Analysis of a 6-DOF redundantly actuated 4-legged parallel mechanism

In this paper, we propose a new 4-legged 6-DOF redundantly actuated UPS parallel mechanism. Kinematics, singularity and dynamics analyses of the proposed mechanism are addressed. Inverse kinematics has a closed-form solution, whereas the forward kinematics has a semi-closed form solution. Also, the Jacobian matrix has been determined using the concept of reciprocal screws. Using the principle of virtual work and minimum norm method, a general formulation for the inverse dynamics of redundantly actuated parallel manipulator is presented. Moreover, the proposed redundant mechanism has been compared with a similar but nonredundant mechanism in three aspects: reachable points, and actuation forces under static and dynamic conditions. We show that the redundancy decreases singular points, and dramatically reduces the actuators’ forces and torques.     

Design and analysis of a compliant parallel pan-tilt platform

In combination of the advantages of both parallel mechanisms and compliant mechanisms, a compliant parallel mechanism with two rotational degrees of freedom is designed to meet the requirement of a lightweight and compact pan-tilt platform. Firstly, two commonly-used design methods i.e. direct substitution and Freedom and Constraint Topology are applied to design the configuration of the pan-tilt system, and similarities and differences of the two design alternatives are compared. Then inverse kinematic analysis of the candidate mechanism is implemented by using the pseudo-rigid-body model, and the Jacobian related to its differential kinematics is further derived to help designer realize dynamic analysis of the 8R compliant mechanism. In addition, the mechanism’s maximum stress existing within its workspace is tested by finite element analysis. Finally, a method to determine joint damping of the flexure hinge is presented, which aims at exploring the effect of joint damping on actuator selection and real-time control. To the authors’ knowledge, almost no existing literature concerns with this issue.     

Disturbance compensation of a dual-arm underwater robot via redundant parallel mechanism theory

Disturbance compensation is one of the major issues for underwater robots to hover as a mobile platform and to manipulate an object in an underwater environment. This paper presents a new strategy of disturbance compensation for a mobile dual-arm underwater robot using internal torques derived from redundant parallel mechanism theory. A model of the robot was analyzed by redundant serial and parallel mechanisms at the same time. The joint torque to operate the robot is obtained from a redundant serial mechanism model with null-space projection due to redundancy. The joint torque derived from the redundant parallel kinematic model is calculated to perfectly compensate for disturbances to the mobile platform and is included in the solution of the joint torque based on the serial redundant model. The resultant joint torque can generate force on the end-effector for required tasks and forces for disturbance compensation simultaneously . A simulation shows the performance of this disturbance compensation strategy. The joint torque based on the algorithm generates the desired task force and the disturbance compensation force together, and a little additional joint torque can generate a large internal force effectively due to the characteristics of a redundant parallel mechanism. The proposed method is more effective than compensation methods using thrusting force on the mobile platform.     

Inverse dynamics of the HALF parallel manipulator with revolute actuators

Recursive matrix relations for kinematics and dynamics of the HALF parallel manipulator are presented in this paper. The prototype of this robot is a spatial mechanism with revolute actuators, which has two translation degrees of freedom and one rotation degree of freedom. The parallel manipulator consists of a base plate, a movable platform and a system of three connecting legs, having wide application in the fields of industrial robots, simulators, parallel machine tools and any other manipulating devices where high mobility is required. Supposing that the position and the motion of the moving platform are known, an inverse dynamics problem is solved using the principle of virtual powers. Finally, some iterative matrix relations and graphs of the torques and powers for all actuators are analysed and determined. It is shown that this approach is an effective means for kinematics and dynamics modelling of parallel mechanisms.     

