Reliability-based approach to the inverse kinematics solution of robots using Elman's networks

The solution of inverse kinematics problem of redundant manipulators is a fundamental problem in robot control. The inverse kinematics problem in robotics is the determination of joint angles for a desired cartesian position of the end effector. For the solution of this problem, many traditional solutions such as geometric, iterative and algebraic are inadequate if the joint structure of the manipulator is more complex. Furthermore, many neural network approaches have been done to this problem. But the neural network-based solutions are not much reliable due to the error at the end of learning. Therefore, a reliability-based neural network inverse kinematics solution approach has been presented, and applied to a six-degrees of freedom (dof) robot manipulator in this paper. The structure of the proposed method is based on using three networks designed parallel to minimize the error of the whole system. Elman network, which has a profound impact on the learning capability and performance of the network, is chosen and designed according to the proposed solution method. At the end of parallel implementation, the results of each network are evaluated using direct kinematics equations to obtain the network with best result.     

An efficient method for inverse dynamics of manipulators based on the virtual work principle

The computational efficiency of inverse dynamics of a manipulator is important to the real-time control of the system. For serial manipulators, the recursive Newton-Euler method has been proven to be the most efficient. However, for more general manipulators, such as serial manipulators with closed kinematic loops or parallel manipulators, it must be modified accordingly and the resultant computational efficiency is degraded. This article presents a computationally efficient scheme based on the virtual work principle for inverse dynamics of general manipulators. The present method uses a forward recursive scheme to compute velocities and accelerations, the Newton-Euler equation to calculate inertia forces/torque, and the virtual work principle to formulate the dynamic equations of motion. This method is equally effective for serial and parallel manipulators. For serial manipulators, its computational efficiency is comparable to the recursive Newton-Euler method. For parallel manipulators or serial manipulators with closed kinematic loops, it is more efficient than the existing methods. As an example, the computations of inverse dynamics (including inverse kinematics) of a general Stewart platform require only 842 multiplications, 511 additions, and 12 square roots.     

Kinematic analysis of a novel 3-DOF actuation redundant parallel manipulator using artificial intelligence approach

Kinematic analysis is one of the key issues in the research domain of parallel kinematic manipulators. It includes inverse kinematics and forward kinematics. Contrary to a serial manipulator, the inverse kinematics of a parallel manipulator is usually simple and straightforward. However, forward kinematic mapping of a parallel manipulator involves highly coupled nonlinear equations. Therefore, it is more difficult to solve the forward kinematics problem of parallel robots. In this paper, a novel three degrees-of-freedom (DOFs) actuation redundant parallel manipulator is introduced. Different intelligent approaches, which include the Multilayer Perceptron (MLP) neural network, Radial Basis Functions (RBF) neural network, and Support Vector Machine (SVM), are applied to investigate the forward kinematic problem of the robot. Simulation is conducted and the accuracy of the models set up by the different methods is compared in detail. The advantages and the disadvantages of each method are analyzed. It is concluded that ν-SVM with a linear kernel function has the best performance to estimate the forward kinematic mapping of a parallel manipulator.     

A New Geometric Subproblem to Extend Solvability of Inverse Kinematics Based on Screw Theory for 6R Robot Manipulators

Geometric inverse kinematics procedures that divide the whole problem into several subproblems with known solutions, and make use of screw motion operators have been developed in the past for 6R robot manipulators. These geometric procedures are widely used because the solutions of the subproblems are geometrically meaningful and numerically stable. Nonetheless, the existing subproblems limit the types of 6R robot structural configurations for which the inverse kinematics can be solved. This work presents the solution of a novel geometric subproblem that solves the joint angles of a general anthropomorphic arm. Using this new subproblem, an inverse kinematics procedure is derived which is applicable to a wider range of 6R robot manipulators. The inverse kinematics of a closed curve were carried out, in both simulations and experiments, to validate computational cost and realizability of the proposed approach. Multiple 6R robot manipulators with different structural configurations were used to validate the generality of the method. The results are compared with those of other methods in the screw theory framework. The obtained results show that our approach is the most general and the most efficient.

     

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.     

Inverse kinematics of binary manipulators by using the continuous-variable-based optimization method

Hyper redundancy, high reliability, and high task repeatability are the main advantages of binary manipulators over conventional manipulators with continuous joints, especially when manipulators are operated under tough and complex work conditions. The precise and complex movement of a binary manipulator necessitates many modules. In this case, numerically efficient inverse kinematics algorithms for binary manipulators usually require impractically large memory size for the real-time calculation of the binary states of all joints. To overcome this limitation by developing a new inverse kinematics algorithm is the objective of this research. The key idea of the proposed method is to formulate the inverse kinematics problem of a binary manipulator as an optimization problem with real design variables, in which the real variables are forced to approach the permissible binary values corresponding to two discrete joint displacements. Using the proposed optimization method, the inverse kinematics of 3-D binary manipulators with many modules can be solved almost in real time (say, less than a second for up to 16 modules) without requiring a large memory size. Furthermore, some manipulation considerations, such as operation power minimization, can be easily incorporated into the proposed formulation. The effectiveness of the proposed method is verified through several numerical problems, including 3-D inverse kinematics problems.     

