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.     

Analytical Inverse Kinematics Solver for Anthropomorphic 7-DOF Redundant Manipulators with Human-Like Configuration Constraints

It is a common belief that service robots shall move in a human-like manner to enable natural and convenient interaction with a human user or collaborator. In particular, this applies to anthropomorphic 7-DOF redundant robot manipulators that have a shoulder-elbow-wrist configuration. On the kinematic level, human-like movement then can be realized by means of selecting a redundancy resolution for the inverse kinematics (IK), which realizes human-like movement through respective nullspace preferences. In this paper, key positions are introduced and defined as Cartesian positions of the manipulator’s elbow and wrist joints. The key positions are used as constraints on the inverse kinematics in addition to orientation constraints at the end-effector, such that the inverse kinematics can be calculated through an efficient analytical scheme and realizes human-like configurations. To obtain suitable key positions, a correspondence method named wrist-elbow-in-line is derived to map key positions of human demonstrations to the real robot for obtaining a valid analytical inverse kinematics solution. A human demonstration tracking experiment is conducted to evaluate the end-effector accuracy and human-likeness of the generated motion for a 7-DOF Kuka-LWR arm. The results are compared to a similar correspondance method that emphasizes only the wrist postion and show that the subtle differences between the two different correspondence methods may lead to significant performance differences. Furthermore, the wrist-elbow-in-line method is validated as more stable in practical application and extended for obstacle avoidance.     

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。     

New Architecture of a Hybrid Two-Fingered Micro–Nano Manipulator Hand: Optimization and Design

This paper presents the synthesis and design optimization of a compact and yet economical hybrid two-fingered micro–nano manipulator hand. The proposed manipulator hand consists of two series modules, i.e., an upper and lower modules. Each of them consists of a parallel kinematics chain with a glass pipette (1 mm diameter and 3–10 cm length) tapered to a very sharp end as an end-effector. It is driven by three piezo-electric actuated prismatic joints in each of the three legs of the parallel kinematics chain. Each leg of the kinematics chain has the prismatic–revolute–spherical joint structure. As the length of the glass pipette end-effector is decreased, the resolution and accuracy of the micro–nano manipulator hand is increased. For long lengths of the glass pipette end-effector, this manipulator works as a micro manipulator and for short lengths it works as a nano manipulator. A novel closed-form solution for the problem of inverse kinematics is obtained. Based on this solution, a simulation program has been developed to optimally choose the design parameters of each module so that the manipulator will have a maximum workspace volume. A computer-aided design model based on optimal parameters is built and investigated to check its workspace volume. Experimental work has been carried out for the purpose of calibration. Also, the system hardware setup of the hybrid two-fingered micro–nano manipulator hand and its practical Jacobian inverse matrices are presented.     

全局和声搜索方法及其在仿人灵巧臂逆运动学求解中的应用

仿人灵巧臂逆运动学(IK)问题可转化为等效的最小化问题,并采用数值优化方法求解.和声搜索(HS)是模拟乐师在音乐演奏中调整音调现象的一种启发式搜索方法,目前还尚未在机器人机械臂逆运动学问题中得到应用.本文提出一种基于粒子群体智能的全局和声搜索方法(GHSA),该方法在和声搜索算法中引入微粒群操作(PSO),采用粒子群策略替代常规和声搜索算法中的搜索法则创作新和声,通过粒子自身认知和群体知识更新和声变量位置信息平衡算法对解空间全局探索与局部开发间能力;同时算法还引入变异操作增强算法跳出局部最优解能力,基准函数测试表明该方法改善了全局搜索能力及求解可靠性.在此基础上以七自由度(7-DOF)冗余仿人灵巧臂为例,考虑以灵巧臂末端位姿误差和“舒适度”指标构建适应度函数并采用GHSA算法求解其逆运动学(IK)问题,数值仿真结果表明了该方法是解决仿人灵巧臂逆运动学问题的一种有效方法.     

