Singularity loci of planar parallel manipulators with revolute actuators

The determination of the singularity loci of planar parallel manipulators is addressed in this paper. The inverse kinematics of two kinds of planar parallel manipulators (a two-degree-of-freedom manipulator and a three-degree-of-freedom manipulator) are first computed and their velocity equations are then derived. At the same time, the branches of the manipulators are distinguished by the introduction of a branch index K_i. Using the velocity equations, the singularity analysis of the manipulators is completed and expressions which represent the singularity of the manipulators are obtained. A polynomial form of the singularity loci is also derived. For the first type of singularity of parallel manipulators, the singularity locus is obtained by finding the workspace limits of the manipulators. For the second type of singularity, the loci are obtained through the solution of nonlinear algebraic equations obtained from the velocity analysis. Finally, the graphical representation of the complete singularity loci of the manipulators is illustrated with examples. The algorithm introduced in this paper allows the determination of the singularity loci of planar parallel manipulators with revolute actuators, which has been elusive to previous approaches.     

Optimal trajectory generation algorithm for serial and parallel manipulators

In this paper, an Optimal Trajectory Generation Algorithm (OTGA) is developed for generating minimum-time smooth motion trajectories for serial and parallel manipulators. OTGA is divided into two phases. The first phase encompasses derivation of minimum-time optimal trajectory using cubic spline due to its less vibration and overshoot characteristics. Although cubic splines are widely used in robotics, velocity and acceleration ripples in the first & last knots can worsen manipulator trajectory. The second phase includes changing cubic spline interpolation in the first and last knots of optimized trajectory with 7th order polynomial for having zero jerk at the beginning and end points of trajectory. Performing this modification eliminate undesired worsening in the trajectory and provide smoother start and stop of joint motions. Particle Swarm Optimization (PSO) is chosen as optimization algorithm because of its easy implementation and successful optimization performance. OTGA has been tested in simulation for PUMA robot and results are compared with algorithms proposed by earlier authors. In addition, a discrete-time PID control scheme for PUMA robot is designed for comparing energy consumption of OTGA with algorithms developed by previous authors. Comparison results illustrated that OTGA is the better trajectory generation algorithm than the others.     

Singularity and Slow Convergence of the EM algorithm for Gaussian Mixtures

Singularities in the parameter spaces of hierarchical learning machines are known to be a main cause of slow convergence of gradient descent learning. The EM algorithm, which is another learning algorithm giving a maximum likelihood estimator, is also suffering from its slow convergence, which often appears when the component overlap is large. We analyze the dynamics of the EM algorithm for Gaussian mixtures around singularities and show that there exists a slow manifold caused by a singular structure, which is closely related to the slow convergence of the EM algorithm. We also conduct numerical simulations to confirm the theoretical analysis. Through the simulations, we compare the dynamics of the EM algorithm with that of the gradient descent algorithm, and show that their slow dynamics are caused by the same singular structure, and thus they have the same behaviors around singularities.     

A robust dynamic programming algorithm for motion detection and estimation

A new robust algorithm for motion detection and precise evaluation of the motion vectors of moving objects in a sequence of images is presented. It is well known that the accuracy of estimating motion vectors estimation is limited by smoothness constraints and mutual occlusions of motion segments. The proposed method is a fusion of block-matching motion estimation and global optimization technique. It is robust to motion discontinuity and moving objects occlusions. To avoid some contradictions between global optimization techniques and piece-wise smooth values of sought motion vectors, a hidden segmentation model is utilized. Computer simulation and experimental results demonstrate an excellent performance of the method in terms of dynamic motion analysis. This article was translated by the authors. Mikhail Mozerov received his MS degree in Physics from the Moscow State University in 1982 and his PhD degree in Image Processing from the Institute of Information Transmission Problems, Russian Academy of Sciences, in 1995. He works at the Laboratory of Digital Optics of the Institute of Information Transmission Problems, Russian Academy of Sciences. His research interests include signal and image processing, pattern recognition, digital holography. Vitaly Kober obtained his MS degree in Applied Mathematics from the Air-Space University of Samara (Russia) in 1984, and his PhD degree in 1992 and Doctor of Sciences degree in 2004 in Image Processing from the Institute of Information Transmission Problems, Russian Academy of Sciences. Now he is a titular researcher at the Centro de Investigación Científica y de Educación Superior de Ensenada (Cicese), México. His research interests include signal and image processing, pattern recognition. Iosif A. Ovseyevich graduated from the Moscow Electrotechnical Institute of Telecommunications. Received candidate’s degree in 1953 and doctoral degree in information theory in 1972. At present, he is Emeritus Professor at the Institute of Information Transmission Problems of the Russian Academy of Sciences. His research interests include information theory, signal processing, and expert systems. He is a Member of IEEE, Popov Radio Society.     

