Workspace Determination of General 6-d.o.f. Cable Manipulators

This paper addresses workspace determination of general 6-d.o.f. cable-driven parallel manipulators with more than seven cables. The workspace under study is called force-closure workspace, which is defined as the set of end-effector poses satisfying the force-closure condition. Having force-closure in a specific end-effector pose means that any external wrench applied to the end-effector can be balanced through a set of non-negative cable forces under any motion condition of the end-effector. In other words, the inverse dynamics problem of the manipulator always has a feasible solution at any pose in the force-closure workspace. The workspace can be determined by the Jacobian matrix and, thus, it is consistent with the usual definition of workspace in the robotics literature. A systematic method of determining whether or not a given end-effector pose is in the workspace is proposed. Based on this method, the shape, boundary, dimensions and volume of the workspace of a 6-d.o.f., eight-cable manipulator are discussed.     

A New Approach for the Dynamic Analysis of Parallel Manipulators

A new approach for the dynamic analysis of parallel manipulators is presented in this paper. This approach is based on the principle of virtual work. The approach is firstly illustrated using a simple example, namely, a planar four-bar linkage. Then, the dynamic analysis of a spatial six-degree-of-freedom parallel manipulator with prismatic actuators (Gough–Stewart platform) is performed. Finally, a numerical example is given in order to illustrate the results. The approach proposed here can be applied to any type of planar and spatial parallel mechanism and leads to faster computational algorithms than the classical Newton–Euler approach when applied to these mechanisms.     

The optimum design of robotic manipulators using dexterity indices

This paper presents new dexterity indices that can be applied to planar and spatial manipulators. These indices are based on the condition number of the Jacobian matrix of the manipulators which is known to be a measure of their kinematic accuracy. Dexterity indices based on that same criterion have been presented elsewhere. However, due to the formulation of the kinematic equations, the existing indices are affected by a scaling of the manipulator when both the position and the orientation of the end effector are included in the kinematic equations. A new formulation of these equations is proposed here to avoid this problem of dimensional dependence. Two dexterity indices are presented for planar manipulators: the first one is based on a redundant formulation of the velocity equations whereas the second one is based on the mininum number of parameters. The corresponding indices are also derived for spatial manipulators. Finally, an example is included to illustrate the use of these indices in the context of design and optimization of manipulators.     

A New Approach to the Architecture Optimization of a General 3-PUU Translational Parallel Manipulator

This paper presents a new approach to the architecture optimization of a general 3-PUU translational parallel manipulator (TPM) based on the performance of a weighted sum of global dexterity index and a new performance index-space utility ratio (SUR). Both the inverse kinematics and forward kinematics solutions are derived in closed form, and the Jacobian matrix is derived analytically. The manipulator workspace is generated by a numerical searching method with the physical constraints taken into consideration. Simulation results illustrate clearly the necessity to introduce a mixed performance index using space utility ratio for architectural optimization of the manipulator, and the optimization procedure is carried out with the goal of reaching a compromise between the two indices. The analytical results are helpful in designing a general 3-PUU TPM, and the proposed design methodology can also be applied to architectural optimization for other types of parallel manipulators.     

Inverse kinematics of planar redundant manipulators via virtual links with configuration index

This article presents a new method for generating inverse kinematic solutions for planar manipulators with large redundancy (hyper-redundant manipulators). The proposed method starts by decomposing a planar redundant manipulator into a series of local planar arms that are either 2-link or 3-link manipulator modules, and connecting the conjunction points between them with virtual links. The manipulator then can be handled by a simple virtual link system, which may be conveniently divided into non-singular and singular cases depending on its configuration. When the virtual link system is no longer effective due to a singular configuration, the displacement of the end-effector is then allocated to virtual links according to a displacement distribution criterion. A dexterity index called the “configuration index” distinguishes the non-singular and singular cases. The concept of virtual link is shown by computer simulations to be simple and effective for the inverse kinematics of a planar hyper-redundant manipulator with a discrete model. In particular, it can be applied to solving the inverse kinematics of a SCARA-type spatial redundant manipulator whose redundancy is included in its planar mechanism. © 1994 John Wiley & Sons, Inc.     

Analysis of duality-based interconnected kinematics of planar serial and parallel manipulators using screw theory

In this paper, a method has been proposed to analyze the planar architectures of serial and parallel manipulators, based on the duality associated with their interconnected kinematics. The interconnected kinematics states that model of one architecture can be derived from the kinematic model of the other, using screw theory approach. The performance of the initial and the derived manipulators was evaluated with three criteria: isotropy, maximum force transmission ratio and local transmission index. Without loss of generality, the serial manipulator derived from parallel has better isotropy, while the parallel manipulator derived from serial can be designed to have better force and power transmission.

