Analysis of a manipulator in consideration of the relative motion between a tray and an object

In this article, equations of motion of a manipulator, whose mechanism has a tray installed with a passive revolute joint, are derived after consideration of the characteristics of the driving source. Considering the relative motion between the tray and the object, the trajectories of the velocity for saving energy are calculated by iterative dynamic programming. Also, the dynamic characteristics of manipulator control based on the trajectory for saving energy are analyzed theoretically and investigated experimentally.     

Trajectory for saving energy of a direct-drive manipulator in throwing motion

In this article, equations of motion of a closed-type manipulator, whose mechanism can easily be made lighter, are derived in consideration of the characteristics of the driving source. Considering the final condition of angular displacement and angular velocity in throwing motion, trajectories of velocity for saving energy are calculated by iterative dynamic programming, and the dynamic characteristics of manipulator control based on the trajectory for saving energy are analyzed theoretically and investigated experimentally. This work was presented in part at the 11th International Symposium on Artificial Life and Robotics, Oita, Japan, January 23–25, 2006     

Analysis of manipulator in consideration of impact absorption between link and object

In this article, equations of motion of a manipulator are derived in consideration of characteristics of driving source. By considering impact force absorption between a link and an object, trajectories for saving energy are calculated by the iterative dynamic programming method. And, the dynamic characteristics of manipulator controlled based on the trajectory for saving energy are also analyzed theoretically and investigated experimentally.     

Analysis of a manipulator in relation to collision between a link and an object

In this article, equations of motion of a manipulator are derived after consideration of the characteristics of the driving source. By considering a collision between a link and an object, and considering the active motion to absorb the kinetic energy of the object, the trajectories for saving energy are calculated by the iterative dynamic programming (IDP) method. The dynamic characteristics of manipulator control based on the trajectory for saving energy are also analyzed theoretically and investigated experimentally.     

Dynamics and Coupling Actuation of Elastic Underactuated Manipulators

This paper investigates the constraint and coupling characteristics of underactuated manipulators by proposing an elastic model of the manipulator and examining the second order constraint equation. A dynamic model and a coupling constraint equation are developed from a Jacobian matrix and the Newton‐Euler formulation. The inertia matrix and the Christoffel tensor are analyzed and decomposed into the part concerning actuated joints and the part concerning passive joints. This decomposition is further extended to the dynamic coupling equation and generates an actuation coupling matrix and a dynamic coupling tensor. Two new dynamic coupling indices are hence identified. One is related to an actuation input and the other is related to centrifugal and Coriolis forces. The former reveals the dynamic coupling between the input and the acceleration of passive joints and gives the actuation effect on the passive joints. The latter reveals the dynamic coupling between the centrifugal and Coriolis forces and the acceleration of passive joints and provides the centrifugal and Coriolis effect on the acceleration of passive joints. The study reveals the coupling characteristics of an underactuated manipulator. This is then demonstrated in a three‐link manipulator and extended to a serial manipulator with passive prismatic joint. © 2003 Wiley Periodicals, Inc.     

Analysis of manipulator in consideration of impact absorption between link and projected object

In this article, equations of motion of a manipulator are derived in consideration of the characteristics of DC servomotors, and a performance criterion for saving energy is defined in consideration of energy consumption of the driving source. When the manipulator is operated in a vertical plane, the system is highly non-linear due to gravity, and an analytical solution cannot be found. By considering for catching the object that moves parabolic, trajectories for saving energy are calculated by iterative dynamic programming method. And, the dynamic characteristics of two-link system controlled based on the trajectory for saving energy are analyzed theoretically. When the object moves parabolic, measurement method for the force of collision between link and object is examined by experiment.     

Kinematic and dynamic models of hybrid robot manipulator for propeller grinding

In this article, we develop a hybrid robot manipulator for propeller grinding and derive its kinematic and dynamic models. The manipulator is constructed by combining a parallel mechanism and a serial one to increase high stiffness as well as workspace. Based on geometric constraints, inverse–direct kinematics and Jacobian are derived to be implemented in real time control. The velocity control is used to measure the surface of a propeller blade and the position control is conducted to grind the removal depth. The dynamic model, which is developed by a motor algebra, can compute the forces and moments acting at a passive joint and an active one. ©1999 John Wiley & Sons, Inc.     

PD Controller for Manipulator with Kinetic Energy Term

A kinetic energy approach to PD control in joint space of a manipulator in terms of the eigenfactor quasi-coordinate velocity (EQV) vector is considered in this paper. The modified PD controller which contains quantities resulting from decomposition of a manipulator mass matrix is proposed. The obtained equations of motion are based on the eigenvalues and eigenvectors of the mass matrix (Junkins, J. L. and Schaub, H. [7]. It is shown that utilizing the EQV vector one can determine directly the kinetic energy of the manipulator and at the same time realize PD control in its joint space. This energy-based strategy gives an interesting insight into position control. The controller presented here was tested in simulation on a 3 d.o.f. direct drive arm manipulator and via experiment on a 2 d.o.f. manipulator. The results confirmed that one can directly determine the kinetic energy for the total manipulator as well for its each joint. Additionally, time response of the system under EQV controller is faster than for the classical controller if mechanical coupling are strong.     

