Path Planning of Free Floating Prismatic-Jointed Manipulators

Reaching a desired position with a specific orientationin space by a robot, mounted on a freely floating base, is an importantpath planning and control problem. Research in this area has mainlyconcentrated on the use of revolute-jointed serial manipulators. It iswell known that the dynamic equations of such manipulators are quitecomplex.In this paper, we propose the use of a 6-link fully prismatic-jointedrobot to achieve a desired position and orientation in space instead of arevolute-jointed robot. The use of pure prismatic-jointed robots forsuch a purpose is counter intuitive. On earth, such a structure is unableto provide a desired orientation to the end-effector. However, it can beshown that in space, arbitrary end-effector orientations are possible.Due to the relative simplicity of kinematics, dynamics and workspace ofprismatic-jointed robots compared to revolute-jointed robots, their useresults in significant computational advantages in path planning andcontrol.Also, in this paper, we adopt an unconventional motion planning methodthat avoids inversion of the Jacobian matrix and results in singularityfree paths for the end-effector. In this method, the joint trajectoriesare considered to be modal sums of basis functions of time. Within this framework, constraints on jointangles and joint rates can be imposed. The results are demonstratedwith an example of a 6-link fully prismatic-jointed robot.     

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.     

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.     

冗余机械臂运动学优化设计

该文主要从机械臂运动学的角度,定义了故障容错机械臂,巧妙地论证了冗余故障容错机械臂应该具备的自由度数,以及针对不同的任务要求,设计故障容错机械臂的方法。通过将任务空间抽象简化为一系列的特征点,建立机械臂参数与理想值相关的罚函数,选择有效的优化算法,设计出了通用一阶故障容错平面位置机械臂,通用一阶故障容错空间位置机械臂,以及特定任务一阶故障容错平面位置机械臂。建立起完整的故障容错机械臂的设计方法。     

On the workspace boundary determination of serial manipulators with non-unilateral constraints

Broadly applicable analytical algorithms for workspace of serial manipulators with non-unilateral constraints are developed and illustrated. The Jacobian row-rank deficiency method is employed to determine the singularities of these manipulators. There are four types of singularity sets: Type I: position Jacobian singularities; Type II: instantaneous singularities that are due to a generalized joint that is reaching its apex; Type III: domain boundary singularities, which are associated with the initial and final values of the time interval; Type IV: coupled singularities, which are associated with a relative singular Jacobian, where the null space is reduced in one sub-matrix due to either of two occurrences: a Type II or a Type III singularity. All of the singular surfaces are hypersurfaces that extend internally and externally the workspace envelope. Intersecting singular surfaces identifies singular curves that partition singular surfaces into subsurfaces, and a perturbation method is used to identify regions (curve segments/surface patches) of the hypersurfaces that are on the boundary. The formulation is illustrated by implementing it to a spatial 3-degree of freedom (DOF) and a spatial 4-DOF manipulator.     

Fuzzy-GA-based trajectory planner for robot manipulators sharing a common workspace

This paper presents a novel fuzzy genetic algorithm (GA) approach to tackling the problem of trajectory planning of two collaborative robot manipulators sharing a common workspace, where the manipulators have to consider each other as a moving obstacle whose trajectory or behaviour is unknown and unpredictable, as each manipulator has individual goals and where both have the same priority. The goals are not restricted to a given set of joint values, but are specified in the workspace as coordinates at which it is desired to place the end-effector of the manipulator. By not constraining the goal to the joint space, the number of possible solutions that satisfies the goal increases according to the number of degrees of freedom of the manipulators. A simple GA planner is used to produce an initial estimation of the movements of the robots' articulations and collision free motion is obtained by the corrective action of the collision-avoidance fuzzy units.     

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.     

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.     

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.     

Stratifying the singularity loci of a class of parallel manipulators

Some in-parallel robots, such as the 3-2-1 and the 3/2 manipulators, have attracted attention because their forward kinematics can be solved by three consecutive trilaterations. In this paper, we identify a class of these robots, which we call flagged manipulators, whose singularity loci admit a well-behaved decomposition, i.e., a stratification, derived from that of the flag manifold. Two remarkable properties must be highlighted. First, the decomposition has the same topology for all members in the class, irrespective of the metric details of each particular robot instance. Thus, we provide explicitly all the singular strata and their connectivity, which apply to all flagged manipulators without any tailoring. Second, the strata can be easily characterized geometrically, because it is possible to assign local coordinates to each stratum (in the configuration space of the manipulator) that correspond to uncoupled rotations and/or translations in the workspace.     

Inverse Kinematics of Binary Manipulators Using a Continuum Model

Binary actuators have only two discrete states, both of which are stable without feedback. As a result, manipulators with binary actuators have a finite number of states. The major benefits of binary actuation are that extensive feedback control is not required, reliability and task repeatability are very high, and two-state actuators are generally very inexpensive, resulting in low cost robotic mechanisms. These manipulators have great potential for use in both the manufacturing and service sectors, where the cost of high performance robotic manipulators is often difficult to justify. The most difficult challenge with a binary manipulator is to achieve relatively continuous end-effector trajectories given the discrete nature of binary actuation. Since the number of configurations attainable by binary manipulators grows exponentially in the number of actuated degrees of freedom, calculation of inverse kinematics by direct enumeration of joint states and calculation of forward kinematics is not feasible in the highly actuated case. This paper presents an efficient method for performing binary manipulator inverse kinematics and trajectory planning based on having the binary manipulator shape adhere closely to a time-varying curve. In this way the configuration of the arm does not exhibit drastic changes as the end effector follows a discrete trajectory.     

