Direct displacement analysis of parallel manipulators

A new numerical method for the direct position analysis of the parallel manipulators is presented. The main feature of the method, making it attractive with respect to the method available in the literature, is the ability to search out the direct solution under any precision quickly. © 2000 John Wiley & Sons, Inc.     

Design and analysis of kinematically redundant parallel manipulators with configurable platforms

Redundancy can, in general, improve the ability and performance of parallel manipulators by implementing the redundant degrees of freedom to optimize a secondary objective function. Almost all published researches in the area of parallel manipulators redundancy were focused on the design and analysis of redundant parallel manipulators with rigid (nonconfigurable) platforms and on grasping hands to be attached to the platforms. Conventional grippers usually are not appropriate to grasp irregular or large objects. Very few studies focused on the idea of using a configurable platform as a grasping device. This paper highlights the idea of using configurable platforms in both planar and spatial redundant parallel manipulators, and generalizes their analysis. The configurable platform is actually a closed kinematic chain of mobility equal to the degree of redundancy of the manipulator. The additional redundant degrees of freedom are used in reconfiguring the shape of the platform itself. Several designs of kinematically redundant planar and spatial parallel manipulators with configurable platform are presented. Such designs can be used as a grasping device especially for irregular or large objects or even as a micro-positioning device after grasping the object. Screw algebra is used to develop a general framework that can be adapted to analyze the kinematics of any general-geometry planar or spatial kinematically redundant parallel manipulator with configurable platform.     

Model-based control of redundantly actuated parallel manipulators in redundant coordinates

Model-based control of parallel kinematics machines (PKM) relies on computationally efficient formulations in terms of a set of independent joint coordinates. Since PKM models are commonly expressed in terms of actuator or end-effector coordinates the models are not valid at input- or output-singularities, respectively. Moreover input-singularities limit the motion range of PKM. Actuation redundancy is a means to increase the singularity-free range of motion. However, due to the redundancy only a subset of the actuator coordinates constitute independent coordinates. This subset corresponds to the actuator coordinates of the non-redundant PKM, which does generally not constitute proper minimal coordinates for the entire workspace. Hence a redundantly actuated PKM (RA-PKM) controlled by a model-based controller in terms of minimal coordinates would exhibit the same limitations as the non-redundant PKM. One approach to tackle this problem is to switch between different minimal coordinates, i.e., different motion equations are used within the controller.In this contribution a computed torque and augmented PD control scheme in redundant coordinates is proposed, as an alternative to coordinate switching, and applied to the control of redundantly actuated PKM. That is, no minimal coordinates are selected. This novel formulation is numerically robust and does not suffer from input- or output-singularities. Even more the formulation is always valid except at configuration space singularities. For the redundancy resolution within the inverse dynamics the pseudoinverse of a rank deficient matrix is required, for which an explicit formulation is presented. For both controllers exponential trajectory tracking is shown. Experimental results are reported for a planar 2 DOF RA-PKM.     

Complete forward displacement solutions for a class of three-branch parallel manipulators

Forward displacement solutions are presented for a class of spatial parallel manipulators. In particular, considered are manipulators consisting of a platform supported through passive spherical joints by three branches, each branch having three-revolute joints forming its main arm. Solutions are described for arbitrary main-arm layouts and for all possible cases of redundant (nine, eight, and seven sensors) and non-redundant (six sensors) sensing of branch main-arm joint displacements. It is demonstrated that closed-form forward displacement solutions can be found for all cases of redundant sensing. Furthermore, it is shown that a closed-form solution can be obtained for one of the two possible cases of non-redundant sensing of the main-arm joint displacements. The only case of joint displacement sensing not allowing a closed-form forward displacement solution is two joints sensed per branch, a case that can be expressed as a 16th-order polynomial of a single variable. Due to the importance of having efficient and failure-safe solutions for the forward displacement problem, it is suggested that appropriate redundancy in displacement sensing should be an important consideration in the design of parallel manipulation devices. © 1994 John Wiley & Sons, Inc.     

Energy efficient redundant configurations for real-time parallel reliable servers

Modular redundancy and temporal redundancy are traditional techniques to increase system reliability. In addition to being used as temporal redundancy, with technology advancements, slack time in a system can also be used by energy management schemes to save energy. In this paper, we consider the combination of modular and temporal redundancy to achieve energy efficient reliable real-time service provided by multiple servers. We first propose an efficient adaptive parallel recovery scheme that appropriately processes service requests in parallel to increase the number of faults that can be tolerated and thus system reliability. Then we explore schemes to determine the optimal redundant configurations of the parallel servers to minimize system energy consumption for a given reliability goal or to maximize system reliability for a given energy budget. Our analysis results show that small requests, optimistic approaches, and parallel recovery favor lower levels of modular redundancy, while large requests, pessimistic approaches and restricted serial recovery favor higher levels of modular redundancy.

