Showing papers on "Kinematics published in 2005"

Geometric control of mechanical systems

Abstract: This talk will outline a comprehensive set of modeling, analysis and design techniques for a class of mechanical systems. We concern ourselves with simple mechanical control systems, that is, systems whose Lagrangian is kinetic energy minus potential energy. Example devices include robotic manipulators, aerospace and underwater vehicles, and mechanisms that locomote exploiting nonholonomic constraints. Borrowing techniques from nonlinear control and geometric mechanics, we propose a coordinateinvariant control theory for this class of systems. First, we take a Riemannian geometric approach to modeling systems dened on smooth manifolds, subject to nonholonomic constraints, external forces and control forces. We also model mechanical systems on groups and symmetries. Second, we analyze some control-theoretic properties of this class of systems, including controllability, averaged response to oscillatory controls, and kinematic reductions. Finally, we exploit the modeling and analysis results to tackle control design problems. Starting from controllability and kinematic reduction assumptions we propose some algorithms for generating and tracking trajectories.

Articulated Body Motion Capture by Stochastic Search

Abstract: We develop a modified particle filter which is shown to be effective at searching the high-dimensional configuration spaces (c. 30 + dimensions) encountered in visual tracking of articulated body motion. The algorithm uses a continuation principle, based on annealing, to introduce the influence of narrow peaks in the fitness function, gradually. The new algorithm, termed annealed particle filtering, is shown to be capable of recovering full articulated body motion efficiently. A mechanism for achieving a soft partitioning of the search space is described and implemented, and shown to improve the algorithm's performance. Likewise, the introduction of a crossover operator is shown to improve the effectiveness of the search for kinematic trees (such as a human body). Results are given for a variety of agile motions such as walking, running and jumping.

Geometric control of mechanical systems : modeling, analysis, and design for simple mechanical control systems

Abstract: Part I: Modeling of mechanical systems Introductory examples and problems Linear and multilinear algebra Differential geometry Simple mechanical control systems Lie groups, systems on groups, and symmetries.- Part II: Analysis of mechanical control systems Stability Controllability Low-order controllability and kinematic reduction Perturbation analysis.- Part III: A sampling of design methodologies Linear and nonlinear potential shaping for stabilization Stabilization and tracking for fully actuated systems Stabilization and tracking using oscillatory controls Motion planning for underactuated systems Appendices Time-dependent vector fields Some proofs.

The aerodynamics of hovering flight in Drosophila.

Abstract: Using 3D infrared high-speed video, we captured the continuous wing and body kinematics of free-flying fruit flies, Drosophila melanogaster, during hovering and slow forward flight. We then `replayed' the wing kinematics on a dynamically scaled robotic model to measure the aerodynamic forces produced by the wings. Hovering animals generate a U-shaped wing trajectory, in which large drag forces during a downward plunge at the start of each stroke create peak vertical forces. Quasi-steady mechanisms could account for nearly all of the mean measured force required to hover, although temporal discrepancies between instantaneous measured forces and model predictions indicate that unsteady mechanisms also play a significant role. We analyzed the requirements for hovering from an analysis of the time history of forces and moments in all six degrees of freedom. The wing kinematics necessary to generate sufficient lift are highly constrained by the requirement to balance thrust and pitch torque over the stroke cycle. We also compare the wing motion and aerodynamic forces of free and tethered flies. Tethering causes a strong distortion of the stroke pattern that results in a reduction of translational forces and a prominent nose-down pitch moment. The stereotyped distortion under tethered conditions is most likely due to a disruption of sensory feedback. Finally, we calculated flight power based directly on the measurements of wing motion and aerodynamic forces, which yielded a higher estimate of muscle power during free hovering flight than prior estimates based on time-averaged parameters. This discrepancy is mostly due to a two- to threefold underestimate of the mean profile drag coefficient in prior studies. We also compared our values with the predictions of the same time-averaged models using more accurate kinematic and aerodynamic input parameters based on our high-speed videography measurements. In this case, the time-averaged models tended to overestimate flight costs.

