Static analysis of cable-driven manipulators with non-negligible cable mass

This paper addresses the static analysis of cable-driven robotic manipulators with non-negligible cable mass. An approach to computing the static displacement of a homogeneous elastic cable is presented. The resulting cable-displacement expression is used to solve the inverse kinematics of general cable-driven robotic manipulators. In addition, the sag-induced stiffness of the cables is derived. Finally, two sample robotic manipulators with dimensions and system parameters similar to a large scale cable-driven manipulator currently under development are analyzed. The results show that cable sag can have a significant effect on both the inverse kinematics and stiffness of such manipulators.     

欠驱动柔性机器人的振动可控性分析

欠驱动柔性机器人的可控性分析是对其进行有效控制的关键问题. 本文以具有柔性杆的3DOF平面欠驱动机器人为例, 分两步分析系统的可控性. 首先,忽略杆件的弹性变形, 研究欠驱动刚性系统在不同驱动电机位置的状态可控性；然后, 考虑柔性因素, 研究欠驱动柔性系统的结构振动可控性. 结果表明振动可控性是随机器人关节位形和驱动电机位置而变化的, 并且欠驱动刚性机器人的状态可控性对相应的柔性系统的振动可控性有很重要的影响. 最后, 将上述研究方法扩展到具有一个被动关节的N自由度平面欠驱动柔性机器人.     

Dynamic modeling and vibration characteristics analysis of flexible-link and flexible-joint space manipulator

With the development of space technology, lighter and larger space manipulators will be born, of which flexible characteristics are more obvious. The manipulator vibration caused by the flexibility not only reduces the efficiency of the manipulator but also affects the accuracy of the operation. The flexibility of space manipulator mainly comes from structural flexibility of links and transmission flexibility of harmonic gear reducer in joints. The vibrations generated by these two kinds of flexibility are coupled and transformed mutually, making the dynamics characteristics of space manipulator system complicated. Therefore it is difficult to assess respective effects of these flexibilities on vibrations of the manipulator tip. And the characteristics of integrated vibration of manipulator tip with different link and joint stiffnesses are not very clear. In this paper, the dynamic equations of multi-link multi-DOF flexible manipulator are established. Then, vibration responses of the tip under different elastic modulus, damping and joint stiffness were studied, and vibration characteristics of the tip with both link and joint were also analyzed. Moreover, the effects of motion planning on the vibration of the tip were analyzed. Finally, the vibration characteristics of the manipulator with flexible joints and links are verified by a two-degree-of-freedom manipulator experimental system. Dynamics analysis results presented some useful rules for the path planning and control to suppress the vibration of the flexible space manipulator.     

Winch-integrated mobile end-effector for a cable-driven parallel robot with auto-installation

International Journal of Control, Automation and Systems - A cable-driven parallel robot (CDPR) is a robot in which rigid links are replaced with cables, unlike conventional serial or parallel...     

Stiffness and dexterous performances optimization of large workspace cable-driven parallel manipulators

Cable-driven parallel manipulators (CDPMs) provide an easy way to achieve large workspace since flexible cables can be readily stored on reels. Generally, cables are treated as massless and inextensible that can only be tensioned. But for large workspace applications, cable curve due to their self-weight must be considered. In this paper, a curved cable is modeled as the series of an inextensible parabolic cable and a flat elastic cable to accurately account for its curve effect. The stiffness and Jacobian matrices of CDPMs are derived, which provide quantitative representations of stiffness and dexterity of manipulators. An optimization model is presented to simultaneously improve the stiffness and dexterity by selecting proper sectional area of cables and other structural parameters. Numerical examples demonstrate the curve effect on the stiffness of manipulators and a remarkable improvement of the performances can be obtained by properly determining structural parameters.     

