Geared robot manipulators with a jointed unit: Kinematic analysis and its application

An efficient and systematic methodology for the kinematic analysis of geared robot manipulators (GRMs) with a jointed unit is presented. It is shown that, by decomposing mechanical transmission lines of a GRM into serially connected jointed and disjointed units, kinematic relation between local inputs and local outputs of admissible jointed units can be systematically formulated. Accordingly, angular displacements of input links with respect to their associated primary links can be symbolically expressed in terms of joint angles by a unit‐by‐unit evaluation procedure. This unit‐by‐unit evaluation procedure provides better kinematic insights into how input torques are transmitted to various joints. It is also shown that an actuator in a GRM with a jointed unit can drive nonconsecutive joints by proper design of its gear train. A 3 degrees of freedom GRM with a jointed unit is used as an illustrative example. © 2001 John Wiley & Sons, Inc.     

On the drive train design of gear coupled manipulators

A systematic methodology for the drive train design of gear coupled manipulators is developed. The approach is based on the idea that the generalized inertia forces contribution to the system's dynamic equations can be divided into the contribution of the virtual open-loop chain and that of the drive train. It is shown that the contribution of the drive train to the system's dynamic equations is a function of the orientations of its rotational axes and the orientations of joints. Conditions to determine these orientations such that the drive train can have configuration-invariant contribution to the system's dynamic equations are derived. From the design conditions, mechanical details of the drive train such as the choice of actuator locations, the arrangements of the drive train and joints, the compatibility between orientations of joints and rotational axes of the drive train can be determined accordingly. This approach, together with the developed design methods for the serial type manipulators, provides a complete design methodology in designing new robots or improving the dynamic performance of existing ones. © 1998 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.

     

Simulation and computer-aided kinematic design of three-degree-of-freedom spherical parallel manipulators

Parallel robotic manipulators are complex mechanical systems that lead to involved kinematic and dynamic equations. Hence, the design of such systems is in general not intuitive, and advanced simulation and design tools specialized for this type of architecture are highly desirable. This article discusses the kinematic simulation and computer-aided design of three-degree-of-freedom spherical parallel manipulators with either prismatic or revolute actuators. The kinematic analysis of spherical parallel manipulators is first reviewed. Solutions for the direct and inverse kinematic problems are given, and the expressions for the singularity loci are then introduced. The determination of the workspace of this type of manipulator is also addressed. Finally, a computer package developed specifically for the CAD of spherical parallel manipulators is presented. This package allows the interactive analysis of manipulators of arbitrary architecture including the representation of the workspace, the representation of singularities, and the graphic animation of trajectories specified either by the direct or the inverse kinematic module. It can be used for the design of any spherical parallel three-degree-of-freedom actuated mechanism, which can find many applications in high-performance robotic systems. © 3995 John Wiley & Sons, Inc.     

Duty-cycle analysis of a human-controlled manipulator

The duty cycles of a human-controlled servomanipulator system have been experimentally measured revealing how humans use manipulators to perform tasks. The use of the kinematic ranges, in both joint and Cartesian space is valuable to engineers in the kinematic design of servomanipulators. The working volume of human manipulation presented here is also of interest to designers of prosthetic systems. These results illuminate the relative merits of various system drive configurations. A graphical representation of mechanical power usage, which displays the total operation time as a function of torque and velocity, is presented for each manipulator joint. These data are compared with data representing idealized joint performance resulting in design criteria for quantitative improvements in joint torque and velocity capacities. A generalized method for applying this representation to any robotic system is discussed.     

A practical method for the deformation of long-stroke hydraulic manipulators in grasping-handling tasks

Long-stroke hydraulic manipulators are utilized in various grasping-handling tasks, and the flexible deformation of these manipulators is the primary obstacle that affects precise position control of the end-effectors in Cartesian space. This deformation is manifested in the following three aspects: joint deformation, structural deformation and clearance variation. Due to deformation uncertainty, methods that model the hydraulic manipulator as a combination of flexible multibody systems and hydraulic actuators are unsuitable. In this article, we propose an incremental inverse kinematics model (IIKM) as a new approach to solving the above deformation difficulties. The projection method is used to obtain the inverse kinematic analytical solution of long-stroke hydraulic manipulators, which is based on the manipulator deformation in the current configuration (current configuration refers to the arrangement of the manipulator links when the manipulator starts to move to the target position). The proposed method avoids complex flexible multibody modeling and parameter identification, allowing long-stroke hydraulic manipulators to be accurately controlled within a certain neighborhood. An evaluation coefficient is proposed to analyze the calculation accuracy of the IIKM in combination with the success rate obtained from 190 grasping experiments. Through these experiments, we determine the optimal calculation height range of the IIKM in the vertical direction and the optimal calculation position area in the horizontal direction and prove that the IIKM result can guarantee the success of grasping-handling tasks when the end-effector is within the optimal calculation height range.     

