Showing papers on "Kinematics published in 1986"

Manipulator Inverse Kinematic Solutions Based on Vector Formulations and Damped Least-Squares Methods

Abstract: Inverse kinematic solutions are used in manipulator controllers to determine corrective joint motions for errors in end-effector position and orientation. Previous formulations of these solutions, based on the Jacobian matrix, are inefficient and fail near kinematic singularities. Vector formulations of inverse kinematic problems are developed that lead to efficient computer algorithms. To overcome the difficulties encountered near kinematic singularities, the exact inverse problem is reformulated as a damped least-squares problem, which balances the error in the solution against the size of the solution. This yields useful results for all manipulator configurations.

A concept for manipulator trajectory planning

Abstract: Following a prescribed trajectory with a manipulator tip in an ideal manner results in a one DOF overall motion whatever the configuration of the manipulator and of the path might be. Thus, a transformation of the equations of motion from joint coordinates to path coordinates leads to a set, which cannot only be solved by formal quadrature but defines as well the phase space of admissible motion constrained by path geometry and joint torques. Time optimal solution representing the maximum mobility of the path-manipulator-configuration can be determined by a field of extremals bounded by a maximum velocity curve, which acts as a trajectory source or sink. Its properties lead to an algorithm for evaluating the time-minimum-curve from a sequence of accelerating/decelerating extremals. Additional optimizing criteria are regarded applying Bellman's principle.

A new geometric notation for open and closed-loop robots

Abstract: This paper presents a new geometric notation for the description of the kinematic of open-loop, tree and closed-loop structure robots. The method is derived from the well-known Denavit and Hartenberg (D-H) notation, which is powerful for serial robots but leads to ambiguities in the case of tree and closed-loop structure robots. The given method has all the advantages of D-H notation in the case of open-loop robots.

Optimal spacecraft rotational maneuvers

Abstract: 1. Introduction. 2. Geometry and Kinematics of Rotational Motion. 3. Basic Principles of Dynamics. 4. Rotational Dynamics of Rigid and Multiple Rigid Body Spacecraft. 5. Dynamics of Flexible Spacecraft. 6. Elements of Optimal Control Theory. 7. Numerical Solution of Two Point Boundary Value Problems. 8. Optimal Maneuvers of Rigid Spacecraft. 9. Optimal Large-Angle Single-Axis Maneuvers of Flexible Spacecraft. 10. Frequency-Shaped Large-Angle Maneuvers of Flexible Spacecraft. 11. Computational Methods for Closed-Loop Control Problems. Appendices: Autonomous Systems of Ordinary Differential Equations. Closed-Form Solution for an Integral Containing Matrix Exponentials. Closed-Form Solutions for Convolution Matrix Integrals and Sensitivity Calculations. Analytical Solution of the Two Body Problem (Keplerian Motion). An Analytic Fourier Transform for a Class of Finite-Time Control Problems. Index.

Robot accuracy analysis based on kinematics

Abstract: The positioning accuracy problem of robot manipulators has long been one of the principal concerns of robot design and control. In a previous work, a linear model that described the robot positioning accuracy due to kinematic errors was developed. However, the previous work considered only the small errors by ignoring the higher order terms and did not address the special case of two consecutive parallel joints. In this work a more detailed model is given that applies to consecutive parallel joints and includes the second-order terms. By comparing the results of the linear model and the second-order model, the accuracy of the linear model can be evaluated for a given manipulator and range of input kinematic errors. The error envelopes obtained using the linear model and the developed second order model for the Puma 560 are plotted and compared for various sets of input kinematic errors. A comparison of the computation complexity for the two models is also given.