     

Kinestatic Analysis of Nonsingular Lower Mobility Manipulators

This paper presents a method of determining exact solutions to kinestatic analyses of lower mobility manipulators by means of the reciprocal Jacobian. The existence and uniqueness of the reciprocal Jacobian are shown, which enables the complete kinestatic analyses of both serial and fully parallel manipulators in a unified way, as well as the derivation of the constraints on the end-effector twist and wrench.      

Force Transmissibility Performance of Parallel Manipulators

In this paper, a new force transmission index called the mean force transmission index (MFTI) is proposed, and the force transmissibility analysis procedure is established for parallel manipulators. The MFTI is an extended definition of the force transmission index (FTI) introduced by the authors previously. It is shown that the FTI is a function of the input velocity ratio (IVR) for a multi‐DOF mechanism of the same configuration. To represent the force transmissibility by a definite value, the MFTI is defined as the mean value of the normalized FTIs function over the whole range of the IVR. The force transmissibility analysis of two planar parallel manipulators is illustrated using the MFTI method. The result is compared with that of the Jacobian matrix method and the joint force index (JFI) method. It shows that, especially for symmetric parallel manipulators, an approximate inverse‐proportionality relationship exists between the JFI and MFTI, and between the maximum input torque/force and MFTI. It is concluded that the MFTI can be used as a quantitative measure of the force transmissibility performance for parallel manipulators. In the end, a design optimization problem is studied by taking the global force transmission index as the objective function. © 2003 Wiley Periodicals, Inc.     

Formulation of unified Jacobian for serial-parallel manipulators

This paper presents a general approach for Jacobian analysis of serial-parallel manipulators (S-PMs) formed by two lower mobility parallel manipulators (PMs) connected in serials. Based on the kinematic relation, coupling and constraint properties of each PM, the unified forward and inverse Jacobian matrices for S-PMs are derived in explicit form. It is shown that the Jacobian matrices of S-PMs have unified forms, which include the complete information of each PM. A (3-RPS)+(3-SPS/UP) S-PM is used as an example to demonstrate the proposed approach. The established model is applicable for S-PMs with various architectures.     

Kinematics and dynamics analyses of a parallel manipulator with three active legs and one passive leg by a virtual serial mechanism

A novel CAD variation geometry approach and a virtual serial mechanism approach are proposed for analyzing the kinematics and dynamics of a parallel manipulator with three SPS-type active legs and one PU-type constrained passive leg. First, a simulation mechanism of this parallel manipulator is created, and some kinematic characteristics are analyzed. Second, the inverse formulae for solving pose and Jocabian matrix are derived, and workspace and singularity are determined. Third, a virtual serial mechanism is created, and the analytic formulae for solving active forces and constrained wrench of these parallel manipulators are derived. The analytic results are verified by using its simulation mechanism.     

A comparison study on the dynamics of planar 3-DOF 4-RRR, 3-RRR and 2-RRR parallel manipulators

This paper presents a comparison study on the dynamics of three planar 3-DOF parallel manipulators, one with 3-RRR structure, and the other two with 2-RRR and 4-RRR structures. The inverse kinematics and Jacobian matrix of these mechanisms are analyzed. The dynamic formulations in the linear form are derived and a dynamic performance index is given to compare their dynamic performances. The results show that the 2-RRR parallel manipulator has the worst dynamic performance.     

Cartesian path generation of robot manipulators using continuous genetic algorithms

In this paper, the authors describe a novel technique based on continuous genetic algorithms (CGAs) to solve the path generation problem for robot manipulators. We consider the following scenario: given the desired Cartesian path of the end-effector of the manipulator in a free-of-obstacles workspace, off-line smooth geometric paths in the joint space of the manipulator are obtained. The inverse kinematics problem is formulated as an optimization problem based on the concept of the minimization of the accumulative path deviation and is then solved using CGAs where smooth curves are used for representing the required geometric paths in the joint space through out the evolution process. In general, CGA uses smooth operators and avoids sharp jumps in the parameter values. This novel approach possesses several distinct advantages: first, it can be applied to any general serial manipulator with positional degrees of freedom that might not have any derived closed-form solution for its inverse kinematics. Second, to the authors’ knowledge, it is the first singularity-free path generation algorithm that can be applied at the path update rate of the manipulator. Third, extremely high accuracy can be achieved along the generated path almost similar to analytical solutions, if available. Fourth, the proposed approach can be adopted to any general serial manipulator including both nonredundant and redundant systems. Fifth, when applied on parallel computers, the real time implementation is possible due to the implicit parallel nature of genetic algorithms. The generality and efficiency of the proposed algorithm are demonstrated through simulations that include 2R and 3R planar manipulators, PUMA manipulator, and a general 6R serial manipulator.     

