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.     

On the decoupling of position and force controllers in constrained robotic tasks

In hybrid control of robot manipulators separate controllers are designed for force and position errors control. Controllers are designed either in task or joint space and their outputs combine to provide input torque to the manipulator. Position and force controllers performance in a constrained robotic task is affected by their interaction to a degree dependent on the controller's ability to reject disturbances. Ideally, decoupling of the two control loops is desired to achieve the best performance in position and force directions. In this article, analysis of control loop interactions is performed for contact and noncontact phases, and controller design requirements are developed to achieve maximum decoupling. Design requirements involve output subspace of each controller leading to control discontinuities for contact and noncontact phases. In the noncontact phase, satisfaction of design requirements leads to a fully linearized and decoupled system. When in contact with the constraining surface, design requirements eliminate disturbances in the force loop, but minimize disturbances in the position loop to an extent dependent on force loop performance. Known hybrid control schemes analysis is performed to reveal existence of control loop interactions in these schemes. Confirmation of theoretical analysis is done through simulation of a three revolute planar manipulator. © 1998 John Wiley & Sons, Inc.     

An algorithmic approach to coordinate transformation for robotic manipulators

Coordinate transformation is one of the most important issues in robotic manipulator control. Robot tasks are naturally specified in work space coordinates, usually a Cartesian frame, while control actions are developed on joint coordinates. Effective inverse kinematic solutions are analytical in nature; they exist only for special manipulator geometries and geometric intuition is usually required. Computational inverse kinematic algorithms have recently been proposed; they are based on general closed-loop schemes which perform the mapping of the desired Cartesian trajectory into the corresponding joint trajectory. The aim of this paper is to propose an effective computational scheme to the inverse kinematic problem for manipulators with spherical wrists. First an insight into the formulation of kinematics is given in order to detail the general scheme for this specific class of manipulators. Algorithm convergence is then ensured by means of the Lyapunov direct method. The resulting algorithm is based on the hand position and orientation vectors usually adopted to describe motion in the task space. The analysis of the computational burden is performed by taking the Stanford arm as a reference. Finally a case study is developed via numerical simulations.     

冗余机械臂运动学优化设计

该文主要从机械臂运动学的角度,定义了故障容错机械臂,巧妙地论证了冗余故障容错机械臂应该具备的自由度数,以及针对不同的任务要求,设计故障容错机械臂的方法。通过将任务空间抽象简化为一系列的特征点,建立机械臂参数与理想值相关的罚函数,选择有效的优化算法,设计出了通用一阶故障容错平面位置机械臂,通用一阶故障容错空间位置机械臂,以及特定任务一阶故障容错平面位置机械臂。建立起完整的故障容错机械臂的设计方法。     

柔性臂漂浮基空间机器人建模与轨迹跟踪控制

利用拉格朗日法和假设模态方法建立了末端柔性的两臂漂浮基空间机器人的非线性动力学方程．通过坐标变换,推导出一种新的以可测关节角为变量的全局动态模型,并在此基础上运用基于模型的非线性解耦反馈控制方法得到关节相对转角与柔性臂的弹性变形部分解耦形式控制方程．最后,讨论了柔性臂漂浮基空间机器人的轨迹跟踪问题,并通过仿真实例计算,表明该模型转换及控制方法对于柔性臂漂浮基空间机器人末端轨迹跟踪控制的有效性．     

A Sequential Bi-criteria Search Algorithm for Robot Path Planning in the Box Pushing Problem

The collision-free trajectory planning method subject to control constraints for mobile manipulators is presented. The robot task is to move from the current configuration to a given final position in the workspace. The motions are planned in order to maximise an instantaneous manipulability measure to avoid manipulator singularities. Inequality constraints on state variables i.e. collision avoidance conditions and mechanical constraints are taken into consideration. The collision avoidance is accomplished by local perturbation of the mobile manipulator motion in the obstacles neighbourhood. The fulfilment of mechanical constraints is ensured by using a penalty function approach. The proposed method guarantees satisfying control limitations resulting from capabilities of robot actuators by applying the trajectory scaling approach. Nonholonomic constraints in a Pfaffian form are explicitly incorporated into the control algorithm. A computer example involving a mobile manipulator consisting of nonholonomic platform (2,0) class and 3DOF RPR type holonomic manipulator operating in a three-dimensional task space is also presented.     