Flight Performance and Visual Control of Flight of the Free-Flying Housefly (Musca Domestica L.) I. Organization of the Flight Motor

Abstract: Free-flying houseflies have been filmed simultaneously from two sides. The orientation of the flies' body axes-in three-dimensional space can be seen on the films. A method is presented for the reconstruction of the flies' movements in a fly-centred coordinate system, relative to an external coordinate system and relative to the airstream. The flies are regarded as three-dimensionally rigid bodies. They move with respect to the six degrees of freedom they thus possess. The analysis of the organization of the flight motor from the kinematic data leads to the following conclusions: the sideways movements can, at least qualitatively, be explained by taking into account the sideways forces resulting from rolling the body about the long axis and the influence of inertia. Thus, the force vector generated by the flight motor is most probably located in the fly's midsagittal plane. The direction of this vector can be varied by the fly in a restricted range only. In contrast, the direction of the torque vector can be freely adjusted by the fly. No coupling between the motor force and the torques is indicated. Changes of flight direction may be explained by changes in the orientation of the body axes: straight flight at an angle of sideslip differing from zero is due to rolling. Sideways motion during the banked turns as well as the decrease of translation velocity observed in curves are a consequence of the inertial forces and rolling. The results are discussed with reference to studies about the aerodynamic performance of insects and the constraints for aerial pursuit.

Coordination of Three-Joint Digit Movements for Rapid Finger-Thumb Grasp

Abstract: Human thumb and index finger kinematics were examined for multiple repetitions of a simple grasp task as a means to evaluate motor planning and execution of these important hand movements. Subjects generated a rapid (approximately 90-ms duration) pinch movement of the index finger and thumb from an open-hand position. Approximately 400 repetitions were obtained from four naive subjects. The two-dimensional trajectory of the fingertip and the angular positions of the metacarpophalangeal (MP) and proximal interphalangeal (PIP) joints of the index finger were recorded along with the angular position of the thumb interphalangeal joint (TH). Individual joint angular positions were transduced using planar electrogoniometers of an exoskeletal linkage design. Except for consistent single-peaked joint angle and digit trajectory velocity profiles, most kinematic features of the grasp varied considerably across trials, including fingertip spatial position at contact, specific finger paths, finger and thumb path distances, finger and thumb peak tangential velocities, and 5) individual joint rotation magnitudes and peak velocities. However, this kinematic variability was not random. Variable TH angular positioning was paralleled by complementary two-dimensional variations in the finger path. These fingertip adjustments were accomplished by actively controlled, reciprocal angular positioning of the MP and PIP joints. Specifically, with natural reductions in thumb flexion, MP flexion was greater while PIP flexion was reduced and vice versa. These adjustments acted to minimize variations in the point contact of the finger on the thumb and yielded a robust and seemingly natural preference for finger-thumb contact at the more distal surfaces of the digits. The kinematic variability was not due to the finger and thumb movements being controlled independently of digit contact. The variable appositional movements of the finger and thumb and the associated contact force were generated as a single action. This was indicated by an absence of kinematic or force adjustments after contact, smooth digit trajectories with a single peak in their tangential velocities, and finger-thumb contact that consistently occurred well after peak velocity. Likewise, because the variability in the kinematics of the grasp was systematic, it apparently was not due simply to sloppiness or noise in motor execution.(ABSTRACT TRUNCATED AT 400 WORDS)

Dynamics of Articulated Structures. Part I. Theory

Abstract: A finite element based method is developed for geometrically nonlinear dynamic analysis of spatial articulated structures; i.e., structures in which kinematic connections permit large relative displacement between components that undergo small elastic deformation. Vibration and static correction modes are used to account for linear elastic deformation of components. Kinematic constraints between components are used to define boundary conditions for vibration analysis and loads for static correction mode analysis. Constraint equations between flexible bodies are derived in a systematic way and a Lagrange multiplier formulation is used to generate the coupled large displacement-small deformation equations of motion. A lumped mass finite element structural analysis formulation is used to generate deformation modes. An intermediate-processor is used to calculate time-independent terms in the equations of motion and to generate input data for a large-scale dynamic analysis code that includes coupled e...