Vibration analysis of cable-driven parallel manipulators

A cable-driven parallel manipulator is a manipulator whose end-effector is driven by a number of parallel cables instead of rigid links. Since cables always have more flexibility than rigid links, a cable manipulator bears a concern of possible vibration. Thus, investigation of vibration of cable manipulators caused by cable flexibility is important for applications requiring high system stiffness or bandwidth. This paper provides a vibration analysis of general 6-DOF cable-driven parallel manipulators. Based on the analysis of the natural frequencies of the multibody system, the study demonstrates that a cable manipulator can be designed stiff enough for special applications like the cable-manipulator based hardware-in-the-loop simulation of contact dynamics. Moreover, under an excitation, a cable may vibrate not only in its axial direction, but also in its transversal direction. The paper also analyzes the vibration of cable manipulators caused by cable flexibilities in both axial and transversal directions. It is shown that the vibration of a cable manipulator due to the transversal vibration of cables can be ignored comparing to that due to the axial flexibility of cables.     

Dynamic control of redundant manipulators

Redundant manipulators provide increased flexibility for the execution of complex tasks. Redundancy is often required to maintain manipulability and avoid obstacles while completing the required task. Self-motion is the internal (joint) motion of the manipulator that does not contribute to the end effector motion. In this article we provide a dynamic feedback control law that guarantees the tracking of a desired end effector trajectory and provides redundancy resolution by making the self-motion of the manipulator flow along the projection of a given arbitrary vector field. By choosing this vector field to be the gradient of a cost function, for example, the manipulator can be made to seek an optimum configuration. The effectiveness of the control law is illustrated with simulation results.     

冗余机械臂角偏差消去方案之原理分析

本文利用优化方法及递归神经网络实时求解器消除冗余机器手臂在运动过程中出现的角偏差问题.鉴于机器手臂都存在着关节物理约束,我们的优化方案也因此考虑关节极限和关节速度极限的躲避.更重要的是,本文详细分析了该成功解决关节角偏差问题的二次型性能指标的设计原理.仿真结果证实了该方法的可行性与有效性.     

冗余机器人系统的自运动控制

研究冗余机器人系统的自运动控制问题，给出一种非连续切换控制算法。该算法可以在保持机器人手端任务向量不变的情况下，使关节构形收敛到期望位置。与以往的算法相比，所提出的算法可以跳出局部最小点，并使关节收敛到期望构形。对三杆平面机器人系统进行的计算机仿真证实了算法的有效性。     

Generation and forward displacement analysis of two new classes of analytic 6‐SPS parallel manipulators

Analytic manipulators are manipulators with a characteristic polynomial of fourth degree or lower. Using the component approach to generate analytic 6‐SPS parallel manipulators (PMs), the generation process is reduced to the generation of analytic components for 6‐SPS PMs. Two new classes of analytic components for 6‐SPS PMs are generated at first. Then, two new classes, IX and X, of analytic 6‐SPS PMs are generated. The forward displacement analysis (FDA) of the new analytic 6‐SPS PMs is also performed. The FDA of the 6‐SPS PMs of class IX is reduced to the solution of one univariate cubic equation and two univariate quadratic equations, in sequence, while that of the 6‐SPS PMs of class X is reduced to the solution of three univariate quadratic equations in sequence. Both of the new analytic 6‐SPS PMs have at most eight assembly modes. © 2001 John Wiley & Sons, Inc.     

Static modeling and control of redundant manipulators

This paper develops unified static models for control of a redundant manipulator. We introduce the Premultiplier Diagram to describe the static behavior of a redundant manipulator. This diagram provides insight into the algebra and physics related to redundant manipulators. We derive redundancy expressions for the joint displacement, joint torque and joint stiffness matrix. These redundancy expressions are composed of a particular (net) part and a homogeneous (null) part. Based on the orthogonality property between the net and the null components, we propose an extension of the stiffness control scheme for redundant manipulators. We also show how the decomposed and decoupled static behavior of redundant manipulators can be used to derive an optimal control strategy.     

Well-conditioned configurations of fault-tolerant manipulators

Fault-tolerant motion of redundant manipulators can be obtained by joint velocity reconfiguration. For fault-tolerant manipulators, it is beneficial to determine the configurations that can tolerate the locked-joint failures with a minimum relative joint velocity jump, because the manipulator can rapidly reconfigure itself to tolerate the fault. This paper uses the properties of the condition numbers to introduce those optimal configurations for serial manipulators. The relationship between the manipulator’s locked-joint failures and the condition number of the Jacobian matrix is indicated by using a matrix perturbation methodology. Then, it is observed that the condition number provides an upper bound of the required relative joint velocity change for recovering the faults which leads to define the optimal fault-tolerant configuration from the minimization of the condition number. The optimization problem to obtain the minimum condition number is converted to three standard Eigen value optimization problems. A solution is for selected optimization problem is presented. Finally, in order to obtain the optimal fault-tolerant configuration, the proposed method is applied to a 4-DoF planar manipulator.     