Singularities in motion and displacement functions for a 7 degree-of-freedom manipulator

The authors propose a method for the determination of singularities in motion and displacement functions for a seven degree-of-freedom manipulator. The manipulator is considered, hereby, as a set of six degree-of-freedom manipulators. It is proven that two types of singularities in motion can occur at link positions that are independent and dependent with respect to the trajectory to be executed. The relations between the structure of singularity equations and displacement equations are discussed. The derivation of displacement equations for a manipulator with singularities of the second type is based on the idea of modeling of a manipulator by two open kinematic chains and invariants that may be found for these chains. The inverse kinematic equations and the equations of singularities in motion have been derived using a symbolic computer program which can handle manipulators of general structure (with five, six, and seven degrees-of-freedom). This program is written in the Symbolic Computation Language REDUCE.     

Learning Control of Robot Manipulators in Task Space

Two important properties of industrial tasks performed by robot manipulators, namely, periodicity (i.e., repetitive nature) of the task and the need for the task to be performed by the end‐effector, motivated this work. Not being able to utilize the robot manipulator dynamics due to uncertainties complicated the control design. In a seemingly novel departure from the existing works in the literature, the tracking problem is formulated in the task space and the control input torque is aimed to decrease the task space tracking error directly without making use of inverse kinematics at the position level. A repetitive learning controller is designed which “learns” the overall uncertainties in the robot manipulator dynamics. The stability of the closed‐loop system and asymptotic end‐effector tracking of a periodic desired trajectory are guaranteed via Lyapunov based analysis methods. Experiments performed on an in‐house developed robot manipulator are presented to illustrate the performance and viability of the proposed controller.     

Visual Motor Control of a 7 DOF Robot Manipulator Using Function Decomposition and Sub-Clustering in Configuration Space

This paper deals with real-time implementation of visual-motor control of a 7 degree of freedom (DOF) robot manipulator using self-organized map (SOM) based learning approach. The robot manipulator considered here is a 7 DOF PowerCube manipulator from Amtec Robotics. The primary objective is to reach a target point in the task space using only a single step movement from any arbitrary initial configuration of the robot manipulator. A new clustering algorithm using Kohonen SOM lattice has been proposed that maintains the fidelity of training data. Two different approaches have been proposed to find an inverse kinematic solution without using any orientation feedback. In the first approach, the inverse Jacobian matrices are learnt from the training data using function decomposition. It is shown that function decomposition leads to significant improvement in accuracy of inverse kinematic solution. In the second approach, a concept called sub-clustering in configuration space is suggested to provide multiple solutions for the inverse kinematic problem. Redundancy is resolved at position level using several criteria. A redundant manipulator is dexterous owing to the availability of multiple configurations for a given end-effector position. However, existing visual motor coordination schemes provide only one inverse kinematic solution for every target position even when the manipulator is kinematically redundant. Thus, the second approach provides a learning architecture that can capture redundancy from the training data. The training data are generated using explicit kinematic model of the combined robot manipulator and camera configuration. The training is carried out off-line and the trained network is used on-line to compute the joint angle vector to reach a target position in a single step only. The accuracy attained is better than the current state of art.     

Feedback control of a flexible cylindrical manipulator

Flexible robotic manipulators have been the subject of numerous studies in the past few years. Past studies, however, have concentrated on flexible manipulators with only revolute joints. This paper considers the case of a structurally flexible manipulator with prismatic and revolute joints; specifically, an algorithm for controlling a structurally flexible three-degree-of-freedom cylindrical manipulator is presented. The control algorithm involves two steps. Using nonlinear feedback, the equations of motion are first decoupled into three subsystems representing the three rigid degrees of freedom together with their associated ‘flexible equations’, if any. Then, using linear optimal control theory, controllers are designed for the three subsystems independently. Computer simulated results for an example system are presented.     

