Showing papers on "Kinematics published in 2000"

Adaptive tracking control of a nonholonomic mobile robot

Abstract: A mobile robot is one of the well-known nonholonomic systems. The integration of a kinematic controller and a torque controller for the dynamic model of a nonholonomic mobile robot has been presented (Fierro and Lewis, 1995). In this paper, an adaptive extension of the controller is proposed. If an adaptive tracking controller for the kinematic model with unknown parameters exists, an adaptive tracking controller for the dynamic model with unknown parameters can be designed by using an adaptive backstepping approach. A design example for a mobile robot with two actuated wheels is provided. In this design, a new kinematic adaptive controller is proposed, then a torque adaptive controller is derived by using the kinematic controller.

Real-time inverse kinematics techniques for anthropomorphic limbs

Abstract: In this paper we develop a set of inverse kinematics algorithms suitable for an anthropomorphic arm or leg. We use a combination of analytical and numerical methods to solve generalized inverse kinematics problems including position, orientation, and aiming constraints. Our combination of analytical and numerical methods results in faster and more reliable algorithms than conventional inverse Jacobian and optimization-based techniques. Additionally, unlike conventional numerical algorithms, our methods allow the user to interactively explore all possible solutions using an intuitive set of parameters that define the redundancy of the system.

Motion analysis system

Abstract: A device comprised of at least a pair of accelerometers and a tilt sensor mounted in fixed relation to a datum plane defining surface (sole of a shoe) may be used for extracting kinematic variables including linear and rotational acceleration, velocity and position. These variables may be resolved into a selected direction thereby permitting both relative and absolute kinematic quantities to be determined. The acceleration is determined using a small cluster of two mutually perpendicular accelerometers mounted on a shoe. Angular orientation of the foot may be determined by double integration of the foot's angular acceleration (which requires a third accelerometer substantially parallel to one of the two orthogonal accelerometers). The two orthogonal accelerations are then resolved into a net horizontal acceleration or other selected direction which may be integrated to find the foot velocity in the selected direction. The average of the foot velocity corresponds to the subject's gait speed.

Mechanism Design: Enumeration of Kinematic Structures According to Function

Abstract: INTRODUCTION A Systematic Design Methodology Links and Joints Kinematic Chains, Mechanisms, and Machines Kinematics of Mechanisms Planar, Spherical, and Spatial Mechanisms Kinematic Inversions BASIC CONCEPT OF GRAPH THEORY Definitions Tree Planar Graph Spanning Trees and Fundamental Circuits Euler's Equation Topological Characteristics of Planar Graphs Matrix Representation of Graphs Contracted Graphs Dual Graphs STRUCTURAL REPRESENTATIONS OF MECHANISMS Functional Schematic Representation Structural Representation Graph Representation Matrix Representation STRUCTURAL ANALYSIS OF MECHANISMS Correspondence between Mechanisms and Graphs Degrees of Freedom Loop Mobility Criterion Lower and Upper Bounds on the Number of Joints on a Link Link Assortments Partition of Binary Link Chains Structural Isomorphism Permutation Group and Group of Automorphisms Identification of Structural Isomorphism Partially Locked Kinematic Chains ENUMERATION OF GRAPHS OF KINEMATIC CHAINS Enumeration of Contracted Graphs Enumeration of Conventional Graphs Atlas of Graphs of Kinematic Chains CLASSIFICATION OF MECHANISMS Planar Mechanisms Spherical Mechanisms Spatial Mechanisms EPICYCLIC GEAR TRAINS Structural Characteristics Buchsbaum-Freudenstein Method Genetic Graph Approach Parent Bar Linkage Method Mechanism Pseudo Isomorphisms Atlas of Epicyclic Gear Trains Kinematics of Epicyclic Gear Trains AUTOMOTIVE MECHANISMS Variable-Stroke Engine Mechanisms Constant-Velocity Shaft Couplings Automatic Transmission Mechanisms Canonical Graph Representation of EGMs Atlas of Epicyclic Gear Transmission Mechanisms ROBOTIC MECHANISMS Parallel Manipulators Robotic Wrist Mechanisms APPENDICES: A. Solving m Equations in n unknowns B. Atlas of Contracted Graphs C. Atlas of Graphs of Kinematic Chains D. Atlas of Planar Bar Linkages E. Atlas of Spatial One-dof Kinematic Chains F. Atlas of Epicyclic Gear Trains G. Atlas of Epicyclic Gear Transmission Mechanisms NOTE: Introduction at the beginning of Chapters 1,3-9 Summary at the end of Chapters 1-6,8-9

