Real-time inverse kinematics techniques for anthropomorphic limbs

In this paper we develop a set of inverse kinematics algorithms suitable for an anthropomorphic arm or leg. We use a combination of analytical and numerical methods to solve generalized inverse kinematics problems including position, orientation, and aiming constraints. Our combination of analytical and numerical methods results in faster and more reliable algorithms than conventional inverse Jacobian and optimization-based techniques. Additionally, unlike conventional numerical algorithms, our methods allow the user to interactively explore all possible solutions using an intuitive set of parameters that define the redundancy of the system.     

Task-directed inverse kinematics for redundant manipulators

This paper presents kinematic algorithms for resolved-rate based inverse kinematics of redundant manipulators. Efficient and robust Jacobian and weighted damped least squares algorithms are given which provide a method that allows full utilization of the redundancy to best achieve task requirements. A nominal set of task space variables is suggested and procedures for modifying this specification or their relative priorities due to changing task requirements or events are discussed. Examples are shown using a simulation of the seven degree-of-freeom Robotics Research manipulator. These simulations demonstrate the singularity robustness of the algorithms and the ability to smoothly transition between task parameterizations and relative priorities.     

Human-like redundancy resolution: An integrated inverse kinematics scheme for anthropomorphic manipulators with radial elbow offset

As a mimic of the human arm structure, anthropomorphic manipulators with radial elbow offset (AMREO) are often deployed on humanoid service robots. However, the unique offset leads to difficulties in solving the analytical inverse kinematics (IK), which poses a challenge for further anthropomorphic control. This paper presents an integrated scheme for solving the path-wise IK problem of a 7-DoF AMREO in the position domain. Unlike other approaches, special attention is paid to the naturalness of the arm configuration, with the aim of making AMREO exhibit human-like behavior in human-centered environments. First, an analytical IK solution of AMREO for a single end-effector pose is derived based on the arm angle parameterization. Then, inspired by the habitual arm configurations in human reaching movements, the natural arm configuration mapped to wrist position is proposed for AMREO. To learn the patterns implied therein, a LSTM-based natural arm angle prediction network (NAPN) is designed and trained based on a human demonstration dataset. Finally, a redundancy resolution framework embedded with NAPN is built to generate smooth and natural joint configurations in the path-wise IK tasks. Comparative experiments show that the proposed analytical IK algorithm has better computational efficiency and precision than conventional methods, and can give complete results for one IK call within 4 μs. In addition, continuous path tracking experiments on a real robot validate the effectiveness and anthropomorphism of the redundancy resolution scheme based on NAPN.     

General-purpose inverse kinematics transformations for robotic manipulators

Real-time robot control requires efficient inverse kinematics transformations to compute the temporal evolution of the joint coordinates from the motion of the end-effector. The development of a coherent, general-purpose framework, incorporating position, velocity and acceleration transformations, is the theme of this paper. In this framework, the computational requirements of a new inverse kinematic algorithm are delineated. The algorithm is applicable to serial (open-chain) manipulators with arbitrary axes of motion. Comparative evaluations of the computational cost of the algorithm demonstrate its efficacy and feasibility for real-time applications.     

Repeatability of inverse kinematics algorithms for mobile manipulators

We introduce and examine the property of repeatability of inverse kinematics algorithms for mobile manipulators. Similarly to stationary manipulators, repeatability of mobile manipulators is defined by requiring that a closed path in the task space should be transformed by the inverse kinematics algorithm into a closed path in the configuration space. In a simply connected, singularity-free region of the task space, a necessary and sufficient condition for repeatability is derived as the integrability condition of a distribution associated with the inverse kinematics algorithm.     

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.     

