欧拉法分别建立了接触碰撞前漂浮基空间机械臂和目标卫星两分体系统的动力学模型;以此为基础借助于空间机械臂与目标卫星接触点间的运动几何关系、力传递关系,计算了接触碰撞所产生的影响效应;捕获卫星后,联立空间机械臂与卫星接触碰撞前的动力学模型,建立了接触碰撞后两系统组合体动力学模型;并设计了增广鲁棒控制算法,以对受碰撞冲击后处于不稳定的组合体系统进行镇定运动控制。上述控制方法能应用于空间机械臂载体位置不受控情况,并能使组合体系统控制方程关于卫星不确定参数呈线性化关系。最后,利用数值仿真模拟捕获过程系统运动状态,验证了上述鲁棒控制镇定运动的效果。     

带有末端集中质量的双连杆柔性机械臂主动控制

对带有末端集中质量的双连杆柔性机械臂的主动控制进行了研究,给出系统的动力学方程,采用非线性解耦反馈控制方法分别得出系统大范围运动方程和柔性臂的动力学方程,采用机械臂逆动力学方法和LQR方法分别设计大范围运动控制律和压电作动器控制律.仿真结果显示,本文控制方法能够有效地进行机械臂的轨迹跟踪,柔性臂的弹性振动可以得到有效抑制.     

Vibration analysis of a planar multilink manipulator using a reduced-order matrix formulation

The main scope of this paper is both to provide an efficient formulation for deriving natural frequencies and mode shapes of a multilink flexible manipulator in an arbitrary posture and discuss the importance of introducing axial deformations along with transversal ones in the same postures. The free vibration problem is solved through a global transfer matrix formulation, which is obtained by opportunely assembling the transfer matrices of links and joints associated with the desired configuration of the robot. The formulation has been chosen in order to keep the same matrix order of the problem, regardless of the number of links of the manipulator. Manipulator links are treated as Timoshenko beams by accounting for both axial loading capability and mass/inertial effects due to the joint actuators. Numerical comparisons between the solutions derived herein and those obtained through existing formulations highlight the importance of the proposed model within the frame of multilink flexible manipulators. A forced vibration analysis is finally presented for a two-link manipulator.     

Screw-matrix method in dynamics of multibody systems

In the present paper the concept of screw in classical mechanics is expressed in matrix form, in order to formulate the dynamical equations of the multibody systems. The mentioned method can retain the advantages of the screw theory and avoid the shortcomings of the dual number notation. Combining the screw-matrix method with the tool of graph theory in Roberson/Wittenberg formalism. We can expand the application of the screw theory to the general case of multibody systems. For a tree system, the dynamical equations for eachj-th subsystem, composed of all the outboard bodies connected byj-th joint can be formulated without the constraint reaction forces in the joints. For a nontree system, the dynamical equations of subsystems and the kinematical consistency conditions of the joints can be derived using the loop matrix. The whole process of calculation is unified in matrix form. A three-segment manipulator is discussed as an example. This work is supported by the National Natural Science Fund.     

多体系统动力学设计灵敏度分析直接微分法

针对受完整约束的多体系统动力学微分／代数方程数学模型动态最优化设计问题，建立了通用的目标函数和约束方程，并以此为基础，用直接微分方法系统地推导出了计算设计灵敏度的通用公式，最后通过平面机械臂模型对理论结果和相应算法进行了验证．     

Dynamics of a Robot Manipulator with Elastic Links

The problems of dynamic and kinematic control of a multilink robot manipulator are formulated. The distributed elasticity and inertia of the manipulator links are taken into account on the basis of the Timoshenko-beam model on the assumption that each of its elements moves complexly. The results obtained here are compared with data on the dynamic characteristics of a manipulator with rigid links and a manipulator with elastic links, whose elastic properties were simulated on the basis of the Euler–Bernoulli-beam model     

The bouncing motion appearing in a robotic system with unilateral constraint

The hopping or bouncing motion can be observed when robotic manipulators are sliding on a rough surface. Making clear the reason of generating such phenomenon is important for the control and dynamical analysis for mechanical systems. In particular, such phenomenon may be related to the problem of Painlevé paradox. By using LCP theory, a general criterion for identifying the bouncing motion appearing in a planar multibody system subject to single unilateral constraint is established, and found its application to a two-link robotic manipulator that comes in contact with a rough constantly moving belt. The admissible set in state space that can assure the manipulator keeping contact with the rough surface is investigated, and found which is influenced by the value of the friction coefficient and the configuration of the system. Painlevé paradox can cause either multiple solutions or non-existence of solutions in calculating contact force. Developing some methods to fill in the flaw is also important for perfecting the theory of rigid-body dynamics. The properties of the tangential impact relating to the inconsistent case of Painlevé paradox have been discovered in this paper, and a jump rule for determining the post-states after the tangential impact finishes is developed. Finally, the comprehensively numerical simulation for the two-link robotic manipulator is carried out, and its dynamical behaviors such as stick-slip, the bouncing motion due to the tangential impact at contact point or the external forces, are exhibited.     

