Numerical solution for designing telescopic manipulators with prescribed workspace points

In this paper a numerical solution is proposed for designing telescopic manipulators when workspace is prescribed through few suitable points. An algorithm is outlined by using an algebraic formulation for the workspace boundary and numerical solution is worked out by using a Newton–Raphson technique to solve a proper design problem. Numerical examples are reported to discuss computational efforts and solution characteristics.     

Interior and exterior boundaries to the workspace of mechanical manipulators

Analytical methods for identifying the boundary to the workspace of serial mechanical manipulators and the boundary to voids in the workspace are presented. The determination of parametric equations of surface patches that envelop the workspace of serial manipulators was presented elsewhere and is extended in this paper to an analytical method for void identification. Because of the ability to identify closed-form surface patches that exist internal and external to the workspace, a mathematical formulation based on the concept of a normal acceleration function is introduced. Admissible motion in the normal direction to a point on a singular surface is delineated and characterized by definiteness properties of a quadratic form. An enclosure bound by surface patches that do not admit normal motion is identified as a void. Several examples are treated using this formulation to illustrate the method.     

Position,Jacobian and workspace analysis of a 3-PSP spatial parallel manipulator

This paper investigates the problems of kinematics, Jacobian, singularity and workspace analysis of a spatial type of 3-PSP parallel manipulator. First, structure and motion variables of the robot are addressed. Two operational modes, non-pure translational and coupled mixed-type are considered. Two inverse kinematics solutions, an analytical and a numerical, for the two operational modes are presented. The direct kinematics of the robot is also solved utilizing a new geometrical approach. It is shown, unlike most parallel robots, the direct kinematics problem of this robot has a unique solution. Next, analytical expressions for the velocity and acceleration relations are derived in invariant form. Auxiliary vectors are introduced to eliminate passive velocity and acceleration vectors. The three types of conventional singularities are analyzed. The notion of non-pure rotational and non-pure translational Jacobian matrices is introduced. The non-pure rotational and non-pure translational Jacobian matrices are combined to form the Jacobian of constraint matrix which is then used to obtain the constraint singularity. Finally, two methods, a discretization method and one based on direct kinematics are presented and robot non-pure translation and coupled mixed-type reachable workspaces are obtained. The influence of tool length on workspace is also studied.     

Optimal design and workspace analysis of a mobile welding robot with a 3P3R serial manipulator

This paper presents the design optimization of a mobile welding robot based on the analysis of its workspace. A welding robot has been developed to be used inside the double-hull structure of ships, and it shows good welding functionality. But there is a need to optimize the kinematic variables ensuring that the required welding functions inside the ships are satisfied. The task-oriented workspace, which is the workspace enabling specific rotations, has been defined in order to validate the welding ability of the robot, and incorporating the required rotational capabilities. To calculate the workspace, a geometric approach is adopted which considers the pitching and yawing angles simultaneously. Based on the workspace analysis, a scenario is compiled for considering a mass reduction, and a ratio between the design parameters and the workspace, with constraints on the workspace margins. The proposed optimization procedure is composed of two steps of coarse and fine searching. In the coarse searching step, a feasible parameter region (FPR) is defined, which satisfies the geometrical design constraints, and can be obtained without any considerations of the objective functions. In the fine searching step, the design parameters are determined by using the optimization technique of the conjugate gradient method in the overall FPRs. The suggested approach to calculating the task-oriented workspace, and the procedure of optimal design, are expected to be applied to general industrial robots.     

On the uniform boundedness of the inertia matrix of serial robot manipulators

In the control of robot manipulators, it is customary to assume that the eigenvalues of the inertia matrix are uniformly bounded from below and above. However, in this article it is shown that not all manipulators possess this property. The class of serial robot manipulators with bounded inertia matrix, referred to as class ℬ︁𝒟 manipulators, is completely characterized and it is shown that it includes manipulators with nontrivial joint configurations. For manipulators of this class, easily computable uniform bounds for the minimum and maximum eigenvalues of the inertia matrix are provided. © 1998 John Wiley & Sons, Inc. 15: 17–28, 1998     

The workspace mapping with deficient-DOF space for the PUMA 560 robot and its exoskeleton arm by using orthogonal experiment design method

