Dynamics of the 6-6 Stewart parallel manipulator

Recursive matrix relations in kinematics and dynamics of the 6-6 Stewart–Gough parallel manipulator having six mobile prismatic actuators are established in this paper. Controlled by six forces, the manipulator prototype is a spatial six-degrees-of-freedom mechanical system with six parallel legs connecting to the moving platform. Knowing the position and the general motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity and acceleration of each manipulator’s link. Further, the inverse dynamics problem is solved using an approach based on the principle of virtual work, but it has been verified the results in the framework of the Lagrange equations with their multipliers. Finally, compact matrix relations and graphs of simulation for the input velocities and accelerations, the input forces and powers are obtained.     

Dynamic formulation and performance evaluation of the redundant parallel manipulator

The dynamic formulation and performance evaluation of the redundant parallel manipulator are presented in this paper. By means of the principle of virtual work and the concept of link Jacobian matrices, the inverse dynamic model of the redundant parallel manipulator is set up. It consists of six linear consistent equations with eight unknown quantities. Then, the optimum solution of the actuating torques is achieved by employing the Moore-Penrose inverse matrix. It is with minimum norm and least quadratic sum among the possible actuating torque vectors. A series of new dynamic performance indices with obvious physical meanings have been proposed in the paper. By decoupling the inverse dynamics in the exhaustive way, a novel dynamic performance index combining the acceleration, velocity and gravity terms of the dynamic equations has been presented to evaluate the dynamic characteristic of the redundant parallel manipulator. With the index, it is possible to control the performance in the different direction. The index has been applied to the dynamic characteristic evaluation of the redundant parallel manipulator in the simulation. It is general and can be used for the dynamic performance evaluation of other types of parallel manipulators.     

Efficient parallel term matching and anti-unification

In this paper we present optimal processor x time parallel algorithms for term matching and anti-unification of terms represented as trees. Term matching is the special case of unification in which one of the terms is restricted to contain no variables. It has wide applicability to logic programming, term rewriting systems and symbolic pattern matching. Anti-unification is the dual problem of unification in which one computes the most specific generalization of two terms. It has application to inductive inference and theorem proving. Our algorithms run in O(log² N) time using N/log² N processors on a shared-memory model of computation that prohibits simultaneous reads or writes (EREW PRAM). These algorithms are the first polylogarithmic-time EREW algorithms with a processor x time product of the same order as that of their sequential counterparts, thereby permitting optimal speed-ups using any number of processors up to N/log² N. We also use the techniques developed in the paper to provide an N/log N-processor, O(log N)-time algorithm for a shared-memory model that allows both simultaneous reads and simultaneous writes (CRCW PRAM).Supported by NSF Grant IRI-88-09324 and NSF/DARPA Grant CCR-8908092.     

Fast parallel algorithms for graph similarity and matching

This paper addresses the problem of global graph alignment on supercomputer-class clusters. We define the alignment of two graphs, as a mapping of each vertex in the first graph to a unique vertex in the second graph so as to optimize a given similarity-based cost function.¹ Using a state of the art serial algorithm for the computation of vertex similarity scores called Network Similarity Decomposition (NSD), we derive corresponding parallel formulations. Coupling this parallel similarity algorithm with a parallel auction-based bipartite matching technique, we obtain a highly efficient and scalable graph matching pipeline. We validate the performance of our integrated approach on a large parallel platform and on diverse graph instances (including Protein Interaction, Wikipedia and Web networks). Experimental results demonstrate that our algorithms scale to large machine configurations (thousands of cores) and problem instances, enabling the alignment of networks of sizes two orders of magnitude larger than reported in the current literature.     

An adjustable linear time parallel algorithm for maximum weight bipartite matching

We present a parallel algorithm for finding a maximum weight matching in general bipartite graphs with an adjustable time complexity of using O(nmax(2ω,4+ω)) processing elements for ω?1. Parameter ω is not bounded. This is the fastest known strongly polynomial parallel algorithm to solve this problem. This is also the first adjustable parallel algorithm for the maximum weight bipartite matching problem in which the execution time can be reduced by an unbounded factor. We also present a general approach for finding efficient parallel algorithms for the maximum matching problem.     

Kinematic analysis of a 3-PRS parallel manipulator

Although the current 3-PRS parallel manipulators have different methods on the arrangement of actuators, they may be considered as the same kind of mechanism since they can be treated with the same kinematic algorithm. A 3-PRS parallel manipulator with adjustable layout angle of actuators has been proposed in this paper. The key issues of how the kinematic characteristics in terms of workspace and dexterity vary with differences in the arrangement of actuators are investigated in detail. The mobility of the manipulator is analyzed by resorting to reciprocal screw theory. Then the inverse, forward, and velocity kinematics problems are solved, which can be applied to a 3-PRS parallel manipulator regardless of the arrangement of actuators. The reachable workspace features and dexterity characteristics including kinematic manipulability and global dexterity index are derived by the changing of layout angle of actuators. Simulation results illustrate that different tasks should be taken into consideration when the layout angles of actuators of a 3-PRS parallel manipulator are designed.     

