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.     

Dynamic simplification of three degree of freedom manipulators with closed chains

A method is presented for designing manipulators to have simplified dynamics. It is based on adding a link group to an open kinematic chain to form a closed chain without changing the degrees of freedom of the open chain. The mass property of the link group is designed to make the closed chain have a diagonal inertia matrix. The conditions of mass distribution are derived under which the inertia matrices become diagonal. The advantage of the proposed method is that the manipulator dynamics can be treated as a decoupled linear system thereby greatly simplifying the control implementation. As examples of the technique we apply it to the design of a 3 DOF planar manipulator and a 3 DOF spatial manipulator.     

Research on the inertia matching of the Stewart parallel manipulator

With the development of the parallel manipulator, inertia matching as an essential factor to realize good potentials of the parallel manipulator is taken serious gradually. However, neither definite inertia index nor inertia matching method has been proposed so far. In this paper, the above issues are discussed by taking the Stewart parallel manipulator as a study object. Firstly, adopting limb Jacobian matrices, the concise algebraic expression of the joint–space inertia matrix of the Stewart parallel manipulator is deduced, based on the dynamic modeling. Next, on the basis of the coupling analysis of the joint–space inertia matrix, the inertia index of the parallel manipulator, the Joint-Reflected Inertia, is proposed. Then, the practical inertia matching principles of the Stewart parallel manipulator are concluded on the basis of simulations, considering multiple factors, such as mechanical resonance frequency, acceleration torque and dynamic performance. Finally, the available range of the motor inertia is deduced, and the inertia matching of the Stewart parallel manipulator is finished as the case study. The inertia index and inertia matching method suggested in this paper can be further used in other parallel manipulators for dynamic analysis and motion system design.     

Gravity compensation of spatial two‐DOF serial manipulators

This article presents the analysis of gravity compensation of a two‐DOF serial manipulator operating in three‐dimensional space by means of linear spring suspension. The physical configuration of the serial manipulator is assumed general. The analysis begins with gravity compensation of a one‐DOF manipulator in order to form the basis which is then extended to a two‐DOF manipulator. The approach taken in the analysis is that of conservation of potential energy. The goal is to seek the location and the stiffness of springs that provide complete compensation of gravity in the manipulator system. It has been found that complete compensation of gravity in a two‐DOF serial manipulator system is possible. Unlike many previous works on spring suspension of a rigid body, which assume that one end of the suspending spring is attached to ground, it is proven in this study that, for complete compensation in a two‐DOF manipulator, the spring that suspends the distal link cannot be connected to ground. Instead, it must be in certain motion relative to the proximal link. The discussion on how to provide such a motion for the spring is given. It is also explained how the problem of gravity compensation of a robot manipulator can be shifted to that of changing gravity environment within a manipulator system. The concept can be applied to simulation and testing of robot manipulators that will be sent to operate in a different gravity environment, such as space. © 2002 Wiley Periodicals, Inc.     

A new composite body method for manipulator dynamics

This article presents a new composite body method for numerically forming the inertia matrix and the bias vector of manipulators, which is more efficient than the other two existing types of composite body methods. The main discrepancy of this one from the existing ones is that all points in a manipulator are observed from the origin of the base frame and the distances are all measured from this origin. The required computations of the present method for the inertia matrix and the bias vector of a manipulator with n rotational joints are (10.5n² + 38.5n - 85)M + (6n² + 39n - 70)A and (12.5n² + 5.5n + 3)M + (9n² + n)A, respectively, where “M” denotes multiplications, “A” does additions. In numerically forming the inertia matrix, the present method is more efficient than other methods in the literature for a manipulator with five or more joints; whereas this method is also superior to the recursive Newton-Euler formulation in computing the bias vector for a manipulator with six or less joints.     