Arm signature identification

Abstract: The positioning accuracy of commercially-available industrial robotic manipulators depends upon a kinematic model which describes the robot geometry in a parametric form Manufacturing errors in machining and assembly of manipulators lead to discrepancies between the design parameters and the physical structure Improving the kinematic performance thus requires identification of the actual kinematic parameters of each individual robot This identification of the individual kinematic parameters is called the arm signature which is then incorporated into the manipulator's controller to improve positional accuracy In this paper, an approach, based on a new parametric model of the kinematics, is introduced for arm signature identification The S-Model utilizes 6n parameters to describe the robot geometry and offers advantages for identification by decomposing the parameters into individually identified subsets The S-Model parameters are then mapped into the equivalent Denavit-Hartenberg parameters for implementation into the controller The S-Model arm signature identification algorithm can be implemented with relatively simple sensors and improves accuracy through statistical averaging This algorithm has been implemented with an external ultrasonic range sensor to measure robot end-effector positions Experimental results of arm signature identification of seven Unimation/Westinghouse Puma 560 robots demonstrated an average reduction in positioning error by a factor of 5-10 for a spectrum of representative test tasks

Kinematic Resonance and Memory Effect in Free Mass Gravitational Antennas

Abstract: Detailed studies are made of two effects in the motion of free masses subject to the influence of gravitational waves: kinematic resonance and the memory effect. In the first of these, besides the oscillatory motion there is a systematic change in the distance between the bodies if they become free in an appropriate phase of the gravitational wave. The second effect takes the form that the distance between a pair of bodies will, in general, be different from the original distance after they have been influenced by a pulse of gravitational radiation. Possible practical applications of these effects in three different experimental programs are discussed. Allowance for these effects should lessen the requirements on the detection systems and ultimately raise the sensitivity of gravitational antennas.

A study of multiple manipulator inverse kinematic solutions with applications to trajectory planning and workspace determination

Abstract: The paper deals with the problem of the multiple solutions of the coordinate transformations for an n-link robot manipulator. Aspect decomposition of the admissible domain of the joint space is introduced and an algorithm for automatic computation of Aspect decomposition is presented. This decomposition takes into account the morphology of the robot arm and the kinematic task definition as well. Two fields of applications are then investigated : - automatic generation of the end effector workspace, - predetermination of trajectories which avoid mechanical limits of the manipulator actuators. Finally an implementation of these methods and algorithms in the CATIA CAD system is given.

The Potential Field Approach And Operational Space Formulation In Robot Control

Abstract: The paper presents a radically new approach to real-time dynamic control and active force control of manipulators In this approach the manipulator control problem is reformulated in terms of direct control of manipulator motion in operational space, the space in which the task is originally described, rather than controlling the task’s corresponding joint space motion obtained after geometric and kinematic transformation The control method is based on the construction of the manipulator end effector dynamic model in operational space Also, the paper presents a unique real-time obstacle avoidance method for manipulators and mobile robots based on the “artificial potential field” concept In this method, collision avoidance, traditionally considered a high level planning problem, can be effectively distributed between different levels of control, allowing real-time robot operations in a complex environment Using a time-varying artificial potential field, this technique has been extended to moving obstacles A two-level control architecture has been designed to increase the system real-time performance These methods have been implemented in the COSMOS system for a PUMA 560 robot arm We have demonstrated compliance, contact, sliding, and insertion operations using wrist and finger sensing, as well as real-time collision avoidance with moving obstacles using visual sensing

Kinematic analysis of manipulators using the zero reference position description

Abstract: This paper presents a new method ofkinematic analysis of manipulators, called the zero reference position method. In this method, the description of the manipulator is in terms of the axes directions and locations in the zero reference posi tion. This position is a conveniently chosen position in which all joint variable values are defined to be zero. This type of manipulator description is easy to learn and is not prone to errors of interpretation. The governing kinematic equations of the manipulator are derived from the principle of similarity. In this paper, it is shown that this method leads to a modular approach to the closed-form solutions of manipulators with ordinary or geared three-roll wrists. Complete solutions for six types of contemporary industrial robots are included.

Computationally efficient kinematics for manipulators with spherical wrists base

Abstract: Most manipulators in use today are kinematically simple, and closed-form symbolic equations are the most efficient means of expressing their kinematics. The analysis presented in this paper is base...

