Showing papers on "Kinematics published in 1987"

A unified approach for motion and force control of robot manipulators: The operational space formulation

Abstract: A framework for the analysis and control of manipulator systems with respect to the dynamic behavior of their end-effectors is developed. First, issues related to the description of end-effector tasks that involve constrained motion and active force control are discussed. The fundamentals of the operational space formulation are then presented, and the unified approach for motion and force control is developed. The extension of this formulation to redundant manipulator systems is also presented, constructing the end-effector equations of motion and describing their behavior with respect to joint forces. These results are used in the development of a new and systematic approach for dealing with the problems arising at kinematic singularities. At a singular configuration, the manipulator is treated as a mechanism that is redundant with respect to the motion of the end-effector in the subspace of operational space orthogonal to the singular direction.

Robot Dynamics Algorithms

Abstract: Spatial Kinematics.- Spatial Dynamics.- Inverse Dynamics - The Recursive Newton-Euler Method.- Forward Dynamics - The Composite-Rigid-Body Method.- Forward Dynamics - The Articulated-Body Method.- Extending the Dynamics Algorithms.- Coordinate Systems and Efficiency.- Contact, Impact, and Kinematic Loops.- Accuracy and Efficiency.- Contact and Impact.

The control of hand equilibrium trajectories in multi-joint arm movements

Abstract: According to the equilibrium trajectory hypothesis, multi-joint arm movements are achieved by gradually shifting the hand equilibrium positions defined by the neuromuscular activity. The magnitude of the force exerted on the arm, at any time, depends on the difference between the actual and equilibrium hand positions and the stiffness and viscosity about the equilibrium position. The purpose of this paper is to test the validity and implications of this hypothesis in the context of reaching movements. A mathematical description of the behavior of an arm tracking the equilibrium trajectory was developed and implemented in computer simulations. The joint stiffness parameters used in these simulations were derived from experimentally measured static stiffness values. The kinematic features of hand equilibrium trajectories which were derived from measured planar horizontal movements gave rise to the suggestion that the generation of reaching movements involves explicit planning of spatially and temporally invariant hand equilibrium trajectories. This hypothesis was tested by simulating actual arm movements based on hypothetical equilibrium trajectories. The success of the predicted behavior in capturing both the qualitative features and the quantitative kinematic details of the measured movements supports the equilibrium trajectory hypothesis. The control strategy suggested here may allow the motor system to avoid some of the complicated computational problems associated with multi-joint arm movements.

Kinematic modeling of wheeled mobile robots

Abstract: We formulate the kinematic equations of motion of wheeled mobile robots incorporating conventional, omnidirectional, and ball wheels.1 We extend the kinematic modeling of stationary manipulators to accommodate such special characteristics of wheeled mobile robots as multiple closed-link chains, higher-pair contact points between a wheel and a surface, and unactuated and unsensed wheel degrees of freedom. We apply the Sheth-Uicker convention to assign coordinate axes and develop a matrix coordinate transformation algebra to derive the equations of motion. We introduce a wheel Jacobian matrix to relate the motions of each wheel to the motions of the robot. We then combine the individual wheel equations to obtain the composite robot equation of motion. We interpret the properties of the composite robot equation to characterize the mobility of a wheeled mobile robot according to a mobility characterization tree. Similarly, we apply actuation and sensing characterization trees to delineate the robot motions producible by the wheel actuators and discernible by the wheel sensors, respectively. We calculate the sensed forward and actuated inverse solutions and interpret the physical conditions which guarantee their existence. To illustrate the development, we formulate and interpret the kinematic equations of motion of Uranus, a wheeled mobile robot being constructed in the CMU Mobile Robot Laboratory.

Stable execution of contact tasks using impedance control

Abstract: This paper presents an experimental evaluation of the performance of a nonlinear robot control algorithm on a contact task involving free motion, constrained motion and transitions between the two. The algorithm is an implementation of impedance control which uses end-point force feedback. Stable control of the force exerted on a rigid surface is achieved without recourse to a soft sensor. Motion control is achieved without inverse kinematic computations. It is unnecessary to switch between different modes of control at the moment of contact as the impedance controller is competent in all phases of the task.