6R机器人实时逆运动学算法研究

提出一套解决各类6R机器人逆运动学问题的实时算法. 一般算法通过矢量计算和16阶矩阵分解得到一般6R机器人的最多16组逆运动学解. 封闭解法直接提取运动学等式求出关节变量的解析解. 组合算法将封闭解法或一般算法的结果作为初始值, 采用牛顿-拉夫森方法迭代出逆运动学精确解, 适用于所有接近满足封闭解条件或一般算法条件的6R机器人. 求解实验结果表明, 整套算法最大算法时间约为2.03 ms, 为任意几何结构的6R机器人应用于强实时系统提供了逆运动学解决方案.     

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。     

Optimal path planning of redundant free-floating revolute-jointed space manipulators with seven links

The path planning of free-floating manipulators is of great interest in space operations. The manipulators in the free-floating mode exhibit nonholonomic characteristics due to the nonintegrability of the angular momentum, which makes the problem complicated. This paper analyzes the path planning of redundant, free-floating space manipulators with revolute joints and 7 degrees of freedom. The primary task of manipulators is to move the manipulator arms so that the desired end-effector position and orientation can be achieved. The motion of the manipulators can produce an attitude disturbance of the base, which has an adverse impact on the spacecraft operation. Thus, it is necessary to minimize the base attitude disturbance in order to reduce the fuel consumption for attitude maintenance. Practically, the path planning of redundant free-floating manipulators with higher degrees of freedom (7 degrees of freedom in this paper) in three-dimensional space is more complicated than path planning with fewer degrees of freedom, including planar or fixed base cases. This paper provides a tractable planning method to solve this problem, which could avoid the pseudo inverse of the Jacobian matrix. The sine functions, whose arguments are the polynomial functions with unknown coefficients, are used to specify the joint paths. The PSODE algorithm (particle swarm optimization combined with differential evolution) is applied to optimize the unknown coefficients of the polynomials in order to achieve the desired end-effector position and orientation and simultaneously minimize the base attitude disturbance. The simulations demonstrate that this method could provide satisfactory smooth paths for redundant free-floating space manipulators.     

Parallel VLSI architectures for real-time kinematics of redundant robots

We describe new architectures for the efficient computation of redundant manipulator kinematics (direct and inverse). By calculating the core of the problem in hardware, we can make full use of the redundancy by implementing more complex self-motion algorithms. A key component of our architecture is the calculation in the VLSI hardware of the Singular Value Decomposition of the manipulator Jacobian. Recent advances in VLSI have allowed the mapping of complex algorithms to hardware using systolic arrays with advanced computer arithmetic algorithms, such as the coordinate rotation (CORDIC) algorithms. We use CORDIC arithmetic in the novel design of our special-purpose VLSI array, which is used in computation of the Direct Kinematics Solution (DKS), the manipulator Jacobian, as well as the Jacobian Pseudoinverse. Application-specific (subtask-dependent) portions of the inverse kinematics are handled in parallel by a DSP processor which interfaces with the custom hardware and the host machine. The architecture and algorithm development is valid for general redundant manipulators and a wide range of processors currently available and under development commercially.     

Extended Jacobian inverse kinematics algorithms for mobile manipulators

We consider the inverse kinematic problem for mobile manipulators consisting of a nonholonomic mobile platform and a holonomic manipulator on board the platform. The kinematics of a mobile manipulator are represented by a driftless control system with outputs together with the associated variational control system. The output reachability map of the driftless control system determines the instantaneous kinematics, while the output reachability map of the variational system plays the role of the analytic Jacobian of the mobile manipulator. Relying on a formal analogy between the kinematics of stationary and mobile manipulators we exploit the extended Jacobian construction in order to design a collection of extended Jacobian inverse kinematics algorithms for mobile manipulators. It has been proved mathematically and confirmed in computer simulations that these algorithms are capable of efficiently solving the inverse kinematic problem. Moreover, a choice of the Jacobian extension may lay down some guidelines for the platform‐manipulator motion coordination. © 2002 Wiley Periodicals, Inc.     

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.     

