Determination of the orientation workspace of parallel manipulators

An important step during the design of a parallel manipulators is the determination of its workspace. For a 6-d.o.f. parallel manipulator workspace limitations are due to the bounded range of their linear actuators, mechanical limits on their passive joints and links interference. The computation of the workspace of a parallel manipulator is far more complex than for a serial link manipulator as its translation ability is dependent upon the orientation of the end-effector.We present in this paper an algorithm enabling to compute the possible rotation of the end-effector around a fixed point. This algorithm enables to take into account all the constraints limiting the workspace. Various examples are presented.     

Efficient workspace generation for binary manipulators with many actuators

Binary actuators have only two discrete states, both of which are stable without feedback. As a result, manipulators with binary actuators have a finite number of states. Major benefits of binary actuation are that extensive feedback control is not required, task repeatability can be very high, and two-state actuators are generally very inexpensive, thus resulting in low-cost robotic mechanisms. Determining the workspace of a binary manipulator is of great practical importance for a variety of applications. For instance, a representation of the workspace is essential for trajectory tracking, motion planning, and the optimal design of binary manipulators. Given that the number of configurations attainable by binary manipulators grows exponentially in the number of actuated degrees of freedom, 0(2), brute force representation of binary manipulator workspaces is not feasible in the highly actuated case. This article describes an algorithm that performs recursive calculations starting at the end-effector and terminating at the base. The implementation of these recursive calculations is based on the macroscopically serial structure and the discrete nature of the manipulator. As a result, the method is capable of approximating the workspace in linear time, O(n), where the slope depends on the acceptable error. © 1995 John Wiley b Sons, Inc.     

Tri-pyramid Robot: Design and kinematic analysis of a 3-DOF translational parallel manipulator

3-DOF translational parallel manipulators have been developed in many different forms, but they still have respective disadvantages in different applications. To overcome their disadvantages, the structure and constraint design of a 3-DOF translational parallel manipulator is presented and named the Tri-pyramid Robot. In the constraint design of the presented manipulator, a conical displacement subset is defined based on displacement group theory. A triangular pyramidal constraint is presented and applied in the constraint designs between the manipulator?s subchains. The structural properties including the decoupled motions, overconstraint elimination, singularity free workspace, fixed actuators and isotropic configuration are analyzed and compared to existing structures. The Tri-pyramid Robot is constrained and realized by a minimal number of 1-DOF joints. The kinematic position solutions, workspace with variation of structural parameters, Jacobian matrix, isotropic and dexterity analysis are performed and evaluated in the numerical simulations.     

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.     

Conceptual design and analysis of the 2T1R mechanism for a cooking robot

This paper deals with the design and analysis of a two-translation and one-rotation (2T1R) mechanism for a novel cooking robot. Firstly the motions involved in stir-fry, the most representative operation in the cooking processes used in Chinese cuisine, are analyzed in details. Then the featured motions are decomposed into four main movements that are used as a design base for a wok motion mechanism. Several three-degrees-of-freedom (DOF) parallel manipulators are considered. From these, a 2T1R mechanism is selected as an ideal candidate. A 4-DOF (2T1R+1T) cooking robot is constructed by combining the 2T1R parallel manipulator with a 1-DOF linear feed mechanism. It is shown that the combined 4-DOF robot can perform the required cooking operations, particularly the stir-fry. The analysis conducted on the proposed 2T1R parallel manipulator includes inverse kinematics, forward kinematics, the velocity analysis, the constant orientation workspace, and the total orientation workspace. A prototype of the cooking robot is developed. The experiments verify that the proposed cooking robot is suitable for performing the required operations.     

