On the Experiment Design for Direct Dynamic Parameter Identification of Parallel Robots

Accurate robot dynamic models require the estimation and validation of the dynamic parameters through experiments. To this end, when performing the experiments, the system has to be properly excited so that the unknown parameters can be accurately estimated. The experiment design basically consists of optimizing the trajectory executed by the robot during the experiment. Due to the restricted workspace with parallel robots this task is more challenging than for serial robots; thus, this paper is focused on the experiment design aimed at dynamic parameter identification of parallel robots. Moreover, a multicriteria algorithm is proposed in order to reduce the deficiencies derived from the single-criterion optimization. The results of the identification using trajectories based on a single criterion and the multicriteria approaches are compared, showing that the proposed optimization can be considered as a suitable procedure for designing exciting trajectories for parameter identification.     

Dynamic and stable reconfiguration of self-reconfigurable planar parallel robots

This paper discusses dynamic and stable reconfigurations of self-reconfigurable planar parallel robots that can be done by coupling and decoupling of two underactuated robots on a horizontal plane. The limbs of the parallel robots are 2R open kinematic chains with their second joints unactuated. Two types of self-reconfigurable parallel robots are considered. One is formed by two limbs, and the other is by a limb and an underactuated robot consisting of two limbs and a platform. Uncertainty singularities enable them to self-reconfigure without additional actuators at their coupling mechanism. In this paper, we propose dynamic contact motion control to move them from an initial contact configuration to an uncertainty singular configuration while maintaining their contact. This paper also considers dynamic stability at their uncertainty singularities as equilibrium and shows that there exist geometrically stable configurations without feedback control, which are useful for decoupling. Experiments with real robots are carried out to verify the effectiveness of the dynamic contact motion control and stability analysis.     

An overview of dynamic parameter identification of robots

Due to the importance to model-based control, dynamic parameter identification has attracted much attention. However, until now, there is still much work for the identification of dynamic parameters to be done. In this paper, an overview is given of the existing work on dynamic parameter identification of serial and parallel robots. The methods for estimating the dynamic parameters are summarized, and the advantages and disadvantages of each method are discussed. The model to be identified and the trajectory optimization are reviewed. Further, the methods for validating the estimated model are summarized and the application of dynamic parameter identification is mentioned. The results of this review are useful for manufacturers of robots in selecting proper identification method and also for researchers in determining further research areas.     

Enlarging parallel robot workspace through Type-2 singularity crossing

In order to increase the reachable workspace of parallel robots, a promising solution consists of the definition of optimal trajectories that ensure the non-degeneracy of the dynamic model in the Type 2 (or parallel) singularity. However, this assumes that the control law can perfectly track the desired trajectory, which is impossible due to modeling errors.This paper proposes a robust multi-model approach allowing parallel robots to cross Type 2 singularities. The main idea is to shift near singularities to a simplified dynamic model that can never degenerate. The two main contributions are the definition of an optimal trajectory crossing Type 2 singularities and the multi-model control law allowing to track this trajectory. The proposed control law is validated experimentally through a Five-bar planar mechanism.     

A procedure to find equivalences among dynamic models of planar biped robots

In this paper, a method to find equivalences among dynamic models is presented. The models are given in different generalized coordinates for the same mechanical system. This novel method is valid for planar biped robots, i.e., those whose motions are executed only in a plane. We show that no matter which generalized coordinates are used to get the dynamic models, there is always an equivalence among them by using a particular input matrix. We exhibit some advantages of getting the dynamic model using absolute coordinates instead of relative coordinates, and we show how to calculate the input matrix for getting the equivalence between these models. Because of its simplicity, a compass-like biped robot model is used as example to explain in detail the novel procedure. In order to appreciate the benefits of the proposed procedure in biped robots of high degrees of freedom, we also present the equivalence between two dynamic models for the single support phase of a 5 degrees of freedom biped robot using absolute coordinates and relative ones.     

