Showing papers on "Kinematics published in 1995"

Control of a nonholonomic mobile robot: backstepping kinematics into dynamics

Abstract: A dynamical extension that makes possible the integration of a kinematic controller and a torque controller for nonholonomic mobile robots is presented. A combined kinematic/torque control law is developed using backstepping and asymptotic stability is guaranteed by Lyapunov theory. Moreover, this control algorithm can be applied to the three basic nonholonomic navigation problems: tracking a reference trajectory, path following and stabilization about a desired posture. A general structure for controlling a mobile robot results that can accommodate different control techniques ranging from a conventional computed-torque controller, when all dynamics are known, to adaptive controllers.

The origin and use of positional frames of reference in motor control

Abstract: A hypothesis about sensorimotor integration (the λ model) is described and applied to movement control and kinesthesia. The central idea is that the nervous system organizes positional frames of reference for the sensorimotor apparatus and produces active movements by shifting the frames in terms of spatial coordinates. Kinematic and electromyographic patterns are not programmed, but emerge from the dynamic interaction among the system s components, including external forces within the designated frame of reference. Motoneuronal threshold properties and proprioceptive inputs to motoneurons may be cardinal components of the physiological mechanism that produces positional frames of reference. The hypothesis that intentional movements are produced by shifting the frame of reference is extended to multi-muscle and multi-degrees-of-freedom systems with a solution of the redundancy problem that allows the control of a joint alone or in combination with other joints to produce any desired limb configuration and movement trajectory. The model also implies that for each motor behavior, the nervous system uses a strategy that minimizes the number of changeable control variables and keeps the parameters of these changes invariant. Examples are provided of simulated kinematic and electromyographic signals from single- and multi-joint arm movements produced by suggested patterns of control variables. Empirical support is provided and additional tests of the model are suggested. The model is contrasted with others based on the ideas of programming of motoneuronal activity, muscle forces, stiffness, or movement kinematics.

Are arm trajectories planned in kinematic or dynamic coordinates? An adaptation study

Abstract: There are several invariant features of pointto-point human arm movements: trajectories tend to be straight, smooth, and have bell-shaped velocity profiles. One approach to accounting for these data is via optimization theory; a movement is specified implicitly as the optimum of a cost function, e.g., integrated jerk or torque change. Optimization models of trajectory planning, as well as models not phrased in the optimization framework, generally fall into two main groups-those specified in kinematic coordinates and those specified in dynamic coordinates. To distinguish between these two possibilities we have studied the effects of artificial visual feedback on planar two-joint arm movements. During self-paced point-to-point arm movements the visual feedback of hand position was altered so as to increase the perceived curvature of the movement. The perturbation was zero at both ends of the movement and reached a maximum at the midpoint of the movement. Cost functions specified by hand coordinate kinematics predict adaptation to increased curvature so as to reduce the visual curvature, while dynamically specified cost functions predict no adaptation in the underlying trajectory planner, provided the final goal of the movement can still be achieved. We also studied the effects of reducing the perceived curvature in transverse movements, which are normally slightly curved. Adaptation should be seen in this condition only if the desired trajectory is both specified in kinematic coordinates and actually curved. Increasing the perceived curvature of normally straight sagittal movements led to significant (P 0.05). The results of the curvature-increasing study suggest that trajectories are planned in visually based kinematic coordinates. The results of the curvature-reducing study suggest that the desired trajectory is straight in visual space. These results are incompatible with purely dynamicbased models such as the minimum torque change model. We suggest that spatial perception-as mediated by vision-plays a fundamental role in trajectory planning.

The kinematics of hyper-redundant robot locomotion

Abstract: This paper considers the kinematics of hyper-redundant (or "serpentine") robot locomotion over uneven solid terrain, and presents algorithms to implement a variety of "gaits". The analysis and algorithms are based on a continuous backbone curve model which captures the robot's macroscopic geometry. Two classes of gaits, based on stationary waves and traveling waves of mechanism deformation, are introduced for hyper-redundant robots of both constant and variable length. We also illustrate how the locomotion algorithms can be used to plan the manipulation of objects which are grasped in a tentacle-like manner. Several of these gaits and the manipulation algorithm have been implemented on a 30 degree-of-freedom hyper-redundant robot. Experimental results are presented to demonstrate and validate these concepts and our modeling assumptions.