In this paper, a particular emphasis is put on the workspace mapping with deficient-DOF space between the PUMA 560 robot and its exoskeleton-arm master-type manipulator, which is proved to be the key step for different structure-based master–slave manipulation. The deficient-DOF space of PUMA 560, made up with the singularity and joint limitation, affects the maneuverability and stability of the master–slave manipulation system. In this work, the deficient-DOF space in the mapped workspace with master–slave control is investigated as a main factor of the workspace mapping. Meanwhile, the orthogonal experiment design method is introduced and two rounds of orthogonal experiments are carried out for this mapping problem, which is simultaneously characterized by many other variables At last the simulation and experiment results demonstrate that the scheme of the mapping is feasible and the orthogonal experiment design method is effective. It is a novel application and exploration of the orthogonal experiment design method in the mechanical or robot optimal design.     

Tracking trajectory in the workspace of rigid manipulators using distributed adaptive control strategy

This paper discusses the tracking trajectory in the workspace of rigid manipulators using distributed adaptive control strategy. This control strategy consists of two steps; first, the classical MIMO dynamical system is decomposed into a set of nonlinear interconnected subsystems. Each subsystem has one joint. Second, the distributed adaptive control strategy is introduced. This control strategy consists of controlling the last subsystem while assuming that the remaining subsystems are stable. Then, going backward to the second last subsystem, the same strategy is applied and so on until the first one. The system parameters are assumed to be unknown. An adaptive control is used to estimate these parameters. Indeed, the unknown parameters existing in the equation of motion of the last subsystem are first estimated and the control law is developed based on these estimated parameters. Then, going backward to the before last joint, the control law is developed using its own estimated parameters and the ones already estimated in the upper level subsystem. Asymptotical stability of the error dynamics is proved using Lyapunov approach. The developed algorithm is experimented on a 4 DOF hyper redundant articulated nimble adaptable trunk robot and compared with the classical computed torque approach. Good tracking in the workspace and joint space is obtained and effectiveness of the results is shown.     

A unified algorithm to determine the reachable and dexterous workspace of parallel manipulators

This paper presents a novel idea for determining the reachable and dexterous workspace of parallel manipulators. Both the reachable workspace and dexterous workspace are utmost important for optimal design and performance comparison of manipulators, because each configuration or point in this region has specified kinematic dexterity by the designer. We propose a uniform algorithm, called stratified workspace boundary determining algorithm (SWBDA), which considers various physical and contrived constraints. The problems of determining the reachable and dexterous workspace boundaries are defined and the unified method is applied to solve all the problems of this kind. The validity and efficiency of the proposed method are verified with two kinds of representative parallel manipulator, since their relational results were studied in literatures. Finally, the advantages of the proposed method are summarized by comparing with other methods.     

带有输出约束的柔性关节机械臂预设性能自适应控制

针对带有输出约束和模型不确定的柔性关节机械臂系统,提出一种基于时变障碍李雅普诺夫函数的预设性能自适应控制方法.通过构造指数衰减的时变约束边界,提出时变正切型障碍李雅普诺夫函数,能够同时适用于约束与非约束情况,进而拓宽传统对数型障碍李雅普诺夫函数的适用范围.此外,通过预先设置时变边界函数的相关参数,使得系统输出在初始阶段...     

Digital control of space robot manipulators with velocity type joint controller using transpose of generalized Jacobian matrix

For free floating space robots having manipulators, we have proposed a discrete-time tracking control method using the transpose of Generalized Jacobian Matrix (GJM). Control inputs of the control method are joint torques of the manipulator. In this paper, the control method is augmented for angular velocity inputs of the joints. Computer simulations have shown the effectiveness of the augmented method. This work was presented in part and awarded as Best Paper Award at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

On the position analysis of a new spherical parallel robot with orientation applications

In this paper, we propose a new spherical parallel robot for celestial orientation, and rehabilitation applications (TV satellite dish, tracking systems, solar panels, cameras, telescopes, table of the machine tools, ankle, shoulder, wrist and etc.). The proposed robot can completely rotate about an axis. After describing the robot and its inverse position analysis, using the genetic algorithm, the dimensional optimization to maximize the workspace of the robot is performed. The workspace analysis shows that the proposed robot has a relatively large workspace. Also, singularity analysis represents that the manipulator is a singularity-free workspace. It is a great advantage of the proposed robot. Next, an optimal approach is proposed for solving the direct position problem of the robot. According to the geometry of the robot, two coupled trigonometric equations are obtained through using a special form of Rodrigues' rotation formula. Next, the two coupled equations are transformed to a 8-degrees polynomial using the Sylvester's Dialytic elimination method. Finally, a numerical example for the robot with an asymmetric structure is given with eight real solutions. Therefore, the polynomial being minimal and the proposed approach is optimal. This greatly decreases computational time, which is necessary for dynamics, control and simulation.     