A simple method for measuring stiffness during running.

Abstract: The spring-mass model, representing a runner as a point mass supported by a single linear leg spring, has been a widely used concept in studies on running and bouncing mechanics However, the measurement of leg and vertical stiffness has previously required force platforms and high-speed kinematic measurement systems that are costly and difficult to handle in field conditions We propose a new "sine-wave" method for measuring stiffness during running Based on the modeling of the force-time curve by a sine function,this method allows leg and vertical stiffness to be estimated from just a few simple mechanical parameters: body mass, forward velocity, leg length, flight time, and contact time We compared this method to force-platform-derived stiffness measurements for treadmill dynamometer and overground running conditions, at velocities ranging from 333 ms-1 to maximal running velocity in both recreational and highly trained runners Stiffness values calculated with the proposed method ranged from 067 % to 693 % less than the force platform method, and thus were judged to be acceptable Furthermore, significant linear regressions (p < 001) close to the identity line were obtained between force platform and sine-wave model values of stiffness Given the limits inherent in the use of the spring-mass model, it was concluded that this sine-wave method allows leg and stiffness estimates in running on the basis of a few mechanical parameters, and could be useful in further field measurements

A new approach to accurate measurement of uniaxial joint angles based on a combination of accelerometers and gyroscopes

Abstract: A new method of measuring joint angle using a combination of accelerometers and gyroscopes is presented. The method proposes a minimal sensor configuration with one sensor module mounted on each segment. The model is based on estimating the acceleration of the joint center of rotation by placing a pair of virtual sensors on the adjacent segments at the center of rotation. In the proposed technique, joint angles are found without the need for integration, so absolute angles can be obtained which are free from any source of drift. The model considers anatomical aspects and is personalized for each subject prior to each measurement. The method was validated by measuring knee flexion-extension angles of eight subjects, walking at three different speeds, and comparing the results with a reference motion measurement system. The results are very close to those of the reference system presenting very small errors (rms=1.3, mean=0.2, SD=1.1 deg) and excellent correlation coefficients (0.997). The algorithm is able to provide joint angles in real-time, and ready for use in gait analysis. Technically, the system is portable, easily mountable, and can be used for long term monitoring without hindrance to natural activities.

Approximating Kinematics for Tracked Mobile Robots

Abstract: In this paper we propose a kinematic approach for tracked mobile robots in order to improve motion control and pose estimation. Complex dynamics due to slippage and track-soil interactions make it difficult to predict the exact motion of the vehicle on the basis of track velocities. Nevertheless, real-time computations for autonomous navigation require an effective kinematics approximation without introducing dynamics in the loop. The proposed solution is based on the fact that the instantaneous centers of rotation (ICRs) of treads on the motion plane with respect to the vehicle are dynamics-dependent, but they lie within a bounded area. Thus, optimizing constant ICR positions for a particular terrain results in an approximate kinematic model for tracked mobile robots. Two different approaches are presented for off-line estimation of kinematic parameters: (i) simulation of the stationary response of the dynamic model for the whole velocity range of the vehicle; (ii) introduction of an experimental setup so that a genetic algorithm can produce the model from actual sensor readings. These methods have been evaluated for on-line odometric computations and low-level motion control with the Auriga-α mobile robot on a hard-surface flat soil at moderate speeds.

