Inverse Dynamics Problem Research Articles

Assessment of Internal Loads in the Joints of the Lower Extremities During the Snatch in Young Weightlifters

The aim of this paper is to present the results of an assessment of internal loads in the joints of the lower limbs during the snatch performed by young weightlifters. A planar model of a weightlifter composed of 7 rigid segments (the lower trunk, thighs, lower legs and feet) connected by six hinge joints was used in the computations. The dynamic equations of the motion of the model were obtained using a projective technique. Kinematic data were recorded by a Vicon system with a sampling frequency of 200 Hz. The ground reactions were measured independently for the left and right limbs on two force platforms. The inverse dynamics problem was solved to assess the internal loads (the muscle forces and joint reactions) in the lower limbs. Relatively high differences in the reactions in the joints and muscle forces in the left and right lower extremities were identified. The obtained results also reveal that the snatch, a lift which tends to be geometrically symmetrical in the sagittal plane, is not necessarily characterized by symmetry of internal loads. Thus, this study has shown that a kinematics analysis of the lifter’s movement, which is commonly used to assess the technique of the snatch, is insufficient and should be supplemented with a dynamics analysis.

Oscillations and control of spherical parallel manipulator

In recent years, there has been a growing number of studies in spherical parallel mechanisms, particularly synthesis, kinematics, and work area singularities. The interaction of degrees of freedom and geometry leads to the nonlinear phenomena, in the dynamics of mechanism. There are few studies into the dynamic properties of such mechanisms. This article deals with the dynamic property of the parallel spherical manipulators, with three degrees of freedom, and presents determination of acceleration input links, oscillations, and the problem of control. Algorithm of control is based on the concept of minimized coordinates, velocities, and acceleration using inverse dynamic problems. This allows synthesis of this algorithm, which can realize a motion in accordance with prescribed trajectories. Finally, the results of calculations are defined.

The dynamical discrepancy method in problems of reconstructing unknown characteristics of a second-order system

This paper considers two problems of dynamical reconstruction of unknown characteristics of a system of nonlinear equations describing the process of innovation diffusion through inaccurate measurements of phase states. A dynamical variant for solving these problems is designed. The system is assumed to operate on a given finite time interval. The evolution of the system's phase state, i.e., the solution of the system, is determined by an unknown input. A precise reconstruction of the real input (acting on the system) is, generally speaking, impossible due to inaccurate measurements. Therefore, some approximation to this input is constructed which provides an arbitrary smallness to the real input if the measurement errors and the step of incoming information are sufficiently small. Based on the dynamical version of the discrepancy method, two algorithms for solving the problems in question are specified. One of them is oriented to the case of measuring all coordinates of the phase vector, and the other, to the case of incomplete measurements. The algorithms suggested are stable with respect to informational noises and computational errors. Actually, they are special regularizing algorithms from the theory of dynamic inverse problems.

Inverse dynamic problem for the wave equation with periodic boundary conditions

Inverse dynamic problem for the wave equation with periodic boundary conditions

A procedure to estimate normal and friction contact parameters in the stance phase of the human gait

A new approach to estimate normal and tangential contact parameters in the foot-ground contact during human gait was proposed. A correct estimation of the contact parameters would be very important in the resolution of predictive forward dynamic problems. The normal contact forces have been well estimated in the literature. But accurate estimation of tangential forces has not been reached yet. This work proposed a new procedure to accurately estimate friction forces. The approach has been based on the consideration of the modulus of the tangential force instead of its components. This modulus was introduced together with the modulus of the normal contact force and its two associated moments in an optimization algorithm to fit the contact forces provided by the model to the experimental data obtained with a force plate. An inverse dynamics problem was solved as a step previous to the optimization algorithm. The results showed that both the normal and tangential forces and the moments in the horizontal plane were in agreement with the experimental measurements. This work also analyzed the influence on the results of the friction law. The results obtained with the general friction law, which considered dry (static and dynamic) and viscous friction, were compared with results provided by simpler laws. The analysis of the components of the friction forces pointed out the importance of the Stribeck component in the resultant force instead of the viscous friction which played a minimal role. But for modelling the stick-slip transition, the implementation of a general friction law is necessary.