海洋核动力平台定位系统多体动力学建模与分析

海洋核动力平台可以为海上油气开发、偏远岛屿和海水淡化等提供稳定的能源供给, 是具有潜力的重要海洋装备. 定位系统作为核动力平台的核心部位, 主要由单点转塔、YOKE刚臂、系泊腿和系泊支架组成, 属于典型的多刚体动力学系统. 对定位系统进行多体动力学分析可以提高核动力平台长期作业的可靠性. 基于多刚体动力学理论, 结合定位系统多铰连接的拓扑结构, 建立了定位系统的多体动力仿真模型; 进而考虑核动力平台作业海洋环境, 通过谱分析与线性叠加原理得到核动力平台在多年重现期下的六自由度运动时程. 以我国首座海洋核动力平台为例, 利用多体动力学模型分别计算了一年一遇、十年一遇和百年一遇海况下定位系统的系泊回复力与连接结构受力行为. 计算结果与准静力学模型、Kane动力学模型进行对比, 给出了定位系统的系泊回复刚度曲线, 并提出了系泊回复力动力放大系数. 研究可为定位系统系泊能力评估和各连接结构受力分析提供参考和借鉴.      

Kinematic analysis of 5-R<Emphasis Type="Underline">P</Emphasis>UR (3T2R) parallel mechanisms

This paper investigates some kinematic properties of a five-degree-of-freedom parallel mechanism generating the 3T2R motion and comprising five identical limbs of the RPUR type. The general mechanism originates from the type synthesis performed for symmetrical 5-DOF parallel mechanism. In this study, two classes of simplified designs are proposed whose forward kinematic problem have either a univariate or a closed-form solution. The principal contributions of this study are the solution of the forward kinematic problem for some simplified designs—which may have more solutions than the FKP of the general 6-DOF Stewart platform with 40 solutions—and the determination of the constant-orientation workspace which is based on the topology of the vertex space (Bohemian dome) and a geometric constructive approach.     

Dynamic modeling and computational efficiency analysis for a spatial 6-DOF parallel motion system

A common approach for simplification analysis of complex dynamic model is presented, and the simplified dynamic model of a spatial 6-DOF parallel motion system with high computational efficiency is proposed for high real time control. By using Kane method, the full dynamic model of a spatial 6-DOF parallel motion system viewed as 13 rigid bodies is built. With rigid body decomposition, the full dynamic model is separated into several parts firstly, and then some separated parts are further divided into many dynamic components in terms of motion separation and the relationship with acceleration or velocity. The contribution of each dynamic term is analyzed for a specified spatial 6-DOF parallel motion system, and the simplified model is derived. Comparing with full dynamic model, the simplified error is analyzed, and the computational efficiency of the simplified model is discussed in a real-time industrial computer. The simplified strategy is confirmed in simulation. The simplified error is less than 8%, the simplified model can improve the computational efficiency by more than 70%, and the execution time is less than 0.1 ms, which can achieve the requirements of high real time control. The numerical results illustrate that the proposed approach is feasible and effective for simplification analysis of dynamics and the derived simplified dynamic model can be used in real-time control system with small simplified error.     

Modeling and motion simulation of a three-wheeled mobile robot with front wheel driven and steered taking into account wheels�� slip

The problem of modeling of dynamics of a three-wheeled mobile robot with front wheel driven and steered is analyzed in this paper. Kinematical structure and kinematics of the robot are described. A universal methodology of analytical modeling of robot??s dynamics is applied. This methodology takes into account wheel-ground contact conditions and wheels?? slip. Its essence is the use of a contact model of deformable tire with rigid ground and division of the robot??s dynamics model into parts connected with wheels, including tire model, and with the mobile platform. The tire model used in this paper results from empirical dependencies determined during investigations of car tires. Ground geometry and type are specified in the environment model. Tire-ground interface is characterized by coefficients of friction and rolling resistance. The robot model takes into account the presence of friction in kinematical pairs. The model of servomotors is included as well. The important part of this work is simulation research performed using Matlab/Simulink package. Simulation research includes solving of the forward and inverse dynamics problems as well as the tracking control task. During simulations, the robot was moving on concrete and on a piece of ice. The simulation research enabled verification of the elaborated solutions.     