Development of an omni-directional mobile robot with 3 DOF decoupling drive mechanism

Abstract: A new driving mechanism for holonomic omnidirectional mobile robots is designed, which enables 3 DOF motion control by three correspondent actuators in a decoupled manner with no redundancy A prototype of the omnidirectional mobile robot with the driving mechanism is developed including a parallel link suspension mechanism The kinematics of the omnidirectional mobile robot is also analyzed, and simulation for velocity control of the robot is performed by a method for velocity modulation with interpolation to achieve the given target position and velocity

Experimental instability in the lumbar spine.

Abstract: Study design An in vivo animal model of lumbar segmental instability, involving both passive and active stabilizing components of the spine, was developed. Objective The aim of this investigation was to dynamically study the alterations in segmental kinematics as a result of interventions to the passive stabilizing components and to the lumbar musculature. Summary of background data Segmental instability in the lumbar spine is associated with abnormal intervertebral motion. The majority of biomechanical studies have examined the in vitro effects of transecting individual stabilizing structures (i.e., intervertebral disc, facet joints, and ligaments), and have not simultaneously considered the effects of active musculature on spinal kinematics, which exist in the in vivo environment. Also, few studies have evaluated the kinematic behavior in the neutral region, for example, the transition phase between flexion and extension. Methods Four experimental groups comprised 33 pigs, each of which followed different surgical injury sequences to the L3-L4 motion segment. An instrumented linkage attached to the L3-L4 motion segment was used to measure the sagittal kinematics during dynamic flexion-extension after each surgical injury and after bilateral stimulation of the lumbar paraspinal musculature. Results Injuries to the disc resulted in greater overall axial translation. Graded injuries to the facet joint mainly caused changes in sagittal rotation and shear translation. When the facet injuries were compounded by removal of the transverse processes, there was significantly greater coupled motion and increased hysteresis in the neutral region for rotation. Extensive muscular stimulation after each of the injuries caused significantly greater rotation and shear translation, along with a tendency toward reduced axial translation, when compared to the unstimulated case. Although increasing the range of motion, increased muscular activity stabilized the injured motion segment by smoothing the erratic rotation pattern of motion, particularly in the neutral region. Conclusions Because of the direct attachment to the vertebrae, both passive and active strain from the musculature influence the spinal kinematics in normal or destabilized motion segments. Although increasing the range of motion, stimulation of the musculature surrounding the injured motion segment has a stabilizing effect by reducing abrupt kinematic behavior, particularly in the neutral region where the muscles are under reduced tension. A facetectomy produces a paradoxical kinematic behavior, which enhances the unstable condition of the motion segment. Surgical and rehabilitative treatments for patients with segmental instability need to consider the physiologic influences of the spinal musculature.

On the mobility and manipulability of general multiple limb robots

Abstract: In this paper, the analysis of the differential kinematics and manipulability measures of robotic systems comprised of multiple cooperating limbs is considered. The goals of this study can be articulated in four points: 1) to enumerate the degrees of freedom of the manipulation system; 2) to describe analytically all possible first-order differential motions of the system at a given configuration; 3) to evaluate in the velocity domain the functionality of a manipulation system, with respect to the task it is required to perform; and 4) to calculate the bounds for the velocities achievable by the system, given bounds on the capabilities of joint actuators. The assumptions made on the robotic system are quite general, so that many complex devices (e.g., dextrous hands, legged vehicles, whole-arm manipulators, etc.) can be dealt with in a unified and convenient framework. >

An implicit loop method for kinematic calibration and its application to closed-chain mechanisms

Abstract: A unified formulation for the calibration of both serial-link robots and robotic mechanisms having kinematic closed-loops is presented and applied experimentally to two 6-degree-of-freedom devices: the RSI 6-DOF hand controller and the MEL "modified Stewart platform". The unification is based on an equivalence between end-effector measurements and constraints imposed by the closure of kinematic loops. Errors are allocated to the joints such that the loop equations are satisfied exactly, which eliminates the issue of equation scaling and simplifies the treatment of multi-loop mechanisms. For the experiments reported here, no external measuring devices are used; instead we rely on measurements of displacements in some of the passive joints of the devices. Using a priori estimates of the statistics of the measurement errors and the parameter errors, the method estimates the parameters and their accuracy, and tests for unmodeled factors. >

The geometries and kinematics of inverted fault systems: a review of analogue model studies