An efficient local approach for the path generation of robot manipulators

In this article an efficient local approach for the path generation of robot manipulators is presented. The approach is based on formulating a simple nonlinear programming problem. This problem is considered as a minimization of energy with given robot kinematics and subject to the robot requirements and a singularities avoidance constraint. From this formulation a closed form solution is derived which has the properties that allows to pursue both singularities and obstacle avoidance simultaneously; and that it can incorporate global information. These properties enable the accomplishment of the important task that while a specified trajectory in the operational space can be closely followed, also a desired joint configuration can be attained accurately at a given time. Although the proposed approach is primarily developed for redundant manipulators, its application to nonredundant manipulators is examplified by considering a particular commercial manipulator.     

Dynamically consistent Jacobian inverse for mobile manipulators

By analogy to the definition of the dynamically consistent Jacobian inverse for robotic manipulators, we have designed a dynamically consistent Jacobian inverse for mobile manipulators built of a non-holonomic mobile platform and a holonomic on-board manipulator. The endogenous configuration space approach has been exploited as a source of conceptual guidelines. The new inverse guarantees a decoupling of the motion in the operational space from the forces exerted in the endogenous configuration space and annihilated by the dual Jacobian inverse. A performance study of the new Jacobian inverse as a tool for motion planning is presented.     

Modelling and simulation of an underwater manipulator

Recently, applications of articulated manipulators have increased to include extreme environments such as underwater and space. Simulation systems to support the design and control of industrial robots have been developed in many laboratories, and some high-speed calculation methods for inverse dynamics analysis of manipulators with series connections have been proposed. This paper deals with the dynamic simulation and modelling of underwater articulated manipulators. The dynamics of the above manipulators are formulated to evaluate the influence of the added mass tensor, the added inertia tensor, and fluid drag, and the lift on each arm according to classical Newton-Euler mechanics. Moreover, by generalizing this model, we can discuss the dynamics of a manipulator with dual arms and simulate some constrained motion of an end-effector. As an example of inverse dynamics analysis, the force and moment of a nine degrees of freedom (d.o.f.) manipulator with dual arms are analysed. As an example of direct dynamics analysis, hybrid control of both the force and the position of a 6 d.o.f. manipulator is simulated.     

无轴承同步磁阻电机逆系统解耦控制仿真研究

研究无轴承同步磁阻电机稳定性控制问题,由于无轴承同步磁阻电机是一个强耦合的非线性系统,为实现负载条件下的稳定悬浮运行,需解除电机转矩和径向悬浮力等多变量之间的耦合关系。针对前馈补偿解耦的缺陷,给出了无轴承同步磁阻电机包含转矩控制和悬浮力控制的统一数学模型,证明电机逆系统存在,设计了一种通过非线性状态反馈的逆系统解耦控制方案,将复杂的无轴承同步磁阻电机系统解耦成两个转子径向位置二阶积分子系统和一个转速一阶积分子系统,并用PI和PID调节器分别对转子位置与转速进行综合设计。运用MATLAB软件对电机控制系统进行仿真。仿真结果证明,解耦控制方案的有效性,为电机系统优化设计提供了保证。     

基于三步法的机械臂轨迹跟踪控制

考虑机械臂末端轨迹跟踪控制问题,以跟踪逆运动学求解出的末端期望轨迹对应的各关节期望角度为控制目标.设计了一种基于三步法的控制器,该控制器由类稳态控制、可变参考前馈控制和误差反馈控制3部分组成.证明了该控制器可以通过控制机械臂的各关节力矩实现各关节实际角度对期望角度的状态跟踪,进而使得末端轨迹渐近跟踪期望轨迹,并且跟踪误差是输入到状态稳定的.仿真表明基于三步法控制器的空间机械臂末端可以渐近跟踪期望轨迹,并且该算法可以克服系统的末端负载质量变化等不确定性的影响.     

