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.

     

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.     

A novel contour error compensator for 3‐PRPS platform

Using a mathematical model to represent the nonlinear characteristics in dynamics of robot manipulators is rather difficult. To reduce the Cartesian space contour error, this study presents a novel contour error compensator influenced by the parameter and unstructured uncertainties in robot manipulators. The proposed compensator is based on the strategy of a Cartesian space cross‐coupled control and the transform relations between Cartesian space and joint space. In addition, the joint space compensated control effort derives reducing the Cartesian space contour error. Consequently, the contour error can be reduced via the theoretical analysis. Moreover, a PC based, 3‐PRPS platform control system is constructed to closely examine the effects of the controller. Experiment results indicate that the controller can reduce the contour error as expected. Furthermore, the forward and the inverse kinematics are derived, along with the forward kinematics solved using the numerical method. The work space of the platform is also described in a three‐dimensional Cartesian space. © 2000 John Wiley & Sons, Inc.     

一种工业机器手的自适应阻抗控制方法

提出一种基于任务空间的直接自适应阻抗方法，它不要求辨识机器手动态模型结构和参数，不需要计算机器手的运动学逆变换，因此，避免了基于机器手模型线性参数辨识的控制方法的缺点。     

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.     

基于三步法的机械臂轨迹跟踪控制

考虑机械臂末端轨迹跟踪控制问题,以跟踪逆运动学求解出的末端期望轨迹对应的各关节期望角度为控制目标.设计了一种基于三步法的控制器,该控制器由类稳态控制、可变参考前馈控制和误差反馈控制3部分组成.证明了该控制器可以通过控制机械臂的各关节力矩实现各关节实际角度对期望角度的状态跟踪,进而使得末端轨迹渐近跟踪期望轨迹,并且跟踪误差是输入到状态稳定的.仿真表明基于三步法控制器的空间机械臂末端可以渐近跟踪期望轨迹,并且该算法可以克服系统的末端负载质量变化等不确定性的影响.     

A Neural Network Controller for Continuum Robots

Continuum or hyper-redundant robot manipulators can exhibit behavior similar to biological trunks, tentacles, or snakes. Unlike traditional rigid-link robot manipulators, continuum robot manipulators do not have rigid joints, hence these manipulators are extremely dexterous, compliant, and are capable of dynamic adaptive manipulation in unstructured environments. However, the development of high-performance control algorithms for these manipulators is quite a challenge, due to their unique design and the high degree of uncertainty in their dynamic models. In this paper, a controller for continuum robots, which utilizes a neural network feedforward component to compensate for dynamic uncertainties is presented. Experimental results using the OCTARM, which is a soft extensible continuum manipulator, are provided to illustrate that the addition of the neural network feedforward component to the controller provides improved performance.     

Kinematics and the implementation of an elephant's trunk manipulator and other continuum style robots

Traditionally, robot manipulators have been a simple arrangement of a small number of serially connected links and actuated joints. Though these manipulators prove to be very effective for many tasks, they are not without their limitations, due mainly to their lack of maneuverability or total degrees of freedom. Continuum style (i.e., continuous "back-bone") robots, on the other hand, exhibit a wide range of maneuverability, and can have a large number of degrees of freedom. The motion of continuum style robots is generated through the bending of the robot over a given section; unlike traditional robots where the motion occurs in discrete locations, i.e., joints. The motion of continuum manipulators is often compared to that of biological manipulators such as trunks and tentacles. These continuum style robots can achieve motions that could only be obtainable by a conventionally designed robot with many more degrees of freedom. In this paper we present a detailed formulation and explanation of a novel kinematic model for continuum style robots. The design, construction, and implementation of our continuum style robot called the elephant trunk manipulator is presented. Experimental results are then provided to verify the legitimacy of our model when applied to our physical manipulator. We also provide a set of obstacle avoidance experiments that help to exhibit the practical implementation of both our manipulator and our kinematic model.     