Comparison of four different heuristic optimization algorithms for the inverse kinematics solution of a real 4-DOF serial robot manipulator

In this study, a 4-degree-of-freedom (DOF) serial robot manipulator was designed and developed for the pick-and-place operation of a flexible manufacturing system. The solution of the inverse kinematics equation, one of the most important parts of the control process of the manipulator, was obtained by using four different optimization algorithms: the genetic algorithm (GA), the particle swarm optimization (PSO) algorithm, the quantum particle swarm optimization (QPSO) algorithm and the gravitational search algorithm (GSA). These algorithms were tested with two different scenarios for the motion of the manipulator’s end-effector. One hundred randomly selected workspace points were defined for the first scenario, while a spline trajectory, also composed of one hundred workspace points, was used for the second. The optimization algorithms were used for solving of the inverse kinematics of the manipulator in order to successfully move the end-effector to these workspace points. The four algorithms were compared according to the execution time, the end-effector position error and the required number of generations. The results showed that the QPSO could be effectively used for the inverse kinematics solution of the developed manipulator.     

TriM: An Ultra-Accurate High-Speed Six Degree-of-Freedom Manipulator Using Planar Stepper Motors

In this paper, we propose a novel six degree-of-freedom positioning system. This mechanism is a tripod structure with inextensible limbs actuated at the base by two-dimensional linear stepper motors (other types of actuators may also be utilized). This manipulator has a closed-chain kinematic structure. Both the direct and the inverse kinematics of the manipulator are presented in detail. While the inverse kinematics are obtained in closed form, the direct kinematics can not be solved in closed form and an algorithm is provided for numerically computing the direct kinematic solution. A detailed dynamic model of the positioning system is also provided. The dynamics of the actuators (Sawyer motors) are also included in the dynamic modeling. The design of the tripod manipulator (TriM) included a kinematic optimization of the system parameters to maximize the manipulator workspace. The proposed manipulator achieves large range of motion in all the 6 degrees of freedom. Furthermore, high resolution and high speed motion may be achieved in all axes due to the actuators used and the direct-drive nature of the manipulator. This work was supported in part by NSF under grants ECS-9977693 and ECS-0501539. An earlier version of this paper was presented at the 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, NV, Oct. 2003.     

Kinematic design of a six-DOF parallel-kinematics Machine with decoupled-motion architecture

The design of a new six-degree-of-freedom (6-DOF) parallel-kinematics machine (PKM) has been proposed. Different from the conventional Stewart-Gough platform which has six extensible legs, the new PKM employs three identical RPRS legs to support the moving platform. Since all joint axes, excluding the three spherical joints at the leg ends, are parallel to each other and perpendicular to the base plane, this 6-DOF PKM presents a promising platform structure with decoupled-motion architecture (DMA) such that translation in a horizontal plane and rotation about a vertical axis are driven by the three active revolute joints, while translation in the vertical direction and rotation about horizontal axes are driven by the three active prismatic joints. As a result, this 6-DOF 3RPRS PKM with DMA has simple kinematics, large cylindrical reachable workspace, and high stiffness in the vertical direction. These features make it appropriate for light machining and heavy parts assembly tasks. Because of the DMA, a projection technique is employed for its kinematics analysis. By projecting the manipulator onto horizontal directions and vertical planes, the kinematics issues such as the displacement, singularity, and workspace analysis are significantly simplified.     

Real-Time Motion Tracking of Robot Manipulators Using Adaptive Genetic Algorithms

The paper presents a genetic algorithm approach to real-time motion tracking of redundant and non-redundant manipulators. The joint angle trajectories are found by applying genetic operators to a set of suitably generated configurations so that the end-effector follows a desired workspace trajectory accurately. The probability of applying a particular genetic operator is adapted on-line to achieve fast convergence to the solution. The adaptation is based on two measures, namely, diversity and fitness of the generated configurations. In order to achieve real time tracking, special provisions are made so that only an appropriate small region in the joint space is searched. The tracking problem is solved at the position level rather the then velocity level. As such the proposed method does not use the manipulator Jacobian inverse or pseudo-inverse matrix and is shown to be free from problems such as excessive joint velocities due to singularities. Simulation results are presented for the 6-DOF Puma and the 7-DOF Robotic Research arm that demonstrate good tracking accuracy and reasonable joint velocities.     

