面向冗余机器人实时控制的逆运动学求解有效方法

针对7自由度冗余机器人实时运动控制,对机器人逆运动学提出了一种新的求解方法.采用位姿分解方式,使7自由度冗余机器人逆运动学简化为4自由度位置逆运动学求解.在梯度投影法得到位置优化解的基础上,利用机器人封闭解公式求得一组优化解.通过对7自由度机器人仿真分析,表明了该方法的有效性.     

A method to learn the inverse kinematics of multi-link robots by evolving neuro-controllers

A general method to learn the inverse kinematic of multi-link robots by means of neuro-controllers is presented. We can find analytical solutions for the most used and well-known robots in the literature. However, these solutions are specific to a particular robot configuration and are not generally applicable to other robot morphologies. The proposed method is general in the sense that it is independent of the robot morphology. The method is based on the evolutionary computation paradigm and works obtaining incrementally better neuro-controllers. Furthermore, the proposed method solves some specific issues in robotic neuro-controller learning: it avoids any neural network learning algorithm which relies on the classical supervised input-target learning scheme and hence it lets to obtain neuro-controllers without providing targets. It can converge beyond local optimal solutions, which is one of the main drawbacks of some neural network training algorithms based on gradient descent when applied to highly redundant robot morphologies. Furthermore, using learning algorithms such as the neuro-evolution of augmenting topologies it is also possible to learn the neural network topology which is a common source of empirical testing in neuro-controllers design. Finally, experimental results are provided when applying the method to two multi-link robot learning tasks and a comparison between structural and parametric evolutionary strategies on neuro-controllers is shown.     

Adaptive inverse dynamics control of robots with uncertain kinematics and dynamics

It has been about two decades since the first globally convergent adaptive tracking controller was derived for robots with dynamic uncertainties. However, not until recently has the problem of concurrent adaptation to both the kinematic and dynamic uncertainties found its solution. This adaptive controller belongs to passivity-based control. Though passivity-based controllers have many attractive properties, in general, they are not able to guarantee the uniform performance of the robot over the entire workspace. Even in the ideal case of perfect knowledge of the manipulator parameters, the closed-loop system remains nonlinear and coupled. Thus the closed-loop tracking performance is difficult to quantify, while the inverse dynamics controllers can overcome these deficiencies. Therefore, in this work, we will develop a new adaptive Jacobian tracking controller based on the inverse manipulator dynamics. Using the Lyapunov approach, we have proved that the end-effector motion tracking errors converge asymptotically to zero. Simulation results are presented to show the performance of the proposed controller.     

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.     

A geometric approach for inverse kinematics of a 4-link redundant In-Vivo robot for biopsy

The presence of a large number of degrees of freedom enables redundant manipulators to have some desirable features like reaching difficult areas and avoiding obstacles. These manipulators in the form of In-Vivo robots will enhance the dexterity and capacity of a surgeon to explore the internal cavity when inserted in the existing tool channel of the endoscope to take a biopsy from the stomach. This paper presents a simple geometric approach, to solve the problem of multiple inverse kinematic solutions of redundant manipulators, to find a single optimum solution and to easily switch from one solution to another depending upon the path and the environment. A simulation model of this approach has been developed and experiments have been conducted on the In-Vivo robot to judge its effectiveness.     

Two optimization algorithms for solving robotics inverse kinematics with redundancy

The kinematic redundancy in a robot leads to an infinite number of solutions for inverse kinematics, which implies the possibility to select a "best" solution according to an optimization criterion. In this paper, two optimization objective functions are proposed, aiming at either minimizing extra degrees of freedom (DOFs) or minimizing the total potential energy of a multilink redundant robot. Physical constraints of either equality or inequality types are taken into consideration in the objective functions. Since the closed-form solutions do not exist in general for highly nonlinear and constrained optimization problems, we adopt and develop two numerical methods, which are verified to be effective and precise in solving the two optimization problems associated with the redundant inverse kinematics. We first verify that the well established trajectory following method can precisely solve the two optimization problems, but is computation intensive. To reduce the computation time, a sequential approach that combines the sequential quadratic programming and iterative Newton-Raphson algorithm is developed. A 4-DOF Fujitsu Hoap-1 humanoid robot arm is used as a prototype to validate the effectiveness of the proposed optimization solutions.     

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.     

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.     

Kinematic control of redundant robots with guaranteed joint limit avoidance

A novel approach for addressing the inverse differential kinematics of redundant manipulators in the presence of hard joint position constraints is presented. A prescribed performance signal for joint limit avoidance guarantees is proposed that can be utilized with both planned and on-line generated trajectories. In the first case, it is a null space velocity for the primary task velocity mapping while in the second case, it modifies the generated reference by acting on the whole velocity space producing a feasible path to the target. Experimental results utilizing a 7DOF KUKA LWR4+ arm demonstrate the performance of the proposed kinematic controller.     

Analytical formula for the pseudoinverse and its application for singular path tracking with a class of redundant robotic limbs

This work introduces a novel formula for calculating the right pseudoinverse, proposed for a class of kinematically redundant robotic limbs with one degree of redundancy. The formula is derived from the Singularity-Consistent method and is expressed as a sum of scalable vector fields parameterized by the desired end link twist. Pseudoinverse properties are ensured by assigning proper vector field intensities. The formula is applied to the IK problem, whereby the end link tracks a degenerate singular path, i.e. a nontangential path that penetrates the workspace boundary, and thus resulting in an unavoidable kinematic singularity. Through this method, the instability of the conventional pseudoinverse solution and the stationary point problem obtained when the solution is stripped from the ill-conditioned denominator is avoided. In addition, the appearance of the ‘inner obstacle’ algorithmic singularity problem known from a previous work can be circumvented. The performance of the method is verified via numerical simulations with an S-R-S-type structure and the Barrett WAM.     