微重力环境下空间机械手的动力学建模新方法

未来空间作业将需要机械手在微重力的环境下完成各种复杂的任务．由于机械手与其本体的动态耦合，给机械手带来了许多运动学、动力学及控制方面的问题．本文提出了一种空间机械手动力学的建模新方法，对空间机械手的正、逆动力学进行了分析．应用该方法，建立了一种基于解出加速度的空间机械手的控制策略．本文所提出的方法不仅适合于单机械手系统，而且适合于多机械手的系统．     

基于行星齿轮机构的牵引式欠驱动机械手设计

为实现夹持力调节和目标物体抓取功能,设计了一种基于行星齿轮机构的牵引式欠驱动机械手。该机械手采用不固定输出轴和内齿圈的行星齿轮机构来分配2种互斥的运动,一种用于手指的转动,实现机械手的夹持功能;另一种用于皮带轮的无限转动,通过皮带实现目标物体的拉入功能。相对于腱绳式和连杆式欠驱动机械手,这种单输入双输出形式不仅能够保持机械手的自适应性,同时还能降低机械手的耦合程度。根据行星齿轮机构的这种传动特点,设计了阻力矩调节机构,实现了机械手的夹持力调节功能。夹持力测试实验表明,在阻力矩调节机构的作用下,机械手能有效调节夹持力。抓取实验结果表明,机械手能够实现对刚性和柔性目标物体的抓取操作,验证了机械手设计的有效性。     

Adaptive stabilization of mobile manipulators

This paper considers the motion control problem for uncertain mobile manipulator systems comprised of a robotic arm mounted on a wheeled mobile platform. More specifically, we address the problem of stabilizing mobile manipulators in the presence of uncertainty regarding the system dynamic model. It is proposed that a simple and effective solution to this problem can be obtained by combining ideas from homogeneous system theory and adaptive control theory. Thus each of the proposed control systems consists of two subsystems: a (homogeneous) kinematic stabilization strategy, which generates a desired velocity trajectory for the mobile manipulator, and an adaptive control scheme, which ensures that this velocity trajectory is accurately tracked. This approach is shown to provide arbitrarily accurate stabilization to any desired configuration and can be implemented without knowledge of the details of the system dynamic model. Moreover, it is demonstrated that exponential rates of convergence can be achieved with this methodology. The efficacy of the proposed stabilization strategies is illustrated through computer simulations with two mobile manipulators. © 1998 John Wiley & Sons, Inc.     

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.     

Parallel and distributed trajectory generation of redundantmanipulators through cooperation and competition among subsystems

Autonomous distributed control (ADC) is one of the most attractive approaches for more versatile and autonomous robot systems. The paper proposes a parallel and distributed trajectory generation method for redundant manipulators through cooperative and competitive interactions among subsystems composing the ADC that is based on a concept of virtual arms. The virtual arm has the same kinematic structure as the manipulator except that its end point is located on a joint or link of the manipulator. Then the redundant manipulator can be represented by a set of the virtual arms. Trajectory generation and point to point control of the redundant manipulator are discussed, and it is shown that the kinematic redundancy of the manipulator can be utilized positively in the generated trajectories by using the virtual arms.     

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.     

A general solution for the position,velocity, and acceleration of hyperredundant planar manipulators

A new approach for the solution of the position, velocity, and acceleration of hyperredundant planar manipulators following any twice‐differentiable desired path is presented. The method is singularity free, and provides a robust solution even in the event of mechanical failure of some of the robot actuators. The approach is based on defining virtual layers, and dividing them into virtual/real three‐link or four‐link subrobots. It starts by solving the inverse kinematic problem for the subrobot located in the lowest virtual layer, which is then used to solve the inverse kinematic equations for the subrobots located in the upper virtual layers. An algorithm is developed that provides a singularity‐free solution up to the full extension through a configuration index. The configuration index can be interpreted as the average of the determinants of the Jacobians of the subrobots. The equations for the velocities and accelerations of the manipulator are solved by extending the same approach, and it is shown that the value of the configuration index is critical in maintaining joint velocity continuity. The inverse dynamic problem of the robot is also solved to obtain the torques required for the robot actuators to accomplish their tasks. Computer simulations of several hyperredundant manipulators using the proposed method are presented as numerical examples. © 2002 John Wiley & Sons, Inc.     