Learning Control of Robot Manipulators in Task Space

Two important properties of industrial tasks performed by robot manipulators, namely, periodicity (i.e., repetitive nature) of the task and the need for the task to be performed by the end‐effector, motivated this work. Not being able to utilize the robot manipulator dynamics due to uncertainties complicated the control design. In a seemingly novel departure from the existing works in the literature, the tracking problem is formulated in the task space and the control input torque is aimed to decrease the task space tracking error directly without making use of inverse kinematics at the position level. A repetitive learning controller is designed which “learns” the overall uncertainties in the robot manipulator dynamics. The stability of the closed‐loop system and asymptotic end‐effector tracking of a periodic desired trajectory are guaranteed via Lyapunov based analysis methods. Experiments performed on an in‐house developed robot manipulator are presented to illustrate the performance and viability of the proposed controller.     

Learning optimal trajectories for non-holonomic systems

Many advanced robotic systems are subject to non-holonomic constraints, e.g. wheeled mobile robots, space manipulators and multifingered robot hands. Steering these mechanisms between configurations in the presence of perturbations is a difficult problem. In fact, the divide et impera strategy (first plan a trajectory, then track it by feedback) has a fundamental drawback in this case: due to the peculiar control properties of non-holonomic systems, smooth feedback cannot provide tracking of the whole trajectory. As a result, it would be necessary to give up either accuracy in the final positioning or predictability of the actual motion. We pursue here a different approach which does not rely on a separation between planning and control. Based on the learning control paradigm, a robust steering scheme is devised for systems which can be put in chained form, a canonical structure for non-holonomic systems. By overparametrizing the control law, other performance goals can be met, typically expressed as cost functions to be minimized along the trajectory. As a case study, we consider the generation of robust optimal trajectories for a car-like mobile robot, with criteria such as total length, maximum steering angle, distance from workspace obstacles, or error with respect to an offline planned trajectory.     

An offset error compensation method for improving ANN accuracy when used for position control of precision machinery

Artificial Neural Networks (ANNs) have recently become the focus of considerable attention in many disciplines, including robot control, where they can be used as a general class of nonlinear models to solve highly nonlinear control problems. Feedforward neural networks have been widely applied for modelling and control purposes. One of the ANN applications in robot control is for the solution of the inverse kinematic problem, which is important in path planning of robot manipulators. This paper proposes an iterative approach and an offset error compensation method to improve the accuracy of the inverse kinematic solutions by using an ANN and a forward kinematic model of a robot. The offset error compensation method offers potential to generate accurately the inverse solution for a class of problems which have an easily obtained forward model and a complicated solution.Now Lecturing in Taiwan.     

面向非完全姿态约束问题的旋转矩阵群中的垂线理论

在很多机器人领域,有很多给定任务要求并不需要3维空间的完整姿态约束,而是只限定了目标姿态某一轴的方向．这类问题称为非完全姿态约束问题．针对该问题,定义了旋转矩阵群中测地线的垂足和垂线,并给出了其解析表达式．基于垂线理论,提出了沿垂线规划的点到点轨迹生成算法．最后通过仿真实验求解操作臂的轨迹规划问题,仿真以6自由度的PUMA 560为平台,并依次固定第6关节、第4关节得到5自由度和4自由度的操作臂．提出的算法不仅适用于具有功能冗余的6自由度操作臂,也可应用于不具有冗余特性的5自由度和4自由度操作臂．实验结果验证了提出的理论和算法在解决非完全姿态约束问题上的通用性．同时,该算法还能避免参数表示方法中的奇异性问题．     

空间机器人的建模及仿真

空间机器人在未来的太空探索中将代替宇航员从事空间作业，而空间机器人在计算机上的寞及仿真是设计及研制中的重要组成部分，此文详细讨论了空间机器人的建模方法，包括建立几何模型和运动学模型，文中第３节介绍了哈尔滨工业大学研制的空间机器人仿真系统的各组成部分及所完成的功能，并在第４节中给出了实验仿真结果，仿真结果表明该仿真系统具有可靠性，实时性。     

A Neural Network Adaptive Controller for End-effector Tracking of Redundant Robot Manipulators

In this paper we propose a neural network adaptive controller to achieve end-effector tracking of redundant robot manipulators. The controller is designed in Cartesian space to overcome the problem of motion planning which is closely related to the inverse kinematics problem. The unknown model of the system is approximated by a decomposed structure neural network. Each neural network approximates a separate element of the dynamical model. These approximations are used to derive an adaptive stable control law. The parameter adaptation algorithm is derived from the stability study of the closed loop system using Lyapunov approach with intrinsic properties of robot manipulators. Two control strategies are considered. First, the aim of the controller is to achieve good tracking of the end-effector regardless the robot configurations. Second, the controller is improved using augmented space strategy to ensure minimum displacements of the joint positions of the robot. Simulation examples are also presented to verify the effectiveness of the proposed approach.     

