Fuzzy logic-based optimization for redundant manipulators

Redundant manipulators have more degrees of freedom (DOF) than the DOF of the task space. This implies that the number of joint position variables is greater than the number of variables specifying the task. The problem of solving the kinematic equations for the joint variables is underspecified unless additional equations/constraints are introduced to obtain a well-posed problem. A dynamic level redundancy resolution is proposed. The joint space model is transformed to a reduced-order model in the pseudovelocity space. The elements of the foregoing transformation matrix indirectly determine the contribution of each joint to the total motion. These elements are selected using two fuzzy logic-based methods so as to minimize the instantaneous manipulator power: (1) in the velocity method, a space vector in the velocity relationship between the two spaces is determined by imposing a constraint on the continuity of the joint velocities at the time instant when the elements of the transformation matrix experience a discontinuity and (2) in the torque method, an alternative approach introduced to reduce the computational complexity, the changes in the transformation matrix are made continuous with respect to time by the appropriate choice of a space vector in the joint torque expression. Simulations are given.     

Gravity compensation of spatial two‐DOF serial manipulators

This article presents the analysis of gravity compensation of a two‐DOF serial manipulator operating in three‐dimensional space by means of linear spring suspension. The physical configuration of the serial manipulator is assumed general. The analysis begins with gravity compensation of a one‐DOF manipulator in order to form the basis which is then extended to a two‐DOF manipulator. The approach taken in the analysis is that of conservation of potential energy. The goal is to seek the location and the stiffness of springs that provide complete compensation of gravity in the manipulator system. It has been found that complete compensation of gravity in a two‐DOF serial manipulator system is possible. Unlike many previous works on spring suspension of a rigid body, which assume that one end of the suspending spring is attached to ground, it is proven in this study that, for complete compensation in a two‐DOF manipulator, the spring that suspends the distal link cannot be connected to ground. Instead, it must be in certain motion relative to the proximal link. The discussion on how to provide such a motion for the spring is given. It is also explained how the problem of gravity compensation of a robot manipulator can be shifted to that of changing gravity environment within a manipulator system. The concept can be applied to simulation and testing of robot manipulators that will be sent to operate in a different gravity environment, such as space. © 2002 Wiley Periodicals, Inc.     

Linearized dynamic models of robot manipulators in cartesian space

This article presents development of the linearized dynamic models of robot manipulators in Cartesian space. A clever method is proposed to formulate the linearized dynamic models of robot manipulators in Cartesian space. Efficient methods are developed to compute various matrices involved in the models (or the manipulator sensitivity matrices in Cartesian space), such as the Jacobian matrix and the first and second derivatives of it with respect to time as well as the manipulator sensitivity matrices in joint space. The proposed methods are simple and systematic and have computational complexity of the order O(n²) only, where n is the number of degrees-of-freedom of the manipulator.     

Spherically actuated platform manipulator

This article presents the inverse and forward pose and rate kinematics solutions for a novel 6‐DOF platform manipulator, actuated by two base‐mounted spherical actuators. The moving platform is connected to the fixed base by two identical spherical‐prismatic‐universal serial chain legs. The S‐joint is active, and the remaining two joints in each chain are passive. An analytical solution is presented for the inverse pose problems, a semi‐analytical solution is presented for the rate problems, and the numerical Newton–Raphson technique is employed to solve the forward pose problem. Unfortunately, the passive joint variables cannot be ignored in the kinematics solutions as they can for the Gough–Stewart platform. Examples are presented and hardware has been built, using two Rosheim Omni‐Wrists on loan from NASA as the spherical actuators. © 2001 John Wiley & Sons, Inc.     

Hypersurfaces of special configurations of serial manipulators and related concepts. part I: Theory and development of the hypersurfaces of special configurations

This article is the first of three companion papers which introduce some novel concepts useful in the kinetmatic design, analysis, motion planning, control, and performance evaluation of serial manipulators. Here an efficient methodology is developed to classify the special configurations of an N DOF manipulator. This classification yields hyper-surfaces in the joint space on each of which the manipulator loses a certain number of its degrees of freedom. The efficiency of the methodology is based on a theorem proved in Appendix B and the utilization of the minimal reference frames. These frames are obtained and tabulated for all possible types of manipulators. Furthermore the adaptability of a manipulator to a common control algorithm is quantified via an index. The numerical values of these indices are listed for all types of manipulators.     

A decomposition approach for the kinematic synthesis of tendon‐driven manipulators

This article describes a decomposition methodology for the kinematic synthesis of tendon‐driven manipulators (TDMs). Based on the QR factorization, the complex transformation between vectors in the tendon‐space and the joint‐space of an n‐DOF TDM with n+1 tendons is decomposed as a two‐step transformation. An orientation matrix is used to characterize the vector transformation between the (n+1)‐dimensional tendon‐space and the n‐dimensional intermediate equivalent tendon‐space. An equivalent structure matrix is also introduced for the vector transformation between the n‐dimensional equivalent tendon‐space and n‐dimensional joint‐space. Design equations for synthesizing a TDM to possess kinematic isotropic transmission characteristics with proper tendon routing and pulley sizes are derived. ©1999 John Wiley & Sons, Inc.     