作业型飞行机器人抓取后重心偏移的轨迹跟踪控制

作业型飞行机器人是指能够对环境施加主动影响的飞行机器人, 它通常由旋翼飞行器与机械臂组合而成. 本文针对作业型飞行机器人在动态飞行抓取后, 重心位置变化产生的系统控制难题, 设计了有效的跟踪控制策略. 首先, 在系统建模时引入重心偏移系统参数和重心偏移控制参数, 并考虑惯性张量不为常数, 提高了系统建模的精度. 然后, 在姿态解算时, 考虑重心偏移对系统性能的影响, 构建包含重心偏移系统参数的解算方法, 得到更高精度的期望翻滚角和期望俯仰角. 接着, 设计了基于滑模控制的重心偏移补偿位置控制器, 实现了有效的位置跟踪控制. 同时, 在姿态反演控制器的基础上, 加入自适应律估计重心偏移控制参数和变化的惯性张量, 再通过小脑神经网络逼近惯性张量的真实值, 提高姿态控制器的精度. 最后, 给出了所设计控制器的稳定性证明, 并在仿真环境下验证了所提出的方法的有效性和优越性.     

机械臂惯性矩阵的并行计算

本文在给出一种非递推形式的逆动力学计算公式的基础上，针对机械臂惯性矩阵的计算提出了一种面向Ｏ（ｎ）个处理器的并行算法，并以ＰＵＭＡ５６０机器人的前３个臂为例进行了计算效率分析。     

作业型飞行机器人动态滑翔抓取的鲁棒自适应控制

作业型飞行机器人是指将多自由度机械臂固连在飞行机器人上的一类新型机器人系统,它能够对周围环境施加主动影响,同时也存在较为复杂的动力学性能.本文针对作业型飞行机器人滑翔抓取物体时所受到的摩擦力和接触力问题以及在飞行过程中产生的转动惯量变化问题,设计了一种整体式鲁棒自适应控制策略.首先在作业型飞行机器人系统动力学建模中引入...     

A new repetitive controller for mechanical manipulators

A new repetitive learning controller for motion control of mechanical manipulators undergoing periodic tasks is developed. This controller does not require exact knowledge of the manipulator dynamic structure or its parameters, and is computationally efficient. In addition, no actual joint accelerations or any matrix inversions are needed in the control law. The global asymptotic stability of the ideal and the robust stability of the nonideal control system is proven, taking into account the full nonlinear dynamics of the manipulator. Simulation results of this algorithm applied to a realistic Scara type manipulator, which includes dry friction, pay-load inertia variations, actuator/sensor noise, and unmodelled dynamics are also presented.     

参数不确定空间机械臂系统的鲁棒自适应混合控制

讨论了载体位置与姿态均不受控制的漂浮基空间机械臂系统的控制问题.对系统运动学、动力学的分析结果表明,结合系统动量守恒及动量矩守恒关系得到的系统广义Jacobi关系以及系统的动力学方程是系统惯性参数的非线性函数.证明了借助于增广变量法可以将系统的增广广义Jacobi矩阵及系统动力学方程表示为一组适当选择的(组合)惯性参数的线性函数.以此为基础,针对系统惯性参数不确定的情况,设计了空间机械臂末端抓手跟踪惯性空间期望轨迹的鲁棒自适应混合控制方案.仿真运算结果证实了方法的有效性.     

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.     

The centralized formulation for complete dynamic modelling of robots

The centralized formulation for the inertia element of robot dynamics found by using the composite rigid body is very efficient. However, the corresponding formulation for the centrifugal, Coriolis, and gravity elements has not been addressed. Based on certain special motion states of a composite rigid body, this article presents the centralized formulation for all the inertial, centrifugal, Coriolis, and gravity elements. This formulation shows a very direct relationship with the mass, inertia, and Jacobian matrix columns of a composite rigid body. Compared with other modelling formulations, it requires the minimum computational complexity. Thus, highly efficient complete dynamic modelling of robots can be achieved. ©2000 John Wiley & Sons, Inc.     

