A direct algorithm for continuous path control of manipulators

This paper presents an algorithm for positioning and orientation of the hand for a redundant or non-redundant manipulator along a continuous path in space. This algorithm minimizes the distance between the actual position of the tip of the end-effector and the desired path. The algorithm does not use the Jacobian matrix for the inverse kinematics of the robot. It takes full advantage of the resolution of the joint drives, avoids singularity problems, and can be used for both redundant manipulators. The algorithm can be used in any situation where continuus motion of the end-effector is required in an open loop mode.     

Intelligent control for avoiding the joint limits of redundant planar manipulators

This article presents an intelligent control system for a redundant manipulator to avoid physical limits such as joint angle limits and joint velocity limits. In this method, a back-propagation neural network (NN) is introduced for the kinematic inversion of the manipulator. Since this inverse kinematics has an infinite number of joint angle vectors, a fuzzy-neuro system is constructed to provide an approximate value for that vector. This vector is fed into the NN as a hint input vector in order to guide the output of the NN within the self-motion. Simulations and a comparative study are made based on a four-link redundant manipulator to prove the efficacy of the proposed control system.     

Collision-avoidance for redundant robots through control of the self-motion of the manipulator

A new method to on-line collision-avoidance of the links of redundant robots with obstacles is presented. The method allows the use of redundant degrees of freedom such that a manipulator can avoid obstacles while tracking the desired end-effector trajectory. It is supposed that the obstacles in the workspace of the manipulator are presented by convex polygons. The recognition of collisions of the links of the manipulator with obstacles results on-line through a nonsensory method. For every link of the redundant manipulator and every obstacle a boundary ellipse is defined in workspace such that there is no collision if the robot joints are outside these ellipses. In case a collision is imminent, the collision-avoidance algorithm compute the self-motion movements necessary to avoid the collision. The method is based on coordinate transformation and inverse kinematics and leads to the favorable use of the abilities of redundant robots to avoid the collisions with obstacles while tracking the end-effector trajectory. This method has the advantage that the configuration of the manipulator after collision-avoidance can be influenced by further requirements such as avoidance of singularities, joint limits, etc. The effectiveness of the proposed method is discussed by theoretical considerations and illustrated by simulation of the motion of three-and four-link planar manipulators between obstacles.     

基于解析法和遗传算法的机械手运动学逆解

研究优化机械手轨迹规划问题,机械手运动时要具有稳定性避障性能。针对平面3自由度冗余机械手优化控制问题,建立机械手的结构模型。提出用解析法和遗传算法相结合满足具有计算量小和适应性强的特点。在给定机械手末端执行器的运动轨迹,按着机械手冗余自由度,运动轨迹上每个点对应的关节角有无穷多个解。而通过算法可以找到一组最优的关节角,可得到优化机械手运动过程中柔顺性和避障点。仿真结果表明,该算法可以快速收敛到全局最优解,可用于计算冗余机械手运动学逆解,并可实现机器人的轨迹规划和避障优化控制。     

自由浮动空间冗余度机械臂避奇异规化的混沌运动抑制控制

推导出自由浮动空间冗余度机械臂的广义雅可比矩阵,讨论空间机械臂避奇异问题,基于梯度投影法选取空间机械臂的运动学可操作度作为避奇异优化目标函数,利用关节空间的自运动,实现自由浮动冗余度空间机械臂的避奇异运动规划,混沌数值计算表明,空间冗余度机械臂避奇异运动时,其关节零空间的自运动处于混沌状态,利用状态延迟反馈控制来实现空间冗余度机械臂避奇异时的混沌抑制,将关节运动镇定到稳定的周期轨道。     

基于ANFIS的机械手运动学逆解的求取

提出一种基于自适应神经模糊推理系统（ANFIS）求取机械手运动学逆解的方法。本文以SCARA（Selective Compliance Assembly Robot Arm）型四自由度机械手为研究对象,研究SCARA机械手末端执行器笛卡儿空间坐标与机械手关节空间关节变量之间的对应关系。首先根据笛卡儿运动轨迹选取起点、终点和中间点,并求得与之对应的关节变量值序列。然后利用插值方法求得关节空间的角度变化曲线,最后在关节曲线上随机选取样本点,进而利用得到的数据训练并验证自适应神经模糊推理系统求解逆解的正确性和精确性。与传统基于BP神经网络求取运动学逆解的方法进行仿真对比分析,结果表明ANFIS在运动学逆解的求取精度和运算时间上均优于BP神经网络。     

Analysis and acceleration of TORM: optimization-based planning for path-wise inverse kinematics

Autonomous Robots - A redundant manipulator can have many trajectories for joints that follow a given end-effector path in the Cartesian space, since it has multiple inverse kinematics solutions...     