Kinematic analysis and error modeling of TAU parallel robot

The TAU robot presents a new configuration of parallel robots with three degrees of freedom. This robotic configuration is well adapted to perform with a high precision and high stiffness within a large working range compared with a serial robot. It has the advantages of both parallel robots and serial robots. In this paper, the kinematic modeling and error modeling are established with all errors considered using Jacobian matrix method for the robot. Meanwhile, a very effective Jacobian approximation method is introduced to calculate the forward kinematic problem instead of Newton–Raphson method. It denotes that a closed form solution can be obtained instead of a numerical solution. A full size Jacobian matrix is used in carrying out error analysis, error budget, and model parameter estimation and identification. Simulation results indicate that both Jacobian matrix and Jacobian approximation method are correct and with a level of accuracy of micron meters. ADAMS's simulation results are used in verifying the established models.     

Fast parallel robots

This paper presents two parallel robots that have been recently designed. The first one is a 3-degree-of-freedom lightweight robot called DELTA and designed in Switzerland by EPFL. We give here the equations corresponding to different models of this robot: forward and inverse kinematics as well as inverse dynamics. The important feature of our method in deriving these models is to use a “good” set of parameters in order to simplify the equations. Based upon these considerations of simplicity, we have tried to extend the principle of the DELTA mechanical structure to a 6-degree-of-freedom parallel robot. We came up with a new design we called the HEXA. We present this robot and show that it should have the same dynamic capabilities as the DELTA, because, like this one, it can be built with light material and it can be easily modeled.     

未知动态环境下非完整移动群机器人围捕

针对未知动态障碍物环境下非完整移动群机器人围捕,提出了一种基于简化虚拟受力模型的自组织方法.首先给出了个体机器人的运动方程,然后给出了未知动态环境下目标和动态障碍物的运动模型.通过对复杂环境下围捕行为的分解,抽象出简化虚拟受力模型,基于此受力模型,设计了个体运动控制方法,接着证明了系统的稳定性并给出了参数设置范围.不同情况下的仿真结果表明,本文给出的围捕方法可以使群机器人在未知动态障碍物环境下保持较好的围捕队形,并具有良好的避障性能和灵活性.最后分析了本文与基于松散偏好规则的围捕方法相比的优势.     

Smart-Structures Technology for Parallel Robots

Industrial robots play an important role in automation technology. A further increase of productivity is desired, especially in the field of handling and assembly, the domain of industrial robots. Parallel robots demonstrated their potential in applications with needs for high-dynamic trajectories in the recent years. Within the scope of the Collaborative Research Center (SFB 562)????Robotic Systems for Handling and Assembly?? the German Aerospace Center (DLR) and the Technical University of Braunschweig investigate smart-structures technology for parallel robots. In this paper the results of the main topics new active components, Finite-Element based elastic position dependent modeling and vibration control are summarized. The latest parallel robot called is equipped with new active rods. The design as well as the dimensioning of the rod with surface mounted piezo patch actuators is described. For trajectory based robot control, rigid body models are required. In parallel robots with vibration reduction a coupled approach is necessary in which elastic and rigid body equations are combined. The derivation of the equations for parallel robot is presented. Finally, the implemented vibration control is explained. In a position-dependent approach several robust controllers are switched to gain optimal control performance. A stability proof for the switching process is derived.     

基于并行蚁群算法的多机器人联盟组成

多机器人联盟组成是多机器人协作的重要方法,如何快速高效的组成最优联盟是工作策略,结合多机器人的协作机制组成多机器人任务最优动态联盟,避免了联盟的死锁问题和资源的浪费,减少联盟组成的计算量和通讯量.     

Kinematic modeling of mobile robots by transfer method of augmented generalized coordinates

A kinematic modeling method, which is directly applicable to any type of planar mobile robots, is proposed in this work. Since holonomic constraints have the same differential form as nonholonomic constraints, the instantaneous motion of the mobile robot at current configuration can be modeled as that of a parallel manipulator. A pseudo joint model denoting the interface between the wheel and the ground (i.e., the position of base of the mobile robot) enables the derivation of this equivalent kinematic model. The instantaneous kinematic structures of four different wheels are modeled as multiple pseudo joints. Then, the transfer method of augmented generalized coordinates, which has been popularly employed in modeling of parallel manipulators, is applied to obtain the instantaneous kinematic models of mobile robots. The kinematic models of six different types of planar mobile robots are derived to show the effectiveness of the proposed modeling method. Lastly, for the mobile robot equipped with four conventional wheels, an algorithm estimating a sensed forward solution for the given information of the rotational velocities of the four wheels is discussed. © 2004 Wiley Periodicals, Inc.     