6-PSS并联机器人操作机平动工作空间解析

提出一种求解6-PSS并联机器人操作机平动工作空 间 边界的解析方法．该方法将平动工作空间问题归结为三类子空间边界求交问题,即分别由六 张球面片交集构成的上、下边界与由六张椭圆柱面交集构成的侧面边界的求交问题．文中还 提出主工作空间的概念和相应的解析表达及工作空间评价指标,并探讨了设计参数对评价指 标的影响规律．     

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.     

A New Approach to the Architecture Optimization of a General 3-PUU Translational Parallel Manipulator

This paper presents a new approach to the architecture optimization of a general 3-PUU translational parallel manipulator (TPM) based on the performance of a weighted sum of global dexterity index and a new performance index-space utility ratio (SUR). Both the inverse kinematics and forward kinematics solutions are derived in closed form, and the Jacobian matrix is derived analytically. The manipulator workspace is generated by a numerical searching method with the physical constraints taken into consideration. Simulation results illustrate clearly the necessity to introduce a mixed performance index using space utility ratio for architectural optimization of the manipulator, and the optimization procedure is carried out with the goal of reaching a compromise between the two indices. The analytical results are helpful in designing a general 3-PUU TPM, and the proposed design methodology can also be applied to architectural optimization for other types of parallel manipulators.     

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.     

Singularity loci of planar parallel manipulators with revolute actuators

The determination of the singularity loci of planar parallel manipulators is addressed in this paper. The inverse kinematics of two kinds of planar parallel manipulators (a two-degree-of-freedom manipulator and a three-degree-of-freedom manipulator) are first computed and their velocity equations are then derived. At the same time, the branches of the manipulators are distinguished by the introduction of a branch index K_i. Using the velocity equations, the singularity analysis of the manipulators is completed and expressions which represent the singularity of the manipulators are obtained. A polynomial form of the singularity loci is also derived. For the first type of singularity of parallel manipulators, the singularity locus is obtained by finding the workspace limits of the manipulators. For the second type of singularity, the loci are obtained through the solution of nonlinear algebraic equations obtained from the velocity analysis. Finally, the graphical representation of the complete singularity loci of the manipulators is illustrated with examples. The algorithm introduced in this paper allows the determination of the singularity loci of planar parallel manipulators with revolute actuators, which has been elusive to previous approaches.     

CAD-based generation of collision-free paths for robotic manipulators

The use of a CAD system can improve the overall efficiency of automated factories. This paper describes the utilization of a CAD system devoted to the off-line generation of collision-free paths for robotic manipulators. This tool is first applied in the case of a robotic manipulator in a moderately cluttered environment, next it is utilized it for planning collision-free paths for two robotic manipulators sharing a common workspace. The implemented off-line programming system is written in C, in X/Windows environment. In this way portability is effectively achieved. Simulation results show the effectiveness of the proposed approach.     

A geometrical workspace calculation method for cable-driven parallel manipulators on minimum tension condition

In this paper, a geometrical expression to delineate the sum of tensions (i.e. minimum 1-norm tensions) of 2-DoF planar cable-driven parallel manipulators (CDPMs) is proposed and proofed, which can be used to reduce calculation time of workspace determination. Furthermore, this paper also presents a systematic analysis on the relation between cable tension and workspace by means of convex analysis. In order to obtain wrench-feasible workspace, a unified and feasible algorithm is adopted in simulation examples of spatial CDPMs with different configurations, which demonstrate that the proposed method is valid and straightforward to calculate workspace.     

基于AutoCAD平台的六自由度并联机器人

本文研究基于AutoCAD平台的六自由度并联机器人在姿态给定情况下工作空间(即位置工作空 间)的几何确定方法,该方法以机器人的运动学反解为基础,得出Stewart并联机器人和6-R TS并联机器人位置工作空间的边界方程,从而得出Stewart并联机器人的位置工作空 间是6个球体的交集,6-RTS并联机器人在姿态给定时其工作空间是6个相同的规则曲面体 的交集．基于AutoCAD平台,其交集以及交集的容积可以很容易的得出,该方法是确定六自 由度并联机器人工作空间的一种简单、有效方法．     

Operating robot manipulators through kinematic singularities using a continuously sliding mode control

Planning the motion of end-effectors of robot manipulators can be carried out more directly in the Cartesian space compared to the joint space. Yet, Cartesian paths may include singular configurations where conventional control schemes suffer from excessive joint velocities and loss of tracking accuracy. The difficulties arise because the Jacobian matrix that is used to establish a linear relation between the velocities in the task and joint spaces loses rank at singularities. The problem can be resolved by using a local second-order approximation of robot kinematics for the joint velocities, which is called Resolved Motion Quadratic Rate Control. In this article, we present a control strategy based on this approach and a recently developed variable structure control scheme. The controller receives Cartesian inputs whenever the manipulator is outside the singular domain. Otherwise, it uses resolved motion quadratic rate control to compute the required joint inputs. Numerical simulation is performed to show that the proposed control scheme provides accurate tracking of the desired motion without inducing excessive control activity when operating robot manipulators through singular configurations. © 1994 John Wiley & Sons, Inc.