Overview of damped least-squares methods for inverse kinematics of robot manipulators

In this paper, we present a tutorial report of the literature on the damped-least squares method which has been used for computing velocity inverse kinematics of robotic manipulators. This is a local optimization method that can prevent infeasible joint velocities near singular configurations by using a damping factor to control the norm of the joint velocity vector. However, the exactness of the inverse kinematic solution has to be sacrificed in order to achieve feasibility.The damping factor is an important parameter in this technique since it determines the trade-off between the accuracy and feasibility of the inverse kinematic solution. Various methods that have been proposed to compute an appropriate damping factor are described.Redundant manipulators, possessing extra degrees of freedom, afford more choice of inverse kinematic solutions than do non-redundant ones. The damped least-squares method has been used in conjunction with redundancy resolution schemes to compute feasible joint velocities for redundant arms while performing an additional subtask. We outline the different techniques that have been proposed to achieve this objective. In addition, we introduce an iterative method to compute the optimal damping factor for one of the redundancy resolution techniques.     

A strictly convergent real-time solution for inverse kinematics of robot manipulators

Inverse Kinematics has been recognized as an important problem in robotics applications. A robot independent solution can only be obtained through numerical methods, but most solutions which use this approach have problems with convergence especially near singularity points. This article develops a strictly convergent algorithm and a special-purpose Inverse Kinematics Processor (IKP) to obtain the solution in real time. While the algorithm is based on open-loop integration of rates, the absolute position deviation is used as a criterion to control the iteration, and a feedback mechanism has been especially designed to eliminate problems with long-term drift or with initial errors in the solution. The architecture of the IKP is based on a high-speed floating-point arithmetic processor and is designed to perform the common matrix-vector operations efficiently with a minimum processor cycle time. The algorithm has been simulated on the proposed architecture, and the results show its robustness and real-time capability. For a six degree-of-freedom robot manipulator (for which no closed-form solution exist), the Inverse Kinematics solution may be obtained at an approximate 2 khz rate with an error which is within standard repeatability limits.     

A solution to the inverse kinematics of redundant manipulators

A solution to the inverse kinematics is a set of joint coordinates which correspond to a given set of task space coordinates (position and orientation of end effector). For the class of kinematically redundant robots, the solution is generically nonunique such that special methods are required for obtaining a solution. The method addressed in the paper, introduced earlier and termed “generalized inverse,” is based on a certain partitioning of the Jacobian functional corresponding to a nonlinear relationship of the inverse kinematics type. The article presents a new algorithm for solving the inverse kinematics using the method of generalized inverse based on a modified Newton-Raphson iterative technique. The new algorithm is efficient, converges rapidly, and completely generalizes the solution of the inverse kinematics problem for redundant robots. The method is illustrated by numerical examples.     

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.     

冗余机械臂逆运动学求解方法研究进展

随着科学技术的发展,冗余机械臂凭借其多自由度的特性获得学者的广泛关注.其中包括执行指定任务时,需要将任务路径转换为关节空间轨迹,进行逆运动学求解,求取非线性函数的连续逆映射.该求解过程尤为重要且非常复杂,国内外学者对此开展了大量研究.这里将冗余机械臂逆运动学求解方法进行分类,归纳整理出各类求解方法,分别概述解析法、数值解法、智能算法以及对应子方法的基本原理、对比及研究现状.最后,指出逆运动学求解方法面临的核心问题以及发展趋势.     

An improved approach to the solution of inverse kinematics problems for robot manipulators

A structured artificial neural-network (ANN) approach has been proposed here to control the motion of a robot manipulator. Many neural-network models use threshold units with sigmoid transfer functions and gradient descent-type learning rules. The learning equations used are those of the backpropagation algorithm. In this work, the solution of the kinematics of a six-degrees-of-freedom robot manipulator is implemented by using ANN. Work has been undertaken to find the best ANN configurations for this problem. Both the placement and orientation angles of a robot manipulator are used to fin the inverse kinematics solutions.     