Space-time behavior of single and bimanual rhythmical movements: data and limit cycle model.

Abstract: How do space and time relate in rhythmical tasks that require the limbs to move singly or together in various modes of coordination? And what kind of minimal theoretical model could account for the observed data? Earlier findings for human cyclical movements were consistent with a nonlinear, limit cycle oscillator model (Kelso, Holt, Rubin, & Kugler, 1981) although no detailed modeling was performed at that time. In the present study, kinematic data were sampled at 200 samples/second, and a detailed analysis of movement amplitude, frequency, peak velocity, and relative phase (for the bimanual modes, in phase and antiphase) was performed. As frequency was scaled from 1 to 6 Hz (in steps of 1 Hz) using a pacing metronome, amplitude dropped inversely and peak velocity increased. Within a frequency condition, the movement's amplitude scaled directly with its peak velocity. These diverse kinematic behaviors were modeled explicitly in terms of low-dimensional (nonlinear) dissipative dynamics, with linear stiffness as the only control parameter. Data and model are shown to compare favorably. The abstract, dynamical model offers a unified treatment of a number of fundamental aspects of movement coordination and control. Language: en

Velocity analysis by iterative profile migration

Abstract: In conventional seismic processing, velocity analysis is performed by using the normal moveout (NMO) equation which is based on the assumption of flat, horizontal reflectors. Imaging by migration (either before or after stack) is done normally in a subsequent step using these velocities. In this paper, velocity analysis and imaging are combined in one step, and migration itself is used as a velocity indicator. Because, unlike NMO, migration can be formulated for any velocity function, migration‐based velocity analysis methods are capable of handling arbitrary structures, i.e., those with lateral velocity variations. In the proposed scheme, each shot gather (profile) is migrated with an initial depth‐velocity model. Profile migration is implemented in the (x, ω) domain, but the actual implementation of profile migration is not critical, as long as it is not done in a spatial‐wavenumber domain, which would preclude handling of lateral velocity variations. After migration with an initial velocity model, the ...

Implications of rotational kinematics for the oculomotor system in three dimensions

Abstract: 1. This paper develops three-dimensional models for the vestibuloocular reflex (VOR) and the internal feedback loop of the saccadic system. The models differ qualitatively from previous, one-dimensional versions, because the commutative algebra used in previous models does not apply to the three-dimensional rotations of the eye. 2. The hypothesis that eye position signals are generated by an eye velocity integrator in the indirect path of the VOR must be rejected because in three dimensions the integral of angular velocity does not specify angular position. Computer simulations using eye velocity integrators show large, cumulative gaze errors and post-VOR drift. We describe a simple velocity to position transformation that works in three dimensions. 3. In the feedback control of saccades, eye position error is not the vector difference between actual and desired eye positions. Subtractive feedback models must continuously adjust the axis of rotation throughout a saccade, and they generate meandering, dysmetric gaze saccades. We describe a multiplicative feedback system that solves these problems and generates fixed-axis saccades that accord with Listing's law. 4. We show that Listing's law requires that most saccades have their axes out of Listing's plane. A corollary is that if three pools of short-lead burst neurons code the eye velocity command during saccades, the three pools are not yoked, but function independently during visually triggered saccades. 5. In our three-dimensional models, we represent eye position using four-component rotational operators called quaternions. This is not the only algebraic system for describing rotations, but it is the one that best fits the needs of the oculomotor system, and it yields much simpler models than do rotation matrix or other representations. 6. Quaternion models predict that eye position is represented on four channels in the oculomotor system: three for the vector components of eye position and one inversely related to gaze eccentricity and torsion. 7. Many testable predictions made by quaternion models also turn up in models based on other mathematics. These predictions are therefore more fundamental than the specific models that generate them. Among these predictions are 1) to compute eye position in the indirect path of the VOR, eye or head velocity signals are multiplied by eye position feedback and then integrated; consequently 2) eye position signals and eye or head velocity signals converge on vestibular neurons, and their interaction is multiplicative.(ABSTRACT TRUNCATED AT 400 WORDS)