An approach to the identifiable parameters of a manipulator

This article deals with the minimal parameters of a manipulator in the least squares sense, so that the minimal parameters are equivalent to the identifiable parameters. The least squares concept is used to introduce terminology for the minimal linear combinations (MLCs) of the system parameters that define a set of linear combinations of the system parameters. The number of elements of the set is minimal, yet the set still completely determines the system. Furthermore, it is shown that the problem of finding a set of MLCs of a manipulator can be simplified to that of finding two individual sets of MLCs that determine the entries of the inertia matrix and the gravity load. Although the approach is applied to the inertia constants of composite bodies to obtain a set of MLCs identical to an earlier one, the result is newly interpreted in the least squares sense. The approach itself is a new method for finding the identifiable parameters of a manipulator, and it yields some new insight into the manipulator dynamics. The crucial feature is that a set of MLCs found by using the present approach is guaranteed to be identifiable. The earlier approaches always require an identification method to verify the results. An equivalence theorem is also presented that rigorously states the equivalence between the different sets of minimal parameters. © 1994 John Wiley & Sons, Inc.     

Robust tracking control design for a 6 DOF parallel manipulator

The focus of this work is on a robust tracking control design for a 6 DOF parallel manipulator in the presence of nonlinearity and fast (or slowly) time‐varying uncertainty. Two types of controllers are presented. The controls are based on the Lyapunov approach and guarantee a practical stability. The controls utilize the information of link displacements and its velocities. The first control scheme uses the quadratic Lyapunov function and other uses the geometry dependent Lyapunov function, which excludes the inverse matrix computation on the inertia matrix. Also, the hydraulic dynamics is considered in the control design and control performance. The control performances of the proposed algorithms are verified by simulations and experiments. © 2000 John Wiley & Sons, Inc.     

基于PMSM驱动的柔性关节空间机械臂轨迹跟踪控制方法

针对目前柔性关节空间机械臂轨迹跟踪控制方法忽略了不同重力影响下的机械臂驱动力变化,导致柔性关节空间机械臂轨迹跟踪控制效果较差的问题,提出了基于PMSM驱动的柔性关节空间机械臂轨迹跟踪控制方法。基于构建PMSM驱动数学模型,采用PMSM的矢量控制方法,分析驱动力矩矢量。根据驱动力矩矢量分析结果,分析不同重力环境下有、无摩擦时的驱动力矩。构建柔性关节模型,分析其在不同重力环境下遇到的重力释放问题,使用自适应反演滑膜控制方法,设计控制率,保证机械臂能够按照既定的方向运动,使机械臂具有鲁棒性。根据柔性关节空间机械臂动力学特性,分析不同重力环境下基于PMSM驱动力矩,确定重力项是随之发生改变的。设计控制器,构建动力学模型,确保空间阶段能够最大限度跟踪运动轨迹。实验结果表明,所提方法X轴、Y轴的末端跟踪结果均与实际运动轨迹一致,误差为0。关节控制力矩在时间为3s时,出现了最大为0.5N.m的误差,说明所提方法的跟踪控制效果较好。     

Dynamics and Coupling Actuation of Elastic Underactuated Manipulators

This paper investigates the constraint and coupling characteristics of underactuated manipulators by proposing an elastic model of the manipulator and examining the second order constraint equation. A dynamic model and a coupling constraint equation are developed from a Jacobian matrix and the Newton‐Euler formulation. The inertia matrix and the Christoffel tensor are analyzed and decomposed into the part concerning actuated joints and the part concerning passive joints. This decomposition is further extended to the dynamic coupling equation and generates an actuation coupling matrix and a dynamic coupling tensor. Two new dynamic coupling indices are hence identified. One is related to an actuation input and the other is related to centrifugal and Coriolis forces. The former reveals the dynamic coupling between the input and the acceleration of passive joints and gives the actuation effect on the passive joints. The latter reveals the dynamic coupling between the centrifugal and Coriolis forces and the acceleration of passive joints and provides the centrifugal and Coriolis effect on the acceleration of passive joints. The study reveals the coupling characteristics of an underactuated manipulator. This is then demonstrated in a three‐link manipulator and extended to a serial manipulator with passive prismatic joint. © 2003 Wiley Periodicals, Inc.     