Canonical parameterization of excess motor degrees of freedom withself-organizing maps

The problem of sensorimotor control is underdetermined due to excess (or "redundant") degrees of freedom when there are more joint variables than the minimum needed for positioning an end-effector. A method is presented for solving the nonlinear inverse kinematics problem for a redundant manipulator by learning a natural parameterization of the inverse solution manifolds with self-organizing maps. The parameterization approximates the topological structure of the joint space, which is that of a fiber bundle. The fibers represent the "self-motion manifolds" along which the manipulator can change configuration while keeping the end-effector at a fixed location. The method is demonstrated for the case of the redundant planar manipulator. Data samples along the self-motion manifolds are selected from a large set of measured input-output data. This is done by taking points in the joint space corresponding to end-effector locations near "query points", which define small neighborhoods in the end-effector work space. Self-organizing maps are used to construct an approximate parameterization of each manifold which is consistent for all of the query points. The resulting parameterization is used to augment the overall kinematics map so that it is locally invertible. Joint-angle and end-effector position data, along with the learned parameterizations, are used to train neural networks to approximate direct inverse functions.     

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.     

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.     

Conceptual design and analysis of the 2T1R mechanism for a cooking robot

This paper deals with the design and analysis of a two-translation and one-rotation (2T1R) mechanism for a novel cooking robot. Firstly the motions involved in stir-fry, the most representative operation in the cooking processes used in Chinese cuisine, are analyzed in details. Then the featured motions are decomposed into four main movements that are used as a design base for a wok motion mechanism. Several three-degrees-of-freedom (DOF) parallel manipulators are considered. From these, a 2T1R mechanism is selected as an ideal candidate. A 4-DOF (2T1R+1T) cooking robot is constructed by combining the 2T1R parallel manipulator with a 1-DOF linear feed mechanism. It is shown that the combined 4-DOF robot can perform the required cooking operations, particularly the stir-fry. The analysis conducted on the proposed 2T1R parallel manipulator includes inverse kinematics, forward kinematics, the velocity analysis, the constant orientation workspace, and the total orientation workspace. A prototype of the cooking robot is developed. The experiments verify that the proposed cooking robot is suitable for performing the required operations.     

A neural-network committee machine approach to the inverse kinematics problem solution of robotic manipulators

In robotics, inverse kinematics problem solution is a fundamental problem in robotics. Many traditional inverse kinematics problem solutions, such as the geometric, iterative, and algebraic approaches, are inadequate for redundant robots. Recently, much attention has been focused on a neural-network-based inverse kinematics problem solution in robotics. However, the result obtained from the neural network requires to be improved for some sensitive tasks. In this paper, a neural-network committee machine (NNCM) was designed to solve the inverse kinematics of a 6-DOF redundant robotic manipulator to improve the precision of the solution. Ten neural networks (NN) were designed to obtain a committee machine to solve the inverse kinematics problem using separately prepared data set since a neural network can give better result than other ones. The data sets for the neural-network training were prepared using prepared simulation software including robot kinematics model. The solution of each neural network was evaluated using direct kinematics equation of the robot to select the best one. As a result, the committee machine implementation increased the performance of the learning.     

Kinematic control of a redundant manipulator using an inverse-forward adaptive scheme with a KSOM based hint generator

This paper proposes an online inverse-forward adaptive scheme with a KSOM based hint generator for solving the inverse kinematic problem of a redundant manipulator. In this approach, a feed-forward network such as a radial basis function (RBF) network is used to learn the forward kinematic map of the redundant manipulator. This network is inverted using an inverse-forward adaptive scheme until the network inversion solution guides the manipulator end-effector to reach a given target position with a specified accuracy. The positioning accuracy, attainable by a conventional network inversion scheme, depends on the approximation error present in the forward model. But, an accurate forward map would require a very large size of training data as well as network architecture. The proposed inverse-forward adaptive scheme effectively approximates the forward map around the joint angle vector provided by a hint generator. Thus the inverse kinematic solution obtained using the network inversion approach can take the end-effector to the target position within any arbitrary accuracy.In order to satisfy the joint angle constraints, it is necessary to provide the network inversion algorithm with an initial hint for the joint angle vector. Since a redundant manipulator can reach a given target end-effector position through several joint angle vectors, it is desirable that the hint generator is capable of providing multiple hints. This problem has been addressed by using a Kohonen self organizing map based sub-clustering (KSOM-SC) network architecture. The redundancy resolution process involves selecting a suitable joint angle configuration based on different task related criteria.The simulations and experiments are carried out on a 7 DOF PowerCube? manipulator. It is shown that one can obtain a positioning accuracy of 1 mm without violating joint angle constraints even when the forward approximation error is as large as 4 cm. An obstacle avoidance problem has also been solved to demonstrate the redundancy resolution process with the proposed scheme.     