A Recursive Formulation for Constrained Mechanical System Dynamics: Part II. Closed Loop Systems

Abstract: A recursive formulation of the equations of motion of constrained mechanical systems with closed loops is derived, using tools of variational and vector calculus. Kinematic couplings between pairs of contiguous bodies presented in Part 1 of this paper are generalized. Lagrange multipliers are introduced to account for the effects of joints that are cut to define a tree structure. Constraint Jacobian terms are added to the reduced variational equations derived in Part I. Cut-joint constraint acceleration equations are derived, to complete the reduced equations of motion. Lagrange multipliers associated with each cut-joint are eliminated at the first junction body encountered that permits closing the loop that constraints in cut joint. The inductive algorithm developed in Part I is used to calculate accelerations for the system. A multi-loop compressor is analyzed to illustrate use of the method.

Constrained relations between two coordinated industrial robots for motion control

Abstract: Tasks for two coordinated industrial robots always bring the robots in contact with the same object. Physically the three form a closed kinematic chain mechanism. When the chain is in motion, the positions and orientations of the two robots must satisfy a set of holonomic equality canstraints for every time instant. To eliminate motion errors between them, we assign one of them to carry the major part of the task. Its motion is planned accordingly. The motion of the second robot is to follow that of the first robot, as specified by the re lations of the joint velocities derived from the constraint conditions. Thus if any modification of the motion is needed in real time, only the motion of the first robot is modified. The modification for the second robot is done implicitly through the constraint conditions. Specifically, when the joint displacements, velocities, and accelerations of the first robot are known for the planned or modified motion, the corre sponding variables for the second robot and the for...

Kinematic stability issues in force control of manipulators

Abstract: In active force or compliance implementations for multi-link manipulators, there is typically a kinematic coordinate transformation in the feedback path. A coordinate transformation will affect the dynamics of the closed-loop system and possibly make it unstable. It is shown that the hybrid force/position control method of Raibert and Craig (1981) exhibits such kinematically induced instabilities for revolute manipulators, whereas other force control methods, such as the stiffness control and the operational space methods, do not. Both theoretical analyses and experimental results on the MIT Serial Link Direct Drive Arm are given.

Controlling dynamic simulation with kinematic constraints

Abstract: Theoretical and numerical aspects of the implementation of a DYNAmic MOtion system, dubbed DYNAMO, for the dynamic simulation of linked figures is presented. The system introduces three means for achieving, control of the resulting motion which have not been present in previous dynamic simulation systems for computer animation. (1) "Kinematic constraints" permit traditional keyframe animation systems to be embedded within a dynamic analysis. Joint limit constraints are also handled correctly through kinematic constraints. (2) "Behavior functions" relate the momentary state of the dynamic system to desired forces and accelerations within the figure. (3) "Inverse dynamics" provides a means of determining the forces required to perform a specified motion.The combination of kinematic and dynamic specifications allows the animator to think about each part of the animation in the way that is most suitable for the task. Successful experimental results are presented which demonstate the ability to provide control without disrupting the dynamic integrity of the resulting motion.

Kinematic Form and Scaling: Further Investigations on the Visual Perception of Lifted Weight

Abstract: Observers are able to judge accurately the weight lifted by another person when only the motions of reflective patches attached to the lifter's major limb joints and head can be seen (Runeson & Frykholm, 1981). What properties of these complex kinematic patterns allow judgments of weight to be made? The pattern of variation in velocity of the lifted object over position is explored as a source of information for weight: It is found to provide limited information. How are variations in kinematic patterns scaled to allow judgments of weight, a kinetic quantity? The possibility of a source of information for scaling in the kinematics is investigated. Judgments based only on patch-light displays are accurate to a degree that is improved by an extrinsic scaling basis. Finally, the sensitivity to scaling of alternative metrics used in judging is explored. Intrinsic metrics are discovered to be less sensitive to the absence of an extrinsic basis for scaling.

Kinematic and electromyographic responses to perturbation of a rapid grasp

Abstract: Kinematic and electromyographic responses of the thumb and index finger to load-induced extension of the thumb during a rapid precision grasp of the thumb and finger were studied in four human subj...