Kinematic Analysis and Optimization of a New Three Degree-of-Freedom Spatial Parallel Manipulator

Abstract: A study of the kinematic characteristics of a three degree-of-freedom (dof) parallel mechanism is presented. The architecture of the mechanism is comprised of a mobile platform attached to a base through three identical prismatic-revolute-spherical jointed serial linkages. The prismatic joints are considered to be actuated. These prismatic actuators lie on a common plane and have radial directions of action. The mechanism's inverse displacement solution is obtained. Since the mechanism has only 3 dof, constraint equations describing the inter-relationship between the six motion coordinates are derived. These constraints allow the definition of parasitic motions, i.e., motions in the three unspecified motion coordinates. Architecture optimization of the device is undertaken demonstrating that specific values of design variables allow minimization of parasitic motion.

Dynamics Filter - concept and implementation of online motion Generator for human figures

Abstract: Humanoid robots are required to make a variety of dynamics and even expressive motions in changing environments. However, the conventional methods for generating humanoid motions fail do achieve this requirement since they can only generate quite artificial and predefined motions through rather complicated optimization processes. In this paper, we propose the concept of "dynamics filter" which transforms a physically inconsistent motion into a consistent one, and provide an example of its implementation using feedback control and local optimization. The optimization is based on the equation of motion of constrained kinematic chains, which is derived from our previously proposed method for computing the dynamics of structure-varying kinematic chains. The proposed method can be applied to online motion generator of humanoid robots.

Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics

Abstract: Volumetric positional accuracy constitutes a large portion of the total machine tool error during machining. In order to improve machine tool accuracy cost-effectively, machine tool geometric errors as well as thermally induced errors have to be characterized and predicted for error compensation. This paper presents the development of kinematic error models accounting for geometric and thermal errors in the Vertical Machining Center (VMC). The machine tool investigated is a Cincinnati Milacron Sabre 750 3 axes CNC Vertical Machining Center with open architecture controller. Using Rigid Body Kinematics and small angle approximation of the errors, each slide of the three axes vertical machining center is modeled using homogeneous coordinate transformation. By synthesizing the machine's parametric errors such as linear positioning errors, roll, pitch and yaw etc., an expression for the volumetric errors in the multi-axis machine tool is developed. The developed mathematical model is used to calculate and predict the resultant error vector at the tool–workpiece interface for error compensation.

Kinematics and Optimization of a Spatial 3-UPU Parallel Manipulator

Abstract: The structural characteristics associated with parallel manipulators are investigated. Using these characteristics a class of 3 degree-of-freedom parallel manipulators are enumerated. Several parallel manipulators with only translational degrees of freedom are identified and the 3-UPU parallel manipulator is chosen for design analysis and optimization. The kinematics of this 3-UPU parallel manipulator is studied. Two geometric conditions that lead to pure translational motion of the moving platform are described. Due to the simple kinematic structure, the inverse kinematics yields two equal and opposite limb lengths whereas the direct kinematics produces two possible manipulator postures with one being the mirror image of the other. The Jacobian matrix is derived and several singular conditions are discussed. Furthermore the conditions for existence of an isotropic point within the workspace are discussed and equations to compute the isotropic configurations of a 3-UPU manipulator are derived. Finally, we undertake architecture optimization and show that certain values of design variables maximize the global condition index of the 3-UPU manipulator.