Design of an arm exoskeleton with scapula motion for shoulder rehabilitation

Abstract: The evolution of an arm exoskeleton design for treating shoulder pathology is examined. Tradeoffs between various kinematics configurations are explored, and a device with five active degrees of freedom is proposed. Two rapid-prototype designs were built and fitted to several subjects to verify the kinematic design and determine passive link adjustments. Control modes are developed for exercise therapy and functional rehabilitation, and a distributed software architecture that incorporates computer safety monitoring is described. Although intended primarily for therapy, the exoskeleton is also used to monitor progress in strength, range of motion, and functional task performance

The human arm kinematics and dynamics during daily activities - toward a 7 DOF upper limb powered exoskeleton

Abstract: Integrating human and robot into a single system offers remarkable opportunities for creating a new generation of assistive technology. Having obvious applications in rehabilitation medicine and virtual reality simulation, such a device would benefit both the healthy and disabled population. The aim of the research is to study the kinematics and the dynamics of the human arm during daily activities in a free and unconstrained environment as part of an on-going research involved in the design of a 7 degree of freedom (DOF) powered exoskeleton for the upper limb. The kinematics of the upper limb was acquired with a motion capture system while performing a wide verity of daily activities. Utilizing a model of the human as a 7 DOF system, the equations of motion were used to calculate joint torques given the arm kinematics. During positioning tasks, higher angular velocities were observed in the gross manipulation joints (the shoulder and elbow) as compared to the fine manipulation joints (the wrist). An inverted phenomenon was observed during fine manipulation in which the angular velocities of the wrist joint exceeded the angular velocities of the shoulder and elbow joints. Analyzing the contribution of individual terms of the arm's equations of motion indicate that the gravitational term is the most dominant term in these equations. The magnitudes of this term across the joints and the various actions is higher than the inertial, centrifugal, and Coriolis terms combined. Variation in object grasping (e.g. power grasp of a spoon) alters the overall arm kinematics in which other joints, such as the shoulder joint, compensate for lost dexterity of the wrist. The collected database along with the kinematics and dynamic analysis may provide the fundamental understanding for designing powered exoskeleton for the human arm

Relationship of biomechanical factors to baseball pitching velocity: within pitcher variation.

Abstract: To reach the level of elite, most baseball pitchers need to consistently produce high ball velocity but avoid high joint loads at the shoulder and elbow that may lead to injury. This study examined the relationship between fastball velocity and variations in throwing mechanics within 19 baseball pitchers who were analyzed via 3-D high-speed motion analysis. Inclusion in the study required each one to demonstrate a variation in velocity of at least 1.8 m/s (range 1.8-3.5 m/s) during 6 to 10 fastball pitch trials. Three mixed model analyses were performed to assess the independent effects of 7 kinetic, 11 temporal, and 12 kinematic parameters on pitched ball velocity. Results indicated that elbow flexion torque, shoulder proximal force, and elbow proximal force were the only three kinetic parameters significantly associated with increased ball velocity. Two temporal parameters (increased time to max shoulder horizontal adduction and decreased time to max shoulder internal rotation) and three kinematic parameters (decreased shoulder horizontal adduction at foot contact, decreased shoulder abduction during acceleration, and increased trunk tilt forward at release) were significantly related to increased ball velocity. These results point to variations in an individual's throwing mechanics that relate to pitched ball velocity, and also suggest that pitchers should focus on consistent mechanics to produce consistently high fastball velocities. In addition, pitchers should strengthen shoulder and elbow musculature that resist distraction as well as improve trunk strength and flexibility to maximize pitching velocity and help prevent injury.

Diffusion-Based Motion Planning for a Nonholonomic Flexible Needle Model

Abstract: Fine needles facilitate diagnosis and therapy because they enable minimally invasive surgical interventions. This paper formulates the problem of steering a very flexible needle through firm tissue as a nonholonomic kinematics problem, and demonstrates how planning can be accomplished using diffusion-based motion planning on the Euclidean group, SE(3). In the present formulation, the tissue is treated as isotropic and no obstacles are present. The bevel tip of the needle is treated as a nonholonomic constraint that can be viewed as a 3D extension of the standard kinematic cart or unicycle. A deterministic model is used as the starting point, and reachability criteria are established. A stochastic differential equation and its corresponding Fokker-Planck equation are derived. The Euler-Maruyama method is used to generate the ensemble of reachable states of the needle tip. Inverse kinematics methods developed previously for hyper-redundant and binary manipulators that use this probability density information are applied to generate needle tip paths that reach the desired targets.

