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.     

Collision-free and smooth joint motion planning for six-axis industrial robots by redundancy optimization

Planning collision-free and smooth joint motion is crucial in robotic applications, such as welding, milling, and laser cutting. Kinematic redundancy exists when a six-axis industrial robot performs five-dimensional tasks, and there are infinite joint configurations for a six-axis industrial robot to realize a cutter location data of the tool path. The robot joint motion can be optimized by taking advantage of the kinematic redundancy, and the collision-free joint motion with minimum joint movement is determined as the optimal. However, most existing redundancy optimization methods do not fully exploit the redundancy of the six-axis industrial robots when they conduct five-dimensional tasks. In this paper, we present an optimization method to solve the problem of inverse kinematics for a six-axis industrial robot to synthesize the joint motion that follows a given tool path, while achieving smoothness and collision-free manipulation. B-spline is applied for the joint configuration interpolation, and the sum of the squares of the first, second, and third derivatives of the B-spline curves are adopted as the smoothness indicators. Besides, the oriented bounding boxes are adopted to simplify the shape of the robot joints, robot links, spindle unit, and fixtures to facilitate collision detections. Dijkstra's shortest path technique and Differential Evolution algorithm are combined to find the optimal joint motion efficiently and avoid getting into a local optimal solution. The proposed algorithm is validated by simulations on two six-axis industrial robots conducting five-axis flank milling tasks respectively.     

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.     

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.     

Motion in human and machine: A virtual fatigue approach

Achieving human-like behavior of a robot is a key issue of the paper. Redundancy in the inverse kinematics problem is resolved using a biological analogue. It is shown that by means of "virtual fatigue" functions, it is possible to generate robot movements similar to movements of a human arm subject to muscle fatigue. Analytic method enabling control of robot motions in a human-like fashion is described. An example of an anthropomorphic robot arm performing a screw-driving task illustrates the method.     

改进末端跟随运动的超冗余蛇形臂机器人运动学逆解

针对超冗余蛇形臂机器人运动学逆解中计算量大、超关节极限和位形偏移量大的问题,提出了一种改进末端跟随运动的逆解算法．在末端跟随法中引入蛇形臂弯曲角度的约束,调整关节位置的更新方式,使关节在蛇形臂轴线上运动．通过依次更新关节的空间位置,将超冗余多节蛇形臂的运动学逆解转化为2自由度单节蛇形臂的运动学逆解．仿真分析了蛇形臂机器人在基座移动和基座固定条件下的轨迹跟踪效果,对比了同一目标位置下不同方法的性能．结果表明,改进后的算法能保证蛇形臂的弯曲角度不超过给定范围,关节的运动量从末端到基座依次减小,机器人的运动更协调;与基于雅可比矩阵的数值法和现有启发式方法相比,该方法运算量降低,机器人整体位形偏移量减小,能用于蛇形臂机器人的实时控制．     

用于机器人逆运动学分析的几何法及应用

本文采用几何法来分析机器人逆运动学问题,将常见的工业机器人机构分为两级来考虑,避免了常用的雅可比逆阵求解机器人逆运动学问题的复杂性.利用文中所述的方法,通过一个喷漆机器人运动学建模说明了采用此方法的优越性.     

Inverse Kinematics Based Human Mimicking System using Skeletal Tracking Technology

Humanoid robots needs to have human-like motions and appearance in order to be well-accepted by humans. Mimicking is a fast and user-friendly way to teach them human-like motions. However, direct assignment of observed human motions to robot’s joints is not possible due to their physical differences. This paper presents a real-time inverse kinematics based human mimicking system to map human upper limbs motions to robot’s joints safely and smoothly. It considers both main definitions of motion similarity, between end-effector motions and between angular configurations. Microsoft Kinect sensor is used for natural perceiving of human motions. Additional constraints are proposed and solved in the projected null space of the Jacobian matrix. They consider not only the workspace and the valid motion ranges of the robot’s joints to avoid self-collisions, but also the similarity between the end-effector motions and the angular configurations to bring highly human-like motions to the robot. Performance of the proposed human mimicking system is quantitatively and qualitatively assessed and compared with the state-of-the-art methods in a human-robot interaction task using Nao humanoid robot. The results confirm applicability and ability of the proposed human mimicking system to properly mimic various human motions.     

Control of biomimetic robots based on analysis of human arm trajectories in 3D movements

In this study, a biomimetic robot arm with joint redundancy movable in a three-dimensional space is taken into consideration. The basic trajectories for controlling all joints are formulated under the minimum angular jerk criterion. Then, a time adjustment of the joint motion of the elbow relative to the shoulder is provided for representing specific properties of joint angular trajectories during a movement. Here, a systematical scheme for formulating the human-like trajectory has been developed by use of a direct kinematics. As the angular trajectories of all joints can be formulated in the proposed manner, the hand trajectory can be uniquely produced once the initial and final postures of the arm and a movement duration are given. The trajectories under the proposed scheme are produced by utilizing the same movement conditions observed by experiments. Then, performance for reproducing human-like trajectories has been evaluated under the comparative analysis between the observed and the produced trajectories.     