A Lagrangian network for kinematic control of redundant robotmanipulators

A recurrent neural network, called the Lagrangian network, is presented for the kinematic control of redundant robot manipulators. The optimal redundancy resolution is determined by the Lagrangian network through real-time solution to the inverse kinematics problem formulated as a quadratic optimization problem. While the signal for a desired velocity of the end-effector is fed into the inputs of the Lagrangian network, it generates the joint velocity vector of the manipulator in its outputs along with the associated Lagrange multipliers. The proposed Lagrangian network is shown to be capable of asymptotic tracking for the motion control of kinematically redundant manipulators.     

Cartesian path generation of robot manipulators using continuous genetic algorithms

In this paper, the authors describe a novel technique based on continuous genetic algorithms (CGAs) to solve the path generation problem for robot manipulators. We consider the following scenario: given the desired Cartesian path of the end-effector of the manipulator in a free-of-obstacles workspace, off-line smooth geometric paths in the joint space of the manipulator are obtained. The inverse kinematics problem is formulated as an optimization problem based on the concept of the minimization of the accumulative path deviation and is then solved using CGAs where smooth curves are used for representing the required geometric paths in the joint space through out the evolution process. In general, CGA uses smooth operators and avoids sharp jumps in the parameter values. This novel approach possesses several distinct advantages: first, it can be applied to any general serial manipulator with positional degrees of freedom that might not have any derived closed-form solution for its inverse kinematics. Second, to the authors’ knowledge, it is the first singularity-free path generation algorithm that can be applied at the path update rate of the manipulator. Third, extremely high accuracy can be achieved along the generated path almost similar to analytical solutions, if available. Fourth, the proposed approach can be adopted to any general serial manipulator including both nonredundant and redundant systems. Fifth, when applied on parallel computers, the real time implementation is possible due to the implicit parallel nature of genetic algorithms. The generality and efficiency of the proposed algorithm are demonstrated through simulations that include 2R and 3R planar manipulators, PUMA manipulator, and a general 6R serial manipulator.     

Redundant grasps,redundant manipulators,and their dual relationships

This article presents a meaningful, practical, and theoretically sound solution that solves the problem of grasping a rigid object with a hand that has redundant (>6) grasping contacts. This is accomplished by introducing compliance at each contact point in such a way as to provide the engineer with the capabilities of object manipulation via controlled forces at the contact points. This method of solution is adapted straight-away to compute the static forces generated in the legs of a redundant in-parallel manipulator that equilibrates a wrench applied to the moving/platform or end-effector. In a way similar to the redundant grasping problem, this is accomplished by introducing the knowledge of the compliances that exist in the legs. The solution thus obtained stems from physical parameters that model the in-parallel manipulator. The in-depth study of the duality between the statics of in-parallel manipulators and the kinematics of serial manipulators reveals a meaningful, practical, and theoretically sound solution for the inverse kinematics of a redundant serial manipulator. This is accomplished by incorporating the knowledge of the compliances that exist or are desired to exist in the joints of the manipulator. (For instance, the torsional compliance in revolute joints or the linear compliance in prismatic joints.) Such information provides a physically meaningful model of the serial manipulator that in turn yields a physically meaningful set of joint increments for a given end-effector twist. © 1992 John Wiley & Sons, Inc.     