Advances in Robot Kinematics

Abstract: From the Publisher: This book presents the most recent research advances in the theory, design, control and application of robotic systems, which are intended for a variety of purposes such as manipulation, manufacturing, automation, surgery, locomotion and biomechanics. The issues addressed are fundamentally kinematic in nature, including synthesis, calibration, redundancy, force control, dexterity, inverse and forward kinematics, kinematic singularities, as well as over-constrained systems. Methods used include line geometry, quaternion algebra, screw algebra, and linear algebra. These methods are applied to both parallel and serial multi-degree-of-freedom systems. The results should interest researchers, teachers, and students, in fields of engineering and mathematics related to robot theory, design, control and application.

Four-degree-of-freedom parallel robot

Abstract: A four-degree-of-freedom parallel robot capable of displacing a traveling plate with four degrees of freedom at a high speed and a high acceleration and positioning the traveling plate with high rigidity and high precision. The four-degree-of-freedom parallel robot has four actuators fixed to a base, four parallel linkages each of which is coupled at its upper end to a tip end of an arm of each of the actuators through a kinematic element such as a universal joint, and a traveling plate whose four corners are coupled to lower ends of the parallel linkages through kinematic elements. By controlling the actuators, a main member of the traveling plate is displaced with four degrees of freedom, i.e., translated in all directions and rotated around a predetermined axis. Only axial forces are applied to rods constituting the parallel linkages. Thus, the traveling plate can be positioned at a high speed and with high rigidity as well as high precision.

Dynamics computation of structure-varying kinematic chains and its application to human figures

Abstract: This paper discusses the dynamics computation of structure-varying kinematic chains which imply mechanical link systems whose structure may change from open kinematic chain to closed one and vice versa. The proposed algorithm can handle and compute the dynamics and motions of any rigid link systems in a seamless manner without switching among algorithms. The computation is developed on the foundation of the dynamics computation algorithms established in robotics, which is superior in efficiency due to explicit use of the generalized coordinates to those used in the general-purpose motion analysis softwares. Although the structure-varying kinematic chains are commonly found in computing human and animal motions, the computation of their dynamics has not been discussed in literature. The developed computation will provide a general algorithm for the computation of motion and control of humanoid robots and computer graphics human figures.

Rigid body attitude tracking without angular velocity feedback

Abstract: In this paper, we revisit the classical problem of attitude tracking for a rigid body. The interesting difference in the formulation is the assumption that only attitude measurements are available. We proceed to construct globally stabilizing control laws in terms of a minimal set of three-dimensional kinematic parameters that enable the rigid body to track any specified trajectory without requiring angular velocity measurements. The results presented here complement and extend some recent developments available for the nonminimal case of Euler parameters (quaternions).

Virtual reality simulation-based training of telekinegenesis system for training sequential kinematic behavior of automated kinematic machine

Abstract: To train the sequential kinematic behavior of an automated telekinegenesis robot system, a virtual reality simulator is driven with kinematic parameter data derived from a teleoperational device, which models the sequential behavior to be exhibited by the target robot. Sensor outputs of the teleoperational device are processed by a geometry conversion algorithm, to generate data representative of the spatial kinematics of the robot's desired travel path. A kinematic machine simulator program within a robotic control simulation workstation simulates a virtual machine based upon the actual parameters of the robot. The virtual reality simulation program is interactive, allowing the workstation operator to selectively interrupt the operation of the machine, modify its control parameters, and then rerun the program, until the desired behavior of the target machine is achieved. When the target machine's simulated kinematic behavior produced by the virtual reality simulation workstation exhibits the desired dynamic spatial geometry profile, the customized spatial parameter data stored in the workstation is processed by the virtual reality simulation program, to produce a sequence of kinematic control instructions that are downloaded into the micro controller of the target machine. When executed, the kinematic control instructions cause the robot to exhibit its intended on-line sequential kinematic behavior.

