Showing papers on "Inertia published in 2008"

On the Passivity-Based Impedance Control of Flexible Joint Robots

Abstract: In this paper, a novel type of impedance controllers for flexible joint robots is proposed. As a target impedance, a desired stiffness and damping are considered without inertia shaping. For this problem, two controllers of different complexity are proposed. Both have a cascaded structure with an inner torque feedback loop and an outer impedance controller. For the torque feedback, a physical interpretation as a scaling of the motor inertia is given, which allows to incorporate the torque feedback into a passivity-based analysis. The outer impedance control law is then designed differently for the two controllers. In the first approach, the stiffness and damping terms and the gravity compensation term are designed separately. This outer control loop uses only the motor position and velocity, but no noncollocated feedback of the joint torques or link side positions. In combination with the physical interpretation of torque feedback, this allows us to give a proof of the asymptotic stability of the closed-loop system based on the passivity properties of the system. The second control law is a refinement of this approach, in which the gravity compensation and the stiffness implementation are designed in a combined way. Thereby, a desired static stiffness relationship is obtained exactly. Additionally, some extensions of the controller to viscoelastic joints and to Cartesian impedance control are given. Finally, some experiments with the German Aerospace Center (DLR) lightweight robots verify the developed controllers and show the efficiency of the proposed control approach.

The transition from inertial to viscous flow in capillary rise

Abstract: We investigate the initial moments of capillary rise of liquids in a tube. In this period both inertia and viscous flow losses balance the pressure generated by the meniscus curvature (capillary pressure). It is known that the very first stage is purely dominated by inertial forces, where subsequently the influence of viscosity increases (visco-inertial flow). Finally the effect of inertia vanishes and the flow becomes purely viscous. In this study we derive the times and meniscus heights at which the transition between the time periods occur. This is done in an attempt to provide a method to determine a priori which terms of the momentum balance are relevant for a given problem. Analytic solutions known from previous literature are discussed and the time intervals of their validity compared. The predicted transition times and the calculated heights show good agreement with experimental results from literature. The results are also discussed in dimensionless form and the limitations of the calculations are pointed out.

Method for determining inertia effects for a hybrid powertrain system

Abstract: A method for controlling a hybrid powertrain system based upon determined inertial effects for a continuously variable operating range state includes monitoring an operator torque request and a rotational speed of the output member, determining an inertial effect on an input speed of the input member for a continuously variable operating range state, and controlling motor torque outputs from the electric machines to meet the operator torque request based upon the inertial effect on the input speed of the input member.

Method for preferential selection of modes and gear with inertia effects for a hybrid powertrain system

Abstract: A method for controlling a hybrid powertrain system selectively operative in one of a plurality of operating range states including an engine includes monitoring an operator torque request and a rotational speed of the output member, determining inertial effects of the transmissions, determining motor torque outputs from the electrical machines and an engine based upon the inertial effects, and selecting a preferred operating range state and a preferred input speed from the engine to the transmission based upon the operator torque request and the inertial effects.

On-Orbit Identification of Inertia Properties of Spacecraft Using a Robotic Arm

Abstract: This paper presents a robotics-based method for on-orbit identification of inertia properties of spacecraft. The method makes use of an onboard robotic arm to change the inertia distribution of the spacecraft system. As a result of the inertia redistribution, the velocity of the spacecraft system will change correspondingly. Because the velocity change is measurable and the inertia redistribution of the robotic arm itself is precisely computable, the inertia parameters of the spacecraft body become the only unknown in the momentum equations and, hence, can be identified from the momentum equations of the spacecraft system. To treat the problem as a linear identification problem, it has to be solved in two steps. The first step is to identify the mass and mass center of the spacecraft; and the second step is to identify the inertia tensor of the spacecraft. The advantages of this method are 1) it does not consume fuel because a robotic subsystem is energized by solar power; 2) it requires measuring velocities only, but not accelerations and forces; and 3) it is not affected by internal forces, which are difficult to accurately measure. The paper investigates the sensitivity of the method with respect to different arm/spacecraft mass ratios, arm motion trajectories, and velocity-measurement errors.