Dynamics of flexible multibody systems with tree topologies

The dynamic equations of flexible multibody systems with tree topological configuration are derived by using the Jourdain's principle. The independent joint coordinates are introduced to describe the large displacements of the bodies, and the modal coordinates are used to describe small deformations of flexible bodies based on the consistent mass finite element method and normal vibration mode analysis. The minimum differential equations are developed, which are compatible with the equations of multi-rigid body systems or structural dynamics. The stiff problem in the numerical integration is thus alleviated effectively. The method used in this paper can be extended to deal with systems with other topological configurations. Finally, the validity and feasibility of the presented mathematical model are demonstrated by a numerical example of a manipulator with two elastic links. The project supported by National Natural Science Foundation of China     

Influence of the flexibility of links on the dynamics of a multilink robot manipulator

The influence of the distributed flexibility of links on the dynamic behavior of a cantilevered multilink robot manipulator is studied. Two dynamic models of the robot are considered. In one of the models, the effectors are flexible. It is described by a hybrid system of ordinary and partial differential equations. In the other model, the manipulator links are perfectly rigid. It is based on the Lagrange formalism and described by a system of ordinary differential equations. To estimate the positioning accuracy, the results of modeling the manipulator in both cases are compared. A three-link manipulator is examined as an example __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 126–137, May 2007.     

多刚体系统动力学的旋量-矩阵方法

本文将经典力学中的旋量概念以矩阵形式表示,用以建立多刚体系统的动力学方程。这种旋量-矩阵方法能保留旋量融矢量与矢量矩于一体的优点,却避免以往对偶数记法的缺点。结合 Roberson/wittenburg的图论工具,旋量-矩阵方法的应用范围可扩大到一般多刚体系统。对于树形系统,利用旋量通路矩阵推导各个由第i铰联结的全部外侧刚体组成的第i子系统的动力学方程,可避免出现铰的约束反力,对于非树系统,则利用回路矩阵导出各子系统动力学方程及运动学相容条件,全部计算过程统一为矩阵运算,以操作机器人作为具体算例。     

Dynamic analysis of a disc brake under frictional and thermomechanical internal loading

The study of the vibratory response of a mechanical system as complex as a disc brake needs to consider the complexity of the problem induced by the coupling of tribological, thermomechanical and dynamical effects. Experimental consideration are discussed here for two set ups at the full scale of the disc brake and at a local scale focussed on the third body interface. A numerical model with thermomechanical and dynamical couplings is then presented, followed by a substantial discussion.     

机械臂臂杆刚度主动控制下的末端振动特性研究

机械臂在运动过程中会因臂杆柔性引发结构变形和弹性振动,降低机械臂末端的定位精度和运动稳定性,将结构振动控制方法用于机械臂的振动抑制研究具有重要意义. 基于变刚度主动控制的设计思想,提出了臂杆刚度主动控制方法,通过改变机械臂臂杆的轴向受力状况来主动改变机械臂的刚度. 采用变形耦合法描述了机械臂的非线性变形,进而结合假设模态法和拉格朗日方程建立了臂杆的变刚度动力学模型,并进行了数值仿真. 在此基础上,设计了基于臂杆刚度主动控制方法的单自由度实验台,分析了不同预紧力下机械臂末端的振动特性. 数值仿真和实验结果表明,随着预紧力的增加,机械臂末端的振动幅值得到衰减,验证了臂杆刚度主动控制方法的有效性. 通过采用响应面法建立了机械臂末端的振动响应与预紧力的关系,并基于内部映射牛顿法的子空间置信域法优化算法对预紧力进行了优化分析,得到了最优预紧力. 该研究可为机械臂的精细动力学建模和振动抑制提供一定的理论依据,并为研究经济型低刚度材料的刚化问题提供了方向,以利用廉价低刚度材料取代目前所应用的昂贵高刚度材料.      