基于模糊神经网络的机器人逆运动学问题

针对机器人逆运动学问题，本文指出了基于模糊神经网络（FNN，Fuzzy Neural Network）的解决方案，阐述了基本设计思想和具体算法过程，给出了二自由度刚性机器人的仿真结果，以表明该方案的有效性和可行性。     

Closed‐loop inverse kinematics algorithm for constrained flexible manipulators under gravity

This work deals with the inverse kinematics problem for a flexible robot manipulator under gravity in contact with a stiff surface. This problem consists of finding the joint and deflection variables for a given tip position and constraint force. The solution algorithm is based on the well‐known closed‐loop inverse kinematics (CLIK) scheme, using the Jacobian transpose, developed for rigid manipulators. The Jacobian employed in the algorithm is obtained by correcting the equivalent rigid manipulator Jacobian with two terms that account for the static deflections due to gravity and contact force, respectively. The algorithm is tested in a number of case studies on a planar two‐link arm. ©1999 John Wiley & Sons, Inc.     

A repeatable inverse kinematics algorithm with linear invariant subspaces for mobile manipulators.

On the basis of a geometric characterization of repeatability we present a repeatable extended Jacobian inverse kinematics algorithm for mobile manipulators. The algorithm's dynamics have linear invariant subspaces in the configuration space. A standard Ritz approximation of platform controls results in a band-limited version of this algorithm. Computer simulations involving an RTR manipulator mounted on a kinematic car-type mobile platform are used in order to illustrate repeatability and performance of the algorithm.     

A geometric method for determining joint rotations in the inverse kinematics of robotic manipulators

An inverse‐kinematics algorithm has been developed to evaluate the joint rotations of a robotic manipulator given the orientation of its hand link. The method mimics the way a person would determine the joint rotations by assembling the links comprising the robot mechanism and making adjustments in the joint displacements until the hand link is in the desired situation. An example is given where it is shown that the method is reasonably robust, can be applied to any design of robot, and is competitive with alternative highly‐mathematical, specific‐robot specialized, computational‐intensive schemes. ©2000 John Wiley & Sons, Inc.     

A neuro-simulated annealing approach to the inverse kinematics solution of redundant robotic manipulators

The neural-network-based inverse kinematics solution is one of the recent topics in the robotics because of the fact that many traditional inverse kinematics problem solutions such as geometric, iterative and algebraic are inadequate for redundant robots. However, since the neural networks work with an acceptable error, the error at the end of inverse kinematics learning should be minimized. In this study, simulated annealing (SA) algorithm was used together with the neural-network-based inverse kinematics problem solution robots to minimize the error at the end effector. The solution method is applied to Stanford and Puma 560 six-joint robot models to show the efficiency. The proposed algorithm combines the characteristics of neural network and an optimization technique to obtain the best solution for the critical robotic applications. Three Elman neural networks were trained using separate training sets and different parameters, since one of them can give better results than the others can. The best result is selected within three neural network results by computing the end effector error via direct kinematics equation of the robotic manipulator. The decimal part of the neural network result was improved up to 10 digits using simulated annealing algorithm. The obtained best solution is given to the simulated annealing algorithm to find the best-fitting 10 digits for the decimal part of the solution. The end effector error was reduced significantly.     

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.     

Computer generation of symbolic kinematics for robot manipulators

Computer generation of symbolic solutions for the direct and inverse robot kinematics is a desired capability not previously available to robotics engineers. In this article, we present a methodology for the design of a software system capable of solving the direct and inverse kinematics for n degree of freedom (dof) manipulators in symbolic form. The inputs to the system are the Denavit-Hartenberg parameters of the manipulator. The outputs of the system are the direct and inverse kinematics solutions in symbolic form. The system consists of a symbolic processor to perform matrix and algebraic manipulations and an expert system to solve the class of nonlinear equations involved in the solution of the inverse kinematics problem. The system can be used to study robot kinematics configurations whose inverse kinematics solutions are not known to exist a priori. Two examples are included to illustrate its capabilities. The first example provides explicit analytical solutions, previously believed nonexistent, for a 3 dof manipulator. A second example is included for a robot whose inverse kinematics solution requires intensive algebraic manipulations.