On an Inverse Dynamic Problem for the Wave Equation with a Potential on a Real Line

The inverse dynamic problem for the wave equation with a potential on a real line is considered. The forward initial-boundary value problem is set up with the help of boundary triplets. As an inverse data, an analog of the response operator (dynamic Dirichlet-to-Neumann map) is used. Equations of the inverse problem are derived; also, a relationship between the dynamic inverse problem and the spectral inverse problem from a matrix-valued measure is pointed out.

Refinement of the Reactor Dynamics Mathematical Model

A mathematical model of reactor dynamics described by a system of integro-differential equations consisting of an unsteady-state multivelocity kinetic transfer equation and a delayed neutrons balance equation is considered. To refine some parameters of this system a number of inverse problems of reactor dynamics with a new definition of integral form are solved. Statements of the linear inverse problem of recovery of a part of the function of inner neutron sources, and non-linear inverse problems of recovery of a part of the absorption coefficient are presented. The sought for parts of the said parameters are functions depending on the velocity and time variables. Theorems of existence and uniqueness of generalized solutions have been proved.

Parametric Optimization of the Transport Operations of a Two-Link Manipulator

We study the problem of optimization of motion of a two-link manipulator, which performs transport operations under the action of controls (moments of forces in the hinges). The initial and the final position of the gripping device of the manipulator and the time of the operation are regarded as known. The quality of motion of the manipulator is estimated by a quadratic functional. Possible configurations of the manipulator at the beginning and at the end of the operation are taken into account. We propose an algorithm for the construction of suboptimal solutions of the problem based on the parametrization of the angular coordinates of the manipulator by the sum of a cubic polynomial and a finite trigonometric series and on the use of the methods of inverse problems of dynamics and numerical procedures of nonlinear programming. The influence of configurations of the manipulator and the parameters of the trigonometric series on the characteristics of the suboptimal process is analyzed.

Reducing of dynamic loads of excavator actuators

In the article, using the example of the walking excavator ESh 20.90, the results of studies on the choice of design parameters of the traction mechanism ensuring the reducing of dynamic loads, based on solving the inverse dynamic problem according to a given type of oscillatory movements of the actuator and using the theory of mechanical circuits are presented. By numerical simulation of the electromechanical system it is shown that the introduction of an additional elastic-damping device in the kinematic scheme of the excavator traction mechanism will allow to reduce the dynamic loads and the duration of their action on the traction mechanism in the start-up and load-step modes and significantly increase the logarithmic decrement of the elastic oscillation.

Predictive Assessment of Operator's Hand Trajectory with the Copying Type of Control for Solution of the Inverse Dynamic Problem

The most important task of modern robotics is the development of robots to perform the work in potentially dangerous fields which can cause the risk to human health. Currently robotic systems can not become a full replacement for man for solving complex problems in a dynamic environment despite an active development of artificial intelligence technologies.
 The robots that implement the copying type of control or the so-called virtual presence of the operator are the most advanced for use in the nearest future. The principle of copying control is based on the motion capture of the remote operator and the formation of control signals for the robot’s drives. A tracking system or systems based on movement planning can be used to control the drives. The tracking systems are simpler, but systems based on motion planning allow to achieve more smooth motion and less wear on the parts of the control object. An artificial delay between the movements of the operator and the control object for necessary data collection is used to implement the control-based motion planning.
 The aim of research is a reduction of delay, which appears when controlling the anthropomorphic manipulator drives based on the solution of the inverse dynamic problem, when real time copying type of control is used . For motion path planning it is proposed to use forecast values of the generalized coordinates for manipulator. Based on the measured values of the generalized coordinates of the operator's hand, time series are formed and their prediction is performed. Predictive values of generalized coordinates are used in planning the anthropomorphic manipulator trajectory and solving the inverse dynamic problem. Prediction is based on linear regression with relatively low computational complexity, which is an important criterion for the system operation in the real time operation mode. The developed mathematical apparatus, based on prediction parameters and maximum permissible accelerations of the manipulator drives, allows to find a theoretical estimate of error values limits for planning the operator's hand trajectory using the proposed approach for specific tasks. The adequacy of the maximum theoretical value of the prediction error, as well as the prospects of the proposed approach for testing in practice is confirmed by the software simulation in Matlab environment.