Optimal design of a 3-PUPU parallel robot with compliant hinges for micromanipulation in a cubic workspace

In recent years, nanotechnology has been developing rapidly due to its potential applications in various fields that new materials and products are produced. In this paper, a novel macro/micro 3-DOF parallel platform is proposed for micro positioning applications. The kinematics model of the dual parallel mechanism system is established by the stiffness model with individual wide-range flexure hinge and the vector-loop equation. The inverse solutions and parasitic rotations of the moving platform are obtained and analyzed, which are based on a parallel mechanism with real parameters. The reachable and usable workspace of the macro motion and micro motion of the mechanism are plotted and analyzed. Finally, based on the analysis of parasitic rotations and usable workspace of micro motion, an optimization for the parallel manipulator is presented. The investigations of this paper will provide suggestions to improve the structure and control algorithm optimization for the dual parallel mechanism in order to achieve the features of both larger workspace and higher motion precision.     

基于运动学模型重构的单关节故障机械臂容错路径规划

针对单关节故障机械臂的路径规划问题,提出一种基于运动学模型重构的容错路径规划方法.首先基于旋量理论进行单关节故障机械臂的通用运动学模型重构;然后分析机械臂的退化工作空间,并以运动性能平稳为约束对其进行栅格化处理;最后通过改进传统的A$^\ast$算法,在退化工作空间中搜索出能够满足任务要求的轨迹.以七自由度机械臂为对象进行仿真实验,验证了所提出方法的正确性和有效性.     

线驱动模块化七自由度机器人轨迹跟踪控制

阐述了一种线驱动与常规串联驱动相结合的混合设计方法．这种设计方法融合了线驱动并联机构和模块化串联机构的优点,而且混合驱动机器人的工作空间大于完全线驱动机器人的工作空间．文章首先介绍了混合驱动机器人的机构设计,也就是机器人的肩关节采用模块化串联结构,而肘、腕关节采用线驱动结构．然后利用几何分析的方法来解机器人前向运动学问题．在分析驱动线长与关节角之间变换关系的基础上,分别利用速度法和关节角增量法来计算机器人逆向运动学解．最后,使用VC++实现混合驱动机器人对直线运动轨迹进行跟踪的仿真,从而证明了文章所描述的设计方法的正确性．     

Evaluation of head-collision safety of a 7-DOF manipulator according to posture variation

As the need for the improvement of the productivity in the manufacturing process grows, industrial robots are brought out of the safety fences and used in the direct collaborative operation with human workers. Consequently, the intended and/or unintended contact between the human and the robot in the collaborative operation is no longer an extraordinary event and is a mundane possibility. The level of the risk of the collision depends on various quantities associated with the collision, for example, inertia, velocity, stiffness, and so on. MSI (manipulator safety index) which is based on HIC (head injury criteria) conventionally used in the automotive industry is one of the practically available measures to estimate the risk of the collision between the human and the manipulator. In this paper MSI is applied to evaluate the collision safety of a 7-DOF articulated human-arm-like manipulator. The risk of the collision could be reduced by choosing different postures without deviating from the given end-effector trajectory using the redundant degree of freedom in the 7-DOF manipulator. The paper shows how the redundant degree of the freedom is utilized to design safer trajectories and/or safer manipulator configurations among many available. A parametric analysis and simulation results for a given trajectory illustrate the usefulness of the concept of the trajectory design for alleviating the risk of the manipulator operation in the human–robot coexisting workspace.     

Analysis and optimization of the 5-RPUR parallel manipulator

Many industrial applications need less than 6 degrees of freedom (DOF) to manipulate. On one hand, the parallel manipulators (PMs) with lower DOF have some advantages such as low manufacturing and control cost. On the other hand, they have more complicated kinematics. Among PMs with lower DOF, the 5-DOF PMs have particularly many industrial applications. Within the group of 5-DOF PMs, the three translational and two rotational (3T2R) type has more industrial applications than three rotational and two translational type. In this paper, we analyze and optimize the 5-RPUR PM which is a 3T2R type. The kinematic analysis is studied using the screw theory. The boundary and volume of the workspace is obtained using a geometrical method. In addition, singularity analysis is studied. Particle swarm optimization is utilized to optimize the workspace and the accuracy simultaneously, and achieve a roughly homogeneous accuracy index over the workspace. The boundary of the optimized workspace is depicted and we show that the optimized workspace is singularity free. The accuracy index of the manipulator is calculated and depicted in several cross-sections of the workspace.     