Step-tracking movements of the wrist in humans. I. Kinematic analysis

Abstract: We have examined the kinematics of the initial trajectory of step- tracking movements performed by human subjects. Each subject tracked a target that required 5–30 degrees of radial or ulnar deviation of the wrist. All movements were to be performed as accurately as possible. Speed instructions were given before each trial. When subjects performed different amplitude movements following the same speed instruction, the peaks of velocity, acceleration, and jerk were linearly related to peak displacement. The peaks of velocity, acceleration, and jerk also changed when the speed instruction was altered. Thus, for any given movement, the peak values of the derivatives of displacement were dependent on both movement amplitude and intended speed. As a result, the peak values of the derivatives cannot be used by themselves to control or monitor peak displacement. When subjects performed different amplitude movements following the same speed instruction, movement duration tended to remain constant. In contrast, movement duration changed when the speed instruction was altered. Movements performed when subjects intended to move slowly had longer durations than when subjects intended to move quickly. These results suggest that subjects volitionally alter intended speed by selecting different movement durations. When both movement amplitude and intended speed were varied, the peak displacement of a step- tracking movement was linearly related to the product of 2 kinematic variables: the initial peak of a derivative of displacement (either velocity, acceleration, or jerk) and movement duration. On the basis of our observations, we propose that central commands generate step- tracking movements of different amplitudes and intended speeds by adjusting both the magnitude and duration of a derivative of displacement.

Using dynamic analysis to animate articulated bodies such as humans and robots

Abstract: A method of animating articulated (linked) bodies such as humans, animals and robots using dynamic analysis is presented. Dynamic analysis predicts motion by analyzing the effect of forces and torques on mass; this is different than the usual kinematic method of specifying motion, where positions, velocities, and accelerations are given without considering the forces and torques producing motion. It is difficult to kinematically specify realistic motion, particularly in cases where the body is moving fast, in complex patterns, or with great freedom. In such cases, animation based on dynamic analysis, though more expensive, may be preferable. Animation using dynamic analysis is also useful in the design and control of robots and other mechanical manipulators, and for analyzing the movement of humans and animals in biomechanics and sports.

Joint control strategies and hand trajectories in multijoint pointing movements.

Abstract: The role of timing in the control of multijoint pointing movements was evaluated. Eight subjects performed rapid pointing movements to a variety of target locations. The subject’s right arm was strapped to a 2° of freedom manupilandum that permitted shoulder and elbow motion in the horizontal plane. Initial and final position of the hand and magnitude of displacement was varied to determine effects on timing characteristics. Kinematics and kinetics of the shoulder, elbow, and hand were analyzed.The hand paths and velocity profiles observed were consistent with prior reports. Multiple regression analysis of kinematic variables disclosed that timing of joint movement onset was independent of initial and final positions of the hand, but was linearly related to joint displacement: the joint that moved farther started moving first. Using computer simulations to create joint movement onset, times that were different from the observed ones always resulted in hand paths with increased curvatures and loss of the s...

Coordinates for molecular dynamics: Orthogonal local systems

Abstract: Systems of orthogonal coordinates for the problem of the motion of three or more particles in classical or in quantum mechanics are considered from the viewpoint of applications to intramolecular dynamics and chemical kinetics. These systems, for which the kinetic energy of relative motion is diagonal, are generated by making extensive use of the concept of kinematic rotations, which act on coordinates of different particles and describe their rearrangements. An explicit representation of these rotations by mass dependent matrices allows to relate different particle couplings in the Jacobi scheme, and to build up alternative systems (such as those based on the Radau–Smith vectors or variants thereof): this makes it possible to obtain coordinates which, while being rigorously orthogonal, may approximate closely the local ones, which are based on actual interparticle distances and are in general nonorthogonal. It is also briefly shown that by defining as variables the parameters describing the kinematic rotations it is possible to obtain nonorthogonal systems of coordinates, which are useful in the treatment of collective modes.

A closed-form solution for the control of manipulators with kinematic redundancy

Abstract: A closed-form equation for inverse kinematics of manipulators with redundancy is derived, using the Lagrangian multiplier method. The proposed equation is proved to provide the exact equilibrium state for the resolved motion method, and is shown to be a general expression that yields the extended Jacobian method. The repeatability problem in the resolved motion method does not exist in the proposed equation. The equation is demonstrated to give more accurate trajectories than the resolved motion method.