Inverse kinematics for humanoid robots

Abstract: Real-time control of the end-effector of a humanoid robot in external coordinates requires computationally efficient solutions of the inverse kinematics problem. In this context, this paper investigates methods of resolved motion rate control (RMRC) that employ optimization criteria to resolve kinematic redundancies. In particular we focus on two established techniques, the pseudo inverse with explicit optimization and the extended Jacobian method. We prove that the extended Jacobian method includes pseudo-inverse methods as a special solution. In terms of computational complexity, however pseudo-inverse and extended Jacobian differ significantly in favor of pseudo-inverse methods. Employing numerical estimation techniques, we introduce a computationally efficient version of the extended Jacobian with performance comparable to the original version. Our results are illustrated in simulation studies with a multiple degree-of-freedom robot, and were tested on a 30 degree-of-freedom humanoid robot.

Online motion retargetting

Abstract: This paper presents a method to retarget the motion of a character to another in real time. The technique is based on inverse rate control, which computes the changes in joint angles corresponding to the changes in end-effector position. While tracking the multiple end-effector trajectories of the original subject or character, our online motion retargetting also minimizes the joint angle differences by exploiting the kinematic redundancies of the animated model. This method can apply a captured motion to another anthropometry so that it can perform slightly different motion, while preserving the original motion characteristics. Because the above is done online, a real-time performance can be mapped to other characters. Moreover, if the method is used interactively during motion capture session, the feedback of retargetted motion on the screen provides more chances to get satisfactory results. As a by-product, our algorithm can be used to reduce measurement errors in restoring captured motion. The data enhancement improves the accuracy in both joint angles and end-effector positions. Experimental results show that our retargetting algorithm preserves high-frequency details of the original motion quite accurately. Copyright © 2000 John Wiley & Sons, Ltd.

On the kinematics of remotely-actuated continuum robots

Abstract: Over the past several years, there has been a rapidly expanding interest in the study and construction of a new class of robot manipulators which utilize high degree of freedom, or continuous, backbone structures. In this paper, we consider and illustrate some basic properties of a class of "hyper-redundant" robots, known as "continuum" robots. We base our analysis around remotely-driven, tendon-actuated manipulators, such as the Rice/Clemson "Elephant's Trunk". We discuss such issues as the kinematic model, the relationship between tendon lengths and bending, and desirable design constraints for continuum robot mechanisms.

Kinematic analysis of translational 3-DOF micro parallel mechanism using matrix method

Abstract: We apply the matrix method to kinematic analysis of our translational 3-DOF micro parallel mechanism for an instance of general flexure mechanisms. The matrix method has been well developed in architecture to analyze a frame structure. We found that this method is well applicable to such a flexure mechanism with circular notched hinges as our micro parallel mechanism because it is approximate to the Rahmen structure. Our matrix method can calculate a compliance matrix with less nodes of matrix than conventional finite element method. First, the compliance matrices of a circular notched hinge and some other beams are defined and the coordinate transformations of compliance matrix are introduced. Next, an analysis of our micro parallel mechanism is demonstrated.

Kinematic Analysis of a New Parallel Machine Tool: The Orthoglide

Abstract: This paper describes a new parallel kinematic architecture for machining applications: the orthoglide. This machine features three fixed parallel linear joints which are mounted orthogonally and a mobile platform which moves in the Cartesian x-y-z space with fixed orientation. The main interest of the orthoglide is that it takes benefit from the advantages of the popular PPP serial machines (regular Cartesian workspace shape and uniform performances) as well as from the parallel kinematic arrangement of the links (less inertia and better dynamic performances), which makes the orthoglide well suited to high-speed machining applications. Possible extension of the orthoglide to 5-axis machining is also investigated.

Three-dimensional kinematic analysis of the snatch of elite Greek weightlifters.