Abstract: Abstract The geometries and kinematics of 2D inverted extensional fault systems are reviewed using the results of scaled physical models together with case histories from inverted basin fault systems. 2D analogue models of detached terranes, listric, planar, ramp/flat listric and domino arrays of planar faults were constructed from homogeneous sandpacks and from anisotropic sand/mica layers. The models were first extended and then subjected to horizontal compression in order to reactivate the extensional fault systems. Upon extension simple listric faults produce a characteristic roll-over anticline and crestal collapse graben. Inversion of this system produces reactivation of the main detachment with the development of a fault-bounded wedge of syn-extensional strata elevated above regional together with tightening of the crestal collapse graben. New thrust faults initiate from the tips of the crestal collapse extensional faults. Characteristic ‘harpoon’ structures develop associated with the reactivation of the main detachment. Similar inversion architectures were also produced for the planar fault systems. Extension of ramp-flat listric fault systems produces an upper roll-over and crestal collapse graben together with a ramp syncline and lower roll-over and crestal collapse graben. Inversion of this system only reactivates a part of the main detachment producing a hangingwall shortcut fault that bypasses the upper roll-over system. Inversion of domino fault arrays produced characteristic harpoon geometries of the syn-rift wedge together with shortcut faults in the footwalls of the main domino faults. Analysis of the progressive deformation during both extension and inversion has been carried out using marker points embedded in the models. In the analogue models of detached terranes hangingwall collapse during extension occurs along planar to curved shear surfaces, whereas upon inversion, different, lower angle shear trajectories are utilized. In the domino fault arrays more complicated shear paths are observed as a result of the footwall shortcut faults developed during inversion. These results have important implications for the analysis of extensional and inverted terranes and for fault reconstruction and section balancing techniques. The architecture of inverted fault systems developed in the analogue models show striking similarities to the inverted basin geometries found in natural fault systems such as those in the North Sea and South East Asia. Examples from these terranes are compared and contrasted with the results of the analogue models. Conceptual models for inversion kinematics and fault system architectures are presented.

Multi-degree-of-freedom mechanisms for machine tools and the like

Abstract: A new generation of hybrid form multi-axis machine tools is described. The hybrid machine tools comprise a position mechanism and an orientation mechanism. Both mechanisms are three-DOF parallel mechanisms that can be connected either in series to form a hybrid parallel-serial manipulator, or in parallel to form a cooperating machine. The position mechanism is used for manipulating the position and the orientation mechanism is used for manipulating the orientation of an object. Six-axes machining of a workpiece is achieved by coordinating the motions of the position and orientation mechanisms. This approach has several important advantages. First of all, a high stiffness, low inertia, and high speed machine tool is realized by using the parallel construction. Secondly, its direct and inverse kinematic solutions could be solved in closed forms which would greatly simplify the control and path planning problems. Thirdly, it has a relatively large workspace in comparison to fully parallel platform manipulators. Fourthly, its position and orientation are completely decoupled. Lastly, it utilizes mostly revolute joints which can be precisely made at low cost.

A Unifying Framework for Classification and Interpretation of Mechanism Singularities

Abstract: This paper presents a generalized approach to the singularity analysis of mechanisms with arbitrary kinematic chains and an equal number of inputs and outputs. The instantaneous kinematics ofa mechanism is described by means of a velocity equation, explicitly including not only the input and output velocities but also the passive-joint velocities. A precise definition of singularity of a general mechanism is provided. On the basis of the six types of singular configurations and the motion space interpretation of kinematic singularity introduced in the paper, a comprehensive singularity classification is proposed.

Overview of damped least-squares methods for inverse kinematics of robot manipulators

Abstract: In this paper, we present a tutorial report of the literature on the damped-least squares method which has been used for computing velocity inverse kinematics of robotic manipulators. This is a local optimization method that can prevent infeasible joint velocities near singular configurations by using a damping factor to control the norm of the joint velocity vector. However, the exactness of the inverse kinematic solution has to be sacrificed in order to achieve feasibility. The damping factor is an important parameter in this technique since it determines the trade-off between the accuracy and feasibility of the inverse kinematic solution. Various methods that have been proposed to compute an appropriate damping factor are described. Redundant manipulators, possessing extra degrees of freedom, afford more choice of inverse kinematic solutions than do non-redundant ones. The damped least-squares method has been used in conjunction with redundancy resolution schemes to compute feasible joint velocities for redundant arms while performing an additional subtask. We outline the different techniques that have been proposed to achieve this objective. In addition, we introduce an iterative method to compute the optimal damping factor for one of the redundancy resolution techniques.