考虑迟滞及变形影响的主被动混合驱动绳驱空间机械臂运动学建模及求解

在绳驱空间机械臂的非结构化环境灵巧作业中,驱动绳索拉伸和臂段形变给机械臂的精确控制带来了困难。为此,本文提出一种改进运动学模型。首先,建立机械臂“驱动绳索长度－关节角度－末端位姿”的多重映射运动学模型;进一步考虑绳索迟滞、运动方向切换和臂段变形3种因素耦合影响,改进“驱动绳索长度－关节角”的映射模型。其次,设计试验平台,开展不同负载下的绳索迟滞量测定试验。最后,对比改进运动学模型仿真结果和绳驱空间机械臂样机试验数据。与理想几何模型的比较结果表明,长1110 mm的两段绳驱空间机械臂的末端绝对位置误差可减小15.2 mm;末端绝对位置误差减小61.4%,证明了改进运动学模型的有效性。     

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.     

Symbolic modeling and dynamic simulation of robotic manipulators with compliant links and joints

The explicit, non-recursive symbolic form of the dynamic model of robotic manipulators with compliant links and joints are developed based on a Lagrangian-assumed mode of formulation. This form of dynamic model is suitable for controller synthesis, as well as accurate simulations of robotic applications. The final form of the equations is organized in a form similar to rigid manipulator equations. This allows one to identify the differences between rigid and flexible manipulator dynamics explixitly. Therefore, current knowledge on control of rigid manipulators is likely to be utilized in a maximum way in developing new control algorithms for flexible manipulators.

Computer automated symbolic expansion of the dynamic model equations for any desired manipulator is accomplished with programs written based on commercial symbolic manipulation programs (SMP, MACSYMA, REDUCE). A two-link manipulator is used as an example. Computational complexity involved in real-time control, using the explicit, non-recursive form of equations, is studied on single CPU and multi-CPU parallel computation processors.     

Vibration Control of a Planar Parallel Manipulator Using Piezoelectric Actuators

This paper presents an active damping control approach applied to piezoelectric actuators attached to flexible linkages of a planar parallel manipulator for the purpose of attenuation of unwanted mechanical vibrations. Lightweight linkages of parallel manipulators deform under high acceleration and deceleration, inducing unwanted vibration of linkages. Such vibration must be damped quickly to reduce settling time of the manipulator platform position and orientation. An integrated control system for a parallel manipulator is proposed to achieve precise path tracking of the platform while damping the undesirable manipulator linkage vibration. The proposed control system consists of a PD feedback control scheme for rigid body motion of the platform, and a linear velocity feedback control scheme applied to piezoelectric actuators to damp unwanted linkage vibrations. In this paper, we apply the proposed vibration suppression algorithm to two different types of piezoelectric actuators and evaluate their respective performances. The two piezoelectric actuators are (i) a PVDF layer applied to the flexible linkage and (ii) PZT actuator segments also applied to the linkage. Simulation results show that both piezoelectric actuators achieve good performance in vibration attenuation of the planar parallel manipulator. The dynamics of the planar parallel platform are selected such that the linkages have considerable flexibility, to better exhibit the effects of the vibration damping control system proposed.     

Analysis of the wrench-closure workspace of planar parallel cable-driven mechanisms

The mobile platform of a parallel cable-driven mechanism is connected in parallel to a base by lightweight links, such as cables. Since the cables can only work in tension, the set of poses of the mobile platform for which the cables can balance any external wrench, i.e., for which the platform of the mechanism is fully constrained, is often limited or even nonexistent. Thus, the study and determination of this set of poses, called the wrench-closure workspace (WCW), is an important issue for parallel cable-driven mechanisms. In this paper, the case of planar parallel cable-driven mechanisms is addressed. Theorems that characterize the poses of the WCW are proposed. Then, these theorems are used to disclose the parts of the reachable workspace which belong to the WCW. Finally, an efficient algorithm that determines the constant-orientation cross-sections of these parts is introduced.     