欠驱动冗余度空间机器人优化控制

欠驱动控制是空间技术中容错技术的重要方面.本文研究了被动关节中有制动器的欠驱动冗余度空间机器人系统的运动优化控制问题.从系统动力学方程出发,分析了欠驱动冗余度空间机器人的优化能力和控制方法;给出了主、被动关节间的耦合度指标;提出了欠驱动冗余度空间机器人系统的“虚拟模型引导控制”方法,在这种方法中采用与欠驱动机器人机构等价的全驱动机器人作为模型来规划机器人的运动,使欠驱动系统在关节空间中逼近给出的规划轨迹,实现了机器人末端运动的连续轨迹运动优化控制;通过末关节为被动关节的平面三连杆机器人进行了仿真,仿真的结果证明了提出算法的有效性.     

Time-scaling control of an underactuated manipulator

Position control of an underactuated manipulator that has one passive joint is investigated. The dynamic constraint caused by the passive joint is second-order nonholonomic. Time scaling of the active joint trajectory and bidirectional motion planning from the initial and the desired configurations provide an exact solution of the positioning trajectory. The active and passive joints can be positioned to the desired angles simultaneously by swinging the active joints only twice. Feedback control constrains the manipulator along the planned path in the configuration space. Simulation and experimental results show the validity of the proposed methods. © 1998 John Wiley & Sons, Inc.     

失重环境下可控柔性臂的模态特性

在非重力场中,考虑控制器动态反馈的影响,对存在控制器定位约束的柔性臂系统进行动力分析,研 究其在相对平衡位置的模态特性．以具有柔性关节和弹性臂杆的可控柔性臂为研究对象,分析了控制器作用下的反 馈约束特性,将控制器位置和速度增益引入力边界条件,得到了耦合控制器参量的模态特征方程,证明了反馈约束 的存在使得系统特征频率为复频率,且模态主振型是复变函数．通过数值仿真,明确了可控柔性臂的模态特性与控 制器增益之间的关系,得到了不同于经典振动理论的结论．设计了可控柔性臂的仿失重实验平台,试验模态结果证 明了理论分析的有效性．     

Dynamic analysis and determination of the joint characteristics of parallel-drive robot manipulators

This article presents a theoretical and experimental study on structural dynamic response and determination of the joint characteristics of a five degree-of-freedom industrial robot manipulator with a parallel-drive mechanism. The joints were modeled as a linear spring in parallel with a viscous damper while the link members were assumed to be rigid in this study. The dynamic equations of motion of the robot manipulator were derived using the principle of virtual work. Based on these equations, the complex structural characteristics of the manipulator were simplified by carefully arranging the manipulator in proper arm configurations to avoid coupling effects among joints. Hence, the joint stiffness and damping ratio of each joint were determined experimentally. Meanwhile, the dynamic responses of the robot manipulator were also investigated. Good correlation between computer simulations and experimental results was achieved. From the experimental study, an additional troublesome flexural mode of about 10 Hz that tends to dominate the whole dynamic response and influence the positioning accuracy of the manipulator was found due to the weakness of the structural member at the base rotation joint, which was not modeled in the dynamic equations. The results of this study will be useful in providing a basis for improving the design of mechanical components and the articulating members of industrial robot manipulators.     

Investigation of joint clearance effects on welding robot manipulators

In this study, effects of joint clearance on a welding robot manipulator are investigated. Theoretical analysis is performed for different clearance sizes. By using the nonlinear spring-damper characteristic, contact model in revolute joint with clearance is established and the friction effect is performed using the Coulomb friction model. Then the simulation is carried out to investigate the kinematic and dynamic characteristics of the welding robot manipulator with joint clearance. For the case of two different clearance sizes, the results show that the joint clearance causes to degradation of kinematic and dynamic performance of the system. Even if the clearance size is small, it has a crucial role on amplitudes of the end-effector's accelerations and joint forces.     

多移动机械臂系统动力学建模以及稳定性分析

随着社会生产力的发展和发展需求的提高,移动机械臂凭借着自身优势,受到学术界和工业界的广泛关注.但在许多工作场景下,单个移动机械臂有着自由度数以及载荷的限制,无法顺利完成任务.为了更好地满足任务需求,多移动机械臂系统应运而生.在上述工业背景下,本文建立了多移动机械臂系统的动力学模型,并针对该动力学方程进行了稳定性分析.首先通过拉格朗日方程建立单个移动机械臂的动力学方程,将多体动力学软件仿真结果同动力学模型数值计算结果进行对比,验证了模型的正确性.随后联立多个移动机械臂的动力学方程和操作对象的动力学方程,得到封闭形式的多移动机械臂系统的动力学方程.再利用关节位置误差和速度误差设计李雅普诺夫函数,通过反步法获得了关节力矩的控制律.最后在多体动力学软件仿真中,察看轨迹是否能跟踪上期望信号来检验控制律的有效性.     