Simulation of Industrial Manipulators Based on the UDU T Decomposition of Inertia Matrix

The UDU ^T – U and D are respectively the upper triangular and diagonal matrices – decomposition of the generalized inertia matrix of an n-link serial manipulator, introduced elsewhere, is used here for the simulation of industrial manipulators which are mainly of serial type. The decomposition is based on the application of the Gaussian elimination rules to the recursive expressions of the elements of the inertia matrix that are obtained using the Decoupled Natural Orthogonal Complement matrices. The decomposition resulted in an efficient order n, i.e., O(n), recursive forward dynamics algorithm that calculates the joint accelerations. These accelerations are then integrated numerically to perform simulation. Using this methodology, a computer algorithm for the simulation of any n degrees of freedom (DOF) industrial manipulator comprising of revolute and/or prismatic joints is developed. As illustrations, simulation results of three manipulators, namely, a three-DOF planar manipulator, and the six-DOF Stanford arm and PUMA robot, are reported in this paper.     

A framework for large‐force task planning of mobile and redundant manipulators

A framework tackling the problem of large wrench application using robotic systems with limited force or torque actuators is presented. It is shown that such systems can apply a wrench to a limited set of Cartesian locations called force workspace (FW), and its force capabilities are improved by employing base mobility and redundancy. An efficient numerical algorithm based on 2ⁿ‐tree decomposition of Cartesian space is designed to generate FW. Based on the FW generation algorithm, a planning method is presented resulting in proper base positioning relative to large‐force quasistatic tasks. Additionally, the case of tasks requiring application of a wrench along a given path is considered. Task workspace, the set of Cartesian space locations that are feasible starting positions for such tasks, is shown to be a subset of FW. This workspace is used for identifying proper base or task positions guaranteeing task execution along desired paths. Finally, to plan redundant manipulator postures during large‐force‐tasks, a new method based on a min–max optimization scheme is developed. Unlike norm‐based methods, this method guarantees no actuator capabilities are exceeded, and force or torque of the most loaded joint is minimized. Illustrative examples are given demonstrating validity and usefulness of the proposed framework. ©1999 John Wiley & Sons, Inc.     

Inverse Dynamic Model and a Control Application of a Novel 6-DOF Hybrid Kinematics Manipulator

Kinematics with six degrees of freedom can be of several types. This paper describes the inverse dynamic model of a novel hybrid kinematics manipulator. The so-called Epizactor consists of two planar disk systems that together move a connecting element in 6 DOF. To do so each of the disk systems has a linkage point equipped with a homokinetic joint. Each disk system can be described as a serial 3-link planar manipulator with unlimited angles of rotation. To compensate singularities, a kinematic redundancy is introduced via a fourth link. The kinematic concept leads to several technical advantages for compact 6-DOF-manipulators when compared to established parallel kinematics: The ratio of workspace volume and installation space is beneficial, the number of kinematic elements is smaller, and rotating drives are used exclusively. For a singularity-robust control-approach, the inverse dynamic model is derived using the iterative Newton–Euler-method. Feasibility is shown by the application of the model to an example where excessive actuator velocities and torques are avoided.     

A new family of hybrid 4‐DOF parallel mechanisms with two platforms and its application to a footpad device

This paper proposes a new family of 4‐degrees‐of‐freedom (DOF) parallel mechanisms with two platforms and its application to a footpad device that can simulate the spatial motions of the human foot. The new mechanism consists of front and rear platforms, and three limbs. Two limbs with 6‐DOF serial joints (P ‐S‐P‐P) are attached to each platform and are perpendicular to the base plate, while the middle limb is attached to the revolute joint that connects the front and rear platforms. The middle limb is driven by the 2‐DOF driving mechanism that is equivalent to active serial prismatic and revolute joints (P_e ‐R_e ), or prismatic and prismatic joints (P_e ‐P_e ) with two base‐fixed prismatic actuators. Since the middle limb perpendicular to the base plate has 3‐DOF serial joints (P_e ‐R_e ‐R or P_e ‐P_e ‐R), two new 4‐DOF parallel mechanisms with two platforms can generate pitch motion of each platform, and roll and heave motions (1T‐3R) or pitch motion of each platform and two translational motions (2T‐2R) at both platforms, according to the type of the 2‐DOF driving mechanism. Kinematic analyses of the 1T‐3R mechanism were performed, including inverse and forward kinematics and velocity analysis. Based on the 1T‐3R mechanism, a footpad device was designed to generate foot trajectories for natural walking. © 2005 Wiley Periodicals, Inc.     

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.     