Singularity avoidance in robotic manipulators: A differential form approach

We examine the avoidability property of singular configurations in redundant robot kinematics. Using a differential form approach a collection of so-called reduced self-motion dynamical systems is attributed to singular configurations distinguished by coranks. The problem of detecting avoidability/unavoidability is transformed to a stability study of the reduced self-motion systems. Sufficient conditions for avoidability and unavoidability are derived.     

Hybrid force and motion control of flexible joint parallel manipulators using inverse dynamics approach

An inverse dynamics control algorithm is developed for hybrid motion and contact force trajectory tracking control of flexible joint parallel manipulators. First, an open-tree structure is considered by the disconnection of adequate number of unactuated joints. The loop closure constraint equations are then included. Elimination of the joint reaction forces and the other intermediate variables yield a fourth-order relation between the actuator torques and the end-effector position and contact force variables, showing that the control torques do not have an instantaneous effect on the end-effector contact forces and accelerations because of the flexibility. The proposed control law provides simultaneous and asymptotically stable control of the end-effector contact forces and the motion along the constraint surfaces by utilizing the feedback of positions and velocities of the actuated joints and rotors. A two degree of freedom planar parallel manipulator is considered as an example to illustrate the effectiveness of the method.     

小波变换在信号奇异性检测中的应用

利用小波变换具有良好的时频局部化特征 ,在特定尺度下 ,求解信号小波变换的模极大值 ,从而找到信号奇异点。该方法应用到输油管道的泄漏检测中 ,结果表明 ,能够排除工况干扰 ,识别有用信号 ,及时准确地检测出管道的泄漏故障。     

Optimal design for robust control of uncertain flexible joint manipulators: a fuzzy dynamical system approach

A novel fuzzy dynamical system approach to the control design of flexible joint manipulators with mismatched uncertainty is proposed. Uncertainties of the system are assumed to lie within prescribed fuzzy sets. The desired system performance includes a deterministic phase and a fuzzy phase. First, by creatively implanting a fictitious control, a robust control scheme is constructed to render the system uniformly bounded and uniformly ultimately bounded. Both the manipulator modelling and control scheme are deterministic and not IF-THEN heuristic rules-based. Next, a fuzzy-based performance index is proposed. An optimal design problem for a control design parameter is formulated as a constrained optimisation problem. The global solution to this problem can be obtained from solving two quartic equations. The fuzzy dynamical system approach is systematic and is able to assure the deterministic performance as well as to minimise the fuzzy performance index.     

时滞柔性关节机械臂自适应位置/力控制

针对具有时滞的柔性关节机械臂自适应位置和力控制问题进行了研究.首先,通过坐标变换得出降维的位置/力控制模型.随后,将时间滞后近似表示成一阶滞后,进行时滞补偿.利用自适应算法修正机械臂系统参数,克服模型参数不确定性对系统的影响.同时,采用反步控制技术设计机械臂位置/力控制器,运用Lyapunov稳定性定理证明控制器能使机械臂位置和力跟踪误差收敛.最后的仿真研究验证了控制方案的有效性.     

Task decoupling in robot manipulators

Task decoupling in robotic manipulators implies that there is a subset of joints primarily responsible for the completion of a subset of the manipulator task. In this paper, we take a novel and general view of task decoupling in which we identify link subsystems primarily responsible for completion of a subset of the manipulator task components, which is not necessarily position or orientation. Our analysis leads to the discovery of other decoupled manipulator geometries never identified before, wherein the decoupled system is responsible for a subset of degress-of-freedom involving a hybrid combination of both position and orientation. Closed-form inverse kinematic solutions for these manipulator geometries are therefore guaranteed. Task decoupling also implied singularity decoupling wherein singularities of decoupled subsystems are equivalent to the manipulator singularities. The analysis leads to a novel and efficient method for identifying the singularities and solving the inverse kinematics problem of six-axes manipulators with decoupled geometries. The practicality of the concepts introduced is demonstrated through an industrial robot example involving a hybrid position and orientation decoupling.     