V01弧焊机器人运动学反解及臂形标志的确定

为了对Ｖ０１弧焊机器人深层次的开发，需要首先剖析其运动学模型，求解的反臂形问题。本文利用几何解法，针对Ｖ０１弧焊机器人建立了相应的逆运动学算法，解决了求解臂形标志问题，从而为Ｖ０１弧焊机器人的离线编程打上了基础。     

Non-linear phase different control for precise output force of bi-articularly actuated manipulators

Bi-articular actuators – actuator spanning two joints – play fundamental role in robot arms designed under the human musculoskeletal actuation paradigm. Unlike kinematic redundancy, actuator redundancy resulting from bi-articular actuation brings advantages such as increasing stability, reducing link's inertia, and decreasing non-linearity of the end-effector force with respect to the force direction. The traditional phase different control (PDC) resolves actuator redundancy on the basis of a linearized model derived from measured human muscle activity. Such linear model produces a non-zero error in calculation between a desired output force and necessary inputs. In this paper, the non-linear phase different control (NLPDC) is proposed to resolve actuator redundancy with no error. The maximum end-effector force of BiWi, bi-articularly actuated, and wire-driven arm, is measured using both PDC and NLPDC. When the robot arm moves towards singular configurations, the measured error in output force remains within the modeling error if using NLPDC, while such error increases significantly for PDC. Furthermore, unlike PDC, the proposed NLPDC allows design of joint stiffness and torque independently, reduction of necessary total muscle input force, and precise calculation of maximum output force.     

Numerical inverse kinematics for modular reconfigurable robots

The inverse kinematics solutions of a reconfigurable robot system built upon a collection of standardized components is difficult to obtain because of its varying configurations. This article addresses the formulation of a generic numerical inverse kinematics model and automatic generation of the model for arbitrary robot geometry including serial and tree‐typed geometries. Both revolute and prismatic types of joints are considered. The inverse kinematics is obtained through the differential kinematics equations based on the product‐of‐exponential (POE) formulas. The Newton–Raphson iteration method is employed for solution. The automated model generation is accomplished by using the kinematic graph representation of a modular robot assembly configuration and the related accessibility matrix and path matrix. Examples of the inverse kinematics solutions for different types of modular robots are given to demonstrate the applicability and effectiveness of the proposed algorithm. ©1999 John Wiley & Sons, Inc.     

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.     

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.     

Inverse kinematics of spherical wrist robot arms: Analysis and simulation

The spherical wrist robot arm is the most common type of industrial robot. This paper presents an efficient analytical computation procedure of its inverse kinematics. It is based on the decomposition of the inverse kinematic problem to two less complex problems; one concerns the robot arm basic structure and the other concerns its hand. The proposed computation procedure is used to obtain the inverse kinematic position models of two robot arms: one contains only revolute joints and the other contains both revolute and prismatic joints. The 1st and 2nd time derivatives of the obtained models give more accurate inverse kinematic velocity and acceleration models than numerical differentiation. These models are verified by simulation for two different trajectories. The obtained results demonstrate the effect of the proposed procedure on reducing the necessary computation time compared to other computation techniques.     

An active hybrid parallel robot for minimally invasive surgery

During the last years, there has been an increase in research in the field of medical robots. This trend motivated the development of a new robotics field called “robotic-assisted minimally invasive surgery”. The paper presents the kinematic and dynamic behavior of a parallel hybrid surgical robot PARASURG-9M. The robot consists of two subsystems: a surgical robotic arm, PARASURG 5M with five motors, and an active robotized surgical instrument PARASIM with four motors. The methodology for the robot kinematics is presented and the algorithm for robot workspace generation is described. PARASURG-9M inverse dynamic simulation is performed using MSC Adams and finally some numerical and simulation results of the developed experimental model with its system control are also described.     

Optimal robot placement with consideration of redundancy problem for wrist-partitioned 6R articulated robots

Rapid set-up of robotic system is critical for realising the high-mix low-volume applications. This paper presents an efficient method to determine the optimal robot base placement for executing required end-effector trajectories while dealing with redundancy problem for wrist-partitioned 6 R articulated robots. The main feature of the method includes the integration of two multi-objectives optimization loops that involve parameterized inverse kinematics of the robot to find the proper robot configurations. Firstly, an optimization scheme is introduced in consideration of all the robot and operational constraints including reachability, singularity avoidance, and collision avoidance. Then, a redundancy resolution scheme is proposed based on a modified particle swarm optimization (MPSO) for the considered target point. Consequently, the optimal robot base placement is obtained via another optimization loop which includes all robot trajectories for the application. The method was applied in a complex robotic welding application. For a set of desired welding torch trajectories on the workpiece, the optimal robot base placement is computed within a few minutes.     

Fast and robust numerical method for inverse kinematics with prioritized multiple targets for redundant robots

In this paper, a new numerical method for inverse kinematics with prioritized multiple targets is proposed. The proposed method is constructed based on the virtual spring model and joint-based damping control. The targets are prioritized by adjusting the effect of the virtual springs. The proposed method has the following three features. First, it does not require complex calculations such as a Jacobian matrix projection into the null space. Second, it can solve prioritized inverse kinematics problems in the position level without integrating the joint velocity. Third, it is robust to parameter variations and singular configurations. The second feature is motivated by the background that most industrial robots in factories are used as position-controlled robots. Simulation experiments using a 9-DOF redundant robot show that the proposed method is faster and more robust than the conventional method. The proposed method is expected to be useful for helping to avoid collisions between links and obstacles using the redundancy.