漂浮基柔性两杆空间机械臂的关节运动鲁棒控制与柔性振动最优控制Robust joint motion control and vibration optimal control for a free-floating two-flexible-link space manipulator

讨论了载体位置、姿态均不受控情况下,具有有界干扰及有界未知参数的漂浮基柔性两杆空间机械臂的具有鲁棒性的关节运动控制与柔性振动最优控制算法设计问题。首先选择合理的联体坐标系,利用拉格朗日方程并结合动量守恒原理得到漂浮基柔性两杆空间机械臂系统的动力学方程。通过合理选择联体坐标系与利用奇异摄动理论,实现了两个柔性杆柔性振动之间、关节运动与两柔性杆柔性振动的解耦,得到了柔性两杆空间机械臂的慢变子系统与柔性臂快变子系统。针对两个子系统设计相应的控制规律,即增广鲁棒慢变子系统控制律与柔性臂快变子系统最优控制律,这两个相应的子系统控制规律综合到一起构成飘浮基柔性两杆空间机械臂总的关节运动与臂柔性振动控制的组合控制律。系统的数值仿真证实了方法的有效性。该控制方案不需要直接测量漂浮基的位置、移动速度和移动加速度。     

A New Parameter Design Method of a 6-DOF Parallel Motion Simulator for a Given Workspace

This paper introduces a new 9-DOF motion simulator that consists of a 3-DOF parallel manipulator and a 6-DOF parallel manipulator. For the 6-DOF manipulator, a new ‘3–3’-PSS parallel mechanism and a new parameter design method for a given workspace are presented. With the kinematic study of this parallel mechanism and the method of Lagrange multipliers, we have found several key points that represent the worst performance of the manipulator within the given workspace. When a position workspace is given, by checking the manipulator's performances at these key points, one can quickly find out whether the manipulator with certain parameters meets the requirements within this workspace. Furthermore, several figures that can find the appropriate parameters are plotted. This key point method can make the design of parameters much quicker and easier for manipulators.     

An Improved Pore Network Model for the Computation of the Saturated Permeability of Porous Rock

A model to estimate the permeability of a porous sample based on a 3D image of its pore space, obtained by X-ray computed tomography (CT) and applying a threshold algorithm on the CT image, is developed. Computational fluid dynamics (CFD) can be used to directly compute the saturated fluid flow in a sample. This is called the direct method. The direct method is relatively accurate, but computationally very expensive. Therefore, a new pore network approach is presented. Pore networks simplify the pore space to a network of nodes that are hydraulically connected by links. A finite difference CFD method is then applied to simulate the fluid flow inside the links and to compute the local permeability values of the links in the network according to Darcy’s law. As these links are relatively small, this demands less computational resources than a CFD simulation on the whole sample. Once the local permeabilities in the network are known, the permeability of the entire network can be calculated.     

Recursive Lagrangian dynamic modeling and simulation of multi-link spatial flexible manipulator arms

The dynamics for multi-link spatial flexible manipulator arms consisting of n links and n rotary joints is investigated. Kinematics of both rotary-joint motion and link deformation is described by 4 - 4 homogenous transformation matrices, and the Lagrangian equations are used to derive the governing equations of motion of the system. In the modeling the recursive strategy for kinematics is adopted to improve the computational efficiency. Both the bending and torsional flexibility of the link are taken into account. Based on the present method a general-purpose software package for dynamic simulation is developed. Dynamic simulation of a spatial flexible manipulator arm is given as an example to validate the algorithm.     

RESEARCH ON VIBRATION CHARACTERISTICS OF THE MANIPULATOR END UNDER ACTIVE CONTROL OF ARM STIFFNESS$^{\bf 1)}$

机械臂在运动过程中会因臂杆柔性引发结构变形和弹性振动,降低机械臂末端的定位精度和运动稳定性,将结构振动控制方法用于机械臂的振动抑制研究具有重要意义. 基于变刚度主动控制的设计思想,提出了臂杆刚度主动控制方法,通过改变机械臂臂杆的轴向受力状况来主动改变机械臂的刚度. 采用变形耦合法描述了机械臂的非线性变形,进而结合假设模态法和拉格朗日方程建立了臂杆的变刚度动力学模型,并进行了数值仿真. 在此基础上,设计了基于臂杆刚度主动控制方法的单自由度实验台,分析了不同预紧力下机械臂末端的振动特性. 数值仿真和实验结果表明,随着预紧力的增加,机械臂末端的振动幅值得到衰减,验证了臂杆刚度主动控制方法的有效性. 通过采用响应面法建立了机械臂末端的振动响应与预紧力的关系,并基于内部映射牛顿法的子空间置信域法优化算法对预紧力进行了优化分析,得到了最优预紧力. 该研究可为机械臂的精细动力学建模和振动抑制提供一定的理论依据,并为研究经济型低刚度材料的刚化问题提供了方向,以利用廉价低刚度材料取代目前所应用的昂贵高刚度材料.