Force,orientation and position control in redundant manipulators in prioritized scheme with null space compliance

This paper addresses the problem of executing multiple prioritized tasks for robot manipulators with compliant behavior in the remaining null space. A novel controller–observer is proposed to ensure accurate accomplishment of various tasks based on a predefined hierarchy using a new priority assignment approach. Force control, position control and orientation control are considered. Moreover, a compliant behavior is imposed in the null space to handle physical interaction without using joint torque measurements. Asymptotic stability of the task space error and external torque estimation error during executing multiple tasks are shown. The performance of the proposed approach is evaluated on a 7R light weight robot arm by several case studies.     

l1鲁棒辨识:一种递推插值方法

针对l¹鲁棒辨识不能有效利用试验数据和进行在线辨识的问题, 提出了一种在线递推插值辨识方法. 用几何方法描述试验信息, 利用系统可行集与新的试验信息所构成的半空间的包含关系判断数据信息, 有效地利用了试验数据, 提高了辨识精度. 同时提出了一种新的计算辨识误差紧界的方法. 仿真结果表明了算法的有效性和可行性.     

l1鲁棒辨识:最小二乘算法及试验设计

现有的l^1鲁棒辨识方法依赖于观测数据窗的起始时刻因而不能用来辨识时变系统,针对该问题基于最小二乘法提出了一种l^1鲁棒辨识算法．该算法与观测窗的起始时刻无关,可用于时变系统的辨识．证明了当试验输入为持续激励信号时所提出的算法为本质最优算法,进一步证明了周期持续激励序列为最优试验信号,并给出了辨识误差紧界的计算公式．最后利用提出的算法研究了慢时变系统的l^1鲁棒辨识问题．     

A robust algorithm for solution of the fuzzy clustering problem on the basis of the fuzzy joint points method

The approach called the method of Fuzzy Joint Points (FJP) is considered in which the fuzziness of clusterization lies in the detailedness of taking into account properties of elements in forming sets of similar elements. Based on this approach, a new robust variant of the FJP algorithm is proposed. The properties of this FJP algorithm are analyzed and a sufficient condition for the correct recognition of the hidden structure of clusters is proved. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 10–22, January–February 2008.     

鲁棒辨识的l_1和H∞误差上界的估计算法

对有限参数线性系统辨识问题的l1误差上界估计和时域H∞ 插值算法误差上界估计等问题转化为一类分片线性函数的最优化问题 ,提出基于分片的混合遗传算法 .吸取进化算法的探索能力 ,并充分利用模型信息 .仿真实验结果表明了它的寻优性能 .     

An approach to automatic generation of dynamic equations of elastic joint manipulators in symbolic language

This paper describes an approach for automatic generation of the equations of motion of elastic joint manipulators in symbolic language. It is based on a vector-parametrization of the Lie groupSO(3) and uses the Lagrange's formalism to derive the dynamical equations, the final forms of which are like the equations generated by a recursive Newton-Eulerian algorithm. These characteristics together increase the computational efficiency of the algorithm and give a very good insight into the dynamical structure of the system. In addition to this, the inertia matrix is explicitly given in the final equations, which is very important for the applicability of a mathematical model in different fields of control and simulation. The suggested algorithm is therefore quite appropriate for the purposes of robot modeling, identification as well as for the applications in real time simulations and control.     

一种基于奇异点检测的光流场去噪方法

针对各种滤波方法对光流场进行去噪处理时会造成目标运动矢量改变的不足,提出一种基于奇异点检测的光流场去噪方法,利用表征信号奇异点特征的Lip指数建立噪声矢量判定准则,可以在目标无损的情况下检测出光流场噪声并消除。实验证明该方法能较好地消除噪声,同时不会造成目标运动矢量的损失。     

基于量子粒子群优化的多波束卫星联合资源分配算法

当使用元启发式算法求解多波束卫星联合资源分配问题时,时延约束和容量约束会导致计算复杂度增大,且算法难以收敛。对此,通过在目标函数中引入惩罚机制,在无效解的目标函数值加入了惩罚值,使得算法的优化解自适应地满足这两个约束。在此基础上,提出了基于量子粒子群优化的联合资源分配算法。仿真结果表明,惩罚策略的引入解决了应用元启发式算法时,难以处理时延约束和容量约束的问题,而带有惩罚机制的量子粒子群算法在分配公平性指数、总系统容量上均优于已有联合分配算法。     

Inverse dynamics based robust control method for position commanded servo actuators in robot manipulators

In this paper, a simple torque to position conversion method is proposed for position commanded servo actuators used in robot manipulators. The torque to position conversion is based on the low level controller of the servomotor. The proposed conversion law is combined with a backstepping sliding mode control method to realize a robust dynamic controller. The proposed torque based method can control a servomotor which can otherwise be operated only through position inputs. This method facilitates dynamic control for position controlled servomotors and it can be extended to position commanded robotic manipulators also. Simulation and experimental studies are conducted to validate the proposed torque to position conversion based robust control method.