STEllar Content and Kinematics from high resolution galactic spectra via Maximum A Posteriori

Abstract: We introduce STECKMAP (STEllar Content and Kinematics via Maximum A Posteriori), a method to recover the kinematical properties of a galaxy simultaneously with its stellar content from integrated light spectra. It is an extension of STECMAP (astro-ph/0505209) to the general case where the velocity distribution of the underlying stars is also unknown. %and can be used as is for the analysis of large sets of data. The reconstructions of the stellar age distribution, the age-metallicity relation, and the Line-Of-Sight Velocity Distribution (LOSVD) are all non-parametric, i.e. no specific shape is assumed. The only a propri we use are positivity and the requirement that the solution is smooth enough. The smoothness parameter can be set by GCV according to the level of noise in the data in order to avoid overinterpretation. We use single stellar populations (SSP) from PEGASE-HR (R=10000, lambda lambda = 4000-6800 Angstrom, Le Borgne et al. 2004) to test the method through realistic simulations. Non-Gaussianities in LOSVDs are reliably recovered with SNR as low as 20 per 0.2 Angstrom pixel. It turns out that the recovery of the stellar content is not degraded by the simultaneous recovery of the kinematic distribution, so that the resolution in age and error estimates given in Ocvirk et al. 2005 remain appropriate when used with STECKMAP. We also explore the case of age-dependent kinematics (i.e. when each stellar component has its own LOSVD). We separate the bulge and disk components of an idealized simplified spiral galaxy in integrated light from high quality pseudo data (SNR=100 per pixel, R=10000), and constrain the kinematics (mean projected velocity, projected velocity dispersion) and age of both components.

A variational formulation of kinematic waves: Solution methods

Abstract: This paper presents improved solution methods for kinematic wave traffic problems with concave flow-density relations As explained in part I of this work, the solution of a kinematic wave problem is a set of continuum least-cost paths in space-time The least cost to reach a point is the vehicle number The idea here consists in overlaying a dense but discrete network with appropriate costs in the solution region and then using a shortest-path algorithm to estimate vehicle numbers With properly designed networks, this procedure is more accurate than existing methods and can be applied to more complicated problems In many important cases its results are exact

A method for deriving displacement data during cyclical movement using an inertial sensor

Abstract: Biomechanical studies often employ optical motion capture systems for the determination of the position of an object in a room-based coordinate system. This is not ideal for many types of study in locomotion since only a few strides may be collected per ;trial', and outdoor experiments are difficult with some systems. Here, we report and evaluate a novel approach that enables the user to determine linear displacements of a proprietary orientation sensor during cyclical movement. This makes experiments outside the constraints of the laboratory possible, for example to measure mechanical energy fluctuations of the centre of mass during over-ground locomotion. Commercial orientation sensors based on inertial sensing are small and lightweight and provide a theoretical framework for determining position from acceleration. In practice, the integration process is difficult to implement because of integration errors, integration constants and the necessity to determine the orientation of the measured accelerations. Here, by working within the constraints of cyclical movements, we report and evaluate a method for determining orientation and relative position using a modified version of a commercial inertial orientation sensor that combines accelerometers, gyroscopes and magnetometers, thus giving a full set of movement parameters (displacement, velocity and acceleration in three dimensions). The 35 g sensor was attached over the spine of a horse exercising on a treadmill. During canter locomotion (9.0 m s-1), the amplitudes of trunk movement in the x (craniocaudal), y (mediolateral) and z (dorsoventral) directions were 99.6, 57.9 and 140.2 mm, respectively. Comparing sensor displacement values with optical motion capture values for individual strides, the sensor had a median error (25th, 75th percentile) in the x, y and z directions of 0.1 (-9.7, +10.8), -3.8 (-15.5, +13.7) and -0.1 (-6.3, +7.1) mm, respectively. High-pass filtering of the displacement data effectively separated non-cyclical from cyclical components of the movement and reduced the interquartile ranges of the errors considerably to (-3.6, 6.2), (-4.0, 3.8) and (-4.5, 5.1) for x, y and z displacement, respectively, during canter locomotion. This corresponds to (-3.2, 5.5)%, (-6.7, 6.3)% and (-3.3, 3.7)% of the range of motion.