空间机器人捕获卫星操作基于柔顺装置的无源模糊避撞柔顺控制

讨论了漂浮基空间机器人在轨捕获非合作卫星过程避免关节受冲击及过载破坏的避撞柔顺控制问题。在关节电机与机械臂之间配置了一种柔顺装置——旋转型串联弹性执行器(RSEA),其作用一是在捕获阶段,通过其内置弹簧的变形来缓冲捕获过程中被捕获卫星对空间机器人关节产生的冲击能量;二是在捕获完成后的镇定运动阶段,结合所设计的避撞柔顺策略来适时开关关节电机以保证关节冲击力矩受限在安全范围。首先,根据拉格朗日法及牛顿-欧拉法分别建立了含柔顺装置空间机器人与目标卫星系统的动力学方程;之后,结合整个系统动量守恒关系、系统运动几何及位置约束关系,建立了捕获操作后两者形成混合体系统的动力学方程。在此基础上,针对捕获操作后不稳定的混合体系统,提出了一种基于无源性理论的避撞柔顺模糊控制方案以实现其镇定控制。最后,通过仿真实验验证了所提避撞柔顺策略的有效性。     

Inverse dynamics of a 3-PRC parallel kinematic machine

Recursive matrix relations for kinematics and dynamics analysis of a three-prismatic-revolute-cylindrical (3-PRC) parallel kinematic machine (PKM) are performed in this paper. Knowing the translational motion of the platform, we develop first the inverse kinematical problem and determine the positions, velocities and accelerations of the robot’s elements. Further, the inverse dynamic problem is solved using an approach based on the principle of virtual work and the results in the framework of the Lagrange equations with their multipliers can be verified. Finally, compact matrix equations and graphs of simulation for input force and power of each of three actuators are obtained. The investigation of the dynamics of this parallel mechanism is made mainly to solve successfully the control of the motion of such robotic system.     

基于柔性机构捕捉卫星的空间机器人动态缓冲从顺控制

研究了空间机器人在轨捕获非合作卫星过程避免关节受碰撞冲击破坏的缓冲从顺控制问题, 为此在机械臂与关节电机之间配置了一种柔性机构, 其作用在于: (1)在接触、碰撞阶段可通过其内置弹簧的变形来吸收被捕获卫星对空间机器人关节产生的冲击力矩; (2)在镇定运动阶段, 结合与之配合的缓冲从顺控制策略来适时开、关关节电机, 以保证关节受到的冲击力矩受限在安全范围. 首先, 利用多刚体系统理论获得配置柔性机构空间机器人及目标卫星分体系统动力学方程; 之后, 结合整个系统动量守恒关系, 捕获操作后系统运动几何关系及力的传递规律, 建立了两者形成联合体系统的动力学方程, 并计算了碰撞过程的冲击效应与冲击力. 为了实现失稳联合体系统的镇定控制, 提出了一种基于动态面的缓冲从顺控制方案. 上述控制方案可在实现吸收捕获操作产生的冲击力矩的同时, 还能在冲击力矩过大时适时开启、关闭关节电机, 以避免关节电机发生破坏; 此外, 动态面的引入避免了反演法存在的计算膨胀问题, 有效减少了计算量. 基于Lyapunov函数法证明了系统的稳定性, 并通过系统数值仿真结果验证了上述缓冲从顺控制策略的正确性.      

Hybrid approach for dynamic model identification of an electro-hydraulic parallel platform

In this paper, a hybrid optimization algorithm is proposed to identify the dynamic parameters of a 6-DOF electro-hydraulic parallel platform. The dynamic model of a parallel platform with arbitrary geometry, inertia distribution and frictions is obtained based on a structured Boltzmann–Hamel–d’Alembert formulation, and then the estimation equations are explicitly expressed in terms of a linear form with respect to the identified inertial and the friction coefficients in accordance with a linear friction model. However, when nonlinear friction models are considered, the parameter identification of the electro-hydraulic parallel platform is considered as an optimization process with an objective function minimizing the errors between the measurement and identification, and then an effective combination of the particle swarm optimization (PSO) method and the local quasi-Newton method is proposed to solve the identification problem. Experimental identification processes are carried out for the identified parameters, and the identified models are compared by the predicted forces between the LS method and the optimization technique as well as between the linear and nonlinear friction models.     