Numerical integration of non‐linear elastic multi‐body systems

Abstract: This paper is concerned with the modelling of nonlinear elastic multi-body systems discretized using the finite element method. The formulation uses Cartesian co-ordinates to represent the position of each elastic body with respect to a single inertial frame. The kinematic constraints among the various bodies of the system are enforced via the Lagrange multiplier technique. The resulting equations of motion are stiff, non-linear, differential-algebraic equations. The integration of these equations presents a real challenge as most available techniques are either numerically unstable, or present undesirable high frequency oscillations of a purely numerical origin. An approach is proposed in which the equations of motion are discretized so that they imply conservation of the total energy for the elastic components of the system, whereas the forces of constraint are discretized so that the work they perform vanishes exactly. The combination of these two features of the discretization guarantees the stability of the numerical integration process for non-linear elastic multi-body systems. Examples of the procedure are presented.

The kinematics of multi-fingered manipulation

Abstract: In this paper, we derive a configuration-space description of the kinematics of the fingers-plus-object system. To do this, we first formulate contact kinematics as a "virtual" kinematic chain. Then, the system can be viewed as one large closed kinematic chain composed of smaller chains, one for each finger and one for each contact point. We examine the underlying configuration space and two ways of moving through this space. The first, kinematics-based velocity control, is a generalization of some previous velocity-based approaches. The second, hyperspace jumps, is a purely configuration-space concept. We conclude with a discussion of how these concepts can be used to understand the task of twirling a baton. >

An efficient assumed strain element model with six DOF per node for geometrically non‐linear shells

Abstract: The present paper describes an assumed strain finite element model with six degrees of freedom per node designed for geometrically non-linear shell analysis. An important feature of the present paper is the discussion on the spurious kinematic modes and the assumed strain field in the geometrically non-linear setting. The kinematics of deformation is described by using vector components in contrast to the conventional formulation which requires the use of trigonometric functions of rotational angles. Accordingly, converged solutions can be obtained for load or displacement increments that are much larger than possible with the conventional formulation with rotational angles. In addition, a detailed study of the spurious kinematic modes and the choice of assumed strain field reveals that the same assumed strain field can be used for both geometrically linear and non-linear cases to alleviate element locking while maintaining kinematic stability. It is strongly recommended that the element models, described in the present paper, be used instead of the conventional shell element models that employ rotational angles.

A multisteering trailer system: conversion into chained form using dynamic feedback

Abstract: This paper examines the kinematic model of an autonomous mobile robot system consisting of a chain of steerable cars and passive trailers, linked together with rigid bars. The state space and kinematic equations of the system are defined, and it is shown how these kinematic equations may be converted into a multiinput chained form. The advantages of the chained form are that many methods are available for the open-loop steering of such systems as well as for point-stabilization; some of these methods are discussed here. Dynamic state feedback is used to convert the system to this multiinput chained form. It is shown how the dynamic state feedback that is used in this paper corresponds to adding, in front of the steerable cars, a chain of virtual axles which diverges from the original chain of trailers. Two different example systems are also presented, along with simulation results for a parallel-parking maneuver.

Design and control of ball wheel omnidirectional vehicles

Abstract: A new class of ball wheel mechanisms for omnidirectional vehicles is presented. This ball wheel mechanism can be designed to yield fully mobile vehicles that are not only free of any kinematic singularity but are configuration invariant in kinematic behavior. Invariant kinematics greatly simplifies the control of smooth and precise vehicle motion. Multiple displacement sensors are easily incorporated into each ball wheel mechanism. This unique feature enables the detection of slip between tires and the floor and also indicates at which tire the slip occurs. This allows traction control to be implemented to fully exploit the available floor friction while accurate dead reckoning navigation continues from two non slipping tires. A prototype vehicle with three ball wheel mechanisms is implemented. Smooth motion and precise dead reckoning are accomplished.

Accuracy analysis of a modified Stewart platform manipulator

Abstract: Relation between the joint displacement errors of Stewart platform manipulators and the end effector accuracy is presented. The position errors of the joints and the actuation errors and backlash are included to the kinematic model. A closed-form forward kinematics solution of the end effector error is derived from the inverse kinematics solution. The method is applied to a modified Stewart platform manipulator, and end effector error ellipsoids are computed. The analysis shows that the method can be used in evaluating the accuracy of prismatic parallel manipulators.

Kinematic calibration of a Stewart platform using pose measurements obtained by a single theodolite

Abstract: This paper focuses on the accuracy enhancement of Stewart platforms through kinematic calibration. The calibration problem is formulated in terms of a measurement residual, which is the discrepancy between the measured leg length and the computed leg length. With this formulation, one is able to identify kinematic error parameters of the Stewart platform without the necessity of solving the forward kinematic problem, thus avoiding the numerical problems associated with the solution of the forward kinematic problem. The error parameters are basically the installation errors of the platform ball and U-joints as well as the leg length offsets. By this formulation, a concise differential error model with a well-structured identification Jacobian, which relates the pose measurement residual to the errors in the parameters of the platform, is derived. A measurement procedure that utilizes a single theodolite was devised to determine the poses of the platform. Experimental studies reveal that the proposed calibration method is effective in enhancing the accuracy performance of Stewart platforms.