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.     

The effect of spine on the bounding dynamic performance of legged system

The effect of the spinal joint on the dynamic performance of a legged system in bounding gait is presented in this paper. We employ the simplified quadruped passive model to discuss the underlying mechanism of the bounding gait pattern. A comparison between the dynamic model with and without the spinal joint suggests that the model with a spinal joint is superior to the model with a rigid body in dynamic indicators including the vertical fluctuation of the centre of mass (CoM), leg forces and energy consumption. The effects of different initial included angles of the spinal joint and different initial vertical positions of the CoM on the dynamics of bounding are also analysed. We found that a low level of the energy consumption and leg forces can be obtained with the proper initial included angle and initial vertical position of the CoM, and there exists an optimal situation for each horizontal running velocity that the lowest energy consumption and the lowest leg forces could be obtained at the same time.     

基于伪逆的导轨机械臂关节速度纠偏运动规划方案

针对导轨机械臂在任务执行过程中出现的关节速度偏离期望值的问题,提出了一种基于伪逆算法的导轨机械臂关节速度纠偏运动规划方案。首先,根据机械臂的关节角状态和末端执行器的运动状态,运用伪逆算法对导轨机械臂在速度层上进行冗余度解析。然后,设计时变函数对关节速度进行约束调整,使偏离后的关节速度收敛于期望值。接着,针对末端执行器出现的位置误差设计了误差修正方法以保证轨迹跟踪任务的顺利执行。最后,将运动规划方案在Matlab软件上以基座直线移动和弧形移动的四连杆冗余度机械臂为例进行了仿真实验。仿真结果表明了该方案能纠正导轨机械臂在任务执行过程中偏离期望值的关节速度,且能使末端执行器的轨迹跟踪达到较高的精度。     

Inverse Velocity and Singularity Analysis of Low‐DOF Serial Manipulators

This paper presents a method for exact inverse velocity analysis of low‐DOF (degrees of freedom n<6) serial manipulators. For a low‐DOF serial manipulator, the number of independently controllable variables in the Cartesian space is equal to the number of joint variables in the joint space, and the remaining 6?n variables are linearly dependent on these independent variables. This paper employs the theory of reciprocal screws to determine a mapping between the independent velocity components in the Cartesian space and the joint rates in the joint space. It is shown that singular conditions of a low‐DOF manipulator depend on choice of independent variables. A 5‐DOF and a 4‐DOF manipulator are analyzed, and a numerical example in which the end effector of a 4‐DOF manipulator is commanded to follow a straight line is used to demonstrate the methodology. © 2003 Wiley Periodicals, Inc.     

基于伪逆的导轨机械臂关节速度纠偏运动规划方案

针对导轨机械臂在任务执行过程中出现的关节速度偏离期望值的问题，提出了一种基于伪逆算法的导轨机械臂关节速度纠偏运动规划方案。首先，根据机械臂的关节角状态和末端执行器的运动状态，运用伪逆算法对导轨机械臂在速度层上进行冗余度解析。然后，设计时变函数对关节速度进行约束调整，使偏离后的关节速度收敛于期望值。接着，针对末端执行器出现的位置误差设计了误差修正方法以保证轨迹跟踪任务的顺利执行。最后，将运动规划方案在Matlab软件上以基座直线移动和弧形移动的四连杆冗余度机械臂为例进行了仿真实验。仿真结果表明了该方案能纠正导轨机械臂在任务执行过程中偏离期望值的关节速度，且能使末端执行器的轨迹跟踪达到较高的精度。     

Robust adaptive control of an underactuated free-flying space robot under a non-holonomic structure in joint space

This paper introduces a robust adaptive control scheme for an underactuated free-flying space robot under non-holonomic constraints. An underactuated robot manipulator is defined as a robot that has fewer joint actuators than the number of total joints. Because, if one of the joints is out of order, it is so hard to repair the joint, especially in space, the control of such a robot manipulator is important. However, it is difficult to control an underactuated robot manipulator because of the reduced dimension of the input space, i.e. the non-holonomic structure of the underactuated system. The proposed scheme does not need to assume that the exact dynamic parameters must be known. It is analysed in joint space to control the underactuated robot mounted on the space station under parametric uncertainties and external disturbances. The simulation results have shown that the proposed method is very feasible and robust for a two-link planar free-flying space robot with one passive joint.