Continuation Method Applied in Kinematics of Parallel Robot

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BUFFER AND COMPLIANT DYNAMIC SURFACE CONTROL OF SPACE ROBOT CAPTURING SATELLITE BASED ON COMPLIANT MECHANISM$^{\bf 1)}$

研究了空间机器人在轨捕获非合作卫星过程避免关节受碰撞冲击破坏的缓冲从顺控制问题, 为此在机械臂与关节电机之间配置了一种柔性机构, 其作用在于: (1)在接触、碰撞阶段可通过其内置弹簧的变形来吸收被捕获卫星对空间机器人关节产生的冲击力矩; (2)在镇定运动阶段, 结合与之配合的缓冲从顺控制策略来适时开、关关节电机, 以保证关节受到的冲击力矩受限在安全范围. 首先, 利用多刚体系统理论获得配置柔性机构空间机器人及目标卫星分体系统动力学方程; 之后, 结合整个系统动量守恒关系, 捕获操作后系统运动几何关系及力的传递规律, 建立了两者形成联合体系统的动力学方程, 并计算了碰撞过程的冲击效应与冲击力. 为了实现失稳联合体系统的镇定控制, 提出了一种基于动态面的缓冲从顺控制方案. 上述控制方案可在实现吸收捕获操作产生的冲击力矩的同时, 还能在冲击力矩过大时适时开启、关闭关节电机, 以避免关节电机发生破坏; 此外, 动态面的引入避免了反演法存在的计算膨胀问题, 有效减少了计算量. 基于Lyapunov函数法证明了系统的稳定性, 并通过系统数值仿真结果验证了上述缓冲从顺控制策略的正确性.     

On human–robot interaction of a 3-DOF decoupled parallel mechanism based on the design and construction of a novel and low-cost 3-DOF force sensor

This paper addresses the extension of a 3-degrees-of-freedom (3-DOF) decoupled parallel mechanism for human–robot interaction purposes. To this end, a low-cost 3-DOF force sensor for human–robot interaction applications is proposed, designed and constructed. In the latter force sensor, five load cells are placed in order to identify the amount of the applied force along each Cartesian direction. In addition, an experimental identification procedure based on least square method is carried out in order to obtain the first and third degree polynomial models of the sensor output model. From the practical tests it has been reveled that the force sensor has a reasonable precision of 0.1 N in both x and y-axes and 0.2 N in z-axis, within a range of 5 N which is suitable for human–robot interaction applications. Then, using the proposed force sensor, two control methods, namely “position control” and “speed control” are applied for human–robot interaction purposes and their performances are compared.     

Image based visual servoing for robot positioning tasks

Visual servoing has become a popular paradigm for the control of complex robotic systems: this sensor based approach exploits the image informations provided by one ore more cameras in a feedback control loop to drive the system to the desired configuration. Here authors will refers to a monocular system where the camera is mounted on the end effector of a 6-DOF manipulator. Among different Visual Servoing approaches Image Based Visual Servoing (IBVS) has been the most investigated in the literature because of its nice properties of robustness with respect to both robot modeling and camera calibration errors: in IBVS the control loop is in fact directly closed in the image; moreover IBVS doesn’t require the knowledge of the target/scene model (model-free approach). Despite its advantages IBVS may be affected by singularity and local minima problems of the control law: these drawbacks arise especially when the initial and the goal camera images respectively corresponding to the actual and desired system configurations are very different (i.e for large system displacements). To overcome these problems an image path planning can be exploited to ensure system convergence. In this paper author presents an off-line image path planning that can be used to execute system positioning task also in presence of large camera displacements: planning trajectories has been developed such as to make the robot end effector move on a 3D helix, connecting the initial and the desired arm configuration, by generating feasible robot twist-screws and keeping the target in the image field of view. During control execution also 3D target informations are retrieved through an adaptive estimation law. Both simulations and experimental results show the feasibility of the proposed approach.     