Vision-Based Task-Level Control of a Flexible-Link Manipulator

This paper discusses a vision-based approach to implement task-level control in flexible-link manipulators. The proposed approach emphasizes the advantage of using vision in the control of flexible manipulators. It is pointed out that taking advantage of the inherent robustness, implementation of an image-based visual servo can be regarded as a synthetic solution to precise task-level control of flexible manipulators. This approach is implemented in a three-dimensional flexible-link manipulator. The implementation makes good use of filters in decoupling task-level control and vibration suppression control. Moreover, we point out that although the robustness of the approach can help to overcome the difficulty in control resulting from the complex measurement of the link's elastic deformation, it lacks in capability of tip trajectory specification. This problem is analyzed in this research and it leads to the proposal for the integration of the image interpolation technique. This technique makes the proposed approach adequate for tasks involved with complex tip trajectories. For flexible-link manipulators, the proposed approach with the remedy is the first vision-based synthetic solution that attempts to make a flexible manipulator usable for a practical task.     

Transputer-based implementation of realtime robot position control

The implementation of the forward kinematics algorithm to position control robot manipulators is discussed. The objective is to control the manipulator in real time by dividing the task between a network of transputers. The underlying strategy is the fine-grain distribution of tasks as opposed to allocating one processor per joint. The network topology used is taken through diagnostic tests for analysis leading to performance maximization.     

Inverse kinematics and geometrically bounded singularities prevention of redundant manipulators: An Artificial Neural Network approach

This article presents an Artificial Neural Network (ANN) approach for fast inverse kinematics computation and effective geometrically bounded singularities prevention of redundant manipulators. Here, some bounded geometrical concepts are properly utilized to establish some characterizing matrices, to yield a simple performance index, and a null space vector for singularities avoidance/prevention and safe path generation. Then, a properly trained ANN is used in a novel scheme for the computation of inverse kinematics. This scheme includes the proposed null space vector being also computed by another properly trained ANN. The efficiency of the proposed ANN approach is demonstrated in the successful singularities prevention of a planar redundant manipulator performing a benchmark test.     

Design and experimental validation of a second-order sliding-mode motion controller for robot manipulators

This article presents an original motion control strategy for robot manipulators based on the coupling of the inverse dynamics method with the so-called second-order sliding mode control approach. Using this method, in principle, all the coupling non-linearities in the dynamical model of the manipulator are compensated, transforming the multi-input non-linear system into a linear and decoupled one. Actually, since the inverse dynamics relies on an identified model, some residual uncertain terms remain and perturb the linear and decoupled system. This motivates the use of a robust control design approach to complete the control scheme. In this article the sliding mode control methodology is adopted. Sliding mode control has many appreciable features, such as design simplicity and robustness versus a wide class of uncertainties and disturbances. Yet conventional sliding mode control seems inappropriate to be applied in robotics since it can generate the so-called chattering effect, which can be destructive for the controlled robot. In this article, this problem is suitably circumvented by designing a second-order sliding mode controller capable of generating a continuous control law making the proposed sliding mode controller actually applicable to industrial robots. To build the inverse dynamics part of the proposed controller, a suitable dynamical model of the system has been formulated, and its parameters have been accurately identified relying on a practical MIMO identification procedure recently devised. The proposed inverse dynamics-based second-order sliding mode controller has been experimentally tested on a COMAU SMART3-S2 industrial manipulator, demonstrating the tracking properties and the good performances of the controlled system.     

机械臂的动态混合控制

本文研究当机械臂的终端受有约束时的控制问题,其中心内容是给出“任务规范投影算子”的概念,利用它首先将机械臂的动态方程解耦为两组方程,它们分别描述了运动与约束力,在此基础上给出了机械臂的控制律,使闭环系统跟踪期望的速度与约束力。