V-Function Method: Some Solutions of Direct and Inverse Dynamics Problems in A New Statement

Abstract Based on the V-function method, the properties of wave nature of object motion are studied for object uniform motion with constant speed and for harmonic oscillator. It follows from the V-function method that object wave motion is inseparably linked with its trajectory motion. The V-function method consists of the principle of local variation and a new statement of the direct and inverse dynamics problems. The proposed approach made it possible to make the optico-mechanical analogy that obtained a new continuation. A comparison is made with the results obtained by Schrödinger for a harmonic oscillator.

Minimum Time Lane Changing Problem of Vehicle Handling Inverse Dynamics Considering the Driver’s Intention

By solving driver’s optimal handling input, this paper presents a novel Lane Changing Assistance System (LCAS) which can provide guidance for driver’s lane changing behavior. In addition, vehicle handling inverse dynamics method is proposed to solve driver’s optimal handling input. Firstly, to recognize driver’s lane changing intention and decrease the false alarm rate of LCAS, a lane changing intention recognition model is established. Secondly, the handling inverse dynamics model is established; and then the inverse dynamics problem is converted into the optimal control problem. Finally, the optimal control problem is converted into a nonlinear programming problem based on GPM; then sequential quadratic programming (SQP) is applied to get the solution. The direct collocation method (DCM) is used as the contrast verification of GPM. The simulation results show that the driver’s optimal handling input can be obtained according to driver’s lane changing intention in the proposed LCAS; and GPM has higher computational accuracy compared with DCM. This method may provide a reference for the research of LCAS and unmanned vehicles.

Forward and Inverse Dynamics of a Unicycle-Like Mobile Robot

In this research work, a new method for solving forward and inverse dynamic problems of mechanical systems having an underactuated structure and subjected to holonomic and/or nonholonomic constraints is developed. The method devised in this paper is based on the combination of the Udwadia-Kalaba Equations with the Underactuation Equivalence Principle. First, an analytical method based on the Udwadia-Kalaba Equations is employed in the paper for handling dynamic and control problems of nonlinear nonholonomic mechanical systems in the same computational framework. Subsequently, the Underactuation Equivalence Principle is used for extending the capabilities of the Udwadia-Kalaba Equations from fully actuated mechanical systems to underactuated mechanical systems. The Underactuation Equivalence Principle represents an efficient method recently developed in the field of classical mechanics. The Underactuation Equivalence Principle is used in this paper for mathematically formalizing the underactuation property of a mechanical system considering a particular set of nonholonomic algebraic constraints defined at the acceleration level. On the other hand, in this study, the Udwadia-Kalaba Equations are analytically reformulated in a mathematical form suitable for treating inverse dynamic problems. By doing so, the Udwadia-Kalaba Equations are employed in conjunction with the Underactuation Equivalence Principle for developing a nonlinear control method based on an inverse dynamic approach. As shown in detail in this investigation, the proposed method can be used for analytically solving in an explicit manner the forward and inverse dynamic problems of several nonholonomic mechanical systems. In particular, the tracking control of the unicycle-like mobile robot is considered in this investigation as a benchmark example. Numerical experiments on the dynamic model of the unicycle-like mobile robot confirm the effectiveness of the nonlinear dynamic and control approaches developed in this work.

From Fixation Probabilities to d-player Games: An Inverse Problem in Evolutionary Dynamics.

The probability that the frequency of a particular trait will eventually become unity, the so-called fixation probability, is a central issue in the study of population evolution. Its computation, once we are given a stochastic finite population model without mutations and a (possibly frequency dependent) fitness function, is straightforward and it can be done in several ways. Nevertheless, despite the fact that the fixation probability is an important macroscopic property of the population, its precise knowledge does not give any clear information about the interaction patterns among individuals in the population. Here we address the inverse problem: from a given fixation pattern and population size, we want to infer what is the game being played by the population. This is done by first exploiting the framework developed in Chalub and Souza (J Math Biol 75:1735-1774, 2017), which yields a fitness function that realises this fixation pattern in the Wright-Fisher model. This fitness function always exists, but it is not necessarily unique. Subsequently, we show that any such fitness function can be approximated, with arbitrary precision, using d-player game theory, provided d is large enough. The pay-off matrix that emerges naturally from the approximating game will provide useful information about the individual interaction structure that is not itself apparent in the fixation pattern. We present extensive numerical support for our conclusions.