Treadmill walking of the pneumatic biped Lucy: Walking at different speeds and step-lengths

Actuators with adaptable compliance are gaining interest in the field of legged robotics due to their capability to store motion energy and to exploit the natural dynamics of the system to reduce energy consumption while walking and running. To perform research on compliant actuators we have built the planar biped Lucy. The robot has six actuated joints, the ankle, knee and hip of both legs with each joint powered by two pleated pneumatic artificial muscles in an antagonistic setup. This makes it possible to control both the torque and the stiffness of the joint. Such compliant actuators are used in passive walkers to overcome friction when walking over level ground and to improve stability. Typically, this kind of robots is only designed to walk with a constant walking speed and step-length, determined by the mechanical design of the mechanism and the properties of the ground. In this paper, we show that by an appropriate control, the robot Lucy is able to walk at different speeds and step-lengths and that adding and releasing weights does not affect the stability of the robot. To perform these experiments, an automated treadmill was built Published in Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 134–142, July 2008.     

Kinematic design of 3-URU pure rotational parallel mechanism to perform precise motion within a large workspace

We present an optimum design of lower-dof parallel mechanism, a 3-URU pure rotational parallel mechanism that reflects issues of workspace and the position error of the center of rotation of the platform. The uncompensatable error determined by position error of center of rotation was used as an evaluation index for the design. The uncompensatable error index, an index used in the optimum design, was proposed taking into account four sources of errors, representing errors between adjacent joints. Based on the application of the mechanism and the error index, the effect of the redundant platform orientation parameter was numerically investigated and the design flow of the mechanism was proposed. We made a kinematic design of a mechanism with a large workspace subject to minimization of platform’s position error of the center of rotation. A prototype of mechanism with a large inclination angle of the platform up to 1.3 rad was shown, and its characteristics are also discussed.     

Explicit dynamics equations of the constrained robotic systems

Recursive matrix relations concerning the kinematics and the dynamics of a constrained robotic system, schematized by several kinematical chains, are established in this paper. Introducing frames and bases, we first analyze the geometrical properties of the mechanism and derive a general set of relations. Kinematics of the vector system of velocities and accelerations for each element of robot are then obtained. Expressed for every independent loop of the robot, useful conditions of connectivity regarding the relative velocities and accelerations are determined for direct or inverse kinematics problem. Based on the general principle of virtual powers, final matrix relations written in a recursive compact form express just the explicit dynamics equations of a constrained robotic system. Establishing active forces or actuator torques in an inverse dynamic problem, these equations are useful in fact for real-time control of a robot.     

Structural synthesis of fully-isotropic translational parallel robots via theory of linear transformations

The paper presents a new structural synthesis approach of fully-isotropic translational parallel robotic manipulators (TPMs) based on the theory of linear transformations. A TPM is a 3-DOF (degree of freedom) parallel mechanism whose output link, called platform, can achieve three independent orthogonal translational motions with respect to the fixed base. The manipulators presented in this paper have three legs connecting the moving platform and the base (fixed platform). Only one kinematic pair per leg is actuated by a linear motor situated on the fixed base. A one-to-one correspondence exists between the actuated joint space and the operational space of the moving platform. The Jacobian matrix of fully-isotropic TPMs presented in this paper is the identity 3×3 diagonal matrix throughout the entire workspace. The synthesis method proposed in this paper allows us to obtain all structural solutions of fully-isotropic TPMs in a systematic manner. Overconstrained/isostatic solutions with elementary/complex and identical/different legs are obtained. Fully-isotropic TPMs have the advantage of simple command and important energy-saving due to the fact that, for a unidirectional translation, only one motor works as in a serial translational manipulator.