Efficient formulations for the manipulator inertia matrix in terms of minimal linear combinations of inertia parameters

This article summarizes four formulations of the composite body method for the inertia matrix of a manipulator in the earlier works and presents a new formulation. These five formulations all use the first moments and the inertia tensors of composite bodies about the origin of the local frame. This paper also presents an algorithm for computing these first moments and inertia tensors. This algorithm utilizes a set of minimal linear combinations of inertia parameters instead of the natural inertia parameters, so that a number of redundant computations are saved. It is found that the new algorithm for the first moments and the inertia tensors of composite bodies is computationally superior to the others in the literature. On the other hand, two among the five formulations for the inertia matrix are more efficient than the other three as well as the others in the literature. The new formulation is one of these two most efficient formulations, and is specially adequate to a manipulator with some translational joints. ©1999 John Wiley & Sons, Inc.     

基于LPV 方法的Stewart 平台关节空间分散控制

为了提高Stewart 平台关节空间分散控制系统的性能,提出一种基于线性变参数(Linear Parameter Varying,LPV) 方法的控制策略．首先建立了平台关节空间动力学模型;通过分析平台惯性矩阵,指出单支路 子系统等效负载变化以及子系统间的耦合干扰是分散控制需要处理的主要问题．然后将平台惯性矩阵分解为 一个对角阵与一个耦合阵之和,子系统间耦合作用视为对单支路的干扰,从而得到每个子系统的动力学方程． 最后针对子系统等效负载随着上平台运动而在较大范围内变化的特点,引入LPV 控制方法,使控制器参数能 够适应子系统负载变化,减少了保守性．仿真结果表明了所提方法的有效性．     

Simulation of Industrial Manipulators Based on the UDU T Decomposition of Inertia Matrix

The UDU ^T – U and D are respectively the upper triangular and diagonal matrices – decomposition of the generalized inertia matrix of an n-link serial manipulator, introduced elsewhere, is used here for the simulation of industrial manipulators which are mainly of serial type. The decomposition is based on the application of the Gaussian elimination rules to the recursive expressions of the elements of the inertia matrix that are obtained using the Decoupled Natural Orthogonal Complement matrices. The decomposition resulted in an efficient order n, i.e., O(n), recursive forward dynamics algorithm that calculates the joint accelerations. These accelerations are then integrated numerically to perform simulation. Using this methodology, a computer algorithm for the simulation of any n degrees of freedom (DOF) industrial manipulator comprising of revolute and/or prismatic joints is developed. As illustrations, simulation results of three manipulators, namely, a three-DOF planar manipulator, and the six-DOF Stanford arm and PUMA robot, are reported in this paper.     

Task-Space Modular Dynamics for Dual-Arms Expressed through a Relative Jacobian

This paper presents modular dynamics for dual-arms, expressed in terms of the kinematics and dynamics of each of the stand-alone manipulators. The two arms are controlled as a single manipulator in the task space that is relative to the two end-effectors of the dual-arm robot. A modular relative Jacobian, derived from a previous work, is used which is expressed in terms of the stand-alone manipulator Jacobians. The task space inertia is expressed in terms of the Jacobians and dynamics of each of the stand-alone manipulators. When manipulators are combined and controlled as a single manipulator, as in the case of dual-arms, our proposed approach will not require an entirely new dynamics model for the resulting combined manipulator. But one will use the existing Jacobians and dynamics model for each of the stand-alone manipulators to come up with the dynamics model of the combined manipulator. A dual-arm KUKA is used in the experimental implementation.