Shape-From-Silhouette Across Time Part II: Applications to Human Modeling and Markerless Motion Tracking

Abstract: In Part I of this paper we developed the theory and algorithms for performing Shape-From-Silhouette (SFS) across time. In this second part, we show how our temporal SFS algorithms can be used in the applications of human modeling and markerless motion tracking. First we build a system to acquire human kinematic models consisting of precise shape (constructed using the temporal SFS algorithm for rigid objects), joint locations, and body part segmentation (estimated using the temporal SFS algorithm for articulated objects). Once the kinematic models have been built, we show how they can be used to track the motion of the person in new video sequences. This marker-less tracking algorithm is based on the Visual Hull alignment algorithm used in both temporal SFS algorithms and utilizes both geometric (silhouette) and photometric (color) information.

A physically-based motion retargeting filter

Abstract: This article presents a novel constraint-based motion editing technique. On the basis of animator-specified kinematic and dynamic constraints, the method converts a given captured or animated motion to a physically plausible motion. In contrast to previous methods using spacetime optimization, we cast the motion editing problem as a constrained state estimation problem, based on the per-frame Kalman filter framework. The method works as a filter that sequentially scans the input motion to produce a stream of output motion frames at a stable interactive rate. Animators can tune several filter parameters to adjust to different motions, turn the constraints on or off based on their contributions to the final result, or provide a rough sketch (kinematic hint) as an effective way of producing the desired motion. Experiments on various systems show that the technique processes the motions of a human with 54 degrees of freedom, at about 150 fps when only kinematic constraints are applied, and at about 10 fps when both kinematic and dynamic constraints are applied. Experiments on various types of motion show that the proposed method produces remarkably realistic animations.

A Kinematic Source-Time Function Compatible with Earthquake Dynamics

Abstract: We propose a new source-time function, to be used in kinematic modeling of ground-motion time histories, which is consistent with dynamic propagation of earthquake ruptures and makes feasible the dynamic interpretation of kinematic slip models. This function is derived from a source-time function first proposed by Yoffe (1951), which yields a traction evolution showing a slip-weakening behavior. In order to remove its singularity, we apply a convolution with a triangular function and obtain a regularized source-time function called the regularized Yoffe function. We propose a parameterization of this slip-velocity time function through the final slip, its duration, and the duration of the positive slip acceleration ( Tacc ). Using this analytical function, we examined the relation between kinematic parameters, such as peak slip velocity and slip duration, and dynamic parameters, such as slip-weakening distance and breakdown-stress drop. The obtained scaling relations are consistent with those proposed by Ohnaka and Yamashita (1989) from laboratory experiments. This shows that the proposed source-time function suitably represents dynamic rupture propagation with finite slip-weakening distances.

Learning and recall of incremental kinematic and dynamic sensorimotor transformations.

Abstract: Numerous studies have shown that when people encounter a sudden and novel sensorimotor transformation that alters perceived or actual movement, they gradually adapt and can later recall what they have learned if they encounter the transformation again. In this study, we tested whether retention and recall of learning is also observed when kinematic and dynamic transformations are introduced incrementally such that participants never experience large movement errors. Participants adapted their reaching movements to either a visuomotor rotation of hand position (kinematic transformation) or a rotary viscous force-field applied to the hand (dynamic transformation). These perturbations were introduced either incrementally or instantaneously. Thus, four groups of participants were tested with an incremental and an instantaneous group for both the kinematic and dynamic perturbations. To evaluate retention of learning, participants from all four groups were tested a day later on the same kinematic or dynamic perturbation presented instantaneously (at full strength). As expected, we found that subjects in the instantaneous group retained learning across days. We also found that, for both kinematic and dynamic perturbations, retention was equally good or better when the transformation was introduced incrementally. Because large and clearly detectable movement errors were not observed during adaptation to incremental perturbations, we conclude that such errors are not required for the learning and retention of internal models of kinematic and dynamic sensorimotor transformations.