A closed-form solution for inverse kinematics of robot manipulators with redundancy

Abstract: A closed-form solution formula for inverse kinematics of manipulators with redundancy is derived using the Lagrangian multiplier method. The proposed method is proved to provide the exact equilibrium state for the resolved-motion method. The repeatability problem in the resolved-motion method does not exist in the proposed method. The method is demonstrated to give more accurate trajectories than the resolved-motion method.

A model of handwriting.

Abstract: The research reported here is concerned with hand trajectory planning for the class of movements involved in handwriting. Previous studies show that the kinematics of human two-joint arm movements in the horizontal plane can be described by a model which is based on dynamic minimization of the square of the third derivative of hand position (jerk), integrated over the entire movement. We extend this approach to both the analysis and the synthesis of the trajectories occurring in the generation of handwritten characters. Several basic strokes are identified and possible stroke concatenation rules are suggested. Given a concise symbolic representation of a stroke shape, a simple algorithm computes the complete kinematic specification of the corresponding trajectory. A handwriting generation model based on a kinematics from shape principle and on dynamic optimization is formulated and tested. Good qualitative and quantitative agreement was found between subject recordings and trajectories generated by the model. The simple symbolic representation of hand motion suggested here may permit the central nervous system to learn, store and modify motor action plans for writing in an efficient manner.

Kinematic and Dynamic Analysis of Parallel Manipulators by Means of Motor Algebra

Abstract: Analyse cinematique et dynamique des manipulateurs ayant une chaine cinematique partiellement fermee (mecanisme parallele)

Using Dynamic Analysis for Realistic Animation of Articulated Bodies

Abstract: A major problem in computer animation is creating motion that appears natural and realistic, particularly in such complex articulated bodies as humans and other animals. At present, truly lifelike motion is produced mainly by copying recorded images, a tedious and lengthy process that requires considerable external equipment. An alternative is the use of dynamic analysis to predict realistic motion. Using dynamic motion control, bodies are treated as masses acting under the influence of external and internal forces and torques. Dynamic control is advantageous because motion is naturally restricted to physically realizable patterns, and many types of motion can be predicted automatically. Use of dynamics is computationally expensive and specifying controlling forces and torques can be difficult. However, there is evidence that dynamics offers hope for more realistic, natural, and automatic motion control. Because such motion simulates real world conditions, an animation system using dynamic analysis is also a useful tool in such related fields as robotics and biomechanics.

Finding collision-free smooth trajectories for a non-holonomic mobile robot

Abstract: Most mobile robots are subject to kinematic constraints (non-holonomic Joints), i.e., the number of degrees of freedom is less than the number of configuration parameters. Such navigate in very constrained space, but at the expense of backing up maneuvers [Laumond 86]. In this paper we study the original problem of finding collision-free smooth trajectories, i.e. with never backing up, for a circular mobile robot whose the turning radius is lower bounded.

A prototype arm signature identification system

Abstract: The S-Model identification algorithm described in [6,7] is a technique which can be used to accurately identify the actual kinematic parameters of serial link robotic manipulators. The actual kinematic parameters of a manipulator differ from the design parameters due to the presence of random manufacturing errors. The set of identified kinematic parameters is called the arm signature. Accurate arm signatures are needed to control and improve the end-effector positioning accuracy of robotic manipulators for a variety of important tasks. This paper describes the hardware and software implementation of a prototype arm signature identification system. This system uses an external ultrasonic range sensor to measure the Cartesian position of target points placed on the links of the robot. Algorithms to compensate the primary range measurements for spatial variations in air temperature and humidity are also incorporated. The relative Cartesian positioning accuracy of the sensor system is ± .02cm. The general characteristics of our sensor design and the overall system design which exploits averaging over many sensor readings offer numerous advantages for arm signature identification. The prototype system has been applied in [6] to improve the kinematic performance of seven Puma 560 robots. For these robots relative positioning accuracy was improved by a factor of 10 on straight'line positioning tasks. Analysis and simulation of systematic errors confirms that the resolution of our sensor system should provide kinematic performance close to the limitations of the joint encoders. Our experimental studies show that sensor bias ultimately limits kinematic performance using this arm signature system. Experience with this prototype system has demonstrated that the S-Model identification algorithm is a practical and viable method for improving the kinematic performance of robotic manipulators.