Abstract: We investigated the linear kinematics and the change in energy of the barbell and the angular kinematics of the trunk and leg during the snatch technique of 12 elite male Greek weightlifters under competitive conditions after the new weight classification. Two S-VHS cameras operating at 60 Hz were used to record the lifts. The spatial coordinates of selected points were calculated using the direct linear transformation procedure; after digital filtering of the raw data, the angular displacements and angular velocities were calculated for the hip, knee and ankle joints. The following variables were also calculated for the barbell: vertical and horizontal displacement, vertical linear velocity and acceleration, external mechanical work and power output. The results revealed that all weightlifters flexed their knees during the transition phase, independently of their weight category. This indicates that the athletes use the elastic energy produced during the stretch-shortening cycle to enhance their performance. In nine athletes, we found that the barbell trajectory did not cross a vertical reference line that passed through the initial position of the barbell. The vertical linear velocity of the barbell was increased continuously from the beginning of the movement until the second maximum extension of the knee joint, with no notable dip being observed. Regarding the change in energy of the barbell, we found that the mechanical work for the vertical displacement of the barbell in the first pull was significantly greater than the mechanical work in the second pull. In contrast, the estimated average mechanical power output of the athletes during the vertical displacement of the barbell was significantly greater in the second pull than in the first pull. We conclude that the major elements of the snatch technique of elite Greek weightlifters have not been affected by the new weight classification.

Randomized single-query motion planning in expansive spaces

Abstract: Random sampling is a fundamental technique for motion planning of objects with many degrees of freedom (dof). This thesis presents efficient randomized algorithms for single-query motion planning of objects with many dofs and under complex motion constraints. Unlike most other probabilistic roadmap planners, our algorithms perform no preprocessing of the environment. They sample collision-free configurations incrementally in the connected components of the space that contain the query configurations, thus avoiding the high cost of pre-computing a roadmap for the entire space. Two specific planners are discussed. One addresses the simpler problem of path planning. The other extends the basic idea and takes into account kinematic and dynamic constraints on motion as well. A control system is used to represent both types of constraints in a unified framework. Our algorithms have been tested extensively on both synthesized examples and real-life CAD data from the industry; they have shown strong performance on rigid-body and articulated objects with up to 18 dofs. We also demonstrate their generality and effectiveness in three practical applications: assembly maintainability checking, motion synthesis for animated characters, and kinodynamic motion planning for an integrated real-time robot system in environments with moving obstacles. The lack of theoretical explanation for the randomized motion planners' success in experiments has motivated us to introduce the notion of expansive spaces as a new way to characterize the complexity of input environments. It provides us a conceptual framework to understand why randomized motion planners work well and under what conditions. We prove that in an expansive space, our algorithms find a solution trajectory with probability that converges to 1 at an exponential rate, if a solution exists. An efficient motion planner is also useful as a primitive for accomplishing more complex tasks. An example of this is the robot placement problem, an important application from the manufacturing industry. By combining a randomized path planner with local iterative optimization, our placement algorithm computes simultaneously a base location and a corresponding collision-free path for a fixed-base robot manipulator to execute specified tasks as efficiently as possible.

Synthesis by screw algebra of translating in-parallel actuated mechanisms

Abstract: A new approach to the study of screw systems variations, for infinitesimal motions, is proposed by analyzing the end-effector acceleration of a serial chain. The developed results are applied to the synthesis of translating in-parallel actuated mechanisms. A novel design method is used. to identify screw systems that present invariable kinematic properties for finite motions.

The direct kinematics of parallel manipulators under joint-sensor redundancy

Abstract: We study, for each of the possible joint-sensor layouts, the subspaces into which the motion of the hip-attachment points of parallel manipulators are completely measured. The projection of the motion of these points onto their subspaces allows us to write the underlying direct kinematics as a linear algebraic system constrained by the proper orthogonality of the rotation matrix. Although the solution of this problem requires a nonlinear technique, we propose a linear procedure that provides what we term a polar least square estimate. The resulting procedure is fast, robust to measurement noise, and produces estimates with about the same accuracy as a nonlinear procedure.