Recursive modelling in dynamics of Agile Wrist spherical parallel robot

Recursive matrix relations for kinematics and dynamics of the 3-RRR Agile Wrist spherical parallel robot are established in this paper. The prototype of the robot is a three-degrees-of-freedom mechanism with three identical legs. Controlled by concurrent torques, which are generated by some electric motors, the active elements of the robot have three independent rotations. Knowing the rotation motion of the moving platform, we develop first the inverse kinematical problem and determine the velocities and accelerations. Further, the principle of virtual work is used in the inverse dynamic problem. Matrix equations offer iterative expressions and graphs for the power requirement comparison of each of three actuators in two computational complexities: complete dynamic model and simplified dynamic model.     

Dynamics of the spherical 3- \mathit{U\underline{P}S/}S parallel mechanism with prismatic actuators

Recursive relations in kinematics and dynamics of the symmetric spherical 3- parallel mechanism having three prismatic actuators are established in this paper. Controlled by three forces, the parallel manipulator is a 3-DOF mechanical system with three parallel legs connecting to the moving platform. Knowing the position and the rotation motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity, and acceleration of each manipulator’s link. Further, the inverse dynamic problem is solved using an approach based on the principle of virtual work, but it has been verified using the results in the framework of the Lagrange equations with their multipliers. Finally, compact matrix relations and graphs of simulation for the input forces and powers are obtained.     

Investigation of joint clearance effects on the dynamic performance of a planar 2-DOF pick-and-place parallel manipulator

In this study, the effects of joint clearance on the dynamic performance of a planar 2-DOF pick-and-place parallel manipulator are investigated. The parallel manipulator is modeled by multi-body system dynamics. The contact effect in revolute joints with clearance is established by using a continuous analysis approach that is combined with a contact force model considering hysteretic damping. The evaluation of the contact force is based on Hertzian contact theory that accounts for the geometrical and material properties of the contacting bodies. Furthermore, the incorporation of the friction effect in clearance joints is performed using a modified Coulomb friction model. By numerical simulation, variations of the clearance joint's eccentric trajectory, the joint reaction force, the input torque, the acceleration, and trajectory of the end-effector are used to illustrate the dynamic behavior of the mechanism when multiple clearance revolute joints are considered. The results indicate that the clearance joints present two obvious separation leaps in a complete pick-and-place working cycle of the parallel manipulator, following a collision. The impact induces system vibration and thus reduces the dynamic stability of the system. The joint clearances affect the amplitudes of the joint reaction force, the input torque, and the end-effector's acceleration, additionally the joint clearances degrade the kinematic and dynamic accuracy of the manipulator's end-effector. Finally, this study proposes related approaches to decrease the effect of joint clearances on the system's dynamic properties for such parallel manipulator and prevent “separation-leap-impact” events in clearance joints.     

Real-time inverse dynamics control of parallel manipulators using general-purpose multibody software

This work deals with the problem of computing the inverse dynamics of complex constrained mechanical systems for real-time control applications. The main goal is the control of robotic systems using model-based schemes in which the inverse model itself is obtained using a general purpose multibody software, exploiting the redundant coordinate formalism. The resulting control scheme is essentially equivalent to a classical computed torque control, commonly used in robotics applications. This work proposes to use modern general-purpose multibody software to compute the inverse dynamics of complex rigid mechanisms in an efficient way, so that it suits the requirements of realistic real-time applications as well. This task can be very difficult, since it involves a higher number of equations than the relative coordinates approach. The latter is believed to be less general, and may suffer from topology limitations. The use of specialized linear algebra solvers makes this kind of control algorithms usable in real-time for mechanism models of realistic complexity. Numerical results from the simulation of practical applications are presented, consisting in a “delta” robot and a bio-mimetic 11 degrees of freedom manipulator controlled using the same software and the same algorithm.     

Dynamic modeling and robust control of a 3-PRC translational parallel kinematic machine

The dynamic modeling and robust control for a three-prismatic-revolute-cylindrical (3-PRC) parallel kinematic machine (PKM) with translational motion have been investigated in this paper. By introducing a mass distribution factor, the simplified dynamic equations have been derived via the virtual work principle and validated on a virtual prototype with the ADAMS software package. Based upon the established model, three dynamics controllers have been attempted on the 3-PRC PKM. The intuitive co-simulations with the combination of MATLAB/Simulink and ADAMS show that the control performance of neither inverse dynamics control nor robust inverse dynamics control is satisfactory in the presence of parametric uncertainties in PKM dynamics. On the contrary, the controller based on the passivity-based robust control scheme is more suitable for tracking control of the PKM in terms of both control performances and controller design procedures. The results presented in the paper provide a sound base for both the mechanical system design and control system design of a 3-PRC PKM.     