On the spatial motion of a rigid body with point contact

Abstract: A study is made of the so-called slide motions between developable ruled surfaces with the line contact under spatial motion. In particular, the authors consider instantaneous time-based kinematics, which includes the contact speeds and rates of change along reference curves on the surfaces, the velocity, acceleration, and jerk of a reference point on the moving surface, and the constraints on the angular velocity and angular acceleration for maintaining line contact. The derived kinematic relationships can be applied to robotic path planning and actual motion calculations in the presence of a tactile sensor to measure the relative motion at the contact line. >

A conceptual approach to teaching kinematics

Abstract: Results from research on student understanding of velocity and acceleration have been used to guide the development of a conceptual approach to teaching kinematics. This paper describes how instruction based on the observation of actual motions can help students: (1) develop a qualitative understanding of velocity as a continuously varying quantity, of instantaneous velocity as a limit, and of uniform acceleration as the ratio of the change in instantaneous velocity to the elapsed time; (2) distinguish the concepts of position, velocity, change of velocity, and acceleration from one another; and (3) make connections among the various kinematical concepts, their graphical representations, and the motions of real objects. Instructional strategies designed to address specific difficulties identified in the investigation are illustrated by example.

Inverse kinematic functions for redundant manipulators

Abstract: A general approach to the kinematic control of redundant manipulators using inverse kinematic functions is presented. The principal objective is to find an inverse kinematic function and a workspace such that the ratio of joint speed to workspace speed is bounded. The definition of such feasible workspaces leads naturally to optimization problems aimed at reducing this bound. The application of these results to the inverse kinematics of a redundant wrist illustrates both the theoretical importance of the approach and its immediate practicality. However, for general redundant manipulators, the development of algorithms for constructing feasible workspaces and the refinement of the optimization problem and its solution remain open questions ripe for further research.

A method for calibrating and compensating robot kinematic errors

Abstract: This paper presents a method of calibrating and compensating for the kinematic errors in robot manipulators. A method of selecting a set of independent kinematic errors for modeling any geometric errors in a manipulator's structure is developed. A calibration algorithm is presented for finding the values of these kinematic errors by measuring the end-effector Cartesian position. These kinematic errors are experimentally determined for a PUMA 560 six joint manipulator. Two general purpose compensation algorithms are developed and the improvement in the Cartesian position of the end-effector is experimentally measured and these results are presented.

Effect of kinematics on motion planning for planar robot arms moving amidst unknown obstacles

Abstract: An approach of dynamic path planning (DPP) was introduced elsewhere, and nonheuristic algorithms were described for planning collision-free paths for a point automaton moving in an environment filled with unknown obstacles of arbitrary shape. The DPP approach was further extended to a planar robot arm with revolute joints; in this case, every point of the robot body is subject to collision. Under the accepted model, the robot, using information about its immediate surroundings provided by the sensory feedback, continuously (dynamically) generates its path. Various kinematic configurations of planar arms with revolute and sliding joints are analyzed in this paper from the standpoint of applying the same strategy. It is shown that, depending on the arm kinematics, specific modifications must be introduced in the path planning algorithm to preserve convergence. The approach presents an attractive method for robot motion planning in unstructured environments with uncertainty.

Coupling effects of kinematics and flexibility in manipulators

Abstract: This paper presents a finite, element-based, nonlinear model of flexibility effects in manipulators. The model allows for the coupling effects due to elastic deformations of the manip ulator links and the kinematics at the manipulator joints. The governing equations of motion are derived including the effects of rotatory inertia, shear deformation. and the effects of gross nonlinear motion of each of the links. Using Timo shenko beam theory, a simple and efficient finite element is proposed for the manipulator links. The complete dynamic model is further integrated with a simplistic representation of actuator-servo effects. The model is described in detail for the case of a planar manipulator with revolute joints. The same model can also be extended to spatial manipulators with prismatic pairs.