Robust adaptive control of redundant manipulators

This paper presents an adaptive scheme for the motion control of kinematically redundant manipulators. The proposed controller is very general and computationally efficient since it does not require knowledge of either the mathematical model or the parameter values of the robot dynamics, and is implemented without calculation of the robot inverse dynamics or inverse kinematic transformation. It is shown that the control strategy is globally stable in the presence of bounded disturbances, and that in the absence of disturbances the size of the residual tracking errors can be made arbitrarily small. The performance of the controller is illustrated through computer simulations with a nine degree-of-freedom (DOF) compound manipulator consisting of a relatively small, fast six-DOF manipulator mounted on a large three-DOF positioning device. These simulations demonstrate that the proposed scheme provides accurate and robust trajectory tracking and, moreover, permits the available redundancy to be utilized so that a high bandwidth response can be achieved over a large workspace.     

Task-based configuration control of redundant manipulators

This article establishes new goals for redundancy resolution based on manipulator dynamics and end-effector characteristics. These goals can be accomplished by employing the recently developed configuration control approach. Redundancy resolution is achieved by controlling the joint inertia matrix or the end-effector mass matrix that affect the inertial torques or by reducing the joint torques due to gravity loading and payload. The manipulator mechanical advantage and velocity ratio are also used as performance measures to be improved by proper utilization of redundancy. Furthermore, end-effector compliance, sensitivity, and impulsive force at impact are introduced as redundancy-resolution criteria. The new goals for redundancy resolution presented in this article allow a more efficient utilization of the redundant joints based on the desired task requirements. Simple case studies using computer simulations are described for illustration.     

Hierarchical trajectory planning of redundant manipulators with structured intelligence

This paper deals with trajectory generation for redundant manipulators with structured intelligence. Recently, behavior engineering for robotic systems has been discussed as a new technological discipline. The intelligence of a robot depends on the structure of hardware and software for processing information, i.e. the structure determines the potentiality of intelligence. This paper proposes a robotic system with structured intelligent based on subsumption-like architecture. Based on perceptual information, a robot with structured intelligence makes decisions and takes action from four levels in parallel. In addition, the robot generates its motion through interaction with the environment and, at the same time, gradually acquires its skill based on the generated motion. To acquire skill and motion, the robot requires internal and external evaluations at least. This paper applies a virus-evolutionary genetic algorithm to trajectory planning for redundant manipulators with structured intelligence. Furthermore, we discuss its effectiveness through computer simulation results.     

Inverse jerk analysis of symmetric zero-torsion parallel manipulators

In this work the inverse velocity, acceleration and jerk analyses of a class of three-degrees-of-freedom parallel manipulators are approached by means of the theory of screws. The concept of reciprocal screws allows to obtain simple and decoupled expressions to compute the joint rates, up to the third time derivative, of the class of manipulators under study given the instantaneous kinematic properties of the center of the moving platform. The interdependency between the angular and linear kinematic properties of the moving platform is also derived. A case study is included.     

Dynamic analysis and driving force optimization of a 5-DOF parallel manipulator with redundant actuation

Redundant actuation can improve the performance and ability of parallel manipulator. In order to deal with coordination and distribution of the driving force of the parallel manipulator with redundant actuation and to realize the control strategy based on dynamics, on the basis of the original 5UPS/PRPU parallel manipulator, it increases a drive for the middle PRPU passive constraint branch to make it a redundant actuation branch. It introduces configurations’ redundant types and compositions of 5UPS/PRPU parallel manipulator with redundant actuation, illustrates that the mechanism is redundant actuation from the perspective of degree of freedom and establishes a dynamic model based on Lagrangian method. On the basis of the weighted optimization principle of driving torque, it optimizes the driving torque of the parallel manipulator and calculates the driving force of the redundant driving chain with cutting force. It carries out the simulation by using ADAMS software and proves validity of dynamic model. Finally it detects the dynamic performance of the parallel manipulator by processing experiment of parallel manipulator with redundant actuation and its non-redundant counterpart.     

冗余机器人的双向自运动路径规划

冗余机器人的自运动路径规划是在保持手端任务向量不变的情况下,在关节空间内寻找一条连接机器人初始关节构形和期望关节构型的几何路径.本文给出一种双向自运动路径规划算法,其基本思想是使位于初始关节构形的真实机器人和位于期望关节构形的虚拟机器人在自运动流形上运动并收敛到同一关节构形,从而得到一条连接初始和期望关节构形的自运动几何路径.该算法克服了以往算法容易陷入局部极小构形的缺陷.仿真结果证实了算法的有效性.