Visual motor control of a 7 DOF robot manipulator using a fuzzy SOM network

A fuzzy self-organizing map (SOM) network is proposed in this paper for visual motor control of a 7 degrees of freedom (DOF) robot manipulator. The inverse kinematic map from the image plane to joint angle space of a redundant manipulator is highly nonlinear and ill-posed in the sense that a typical end-effector position is associated with several joint angle vectors. In the proposed approach, the robot workspace in image plane is discretized into a number of fuzzy regions whose center locations and fuzzy membership values are determined using a Fuzzy C-Mean (FCM) clustering algorithm. SOM network then learns the inverse kinematics by on-line by associating a local linear map for each cluster. A novel learning algorithm has been proposed to make the robot manipulator to reach a target position. Any arbitrary level of accuracy can be achieved with a number of fine movements of the manipulator tip. These fine movements depend on the error between the target position and the current manipulator position. In particular, the fuzzy model is found to be better as compared to Kohonen self-organizing map (KSOM) based learning scheme proposed for visual motor control. Like existing KSOM learning schemes, the proposed scheme leads to a unique inverse kinematic solution even for a redundant manipulator. The proposed algorithms have been successfully implemented in real-time on a 7 DOF PowerCube robot manipulator, and results are found to concur with the theoretical findings.     

Inverse kinematics of planar redundant manipulators via virtual links with configuration index

This article presents a new method for generating inverse kinematic solutions for planar manipulators with large redundancy (hyper-redundant manipulators). The proposed method starts by decomposing a planar redundant manipulator into a series of local planar arms that are either 2-link or 3-link manipulator modules, and connecting the conjunction points between them with virtual links. The manipulator then can be handled by a simple virtual link system, which may be conveniently divided into non-singular and singular cases depending on its configuration. When the virtual link system is no longer effective due to a singular configuration, the displacement of the end-effector is then allocated to virtual links according to a displacement distribution criterion. A dexterity index called the “configuration index” distinguishes the non-singular and singular cases. The concept of virtual link is shown by computer simulations to be simple and effective for the inverse kinematics of a planar hyper-redundant manipulator with a discrete model. In particular, it can be applied to solving the inverse kinematics of a SCARA-type spatial redundant manipulator whose redundancy is included in its planar mechanism. © 1994 John Wiley & Sons, Inc.     

Adaptive control of redundant multiple robots in cooperative motion

A redundant robot has more degrees of freedom than what is needed to uniquely position the robot end-effector. In practical applications the extra degrees of freedom increase the orientation and reach of the robot. Also the load carrying capacity of a single robot can be increased by cooperative manipulation of the load by two or more robots. In this paper, we develop an adaptive control scheme for kinematically redundant multiple robots in cooperative motion.In a usual robotic task, only the end-effector position trajectory is specified. The joint position trajectory will therefore be unknown for a redundant multi-robot system and it must be selected from a self-motion manifold for a specified end-effector or load motion. In this paper, it is shown that the adaptive control of cooperative multiple redundant robots can be addressed as a reference velocity tracking problem in the joint space. A stable adaptive velocity control law is derived. This controller ensures the bounded estimation of the unknown dynamic parameters of the robots and the load, the exponential convergence to zero of the velocity tracking errors, and the boundedness of the internal forces. The individual robot joint motions are shown to be stable by decomposing the joint coordinates into two variables, one which is homeomorphic to the load coordinates, the other to the coordinates of the self-motion manifold. The dynamics on the self-motion manifold are directly shown to be related to the concept of zero-dynamics. It is shown that if the reference joint trajectory is selected to optimize a certain type of objective functions, then stable dynamics on the self-motion manifold result. The overall stability of the joint positions is established from the stability of two cascaded dynamic systems involving the two decomposed coordinates.     

Robot arm reaching through neural inversions and reinforcement learning

We present a neural method that computes the inverse kinematics of any kind of robot manipulators, both redundant and non-redundant. Inverse kinematics solutions are obtained through the inversion of a neural network that has been previously trained to approximate the manipulator forward kinematics. The inversion provides difference vectors in the joint space from difference vectors in the workspace. Our differential inverse kinematics (DIV) approach can be viewed as a neural network implementation of the Jacobian transpose method for arm kinematic control that does not require previous knowledge of the arm forward kinematics. Redundancy can be exploited to obtain a special inverse kinematic solution that meets a particular constraint (e.g. joint limit avoidance) by inverting an additional neural network The usefulness of our DIV approach is further illustrated with sensor-based multilink manipulators that learn collision-free reaching motions in unknown environments. For this task, the neural controller has two modules: a reinforcement-based action generator (AG) and a DIV module that computes goal vectors in the joint space. The actions given by the AG are interpreted with regard to those goal vectors.     