Adaptive end-effector pose control for tomato harvesting robots

This paper investigates the development of a tomato-harvesting robot operating on a plant factory and primarily studies the reachable pose of tomatoes in the nondexterous workspace of manipulator. The end-effector can only reach the tomatoes with reachable poses when the tomatoes are within the nondexterous workspace. If the grasping pose is not reachable, it will lead to grasping failure. An adaptive end-effector pose control method based on a genetic algorithm (GA) is proposed to find a reachable pose. The inverse kinematic solution based on analysis method of the manipulator is analyzed and the objective function of whether the manipulator has a solution or not is obtained. The grasping pose is set as an individual owing to the position of the tomatoes is fixed and the grasping pose is variable. The GA is used to solve until a pose that can make the inverse kinematics have a solution is generated. This pose is the reachable grasping pose of the tomato at this position. The quintic interpolation polynomial is used to plan the trajectory to avoid damage to tomatoes owing to fast approaching speed and a distance based background filtering method is proposed. Experiments were performed to verify the effectiveness of the proposed method. The radius of the workspace of the UR3e manipulator with the end-effector increased from 550 to 800 mm and the grasping range expanded by 208%. The harvesting success rate using the adaptive end-effector pose control method and trajectory planning method was 88%. The cycle of harvesting a tomato was 20 s. The experimental results indicated that the proposed tomato-recognition and end-effector pose control method are feasible and effective.     

Singularity-robust decoupled control of dual-elbow manipulators

The ability of a robot manipulator to move inside its workspace is inhibited by the presence of joint limits and obstacles and by the existence of singular positions in the configuration space of the manipulator. Several kinematic control strategies have been proposed to ameliorate these problems and to control the motion of the manipulator inside its workspace. The common base of these strategies is the manipulability measure which has been used to: (i) avoid singularities at the task-planning level; and (ii) to develop a singularity-robust inverse Jacobian matrix for continuous kinematic control. In this paper, a singularity-robust resolved-rate control strategy is presented for decoupled robot geometries and implemented for the dual-elbow manipulator. The proposed approach exploits the decoupled geometry of the dual-elbow manipulator to control independently the shoulder and the arm subsystems, for any desired end-effector motion, thus incurring a significantly lower computational cost compared to existing schemes.     

An analysis of the inverse kinematics for a 5-DOF manipulator

This paper proposes an analytical solution for a 5-DOF manipulator to follow a given trajectory while keeping the orientation of one axis in the end-effector frame. The forward kinematics and inverse kinematics for a 5-DOF manipulator are analyzed systemically. The singular problem is discussed after the forward kinematics is provided. For any given reachable position and orientation of the end-effector, the derived inverse kinematics will provide an accurate solution. In other words, there exists no singular problem for the 5-DOF manipulator, which has wide application areas such as welding, spraying, and painting. Experiment results verify the effectiveness of the methods developed in this paper.     

Cable-Direct-Driven Robot (CDDR) with Passive SCARA Support: Theory and Simulation

This article presents a new planar translational cable-direct-driven robot (CDDR) with actuation redundancy and supported against loading normal to the motion plane with a passive planar two-degree-of-freedom SCARA-type (Selective Compliance Assembly Robot Arm) serial manipulator. This allows the robot to resist cable sag without being supported on the motion plane. The proposed robot architecture may assure high payload-to-weight ratio, resistance to forces normal to the plane of motion, and a potentially large workspace. Another benefit is that the passive SCARA has structure to provide end-effector moment resistance, which is not possible with many proposed translational CDDRs. Moreover, the passive robot can also serve as an independent Cartesian metrology system. This article derives the kinematics and dynamics models for the proposed hybrid serial/parallel architecture. Additionally it proposes a dynamic Cartesian controller always ensuring positive cable tensions while minimizing the sum of all the torques exerted by the actuators. Simulation examples are also presented to demonstrate the novel CDDR concept, dynamics, and controller.Category (7) – System Modelling/Simulation/Control/Computer–Aided Design/Robot Control/Teleoperation/Moving Robots