Integrated Development of the Equations of Motion for Elastic Hypersonic Flight Vehicles

Abstract: An integrated, consistent analytical framework is developed for modeling the dynamics of elastic hypersonic flight vehicles. A Lagrangian approach is used to capture the dynamics of rigid-body motion, elastic deformation, fluid flow, rotating machinery, wind, and a spherical rotating Earth model and to account for their mutual interactions. The resulting equations of motion govern the rigid-body and elastic degrees of freedom (DOF). The elastic motion is represented in terms of modal displacement coordinates relative to the elastic mean axes system, and the rigid-body motion is represented in terms of the translational and rotational velocities of this axes system. A vector form of the force, moment, and elastic-deformation equations is developed from Lagrange's equation; a usable scalar form of these equations is also presented. The appropriate kinematic equations are developed and are presented in a usable form. The characteristics of the three-DOF point-mass dynamic model are also outlined, and the corresponding equations are presented. A preliminary study of the significance of selected terms in the equations of motion is conducted. Using generic data for a single-stage-to-orbit vehicle, it was found that the Coriolis force can reach values up to 6 % of the vehicle weight and that the forces and moments attributable to fluid-flow terms can be significant.

An interactive objective kinematic analysis system

Abstract: The need for high-quality wind fields for ocean response models arises in hindcast studies of operational and extreme climate, in coastal and offshore structure design, and in forecasting for ocean platform operation and ships. Ocean response models such as the third generation (3G) wave model (WAM) and the Oceanweather’s 3G wave model have shown great skill in producing nearly perfect hindcasts of significant wave height and peak period in severe tropical and extratropical systems when driven by high quality wind fields. The Surface Wave Dynamics (SWADE) study special Intense Observational Period (IOP) of the October 1990 US East coast event put several wind fields using both objectively derived and handdrawn man-intensive wind fields through a common wave model (WAM 3G). The results show (Cardone et.al., 1995) that the suite of hindcasts produced by very sophisticated purely objective analysis schemes was clearly beaten by hand-drawn kinematic analysis (Figure 1). Unfortunately, this man-intensive, tediously produced analysis took approximately 100 manhours to produce a 10 day hindcast, which is a time frame clearly inapplicable to long term hindcast studies and forecasting applications.

Interface apparatus for automatic test equipment

Abstract: A kinematic coupling for a test system with a test head which must be docked with a handling device. The coupling is implemented with a plurality of modules attached to the test head. Each module has one kinematic surface and is designed to mate with another kinematic surface on the handling device. Each module includes a motor which can extend or retract the kinematic surface. These modules allow docking of the test head to the handling device with a final motion perpendicular to the handler. They also allow the tilt angle between the test head and the handler to be adjusted to achieve planarization.

The mechanics of undulatory locomotion: the mixed kinematic and dynamic case

Abstract: This paper studies the mechanics of undulatory locomotion. This type of locomotion is generated by a coupling of internal shape changes to external non-holonomic constraints. Employing methods from geometric mechanics, the authors use the dynamic symmetries and kinematic constraints to develop a specialized form of the dynamic equations which govern undulatory systems. These equations are written in terms of physically meaningful and intuitively appealing variables that show the role of internal shape changes in driving locomotion.

Periodic forcing, dynamics and control of underactuated spacecraft and underwater vehicles

Abstract: In this paper we describe spacecraft and underwater vehicle dynamics with small-amplitude, periodically time-varying forcing. The dynamic descriptions are derived so that they can be used to prescribe forcing laws for controlling the motion of these systems when they are underactuated, i.e., when the number of force inputs is less than the dimension of the configuration space. The use of periodic force inputs is motivated by the demonstrated success of using periodic velocity inputs in the associated nonholonomic kinematic spacecraft and underwater vehicle motion control problems, e.g., controlling underactuated spacecraft driven with internal rotors and underwater vehicles at low Reynolds number. By now addressing dynamic as well as kinematic response, we provide results that are useful in many practical problems in which the system cannot be modelled as purely kinematic, e.g., controlling underactuated spacecraft driven with gas jets and underwater vehicles at high Reynolds number.