Energy analysis of robot task motions

An energy criterion for choosing the best type of manipulator for a specified task is developed. First, the energy required to perform the robotic task is calculated. Then the lower bound of the mechanical energy consumed by the various kinds of manipulators during their motion, while performing a task, is calculated. Thus, the efficiency of a manipulator for the task is determined. Some examples show that the proper selection of the manipulator configuration can reduce the required energy to a quarter of that of a less suitable one. Once the most suitable manipulator is chosen, the criterion for its most energy efficient motion is developed. The model takes into account the kinematic configuration of the robot, gravitational and other external and internal forces acting on the robot during its operation, and the electric motor driving the robot links. Energy optimization of different paths of motion in joint coordinates is discussed briefly.     

Forward displacement analysis and uncertainty configurations of parallel manipulators with a redundant branch

The effect of adding a redundant branch in terms of reduction of the number of assembly modes and elimination of potential uncertainty configuration types is investigated for a class of parallel manipulators. Considered is a broad class that includes all three-branch manipulators where each branch is comprised of a serial arrangement of three main-arm joints supporting a common payload platform through a passive spherical branch end joint-group. The addition of a redundant branch effectively yields a four-branch manipulator class. Considered in particular is a 3–4 form of the manipulator where two branch ends meet at one point on the mobile platform. Symmetric main-arm joint sensing and actuation (two sensed/acutated main-arm joints per branch) is utilized. Synthetic geometry is used to study the number of assembly configurations of the resulting 3–4 four-branch parallel manipulators. It is presented that the number of assembly modes of three-branch parallel manipulators with passive spherical branch end joints can be reduced by utilizing a redundant branch. It is shown that there exist up to eight and up to four assembly modes when all unsensed joints are revolute and when all unsensed joints are prismatic, respectively. Combinations of unsensed prismatic and revolute joints are also investigated. It is determined that there are up to eight and up to four assembly modes when the unsensed main-arm joint of one of the concurrent branches is prismatic and when the unsensed joints of both concurrent branches are prismatic joints, respectively. Resolving the potential assembly modes require only the consideration of, at highest, second-order single-variable polynomials. In addition, kinematic design considerations allowing reduction of feasible assembly modes are discussed. The investigation of potential uncertainty configuration types is based on examining degeneracies of the screw systems formed by wrenches associated with the forces that the actuated-joints can apply. All linear dependency cases that could potentially cause uncertainties for the class of four-branch manipulators are identified. It is shown that while significantly reducing potential uncertainty configuration types, the addition of a redundant branch number cannot eliminate all potential dependency (uncertainty) cases completely. For the remaining potential uncertainty configuration types, the characteristics of the corresponding unconstrained instantaneous degrees of freedom are discussed. © 1996 John Wiley & Sons, Inc.     

Parametric motor control: A new approach to the control of point-to-point manipulator movements

We propose a control scheme for point-to-point movements of robotic manipulators, which is based on an established concept about human movement control. In this approach, actuator drive signals have an invariant shape and are parametrically modified to fit the requirements of different tasks. The appropriate parameter values are provided by an Artificial Neural Network before movement onset. Explicit solutions of the inverse kinematic and inverse dynamic equations, or multiple feedback loops, are not required for this approach. We found that Parametric Motor Control yields satisfactory performance, allowing the manipulator to discriminate between targets in a 5×3 grid and to generalize to new target locations. The new control scheme has potential benefits for scenarios where complex manipulators must be controlled in real time. © 1997 John Wiley & Sons, Inc.     

Manipulability and Static Stability of Parallel Manipulators

The design of reliable parallel robots demands a priori determination oftheir kinematic and dynamic properties. An important issue of the designof robotic manipulators is to ensure a high manipulability and theability to reach a desired spatial position. For parallel mechanisms themanipulability highly depends on its actual configuration and can bedescribed by several local measures each having a different sensitivityto singular configurations of the structure. Global manipulabilitymeasures are introduced which globally characterize the kinematicdexterity of parallel manipulators. Beside purely kinematiccharacteristics the stability of manipulator configurations is ofparticular interest. To facilitate such analyses a stability measure isintroduced taking into account the actual load and elastic members ofthe structure. A Hexapod structure clarifies the relevance of theproposed measures.     

Virtual joint method for kinematic modeling of wheeled mobile manipulators

In this paper, we propose a virtual joint method that better utilizes quasi-velocities for the kinematic modeling of wheeled mobile manipulators. By identifying quasi-velocities as motions of imaginary revolute and prismatic kinematic pairs, our method enables one to regard a mobile manipulator as an ordinary articulated manipulator for the purposes of velocity analysis. We also propose an inverse kinematic scheme for the mobile manipulators along the line with the virtual joint based kinematic framework. Details are worked out for mobile manipulators with representative differential-drive and car-like mobile platforms.     

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.