Comparative study of performance indices for fundamental robot manipulators

In this paper, conventional global and local indices–structural length index, manipulability measure, condition number and Global Conditioning Index (GCI)–have been examined for the workspace optimization of the sixteen fundamental robot manipulators classified by B. Huang and V. Milenkovic [Kinematics of major robot linkages, Robotics International of SME 2 (1983) 16–31]. To find the optimum link length and volumes of these robot manipulators, two design objectives have been used: maximize the workspace area covered by the robot manipulator and maximize the local indices. As an example, a three-link robot manipulator has been studied based on the above design objectives. Also, optimization results of the sixteen robot manipulators have been compared to each other and summarized in tables.     

The power manipulability – A new homogeneous performance index of robot manipulators

Jacobian-based performance indices such as the manipulability ellipsoid, the condition number and the minimum singular value, have been very helpful tools both for mechanical manipulator design and for determining suitable manipulator postures to execute a given task. For a manipulator having complex degrees of freedom (translations and rotations), Jacobian matrix becomes non-homogeneous, i.e. it contains elements with different physical units; therefore, the evaluation of its determinant, eigenvalues or singular values needs the combination of quantities of different nature, which is physically inconsistent and moreover it corresponds to a noncommensurable system. In this paper, a new performance index of robot manipulators is proposed. It is fully homogeneous and it constitutes a physically consistent system whether the manipulator contains joints of different natures, or the task space combines both translation and rotation motion. The development is concerned with the study of power within the mechanism. Given that the power has the same physical units in translation and rotation, it can be used as a homogeneous or natural performance index of manipulators by examining the behaviour of its basic components namely, force and speed, at different kinematics configurations. Furthermore, the new concept of vectorial power is introduced, followed by to the quadrivector of apparent power, and leading to the final homogeneous performance index of the power manipulability (PM). This new approach matches perfectly with mechanisms having joints of different natures, as well as with a task space combining both translation and rotation.     

Procedure for manipulator inverse kinematics computation and proper pseudoinverse perturbation

In this article, an efficient procedure for the proper pseudoinverse perturbation and the numerical inverse kinematics computation of robot manipulators is presented. The approach is based on solving a linear system of equations and using an original scheme for the appropriate perturbation of the pseudoinverse matrix in the next iteration. The resultant algorithm is tested on the simulation of an industrial robot manipulator. From the results obtained, it is observed that the proposed approach compares favorably with the approaches using a Gaussian elimination procedure and with pseudoinverse robustness based on a manipulability measure.     

A Sequential Bi-criteria Search Algorithm for Robot Path Planning in the Box Pushing Problem

The collision-free trajectory planning method subject to control constraints for mobile manipulators is presented. The robot task is to move from the current configuration to a given final position in the workspace. The motions are planned in order to maximise an instantaneous manipulability measure to avoid manipulator singularities. Inequality constraints on state variables i.e. collision avoidance conditions and mechanical constraints are taken into consideration. The collision avoidance is accomplished by local perturbation of the mobile manipulator motion in the obstacles neighbourhood. The fulfilment of mechanical constraints is ensured by using a penalty function approach. The proposed method guarantees satisfying control limitations resulting from capabilities of robot actuators by applying the trajectory scaling approach. Nonholonomic constraints in a Pfaffian form are explicitly incorporated into the control algorithm. A computer example involving a mobile manipulator consisting of nonholonomic platform (2,0) class and 3DOF RPR type holonomic manipulator operating in a three-dimensional task space is also presented.     

A new index of serial-link manipulator performance combining dynamic manipulability and manipulating force ellipsoids

The inertia matching ellipsoid (IME) is proposed as a new index of dynamic performance for serial-link robotic manipulators. The IME integrates the existing dynamic manipulability and manipulating-force ellipsoids to achieve an accurate measure of the dynamic torque-force transmission efficiency between the joint torque and the force applied to a load held by an end-effector. The dynamic manipulability and manipulating-force ellipsoids can both be derived from the IME as limiting forms, with respect to the weight of the load. The effectiveness of the IME is demonstrated numerically through the selection of an optimal leg posture for jumping robots and optimal active stiffness control, and experimentally through application to a pick-up task using a commercial manipulator. The index is also extended theoretically to the case of a manipulator mounted on a free-flying satellite.     

Analyses of biped walking posture by dynamical-evaluating index

In this paper, biped walking posture and design are evaluated through dynamic reconfiguration manipulability shape index (DRMSI). DRMSI is the concept derived from dynamic manipulability and reconfiguration manipulability with remaining redundancy. DRMSI represents the ability of dynamical system of manipulators possessing shape changing acceleration in task space by normalized torque inputs, while the hand motion is assigned as the primary task. Besides, we use visual lifting approach to stabilize the walking and stop falling down. In this research, the primary task is to make the position of the head direct to the desired one as much as possible. And realizing the biped walking is the second task. This research indicates that proposed dynamical-evaluating index is effective in evaluating the biped walking motion and biped humanoid robot has the adjustable configuration to walk with higher flexibility. Flexibility represents the dynamical shape changeability of humanoid robot based on redundancy of the humanoid robot with the premise of the primary task given to keeping the head position high.     