On the adaptive control of robot manipulators with velocity observers

To achieve accurate tracking control of robot manipulators many schemes have been proposed. A common approach is based on adaptive control techniques, which guarantee trajectory tracking under the assumption that the robot model structure is perfectly known and linear in the unknown parameters, while joint velocities are available. Despite tracking errors tend to zero, parameter errors do not unless some persistent excitation condition is fulfilled. There are few works dealing with velocity observation in conjunction with adaptive laws. In this note, an adaptive control/observer scheme is proposed for tracking position of robot manipulators. It is shown that tracking and observation errors are ultimately bounded, with the characteristic that when a persistent excitation condition is matched then they, as well as the parameter errors, tend to zero. Simulation results are in good agreement with the developed theory.     

A new Image Registration technique with free boundary constraints: application to mammography

In this paper, a new image-matching mathematical model is presented with its application to mammogram registration. In a variational framework, an energy minimization problem is formulated and a multigrid resolution algorithm is designed. The model focuses on the matching of regions of interest. It also combines several constraints which are both intensity- and segmentation-based. A new feature of our model is combining region matching and segmentation by formulation of the energy minimization problem with free boundary conditions. Moreover, the energy has a new registration constraint. The performances of the new model and an equivalent model with fixed boundary conditions are compared on simulated mammogram pairs. It is shown that the model with free boundary is more robust to initialization inaccuracies than the one with fixed boundary conditions. Both models are applied to several real bilateral mammogram pairs. The model ability to compensate significantly for some normal differences between mammograms is illustrated. Results suggest that the new model could enable some improvements of mammogram comparisons and tumor detection system performances.     

On the planning of collision-free movements of manipulators

This paper proposes an efficient position identification method for mobile robots in the environment of a building corridor using colour images and map information. A robot can usually estimate its position from its motion history (so-called dead reckoning); however, there are occasions when the robot's position needs to be estimated without the motion history, for example when self-tracking of the motion has failed, or just after the robot power is on. The proposed method is to identify the robot's position without the motion history. The method consists of the following three steps: (1) map information for the mobile robot is prepared; (2) a colour image is processed to detect a vanishing point and to generate an abstracted image. The robot moves to an appropriate position for the identification, if it is unable to identify the current position; and (3) the current robot position is identified from the map information, the vanishing point, and the abstracted image. The effectiveness of the proposed method is shown by the experimental results.     

On generating the motion of industrial robot manipulators

In this study, an intelligent search algorithm is proposed to define the path that leads to the desired position and orientation of an industrial robot׳s manipulator end effector. The search algorithm gradually approaches the desired configuration by selecting and evaluating a number of alternative robot׳s configurations. A grid of the robot׳s alternative configurations is constructed using a set of parameters which are reducing the search space to minimize the computational time. In the evaluation of the alternatives, multiple criteria are used in order for the different requirements to be fulfilled. The alternative configurations are generated with emphasis being given to the robot׳s joints that mainly affect the position of the end effector. Grid resolution and size parameters are set on the basis of the desired output. High resolution is used for a smooth path and lower for a rough estimation, by providing only a number of the intermediate points to the goal position. The path derived is a series of robot configurations. This method provides an inexperienced robot programmer with flexibility to generate automatically a robotic path that would fulfill the desired criteria without having to record intermediate points to the goal position.     

含有LuGre摩擦并联机械臂的自适应控制

本文研究了含有LuGre摩擦的并联机械臂自适应控制问题.首先,在并联机械臂动力学模型中引入LuGre摩擦模型来描述伺服关节内部的摩擦行为;其次,构造含有动态摩擦补偿的自适应控制算法,并使用Lyapunov方法证明控制算法的有效性;最后,通过平面3 RRR并联机械臂数值算例,验证所提出控制算法的效果以及LuGre摩擦补偿的必要性.