Optimal Design of a 4-DOF Parallel Manipulator: From Academia to Industry

This paper presents an optimal design of a parallel manipulator aiming to perform pick-and-place operations at high speed and high acceleration. After reviewing existing architectures of high-speed and high-acceleration parallel manipulators, a new design of a 4-DOF parallel manipulator is presented, with an articulated traveling plate, which is free of internal singularities and is able to achieve high performances. The kinematic and simplified, but realistic, dynamic models are derived and validated on a manipulator prototype. Experimental tests show that this design is able to perform beyond the high targets, i.e., it reaches a speed of 5.5 m/s and an acceleration of 165 m/s². The experimental prototype was further optimized on the basis of kinematic and dynamic criteria. Once the motors, gear ratio, and several link lengths are determined, a modified design of the articulated traveling plate is proposed in order to reach a better dynamic equilibrium among the four legs of the manipulator. The obtained design is the basis of a commercial product offering the shortest cycle times among all robots available in today's market.     

Experimental kinematic calibration of parallel manipulators using a relative position error measurement system

Because of errors in the geometric parameters of parallel robots, it is necessary to calibrate them to improve the positioning accuracy for accurate task performance. Traditionally, to perform system calibration, one needs to measure a number of robot poses using an external measuring device. However, this process is often time-consuming, expensive and difficult for robot on-line calibration. In this paper, a methodical way of calibration of parallel robots is introduced. This method is performable only by measuring joint variable vector and positioning differences relative to a constant position in some sets of configurations that the desired positions in each set are fixed, but the moving platform orientations are different. In this method, measurements are relative, so it can be performed by using a simple measurement device. Simulations and experimental studies on a Hexaglide parallel robot built in the Sharif University of Technology reveal the convenience and effectiveness of the proposed robot calibration method for parallel robots.     

Vision-based Control of a Delta Parallel Robot via Linear Camera-Space Manipulation

One of the open problems to control a parallel robot in real-time is the larger number of parameters to be incorporated in the control model when compared to serial robots. This paper presents an innovative vision-based method to control a delta-type parallel robot based on Linear Camera-Space Manipulation. The proposed method is a simple and robust technique capable of achieving real-time control of robots without relying on the calibration of either the robot or the environment parameters. To document the robustness of this technique, a sensitivity analysis was performed in simulation where the effect of two sources of error on the end-point positioning are considered. Such sources are the variability of each link’s parameters, and the uncertainty of the visual measurements. Experimental results on a Clavel’s delta parallel robot show that end-point positioning errors obtained with Linear Camera-Space Manipulation are less than 1.5 mm, demonstrating a low sensitivity to parameter uncertainty in qualitative agreement with the simulation results. The results show that the developed approach is advantageous to control parallel robots for industrial applications in real-time and can obviate to a number of open problems common with the control of parallel robots.     

Finite-time Stable Robust Sliding Mode Dynamic Control for Parallel Robots

To address the tracking control problem for n-DOF parallel robots in presence of the lumped disturbance, including modeling errors, friction and external disturbance, a finite-time stable robust sliding mode dynamic control (FRSMDC) for parallel robots is explored. From the implementation condition of the FRSMDC for parallel robots, the limitation on the change rate of the lumped disturbance is relaxed for easy realization. From the results of the FRSMDC for parallel robots, the finite-time stability of the sliding variable is proved and the settling time is derived; the switching gain required is only larger than the upper bound of the disturbance estimation error, instead of the upper bound of the disturbance, due to the feed-forward compensation to the lumped disturbance via a disturbance observer. Consequently, the system robustness is improved and the chattering of FRSMDC is alleviated. The finite-time stability of the closed-loop system is confirmed with Lyapunov theory. Besides, the application of the proposed method is extended to a general multi-input multi-output nonlinear system with the relative degree m by analogy. Finally, the case of the dynamic control of a 6-DOF parallel robot for automobile electro-coating conveying is studied for simulation and experiment, so as to attest the validity of the FRSMDC for parallel robots.