冗余度机器人操作手的运动灵活性测度

本文在速度水平上讨论了机器人操作手的运动灵活性,根据机器人操作手的运动灵活性完全取决于雅可比矩阵列向量的相关性这一分析,提出用雅可比矩阵的子阵 J_m 的总体相关性指标和相对相关性指标作为机器人操作手的运动灵活性测度,定义了运动灵活性的两个度量指标——绝对灵活度 D_α和相对灵活度 D_r;并论证了绝对灵活度 D_α和可操作度 W,相对灵活度 D_r 和可操作度 W、条件数 K 及最小奇异值σ_m 之间的关系;证明了绝对灵活度 D_α和可操作度 W 的等价性,并给出了可操作度的新的定义.从而全面论证了本文提出的操作手的运动灵活性测度的合理性.     

Geometrical approach of planar hyper-redundant manipulators: Inverse kinematics,path planning and workspace

A new method for inverse kinematics for hyper-redundant manipulators is proposed in this paper to plan the path of the end-effector. The basic idea is that for a given smooth path consisting of points close enough to each other; computing the inverse kinematics for these points is carried out geometrically using the proposed method. In this method, the angles between the adjacent links are set to be the same, which makes lining up of two or more joint axes impossible; therefore, avoiding singularities. The manipulability index has been used to show how far the manipulator from the singularity configuration is. The determination of the workspace of the manipulator using the proposed method has been presented in this paper. The simulation results have been carried out on a planar and a three dimensional manipulators. The effectiveness of the proposed method is clearly demonstrated by comparing its result with results calculated by the well-known method of measuring manipulability which is used for singularity avoidance for the last two decades.     

A kinetostatic index to measure the task-executing ability of robotic manipulators with limit-driven characteristics of actuators

Dexterity is an important issue for the design, trajectory planning and control of robotic manipulators. However, even though a lot of robot manipulators are driven by DC motors, no dexterity measures were introduced to evaluate how efficient a manipulator system is for performing a required task in the case of taking the limit-driven characteristics of the DC motor into consideration. In this study, we introduce a new kinetostatic dexterity index to measure the task-executing ability of robotic manipulators where the possible maximum velocity and force of the required task are derived subject to the heat-converted power limit of the DC motor. The measure is to evaluate how efficient a manipulator system is to execute a required task, while the limit-driven characteristics of its actuators are taken into consideration. Two examples are used to show that the proposed dexterity index is task-dependent and changed due to the tasks.     

Repetitive motion of redundant robots planned by three kinds of recurrent neural networks and illustrated with a four-link planar manipulator’s straight-line example

In this paper, a dual neural network, LVI (linear variational inequalities)-based primal-dual neural network and simplified LVI-based primal-dual neural network are presented for online repetitive motion planning (RMP) of redundant robot manipulators (with a four-link planar manipulator as an example). To do this, a drift-free criterion is exploited in the form of a quadratic performance index. In addition, the repetitive-motion-planning scheme could incorporate the joint physical limits such as joint limits and joint velocity limits simultaneously. Such a scheme is finally reformulated as a quadratic program (QP). As QP real-time solvers, the aforementioned three kinds of neural networks all have piecewise-linear dynamics and could globally exponentially converge to the optimal solution of strictly-convex quadratic-programs. Furthermore, the neural-network based RMP scheme is simulated based on a four-link planar robot manipulator. Computer-simulation results substantiate the theoretical analysis and also show the effective remedy of the joint angle drift problem of robot manipulators.     

Posture measure and control for robot compliance tasks

Various measures have been proposed for evaluating the compatibility of manipulator postures with respect to task requirements from kinematic and dynamic standpoints. In most previous studies, the measures were used to determine optimal postures for manipulators in advance, and their effects on system performance were generally examined statically. When posture measures are applied to controlled dynamic systems, however, their effects are usually not evident, because deficiencies (merits) caused by bad (good) postures can be compensated for by the controller. On the other hand, postures determined according to proper measures can still alleviate the controller's load and be helpful in control strategy realization. In this paper, we propose that planned compliant motion trajectories should be accompanied by proper postures for compliance tasks. Thus, we analyze manipulator dynamic behavior by using postures specified according to various measures. And, because different postures are used in different phases of the compliance task, a posture selection and control scheme is also proposed to govern the sequence of postures selected according to task requirements and environments. Redundant robot manipulators were used for investigation because of their better manipulability. Simulations that demonstrate the effectiveness of the proposed scheme are described. © 1998 John Wiley & Sons, Inc.     