Calibration of stewart platforms and other parallel manipulators by minimizing inverse kinematic residuals

This paper focuses on the accuracy enhancement of Stewart platforms through kinematic calibration. The calibration problem is formulated in terms of a measurement residual, which is the discrepancy between the measured leg length and the computed leg length. With this formulation, one is able to identify kinematic error parameters of the Stewart platform without the necessity of solving the forward kinematic problem; thus avoiding the numerical problems associated with any forward kinematic solution. By this formulation, a concise differential error model with a well-structured identification Jacobian, which relates the pose measurement residual to the errors in the parameters of the platform, is derived. Experimental studies confirmed the effectiveness of the method. It is also shown in this paper that the proposed approach can be applied to other types of parallel manipulators, assuming that their inverse kinematic solution is simpler than its forward kinematic solution. Because this condition is satisfied by almost all parallel manipulators, the method is very useful for kinematic calibration of such machines. © 1998 John Wiley & Sons, Inc.     

漂浮基空间机械臂分解运动控制的增广自适应算法

本文讨论了载体位置与姿态均不受控制的漂浮基两杆空间机械臂系统的逆运动学问题 ,推导了系统的运动学、动力学方程．分析表明,结合系统动量守恒及动量矩守恒关系得到 的系统广义Jacobi关系为系统惯性参数的非线性函数．本文证明了,借助于增广变量法可以 将增广广义Jacobi矩阵表示为一组适当选择的惯性参数的线性函数．并在此基础上,给出了 系统参数未知时由空间机械臂末端惯性空间期望轨迹产生机械臂关节铰期望角速度、角加速 度的增广自适应控制算法．仿真运算,证实了方法的有效性．     

Solving the forward kinematics of parallel manipulators with a genetic algorithm

A floating point genetic algorithm is proposed to solve the forward kinematic problem for parallel manipulators. This method, adapted from studies in the biological sciences, allows the use of inverse kinematic solutions to solve forward kinematics as an optimization problem. The method is applied to two 3-degree-of-freedom planar parallel manipulators and to a 3-degree-of-freedom spherical manipulator. The method converges to a solution within a broader search domain compared to a Newton-Raphson scheme. © 1996 John Wiley & Sons, Inc.     

Iterative learning control and the singularity robust Jacobian inverse for mobile manipulators

The method of iterative learning control, to a large extent, has been inspired by robotics research, focused on the control of stationary manipulators. In this article we deal with the inverse kinematics problem for mobile manipulators, and show that a very basic singularity robust Jacobian inverse can be derived in a natural way within the framework of iterative learning control. To achieve this objective we have exploited the endogenous configuration space approach. The introduced Jacobian inverse defines the singularity robust Jacobian inverse kinematics algorithm for mobile manipulators. A Kantorovich-type estimate of the region of guaranteed convergence of the algorithm is derived. For two example kinematics, this estimate has been computed efficiently.     

Singularity Analysis of Lower Mobility Parallel Manipulators Using Grassmann–Cayley Algebra

This paper introduces a methodology to analyze geometrically the singularities of manipulators, of which legs apply both actuation forces and constraint moments to their moving platform. Lower mobility parallel manipulators and parallel manipulators, of which some legs have no spherical joint, are such manipulators. The geometric conditions associated with the dependency of six PlUumlcker vectors of finite lines or lines at infinity constituting the rows of the inverse Jacobian matrix are formulated using Grassmann-Cayley algebra (GCA). Accordingly, the singularity conditions are obtained in vector form. This study is illustrated with the singularity analysis of four manipulators.     

Adaptive control of parallel manipulators via fuzzy-neural network algorithm

This paper considers adaptive control of parallel manipulators combined with fuzzy-neural network algorithms （FNNA）. With this algorithm, the robustness is guaranteed by the adaptive control law and the parametric uncertainties are eliminated. FNNA is used to handle model uncertainties and external disturbances. In the proposed control scheme, we consider modifying the weight of fuzzy rules and present these rules to a MIMO system of parallel manipulators with more than three degrees-of-freedom （DoF）. The algorithm has the advantage of not requiring the inverse of the Jacobian matrix especially for the low DoF parallel manipulators. The validity of the control scheme is shown through numerical simulations of a 6-RPS parallel manipulator with three DoF.