绳索牵引并联机器人的双空间自适应同步控制

在绳索牵引并联机器人(CDPR)的运动过程中,关键的问题就是绳索必须保持张紧,且多根绳索之间需要相互协调.而且,模型参数的不确定性也会在一定程度上影响其运动控制,必须加以考虑.为了解决这些挑战,将绳长空间自适应同步与工作空间自适应补偿结合起来,提出了一种新型的双空间自适应同步控制器.通过绳长同步误差来表示绳索之间的协调运动,并通过双空间自适应的方法来实时补偿不同空间中的模型参数不确定性.随后,严格证明了双空间自适应同步控制系统的闭环稳定性.将实验结果与现有的增广PD控制器进行对比发现,提出的双空间自适应同步控制器可以显著地提高绳长的跟踪精度、改善绳索之间的协调关系,从而最终提高动平台的控制精度.同时,控制器中的自适应作用可以有效地补偿末端动平台的质量变化带来的影响.     

位－力驱动的线驱连续型机器人的动力学建模及实验验证

提出了一种位－力混合驱动的线驱连续型机器人的动力学模型。首先,基于集中质量矩阵法进行机器人动力学建模,将机器人动能的连续积分等效离散为三点求和形式,可简化建模过程并提升仿真的计算效率。其次,分析了驱动力与驱动线几何约束的力学关系,将线驱动作用等效建模为电机的驱动参数与牵引线张力的线性方程组,不仅可以精确地满足牵引线对系统的约束条件,还可以在不使用拉力传感器的条件下得到线的驱动力,降低了机器人成本及控制难度,这种方法适用于任意数量牵引线的连续型机器人。最后,将线驱连续型机器人的仿真和实验结果进行对比,机器人末端点的轨迹最大误差为3.85%,验证了所提模型的有效性。     

Optimization of Actuator Forces in Cable-Based Parallel Manipulators Using Convex Analysis

In cable-driven parallel manipulators (CPMs), cables can perform only under tension, and therefore, redundant actuation, which can be provided by redundant limbs, is needed to maintain the cable tensions. By optimizing the distribution of the forces in the cables and the redundant limbs, the average size of actuators can be reduced resulting in lower cost. Optimizing the force distribution in CPMs requires consideration for the inequality constraints imposed on the cable forces as a result of the unilateral driving property of the cables. In this study, a projection method is presented to calculate optimum solutions for the actuators force distribution in CPMs. Two solutions are presented: 1) a minimum-norm solution that minimizes the 2-norm of all forces in the cables and redundant limbs and 2) a solution that minimizes the 2-norm of the forces in the cables only. The optimization problem is formulated as a projection on an intersection of convex sets and the Dykstra's projection method is used to obtain the solutions. This method is successfully applied to a 3-DOF CPM.     

Dynamics and flatness-based control of a kinematically undetermined cable suspension manipulator

A kinematically undetermined cable suspension manipulator moves a payload platform in space by several cables with computer-controlled winches, whereby the position of the payload platform is not determined by the lengths of the cables. Trajectory tracking control of the payload platform is achieved by means of the concept of flat systems. A flat system has the property that the state variables and the control inputs can be algebraically expressed in terms of the so-called flat output and a finite number of time derivatives of the flat output. Its application to kinematically undetermined manipulators represents a generalization of computed-torque control. The control forces are algebraically calculated from the desired trajectories of the payload platform and their time derivatives up to the fourth order leading to a feedforward control strategy. Asymptotically stable tracking behavior is achieved by exact linearization of the nonlinear dynamics by means of a so-called quasi-static state feedback. The procedure is described for the trajectory tracking control of the prototype three-cable suspension manipulator CABLEV.     

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．     

Underactuated Flexible Aerial Manipulators: a New Framework for Optimal Trajectory Planning Under Constraints Induced by Complex Dynamics