On Certain Conventional Misconceptions in Seismology

The history of science abounds in examples when misconceptions dominated the scientific community and did it significant harm. New ideas in science have always cut their paths with great difficulty. Inertial thinking and the temptation to adhere to stereotypes often hamper the development of knowledge and lead to erroneous interpretations of experimental data. Often a scientist has to face the skepticism of his colleagues and even the distrust of the community. Moreover, if new knowledge contradicts the established methodological schemes that are generally accepted in a particular scientific field, a creator of innovations can almost inevitably expect attack. Misconceptions inhibit, but sometimes lead to the development of our knowledge in understanding processes occurring deep in the Earth’s interior. These examples, of course, do not exhaust all misconceptions in the earth sciences, and any researcher, if desired, can easily supplement this list. Misconceptions in science culminate in researchers obtaining incorrect results or simply hitting a dead end. Thus, if the coordinates of hypocenters are incorrectly determined, a subsequent chain of incorrect conclusions arises when studying particular regions. In addition to the objective consequences of misconceptions, subjective consequences cause considerable harm. Subjective consequences entail the effect of when individual scientists are held captive by misconceptions—due to ignorance or misunderstanding of individual aspects of certain problems—on the emergence of new ideas and approaches in a particular field. Most often, this manifests itself when scientists review articles and dissertations by their peers. In this article, the author gives several examples of misconceptions, which, in his opinion, are typical of the field in which he has worked for many years. In particular, this concerns misconceptions related to determining the hypocentral coordinates of earthquakes, seismic tomography, the inverse dynamic problem, reversal of seismic wave travel-time curves, etc. Twelve misconceptions are considered in all, which in one way or another affect the development of alternative methods for interpreting seismological data and our understanding of the Earth’s structure.

Two gesture-computing approaches by using electromagnetic waves

We are concerned with a novel sensor-based gesture input/ instruction technology which enables human beings to interact with computers conveniently. The human being wears an emitter on the finger or holds a digital pen that generates a time harmonic point charge. The inputs/instructions are performed through moving the finger or the digital pen. The computer recognizes the instruction by determining the motion trajectory of the dynamic point charge from the collected electromagnetic field measurement data. The identification process is mathematically modelled as a dynamic inverse source problem for time-dependent Maxwell's equations. From a practical point of view, the point source should be assumed to move in an unknown inhomogeneous background medium, which models the human body and the surroundings. Moreover, a salient feature is that the electromagnetic radiated data are only collected in a limited aperture. For the inverse problem, we develop, from the respectively deterministic and stochastic viewpoints, a dynamic direct sampling method and a modified particle filter method. Both approaches can effectively recover the motion trajectory. Rigorous theoretical justifications are presented for the mathematical modelling and the proposed recovery methods. Extensive numerical experiments are conducted to illustrate the promising features of the two proposed recognition approaches.

Новый метод количественной диагностики технического состояния установок скважинных штанговых насосов решением обратных задач методами многомерной оптимизации

Новый метод количественной диагностики технического состояния установок скважинных штанговых насосов решением обратных задач методами многомерной оптимизации

Nonparametric Method for Aircraft Flight Control

This paper is a part of a series of articles on nonparametric methods in dynamic systems theory. Here the authors propose a new method for inverse dynamic problem solution based only on some past measurements of controlled system input-output signals. The described nonparametric control method needs no any priori information on controlled system model parameters and does not require identification, training or statistical calculations. An example of nonparametric aircraft flight control is presented.

ПРИМЕНЕНИЕ МЕТРИКИ ВАССЕРШТЕЙНА ДЛЯ РЕШЕНИЯ ОБРАТНОЙ ДИНАМИЧЕСКОЙ ЗАДАЧИ СЕЙСМИКИ

The inverse dynamic problem of seismic consists in recovering the velocity model of elastic medium based on the observed seismic data. In this work it is proposed to use the Wasserstein metric since its use reduces the number of local extremes of the target functional in comparison with the L2-norm. This work also presents and discusses the results of numerical experiments including a comparative analysis of the velocity models recovered using the Wasserstein metric and L2-norm.

Dynamic inverse problem for Jacobi matrices

We consider the inverse dynamical problem for the dynamical system with discrete time associated with the semi-infinite Jacobi matrix. We solve the inverse problem for such a system and answer a question on the characterization of the inverse data. As a by-product we give a necessary and sufficient condition for the measure on the real line line to be the spectral measure of semi-infinite discrete Schrodinger operator.