Strategy of approach for seizure of an assistive mobile manipulator

In assistive robotics, a manipulator arm constitutes one possible solution for restoring some manipulation functions to victims of upper limb disabilities. The aim of this paper is to present a global strategy of approach of an assistive mobile manipulator (manipulator arm mounted on a mobile base). A manipulability criterion is defined to deal with the redundancy of the system. The aim is to keep the arm manipulable, i.e. capable of moving by itself. The strategy is based on human-like behaviour to help the disabled operator to understand the action of the robot. When the robot is far from its objective, only the mobile base moves, thus avoiding obstacles if necessary. When the objective is close to the robot, both mobile base and arm move and redundancy can be used to maximise a manipulability criterion. All the situations are tested separately and a global mission is realised in which all the previous situations are encountered. The partial results obtained with the real robot consolidate the results of simulation. This paper does not propose an autonomous path planning and navigation of the mobile arm but an assistance to the user for remote controlling it.     

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.     

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.     

冗余机械臂运动学优化设计

该文主要从机械臂运动学的角度,定义了故障容错机械臂,巧妙地论证了冗余故障容错机械臂应该具备的自由度数,以及针对不同的任务要求,设计故障容错机械臂的方法。通过将任务空间抽象简化为一系列的特征点,建立机械臂参数与理想值相关的罚函数,选择有效的优化算法,设计出了通用一阶故障容错平面位置机械臂,通用一阶故障容错空间位置机械臂,以及特定任务一阶故障容错平面位置机械臂。建立起完整的故障容错机械臂的设计方法。     

B-splines joint trajectory planning

This paper describes how B-splines can be used to construct joint trajectories for robot manipulators. The motion is specified by a sequence of Cartesian knots, i.e., positions and orientations of the end effector of a robot manipulator. For a six joint robot manipulator, these Cartesian knots are transformed into six sets of joint variables, with each set corresponding to a joint. Splines, represented as linear combinations of B-splines, are used to fit the sequence of joint variables for each of the six joints. A computationally very simple recurrence formula is used to generate the B-splines. This approach is used for the first time to establish the mathematical model of trajectory generation for robot manipulators, and offers flexibility, computational efficiency, and a compact representation.     

Torque Optimizing Control with Singularity-Robustness for Kinematically Redundant Robots

A new control method for kinematically redundant manipulators having the properties of torque-optimality and singularity-robustness is developed. A dynamic control equation, an equation of joint torques that should be satisfied to get the desired dynamic behavior of the end-effector, is formulated using the feedback linearization theory. The optimal control law is determined by locally optimizing an appropriate norm of joint torques using the weighted generalized inverses of the manipulator Jacobian-inertia product. In addition, the optimal control law is augmented with fictitious joint damping forces to stabilize the uncontrolled dynamics acting in the null-space of the Jacobian-inertia product. This paper also presents a new method for the robust handling of robot kinematic singularities in the context of joint torque optimization. Control of the end-effector motions in the neighborhood of a singular configuration is based on the use of the damped least-squares inverse of the Jacobian-inertia product. A damping factor as a function of the generalized dynamic manipulability measure is introduced to reduce the end-effector acceleration error caused by the damping. The proposed control method is applied to the numerical model of SNU-ERC 3-DOF planar direct-drive manipulator.     

On the boundedness of the Hessian of the potential energy of robot manipulators

Several results on robot manipulator motion control require a uniform bound for the Hessian of the potential energy or equivalently the Jacobian of the gravity vector. Not all robot manipulators, however, ensure the existence of such a uniform bound. The first contribution of this article is the complete characterization of this class which is referred to as class ℬ︁𝒢𝒥 manipulators. The uniform bound of the Hessian is typically part of the control law expression and hence it plays an important role in controller gain synthesis. The second contribution of this article consists of deriving, for class ℬ︁𝒢𝒥 robot manipulators, an easy to compute explicit expression of the uniform bound in terms of kinematic and inertial link parameters. If for a particular robot manipulator the Hessian of potential energy is not uniformly bounded, a bound exists that is valid within the physical workspace of the manipulator. The third contribution of this article is the derivation of an explicit expression for the latter bound which is useful in the design and controller gain synthesis of control laws that are valid locally. ©1999 John Wiley & Sons, Inc.     

A systematic formulation of dynamic equations for robot manipulators with elastic links

Although a variety of formulation schemes for the dynamic equations of robot manipulators with rigid links can be found in the literature, an efficient method of the formulation for robot manipulators with elastic links is not well known. Accordingly, this work presents the derivation of the equations of motion for application to mechanical manipulators with elastic links. The formulation is conducted analytically using Hamilton's principle. The resultant equations consist of the terms of inertial, Coriolis, centrifugal, gravitational, and exerted forces. They are expressed in terms of a set of independent generalized coordinates. In contrast to conventional variational approaches, the present method provides an efficient and systematic way for obtaining the compact symbolic equations of flexible manipulator systems. Two examples are presented to illustrate the proposed methodology. Firstly, a three-link flexible manipulator with three revolute joints is studied. A flexible manipulator consisting of a prismatic joint and a discrete mass is the second model.