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.     

Kinematic design of a 6-DOF parallel manipulator with decoupled translation and rotation

A new three-limb, six-degree-of-freedom (DOF) parallel manipulator (PM), termed a selectively actuated PM (SA-PM), is proposed. The end-effector of the manipulator can produce 3-DOF spherical motion, 3-DOF translation, 3-DOF hybrid motion, or complete 6-DOF spatial motion, depending on the types of the actuation (rotary or linear) chosen for the actuators. The manipulator architecture completely decouples translation and rotation of the end-effector for individual control. The structure synthesis of SA-PM is achieved using the line geometry. Singularity analysis shows that the SA-PM is an isotropic translation PM when all the actuators are in linear mode. Because of the decoupled motion structure, a decomposition method is applied for both the displacement analysis and dimension optimization. With the index of maximal workspace satisfying given global conditioning requirements, the geometrical parameters are optimized. As a result, the translational workspace is a cube, and the orientation workspace is nearly unlimited.     

基于改进天牛须算法的电力攀爬机器人运动学逆解算法

为了提高电力系统的自动化水平,减轻电力工人在检修高压输电系统时的劳动强度,同时保障电力工人人身安全,提出并设计一种可以攀爬电力铁塔的六自由度关节式机器人,针对该构型进行运动学分析和求解.为解决传统的解析法用于机械臂逆运动学求解过程中存在操作繁琐和奇异点无法逆运算等问题,提出一种基于改进天牛须算法的电力攀爬机器人运动学逆解算法.首先,对电力攀爬机器人进行DH建模,得到正运动学方程;然后,使用正运动学方程和目标位姿建立代价函数,采用改进天牛须算法对代价函数优化;最后,使用Matlab实现此算法进行仿真验证.实验结果表明,与传统的天牛须算法、改进遗传算法以及改进粒子群算法相比,所提出算法具有较好的收敛性,求解精度较高.     

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.     

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.     

Task-oriented approaches to the inverse kinematics problem for a reclaimer excavating and transporting raw material

The inverse kinematics problem of the reclaimer that excavates and transports raw materials in a raw yard is investigated. Link coordinates are introduced by the Denavit-Hartenberg representation. The middle bucket, among the buckets which are in contact with the raw material pile, is treated as the end-effector of a reclaimer. Two task-oriented approaches are investigated. The first approach assumes the complete removal of a pile via a level plan on the pile. In this case, the end-effector is assumed to be a particle moving in the three-dimensional (3D) space. A closedform solution is provided. The second approach assumes the reclamation of an arbitrary pile. The end-effector is regarded as a rigid body which requires both position and orientation information. Because there is no solution for the second approach in general, an approximate solution is provided by exploiting a geometric constraint. The 3D information near the excavation point is approximated as a plane and the orientation of the end-effector is given in the normal direction of the plane.     

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.     

Kinematic calibration of modular reconfigurable robots using product-of-exponentials formula

A modular reconfigurable robot system is a collection of individual link and joint components that can be assembled into different robot geometries for specific task requirements. However, the machining tolerance and assembly errors at the module interconnections affect the positioning accuracy of the end-effector. This article describes a novel kinematic calibration algorithm for modular robots based on recursive forward dyad kinematics. The forward kinematic model derived from the Product-of-Exponentials formula is configuration independent. The error correction parameters are assumed to be in the relative initial positions of the dyads. Two calibration models, namely the six- and seven-parameter methods, are derived on the grounds of the linear superposition principle and differential transformation. An iterative least square algorithm is employed for the calibration solution. Two simulation examples of calibrating a three-module manipulator and a 4-DOF SCARA type manipulator are demonstrated. The result has shown that the average positioning accuracy of the end-effector increases two orders of magnitude after the calibration. © 1997 John Wiley & Sons, Inc.