     

Forward and inverse kinematics of a 5-DOF hybrid robot for composite material machining

Hybrid robots consist of both serial and parallel mechanisms, which have advantages in stiffness and workspace compared with serial/parallel robots when machining composite material. However, the forward and inverse kinematics of hybrid robots generally do not have analytic solutions. This paper deals with the analytic forward and inverse kinematics solutions of a 5-degree-of-freedom (DOF) hybrid robot which consists with a 3-DOF 2UPU/SP parallel mechanism (PM) and a 2-DOF rotating head. In the forward kinematic problem, a method is proposed to transfer the high order kinematic equation to a 4th-order polynomial based on the Sylvester's dialytic elimination, and the analytic solutions can be further obtained by Ferrari's method. In the inverse problem, the redundant Euler angles expressed by four rotations are firstly proposed for decoupling different motions, then, the closed-form solution of inverse kinematics can be found. Finally, a simulation trajectory is given, and the result shows that the accuracy of the solutions’ calculation reaches femtometer grade and the efficiency reaches microsecond grade; furthermore, an experiment is performed on the prototype to validate the effectiveness of the proposed forward and inverse kinematics.     

模块化可重构机器人动力学研究进展

模块化可重构机器人由于其构型多变,运动形式丰富等特点,可以在非结构化环境或未知环境中执行任务,在最近几年迅速成为机器人研究领域的前沿和热点. 模块化可重构机器人在军事、医疗、教育等众多工程领域具有广泛的应用前景,其典型代表包括仿生多足模块化机器人、模块化可重构机械臂、晶格式模块化机器人等. 模块化可重构机器人丰富的构型设计、多样的连接特征、不断拓展的应用范围,给动力学建模与控制带来了很多挑战和机遇. 本文首先阐述了模块化可重构机器人的研究背景和意义,并概述了其构型分类与设计、构型描述与运动学建模方法.随后,本文系统回顾了模块化可重构机器人动力学研究中相关问题的最新进展,包括：(1)系统整体动力学建模;(2)结合面以及对接机构动力学建模;(3)基于动力学模型的控制方法. 本文最后提出了模块化可重构机器人动力学研究中若干值得关注的问题.     

Dynamics and input–output feedback linearization control of a wheeled mobile cable-driven parallel robot

In comparison to the conventional parallel robots, cable-driven parallel robots (CDPRs) have generally superior features such as simple production technology, low energy consumption, large workspace, high payload to moving weight ratio, and also low cost. On the other hand, a wheeled mobile robot (WMR) which is capable of covering a vast area can be used when no specific space is designated for the stationary accessories of a robot. In this paper, the integration of a CDPR with a WMR is proposed to overcome some of the issues related to each of these robots. The kinematic equations of the robot are presented. To derive the dynamic equations, Gibbs–Appel (G–A) formulation is used, which in contrary to the Lagrange formulation benefits from advantages of quasi-velocities over generalized coordinates as well as not requiring Lagrange multipliers. The dynamic equations of the two parts are coupled, and the interacting effects are observable from the governing equations. By considering non-holonomic wheels for the robot, internal dynamics appears in the equations. However, based on some conditions, the equations are input–output linearizable via a static feedback. The platform trajectory is designed based on the given end-effector trajectory. The effectiveness of the controller is shown through simulations and experimental tests.     

复杂环境下群机器人自组织协同多目标围捕

针对动态多目标围捕,提出了一种复杂环境下协同自组织多目标围捕方法.首先设计了多目标在复杂环境下的运动模型,然后通过对生物群体围捕行为的研究,构建了多目标简化虚拟受力模型.基于此受力模型和提出的动态多目标自组织任务分配算法,提出了群机器人协同自组织动态多目标围捕算法,这两个算法只需多目标和个体两最近邻位置信息以及个体面向多目标中心方向的两最近邻任务信息,计算简单高效,易于实现.接着获得了系统稳定时参数的设置范围.由仿真可知,所提的方法具有较好的灵活性、可扩展性和鲁棒性.最后给出了所提方法相较于其它方法的优势.     

A real-time path planning algorithm for cable-driven parallel robots in dynamic environment based on artificial potential guided RRT

Microsystem Technologies - This paper deals with the collision-free path planning of cable-driven parallel robots (CDPRs) in a dynamic three-dimensional environment. The proposed algorithm is based...