基于 Hadoop平台的并行特征匹配算法研究

很多大企业采用Hadoop分布式文件系统来存储海量数据,而传统的病毒扫描主要针对单机系统环境。研究如何并行化病毒扫描中的核心特征匹配算法来处理分布式海量数据。在Hadoop平台下,基于MapReduce并行编程模型来实现大数据高效的病毒扫描,特别是针对Hadoop处理海量小文件效率低的问题,通过将小文件合并,再利用索引来提高海量小文件的处理效率。实验结果表明,提出的并行特征匹配算法可以显著降低处理时间,适用于大数据的病毒扫描。     

The singularities and dynamics of a Stewart platform manipulator

The Stewart platform manipulator is a fully parallel kinematic linkage system that has major mechanical differences over typical serial link robots. Its closed kinematic chain and parallel linkage structure give it great rigidity and a high force-to-weight ratio. In this paper, based on the forward and inverse kinematic analysis, the Jacobian matrix and the dynamic equations of the six-degree-of-freedom Stewart platform are derived. The singularities of the Stewart platform are also studied. Four singular positions are proved and some other conditions under which the possible singular positions may occur are given. These results provide us with the necessary information to avoid passing through singular points. The dynamic equations in Cartesian space appear in a very simple form. Especially in some applications if there is no rotation about the fixed X-axis, then the inertia matrix reduces to a constant, diagonal matrix and the Coriolis and centrifugal matrix goes to zero, which makes the Stewart platform become a decoupled, linear system in Cartesian space.     

Jerk analysis of a six-degrees-of-freedom three-legged parallel manipulator

In this work the jerk analysis of a 3-RRPS parallel manipulator to realize six degrees of freedom is approached by means of the theory of screws. The input/output equations of velocity, acceleration and jerk of the moving platform with respect to the fixed platform are obtained systematically by resorting to reciprocal-screw theory. A numerical example is included in order to show the application of the method of kinematic analysis. Furthermore, the numerical results obtained via screw theory are satisfactorily compared with simulations generated with the aid of commercially available software.     

Forward kinematics,performance analysis,and multi-objective optimization of a bio-inspired parallel manipulator

In this paper, a bio-inspired parallel manipulator with one translation along z-axis and two rotations along x- and y- axes is developed as the hybrid head mechanism of a groundhog robotic system. Several important issues including forward kinematic modeling, performance mapping, and multi-objective improvement are investigated with specific methods or technologies. Accordingly, the forward kinematics is addressed based on the integration of radial basis function network and inverse kinematics. A novel performance index called dexterous stiffness is defined, derived and mapped. The multi-objective optimization with particle swarm algorithm is conducted to search for the optimal dexterous stiffness and reachable workspace.     

Dynamics and control of a novel 3-DOF parallel manipulator with actuation redundancy

This paper deals with the dynamics and control of a novel 3-degrees-of-freedom （DOF） parallel manipulator with actuation redundancy. According to the kinematics of the redundant manipulator, the inverse dynamic equation is formulated in the task space by using the Lagrangian formalism, and the driving force is optimized by utilizing the minimal 2-norm method. Based on the dynamic model, a synchronized sliding mode control scheme based on contour error is proposed to implement accurate motion tracking control. Additionally, an adaptive method is introduced to approximate the lumped uncertainty of the system and provide a chattering-free control. The simulation results indicate the effectiveness of the proposed approaches and demonstrate the satisfactory tracking performance compared to the conventional controller in the presence of the parameter uncertainties and un-modelled dynamics for the motion control of manipulators.     

Derivation of a parallel string matching algorithm

We derive an efficient parallel algorithm to find all occurrences of a pattern string in a subject string in O(logn) time, where n is the length of the subject string. The number of processors employed is of the order of the product of the two string lengths. The theory of powerlists [J. Kornerup, PhD Thesis, 1997; J. Misra, ACM Trans. Programming Languages Systems 16 (6) (1994) 1737-1740] is central to the development of the algorithm and its algebraic manipulations.     

基于OpenMP的Stewart并联机器人控制系统

针对Stewart并联机器人控制难度大的问题,实现了一种基于OpenMP的Stewart并联机器人上位机控制系统,对机器人实现了快速有效直观的振动控制.系统共包含了动力学解算模块、数据传输模块和人机交互模块,不仅能够准确地计算出振动数据,控制机器人振动,而且也设计了简洁明了的用户界面,提升用户体验.为了提高软件的执行效率,还加入了OpenMP多线程并行计算技术加速控制算法,最高达到了2.18倍的加速比.验证了软件计算的正确性、控制的稳定性和执行的高效性.     

Generation and application of prestress in redundantly full-actuated parallel manipulators

This paper addresses the inverse dynamics of redundantly actuated parallel manipulators. Such manipulators feature advantageous properties, such as a large singularity-free workspace, a high possible acceleration of the moving platform, and higher dexterity and manipulability. Redundant actuation further allows for prestress, i.e., internal forces without generating end-effector wrenches. This prestress can be employed for various goals. It can potentially be used to avoid backlash in the driving units or to generate a desired tangential end-effector stiffness. In this paper, the application of prestress is addressed upon the inverse dynamics solution. A general formulation for the dynamics of redundantly actuated parallel manipulators is given. For the special case of simple redundancy, a closed-form solution is derived in terms of a single prestress parameter. This yields an explicit parametrization of prestress. With this formulation an open-loop prestress control is proposed and applied to the elimination of backlash. Further, the generation of tangential end-effector stiffness is briefly explained. The approach is demonstrated for a planar 4RRR manipulator and a spatial heptapod.