Kinematics modeling and analyses of articulated rovers

Abstract: This paper describes a general approach to the kinematics modeling and analyses of articulated rovers traversing uneven terrain. The model is derived for full 6DOF (6-degree-of-freedom) motion, enabling movements in the x,y, and z directions, as well as pitch, roll, and yaw rotations. Differential kinematics is derived for the individual wheel motions in contact with the terrain. The resulting equations of the individual wheel motions are then combined to form the composite equation for the rover motion. Three types of kinematics, i.e., navigation, actuation, and slip kinematics are identified, and the equations and application of each are discussed. The derivations are specialized to Rocky 7, a highly articulated prototype Mars rover, to illustrate the developed methods. Simulation results are provided for the motion of the Rocky 7 over several terrains, and various motion profiles are provided to explain the behavior of the rover.

Task-oriented whole body motion for humanoid robots

Abstract: We present a whole body motion control algorithm for humanoid robots It is based on the framework of Liegeois and solves the redundant inverse kinematics problem on velocity level We control the hand positions as well as the hand and head attitude The attitude is described with a novel 2-dof description suited for symmetrical problems Task-specific command elements can be assigned to the command vector at any time, such enabling the system to control one or multiple effectors and to seamlessly switch between such modes while generating a smooth, natural motion Further, kinematic constraints can be assigned to individual degrees of freedom The underlying kinematic model does not consider the leg joints explicitly Nevertheless, the method can be used in combination with an independent balance or walking control system, such reducing the complexity of a complete system control We show how to incorporate walking in this control scheme and present experimental results on ASIMO

Computational Modelling of Isotropic Multiplicative Growth

Abstract: The changing mass of biomaterials can either be modelled at the constitutive level or at the kinematic level. This contribution attends on the description of growth at the kinematic level. The deformation gradient will be multiplicatively split into a growth part and an elastic part. Hence, in addition to the material and the spatial configuration, we consider an intermediate configuration or grown configuration without any elastic deformations. With such an ansatz at hand, contrary to the modelling of mass changes at the constitutive level, both a change in density and a change in volume can be modelled. \\ The algorithmic realisation of this framework within a finite element setting constitutes the main contribution of this paper. To this end the key kinematic variable, i.e. the isotropic stretch ratio, is introduced as internal variable at the integration point level. The consistent linearisation of the stress update based on an implicit time integration scheme is developed. Basic features of the model are illustrated by means of representative numerical examples.

Can co-activation reduce kinematic variability? A simulation study

Abstract: Impedance modulation has been suggested as a means to suppress the effects of internal ‘noise’ on movement kinematics. We investigated this hypothesis in a neuro-musculo-skeletal model. A prerequisite is that the muscle model produces realistic force variability. We found that standard Hill-type models do not predict realistic force variability in response to variability in stimulation. In contrast, a combined motor-unit pool model and a pool of parallel Hill-type motor units did produce realistic force variability as a function of target force, largely independent of how the force was transduced to the tendon. To test the main hypothesis, two versions of the latter model were simulated as an antagonistic muscle pair, controlling the position of a frictionless hinge joint, with a distal segment having realistic inertia relative to the muscle strength. Increasing the impedance through co-activation resulted in less kinematic variability, except for the lowest levels of co-activation. Model behavior in this region was affected by the noise amplitude and the inertial properties of the model. Our simulations support the idea that muscular co-activation is in principle an effective strategy to meet accuracy demands.