The aerial manipulators (AMs) are a new class of unmanned aerial systems (UASs) that are created in response to the ever-increasing demand for autonomous object transportation and manipulation. Because of power supply restrictions, the load carrying capacity is limited and therefore it is necessary to reduce the overall weight of these UASs. The past works in the field of AMs consider the multi-rotor unmanned aerial vehicles (UAVs) as the base and manipulators with rigid links as the interactive elements with the environment which are bulky and heavy. To overcome the issue, this paper introduces the AMs endowed with flexible manipulators, their dynamic modeling, a new method for trajectory planning and control algorithm such that the unfavorable effects of using flexible elements like vibrations are minimized. Due to lack of kinematic constraints and the presence of flexibility conditions, conventional methods of trajectory planning for ground wheeled-mobile manipulators (GWMMs) such as extended and augmented Jacobian matrix cannot be applied to AMs. The addition of flexibility to the manipulator increases underactuation degrees (UADs), the complexity of trajectory planning and control synthesis. Considering large deformation assumption for flexible links, the dynamic equations and their induced nonholonomic constraints are derived applying Lagrangian formulation. Then, these constraints with that part of equations of motion corresponding to the links flexibility are solved simultaneously in the context of an optimization algorithm resulting in optimized trajectories. Through simulation results, the proposed method of trajectory planning and vibration control of underactuated flexible AMs has been shown to be effective.     

Observer-Based Optimal Control of Flexible Stewart Parallel Robots

The design and simulation of two optimal control schemes for a parallel flexible link manipulator of the Stewart type is presented. The first control scheme combines a nonlinear rigid model of the flexible manipulator with a linear rigid observer, whereas the second scheme uses a nonlinear flexible manipulator model with a linear flexible observer. The majority of the results available in the literature do not address the optimal control problem through the use of observers, as it is done in this paper, for the control of parallel robots. The simulation results have shown in both cases that indeed optimal state-obscrver-based control is a good candidate for controlling parallel-link manipulators in practice. As expected, the second scheme (flexible model plus flexible observer) gives better results than the first one, achieving faster trajectory tracking. The effects of white noises, applied forces, and zero gravity environment were taken under consideration.     

轮式移动机械臂的建模与仿真研究

移动机械臂系统一般由移动平台和机器臂组成，它既具有机器臂的操作灵活性，又具有移动机器人的可移动性，因此其应用范围要比单个系统宽得多。这篇文章主要研究了由非完整移动平台和完整机械臂组成的轮式移动机械臂系统的建模、跟踪控制及仿真问题。首先。利用拉格朗日动力学方程和非完整动力学罗兹方程建立了移动机械臂系统的精确数学模型；然后。利用非线性反馈将系统解耦。采用类PD控制器进行控制。在考虑了非完整约束及移动平台和机械臂的动态交互影响情况下，该控制算法保证系统同时跟踪给定的终端执行器和平台轨迹；最后，使用Maflah6．5对系统进行了仿真研究，仿真结果表明了其数学模型及控制方法的正确有效性。     

Trajectory planning of a suspended cable driven parallel robot with reconfigurable end effector

In this paper, a new suspended cable driven parallel robot (CDPR) with reconfigurable end effector is presented. This robot has been conceived for pick and place operations in industrial environments. For such applications, the possibility to change the configuration of the cables at the end-effector level is a promising way to avoid collisions with obstacles in the approaching phases, while reducing at the same time the duration of motion in the remaining part of the trajectory. An optimized trajectory planning algorithm is proposed, which implements a pick and place operation in the operational space with dynamic on-line reconfiguration of the end effector. The results on a simplified scenario demonstrate the ability of the system to obtain reduced movement times together with obstacle avoidance.     

The design of a new remote manipulator for space operation using a 4-cable-driven thrusters-embedded configuration

A new remote manipulator based on cable-driven parallel mechanism (CDPM) is designed for space long-distance operations (e.g. space capture/docking and other long-distance space activities) in this paper. By controlling the cables and thrusters which are equipped on the manipulator simultaneously, the new remote manipulator can achieve expected position, linear velocity, and angular velocity. The new manipulator has a larger controllable workspace compared with usual CDPMs. The structure and characteristics of this manipulator are discussed in this paper. The volume and characteristics of the workspace are also discussed. The influence of the distance on the static equilibrium is studied. The simulation results show that the workspace of this new manipulator is larger than usual CDPM’s. The results also indicate that the cable forces and thruster vectors can completely constrain the manipulator and meet the requirements of space activities. The results of the simulation also show that the controllable workspace of the manipulator is not continuous at some regions. Hence, trajectory planning is necessary.