Estimation model for kinematic calibration of manipulators with a parallel structure

This article provides an estimation model for calibrating the kinematics of manipulators with a parallel geometrical structure. Parameter estimation for serial link manipulators is well developed, but fail for most structures with parallel actuators, because the forward kinematics is usually not analytically available for these. We extend parameter estimation to such parallel structures by developing an estimation method where errors in kinematical parameters are linearly related to errors in the tool pose, expressed through the inverse kinematics, which is usually well known. The method is based on the work done to calibrate the MultiCraft robot. This robot has five linear actuators built in parallel around a passive serial arm, thus making up a two-layered parallel-serial manipulator, and the unique MultiCraft construction is reviewed. Due to the passive serial arm, for this robot conventional serial calibration must be combined with estimation of the parameters in the parallel actuator structure. The developed kinematic calibration method is verified through simulations with realistic data and real robot kinematics, taking the MultiCraft manipulator as the case. © 1994 John Wiley & Sons, Inc.     

Hybrid adaptive control laws solving a path following problem for non-holonomic mobile manipulators

In this paper a general solution to the path following problem for mobile manipulators with non-holonomic mobile platform has been presented. New proposed control algorithms — for mobile manipulators with fully known dynamics or with parametric uncertainty in the dynamics — take into considerations the kinematics as well as the dynamics of the non-holonomic mobile manipulator. The convergence of the control algorithms is proved using the LaSalle's invariance principle.     

Endogenous configuration space approach to mobile manipulators: A derivation and performance assessment of Jacobian inverse kinematics algorithms

By a mobile manipulator we mean a robotic system composed of a non-holonomic mobile platform and a holonomic manipulator fixed to the platform. A taskspace of the mobile manipulator includes positions and orientations of its end effector relative to an inertial coordinate frame. The kinematics of a mobile manipulator are represented by a driftless control system with outputs. Admissible control functions of the platform along with joint positions of the manipulator constitute the endogenous configuration space. Endogenous configurations have a meaning of controls. A map from the endogenous configuration space into the taskspace is referred to as the instantaneous kinematics of the mobile manipulator. Within this framework, the inverse kinematic problem for a mobile manipulator amounts to defining an endogenous configuration that drives the end effector to a desirable position and orientation in the taskspace. Exploiting the analogy between stationary and mobile manipulators we present in the paper a collection of regular and singular Jacobian inverse kinematics algorithms. Their performance is evaluated on the basis of intense computer simulations.     

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 new inverse kinematics algorithm for binary manipulators with many actuators

In this paper we present a new, and extremely fast, algorithm for the inverse kinematics of discretely actuated manipulator arms with many degrees of freedom. Our only assumption is that the arm is macroscopically serial in structure, meaning that the overall structure is a serial cascade of units with each unit having either a serial or parallel kinematic structure. Our algorithm builds on previous works in which the authors and coworkers have used the workspace density function in a breadthfirst search for solving the inverse kinematics problem. The novelty of the method presented here is that only the 'mean' of this workspace density function is used. Hence the requirement of storing a sampled version of the workspace density function (which is a function on a six-dimensional space in the case of a spatial manipulator) is circumvented. We illustrate the technique with both planar revolute and variable-geometry-truss manipulators, and briefly describe a new manipulator design for which this algorithm is applicable.     

Analysis of duality-based interconnected kinematics of planar serial and parallel manipulators using screw theory

In this paper, a method has been proposed to analyze the planar architectures of serial and parallel manipulators, based on the duality associated with their interconnected kinematics. The interconnected kinematics states that model of one architecture can be derived from the kinematic model of the other, using screw theory approach. The performance of the initial and the derived manipulators was evaluated with three criteria: isotropy, maximum force transmission ratio and local transmission index. Without loss of generality, the serial manipulator derived from parallel has better isotropy, while the parallel manipulator derived from serial can be designed to have better force and power transmission.

     

Solving the forward kinematics of parallel manipulators with a genetic algorithm

A floating point genetic algorithm is proposed to solve the forward kinematic problem for parallel manipulators. This method, adapted from studies in the biological sciences, allows the use of inverse kinematic solutions to solve forward kinematics as an optimization problem. The method is applied to two 3-degree-of-freedom planar parallel manipulators and to a 3-degree-of-freedom spherical manipulator. The method converges to a solution within a broader search domain compared to a Newton-Raphson scheme. © 1996 John Wiley & Sons, Inc.     

A study of neural network based inverse kinematics solution for a three-joint robot

A neural network based inverse kinematics solution of a robotic manipulator is presented in this paper. Inverse kinematics problem is generally more complex for robotic manipulators. Many traditional solutions such as geometric, iterative and algebraic are inadequate if the joint structure of the manipulator is more complex. In this study, a three-joint robotic manipulator simulation software, developed in our previous studies, is used. Firstly, we have generated many initial and final points in the work volume of the robotic manipulator by using cubic trajectory planning. Then, all of the angles according to the real-world coordinates (x, y, z) are recorded in a file named as training set of neural network. Lastly, we have used a designed neural network to solve the inverse kinematics problem. The designed neural network has given the correct angles according to the given (x, y, z) cartesian coordinates. The online working feature of neural network makes it very successful and popular in this solution.