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.     

Neural networks and the inverse kinematics problem

Inverse kinematics is a fundamental problem in robotics. Past solutions for this problem have been realized through the use of various algebraic or algorithmic procedures. In this paper the use of feedforward neural networks to solve the inverse kinematics problem is examined for three different cases. A closed kinematic linkage is used for mapping input joint angles to output joint angles. A three-degree-of-freedom manipulator in 3D space is used to test mappings from both cartesian and spherical coordinates to manipulator joint coordinates. A majority of the results have average errors which fall below 1% of the robot workspace. The accuracy indicates that neural networks are an alternate method for performing the inverse kinematics estimation, thus introducing the fault-tolerant and high-speed advantages of neural networks to the inverse kinematics problem.This paper also shows the use of a new technique which reduces neural network mapping errors with the use of error compensation networks. The results of the work are put in perspective with a survey of current applications of neural networks in robotics.     

A projected back-tracking line-search for constrained interactive inverse kinematics

Inverse kinematics is the problem of manipulating the pose of an articulated figure in order to achieve a desired goal disregarding inertia and forces. One can approach the problem as a non-linear optimization problem or as non-linear equation solving. The former approach is superior in its generality and ability to generate realistic poses, whereas the latter approach is recognized for its low iteration cost. Therefore, many prefer equation solving over optimization for interactive applications. In this paper we present a projected-gradient method for solving an inverse kinematics problem interactively, which exhibit good performance and precision. The method is compared to existing work in terms of visual quality and accuracy. Our method shows good convergence properties and deals with joint constraints in a simple and elegant manner. Our main contribution lies in an explicit incorporation of joint limits in an interactive solver. This makes it possible to compute the pose in each frame without the discontinuities exhibited by existing key frame animation techniques.     

Contribution to the kinematics and dynamics of redundant robots via distributed positioning

The concept of distributed positioning is based on the separation of the required end-effector motion into two components according to a criterion. The external-to-internal transformation of the motion is made in such a way that some of the joints become responsible for the first and others for the second component. Thus, the redundancy could be compensated and the unique solution of the inverse kinematics achieved. If the separation is made according to the acceleration criterion, then the ‘smooth’ and the ‘fast’ components of the end-effector motion are obtained. The paper shows that this concept results in the improvement of robot dynamic capabilities.This work was supported by the Science Fund of the Republic of Serbia (project: Robotics).     

An analysis of the inverse kinematics for a 5-DOF manipulator

This paper proposes an analytical solution for a 5-DOF manipulator to follow a given trajectory while keeping the orientation of one axis in the end-effector frame. The forward kinematics and inverse kinematics for a 5-DOF manipulator are analyzed systemically. The singular problem is discussed after the forward kinematics is provided. For any given reachable position and orientation of the end-effector, the derived inverse kinematics will provide an accurate solution. In other words, there exists no singular problem for the 5-DOF manipulator, which has wide application areas such as welding, spraying, and painting. Experiment results verify the effectiveness of the methods developed in this paper.     

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.     

实时解析法在NAO模型运动学求逆解中的应用

为了提高RoboCup3D仿真平台中球员在运动过程中的精确性和稳定性,提出一种针对仿人机器人NAO模型的运动学实时求逆解方法。首先,分析了NAO模型的下肢拓扑结构,并且建立了其前向运动学模型;然后,通过实时的逆运动学解析法推导出机器人下肢关节各个关节角的求解方程;最后,通过编码实现该算法。实验结果验证了该方法的求解数值稳定性和在线实施的可行性,提升了RoboCup3D仿真球队的整体竞技水平。     

6R关节型机器人运动学建模

为满足新开发的多机器人实验系统编程需要,研究了6R机器人运动学逆解问题.推导了代数逆解结果,并研究了将其用于实际控制系统时,逆解的漏解、增根和多解问题.与传统方法比较,采用了便于程序模块化的坐标系设置方式,在需要经常更换作业工具的多机器人系统中更为适用.推导过程只需2次矩阵逆乘,步骤简单.基于VC++和OpenGL技术编制了系统程序,检验了方法的有效性.以其中一个位姿为例,对比几何方法得出的结果,验证了算法的正确性.研究的结果适用于MOTOMAN-UP6和PUMA560等相似构型的所有机器人.     

Evaluation of on-line analytic and numeric inverse kinematics approaches driven by partial vision input

Despite its central role in the constitution of a truly enactive interface, 3D interaction through human full body movement has been hindered by a number of technological and algorithmic factors. Let us mention the cumbersome magnetic equipments, or the underdetermined data set provided by less invasive video-based approaches. In the present paper, we explore the recovery of the full body posture of a standing subject in front of a stereo camera system. The 3D position of the hands, the head and the center of the trunk segment are extracted in real-time and provided to the body posture recovery algorithmic layer. We focus on the comparison between numeric and analytic inverse kinematics approaches in terms of performances and overall quality of the reconstructed body posture. Algorithmic issues arise from the very partial and noisy input and the singularity of the human standing posture. Despite stability concerns, results confirm the pertinence of this approach in this demanding context.