Calculation of repeatable control strategies for kinematically redundant manipulators

A kinematically redundant manipulator is a robotic system that has more than the minimum number of degrees of freedom that are required for a specified task. Due to this additional freedom, control strategies may yield solutions which are not repeatable in the sense that the manipulator may not return to its initial joint configuration for closed end-effector paths. This paper compares two methods for choosing repeatable control strategies which minimize their distance from a nonrepeatable inverse with desirable properties. The first method minimizes the integral norm of the difference of the desired inverse and a repeatable inverse while the second method minimizes the distance of the null vectors associated with the desired and the repeatable inverses. It is then shown how the two techniques can be combined in order to obtain the advantages of both methods. As an illustrative example the pseudoinverse is approximated in a region of the joint space for a seven-degree-of-freedom manipulator.     

冗余度机器人自运动中的混沌运动及其控制

以一个平面3R刚性冗余度机器人为研究对象,采用PD调节器进行工作空间内的负反馈,控制机器人末端重复跟踪工作空间内封闭路径,对此过程中机器人自运动中可能存在的混沌运动进行了研究.通过运动仿真和相图,以及计算系统的最大李亚普诺夫指数,研究发现,基于雅可比矩阵的伪逆,求解冗余度机器人运动学逆解时其自运动是混沌的.首次应用延迟反馈控制法对所发现的混沌运动进行控制,在适当的参数条件下,成功地将混沌运动转变为规则的周期运动.􀁱 􀁽     

Comparison of four different heuristic optimization algorithms for the inverse kinematics solution of a real 4-DOF serial robot manipulator

In this study, a 4-degree-of-freedom (DOF) serial robot manipulator was designed and developed for the pick-and-place operation of a flexible manufacturing system. The solution of the inverse kinematics equation, one of the most important parts of the control process of the manipulator, was obtained by using four different optimization algorithms: the genetic algorithm (GA), the particle swarm optimization (PSO) algorithm, the quantum particle swarm optimization (QPSO) algorithm and the gravitational search algorithm (GSA). These algorithms were tested with two different scenarios for the motion of the manipulator’s end-effector. One hundred randomly selected workspace points were defined for the first scenario, while a spline trajectory, also composed of one hundred workspace points, was used for the second. The optimization algorithms were used for solving of the inverse kinematics of the manipulator in order to successfully move the end-effector to these workspace points. The four algorithms were compared according to the execution time, the end-effector position error and the required number of generations. The results showed that the QPSO could be effectively used for the inverse kinematics solution of the developed manipulator.     

一种仿人机械臂的运动学逆解的几何求解方法

运用几何方法求解一种具有7个旋转自由度的仿人机械臂的运动学逆解,并运用特定的寻优指标,搜索与指定末端位姿对应的关节角空间最优解.这种解法没有理论误差并且解算速度足够快,有利于在线实时控制机械臂的运动.     

Kinematic control of redundant free-floating robotic systems

This paper is aimed at presenting solution algorithms to the inverse kinematics of a space manipulator mounted on a free-floating spacecraft. The reaction effects of the manipulator's motion on the spacecraft are taken into account by means of the so-called generalized Jacobian. Redundancy of the system with respect to the number of task variables for spacecraft attitude and manipulator end-effector pose is considered. Also, the problem of both spacecraft attitude and end-effector orientation representation is tackled by means of a non-minimal singularity-free representation: the unit quaternion. Depending on the nature of the task for the spacecraft/manipulator system, a number of closed-loop inverse kinematics algorithms are proposed. Case studies are developed for a system of a spacecraft with a six-joint manipulator attached.     

Geometrical approach of planar hyper-redundant manipulators: Inverse kinematics,path planning and workspace

A new method for inverse kinematics for hyper-redundant manipulators is proposed in this paper to plan the path of the end-effector. The basic idea is that for a given smooth path consisting of points close enough to each other; computing the inverse kinematics for these points is carried out geometrically using the proposed method. In this method, the angles between the adjacent links are set to be the same, which makes lining up of two or more joint axes impossible; therefore, avoiding singularities. The manipulability index has been used to show how far the manipulator from the singularity configuration is. The determination of the workspace of the manipulator using the proposed method has been presented in this paper. The simulation results have been carried out on a planar and a three dimensional manipulators. The effectiveness of the proposed method is clearly demonstrated by comparing its result with results calculated by the well-known method of measuring manipulability which is used for singularity avoidance for the last two decades.