Robust nonlinear task space control for 6 DOF parallel manipulator

This paper presents a robust nonlinear controller equipped with a friction estimator for a 6 degree of freedom (DOF) parallel manipulator in the task space coordinates. The requisite 6 DOF system states for the task space control are acquired by an alpha-beta tracker and a numerical forward kinematic solution. The Friedland-Park friction observer in the joint space coordinates provides friction estimates that help to improve the control performance. Finally, the RNTC turns out to outper form a nonlinear task space control and a popularly adopted PID control with the friction estimator in the joint space coordinates.     

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．     

Velocity degeneracy determination for the kinematically redundant CSA/ISE STEAR testbed manipulator

The Canadian Space Agency (CSA)/International Submarine Engineering (ISE) STEAR Testbed Manipulator (STM) is a ground‐based manipulator similar to the arms of the Special Purpose Dextrous Manipulator (SPDM) being built for the International Space Station (ISS). This work presents the determination of the velocity‐degenerate (singular) configurations for the STM, a system comprised of two seven‐jointed redundant manipulators. The two “arms” of the STM are mirror images of one another. The analysis presented is for the STM‐1 or “right” arm, but it applies to the STM‐2 or “left” arm since they are mirror images and have similar dimensions and joint ranges. A methodology based on reciprocity of screws is used to identify all configurations causing one degree‐of‐freedom (DOF) instantaneous motion loss in the STM. It is shown that there are five families of two‐condition configurations resulting in a single DOF loss for manipulators kinematically similar to the STM‐1. Reciprocal screws characterizing the lost motion DOF for each of the degenerate configurations are derived. Analysis of the velocity degeneracies shows that for the STM‐1 dimensions and joint limits, only four of the five velocity‐degenerate configurations are feasible. © 2000 John Wiley & Sons, Inc.     

New inverse kinematic algorithms for redundant robots

New inverse kinematic algorithms for generating redundant robot joint trajectories are proposed. The algorithms utilize the kinematic redundancy to improve robot motion performance (in joint space or Cartesian space) as specified by certain objective functions. The algorithms are based on the extension of the existing “joint-space command generator” technique in which a null space vector is introduced which optimizes a specific objective function along the joint trajectories. In this article, the algorithms for generating the joint position and velocity (PV) trajectories are extensively developed. The case for joint position, velocity, and acceleration (PVA) generation is also addressed. Application of the algorithms to a four-link revolute planar robot manipulator is demonstrated through simulation. Several motion performance criteria are considered and their results analyzed.     

A Modular Scheme for Controller Design and Performance Evaluation in 3D Visual Servoing

In this paper we present a modular scheme for designing and evaluating different control systems for position based dynamic look and move visual servoing systems. This scheme is particularly applied to a 6 DOF industrial manipulator equipped with a camera mounted on its end effector. The manipulator with its actuators and its current feedback loops can be modeled as a Cartesian device commanded through a serial line. In this case the manipulator can be considered as a decoupled system with 6 independent loops. The use of computer vision as feedback transducer strongly affects the closed loop dynamics of the overall system, so that a visual controller is required for achieving fast response and high control accuracy. Due to the long delay in generating the control signal, it is necessary to carefully select the visual controller. In this paper we present a framework that allows the study of some conventional and new techniques to design this visual controller. Besides an experimental setup has been built and used to evaluate and compare the performance of the position based dynamic look and move system with different controllers. Some criterions for selecting the best strategy for each task are established. Quite a lot of results relative to different trajectory tracking control strategies are presented, showing both simulation and real platform responses.     

Algebraic solution to forward kinematics of a 3‐DOF spherical parallel manipulator

A three degree‐of‐freedom (3‐DOF) spherical parallel manipulator consists of two tetrahedrons (pyramids). The base tetrahedron is fixed while the moving tetrahedron is rotating at the joint apex of the two tetrahedrons. This article studies the forward kinematics to a special 3‐DOF spherical parallel manipulator, where the three apical angles of the moving tetrahedron are equal to their counterparts in the base tetrahedron, respectively. The final result of the forward kinematics to this parallel manipulator is a univariate quartic polynomial equation, which has a direct algebraic solution. In addition, a special right‐angle case of the manipulator is investigated and its forward kinematics can be obtained directly. © 2001 John Wiley & Sons, Inc.     

Gain Scheduled LPV H∞ Control Based on LMI Approach for a Robotic Manipulator

A new approach to the design of a gain scheduled linear parameter‐varying (LPV) H_∞ controller, which places the closed‐loop poles in the region that satisfies the specified dynamic response, for an n‐joint rigid robotic manipulator, is presented. The nonlinear time‐varying robotic manipulator is modeled to be a LPV system with a convex polytopic structure with the use of the LPV convex decomposition technique in a filter introduced. State feedback controllers, which satisfy the H_∞ performance and the closed‐loop pole‐placement requirements, for each vertex of the convex polyhedron parameter space, are designed with the use of the linear matrix inequality (LMI) approach. Based on these designed feedback controllers for each vertex, a LPV controller with a smaller on‐line computation load and a convex polytopic structure is synthesized. Simulation and experiment results verify that the robotic manipulator with the LPV controller always has a good dynamic performance along with the variations of the joint positions. © 2002 Wiley Periodicals, Inc.