Realization of task-based designs involving DH parameters: a modular approach

Task-based designs—proven to be successful for constrained environments—may face challenges at prototype development phase. To assist in generalized design and development of task-based serial manipulators for cluttered environments, a parameters-based modular approach is proposed. First, a task-based design strategy for serial manipulators is exhibited, using all the robotic parameters (DH parameters) as variables. The flexibility in robotic parameters enhances the possibility of good designs even for highly cluttered workspaces, but the realization of the resulting complicated designs is challenging. This work is an attempt to develop modular manipulators in correspondence to the task-based designs. The DH parameters-based proposed link modules, with reconfigurable architecture, can be adjusted and assembled to acquire the serial manipulators with designed robotic parameters. To validate the concept, some standardized 3R-configurations have been modelled using the proposed link modules. Case studies are presented on task-based design of robotic manipulators, with six and eight degrees of freedom, for service applications in realistic environments. The selected case studies include the robot design processes for applications of cleaning solar panels, and for the maintenance of the nuclear plants.     

Robust adaptive control for robot manipulators

A composite adaptive control law for robot manipulators in task space, which uses both the tracking error and the prediction error to drive parameter estimation, is developed in this paper. It is shown that global stability and convergence can be achieved for the adaptive control algorithm in the ideal case, and furthermore that the algorithm can be easily modified by using parameter projection to achieve robustness with respect to a class of unmodelled dynamics. In addition, the algorithm has the advantage that no requirement is needed for the inverse of the jacobian matrix or for the bounded inverse of the estimated inertia matrix. A simulation example is provided for performance demonstration.     

A heterogeneous modular robotic design for fast response to a diversity of tasks

This paper describes a heterogeneous modular robot system design which attempts to give a quick solution to a diversity of tasks. The approach is based on the use of an inventory of three types of modules i.e., power and control module, joint module and specialized module. Each module type aims to balance versatility and functionality. Their design permits rapid and cost effective design and fabrication. They are interchangeable in different ways to form different robot or system configurations. Depending on the task, the operator decides what type of robot can provide the best performance within the mission. A spherical joint module is described and used to build different robots, hence, forward and inverse kinematics models are obtained. Finally, from the modules described in this work, several robot configurations such as robotic arms, leg-based robots and wheel-based robots are assembled to demonstrate the execution of manipulation and locomotion tasks.     

Robot trajectory planning using simulation

This paper presents a near-optimal trajectory-planning method for industrial robot manipulators. Trajectory planning is discussed considering robot dynamics, singular configurations and collision-free constraints. The problem is formulated as a non-linear mathematical programming model. Owing to the highly non-linear and non-convex constraints involved, a robust simulation-based method is introduced to solve this optimization problem heuristically. This simulation method was tested on a CRS-PLUS robot with a sphere obstacle in three-dimensional work space. Numerical analysis and computational results are presented.     

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.     

Customized computational robot dynamics

In 1983 the authors implemented the computer program Algebraic Robot Modeler (ARM) to generate symbolically complete closed-form and recursive dynamic robot models.^1–3 Then, in 1985, we incorporated in ARM heuristic rules for the systematic organization of dynamic robot models to reduce the computational requirements of customized forward and inverse dynamics calculations. We resolve the issue of numerical efficiency of customized closed-form and recursive forward and inverse dynamics algorithms for kinematically and dynamically structured manipulators. We find that ARM-generated customized closed-form algorithms are the most computationally efficient calculators of forward and inverse dynamics of three degree-of-freedom manipulators. For six DOF predominantly rotational manipulators, ARM-generated customized recursive algorithms are the most computationally efficient foward and inverse dynamics algorithms; inverse dynamics can be computed in less than one millisecond on commercially-available processors (in software, without special-purpose hardware). In our companion article,⁴ we compare the symbolic efficiencies of six robot dynamics formulations for generating closed-form and recursive models.