Electric power steering device

Abstract: PROBLEM TO BE SOLVED: To provide an electric power steering device capable of ensuring superior steering response characteristic not depending on inertia main shaft arrangement of an actual vehicle. SOLUTION: The electric power steering device 1 is provided with a torque sensor 10 for detecting steering torque generated by steering operation; a vehicle speed sensor 11 for detecting a vehicle speed; and an ECU 12. The ECU 12 has an assist amount operation part 13 for determining an assist amount based on a detection value of the torque sensor 10 and the vehicle speed sensor 11; an assist amount correction part 14 for correcting the assist amount using a transmission function obtained by vehicle item data including a parameter regarding the actual inertia main shaft arrangement and target inertia main shaft arrangement; and a motor driving control part 15 for controlling driving of a motor 8 according to the assist amount after correction. The vehicle item data including the parameter regarding the actual inertia main shaft arrangement and the target inertia main shaft arrangement are previously memorized in a memory 16. COPYRIGHT: (C)2008,JPO&INPIT

Principles of Mechanics

Abstract: The response of bodies to slowly varying loads is static or quasistatic. For slowly varying loads, the sum of all forces acting on any segment of a body are in balance since there are no accelerations; i.e. for any segment of the body, the resultant of tractions on the surface of the segment is equal in magnitude but opposite in direction to any external force acting on the segment. On the other hand, rapid changes in load cause the body to accelerate; in this case the resultants of stresses acting on any part of the body are related to the product of acceleration and inertia by the laws of motion. For these two broad classes of loading the differential equations for variations in stress (or stress resultant) across an arbitrary segment of the body are obtained from either equilibrium equations or the laws of motion. These laws form the basis of several useful principles. In this chapter special forms of these principles will be developed that apply to small deflection theory for planar displacements of slender bodies.

Mass redistribution method for finite element contact problems in elastodynamics

Abstract: This paper is devoted to a new method dealing with the semi-discretized finite element unilateral contact problem in elastodynamics. This problem is ill-posed mainly because the nodes on the contact surface have their own inertia. We introduce a method based on an equivalent redistribution of the mass matrix such that there is no inertia on the contact boundary. This leads to a mathematically well-posed and energy conserving problem. Finally, some numerical tests are presented.

Optimal protocols for minimal work processes in underdamped stochastic thermodynamics.

Abstract: For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between two given equilibrium states. For overdamped dynamics which ignores inertia effects, the optimal protocol has been found to involve jumps of the control parameter at the beginning and end of the process. Including the inertia term, we show that this feature not only persists but that even delta-peak-like changes of the control parameter at both boundaries make the process optimal. These results are obtained by analyzing two simple paradigmatic cases: First, a Brownian particle dragged by a harmonic optical trap through a viscous fluid and, second, a Brownian particle subject to an optical trap with time-dependent stiffness. These insights could be used to improve free energy calculations via either thermodynamic integration or “fast growth” methods using Jarzynski’s equality.

Nonisothermal Transient Flow in Natural Gas Pipeline

Abstract: The fully implicit finite-difference method is used to solve the continuity, momentum, and energy equations for flow within a gas pipeline. This methodology (1) incorporates the convective inertia term in the conservation of momentum equation, (2) treats the compressibility factor as a function of temperature and pressure, and (3) considers the friction factor as a function of the Reynolds number and pipe roughness. The fully implicit method representation of the equations offers the advantage of guaranteed stability for a large time step, which is very useful for gas pipeline industry. The results show that the effect of treating the gas in a nonisothermal manner is extremely necessary for pipeline flow calculation accuracies, especially for rapid transient process. It also indicates that the convective inertia term plays an important role in the gas flow analysis and cannot be neglected from the calculation.

Reliability of Strongly Nonlinear Single Degree of Freedom Dynamic Systems by the Path Integration Method

Abstract: This paper presents a first passage type reliability analysis of strongly nonlinear stochastic single-degree-of-freedom systems. Specifically, the systems considered are a dry friction system, a stiffness controlled system, an inertia controlled system, and a swing. These systems appear as a result of implementation of the quasioptimal bounded in magnitude control law. The path integration method is used to obtain the reliability function and the first passage time.

Optimal protocols for minimal work processes in underdamped stochastic thermodynamics

Abstract: For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between two given equilibrium states. For overdamped dynamics which ignores inertia effects, the optimal protocol has been found to involve jumps of the control parameter at the beginning and end of the process. Including the inertia term, we show that this feature not only persists but that even delta peak-like changes of the control parameter at both boundaries make the process optimal. These results are obtained by analyzing two simple paradigmatic cases: First, a Brownian particle dragged by a harmonic optical trap through a viscous fluid and, second, a Brownian particle subject to an optical trap with time-dependent stiffness. These insights could be used to improve free energy calculations via either thermodynamic integration or "fast growth" methods using Jarzynski's equality.

A Model of Consumer Inertia With Applications to Dynamic Pricing

Abstract: This paper introduces a model to capture the behavioral phenomenon of inertia in inter-temporal consumer purchase decisions. We define inertia as the inherent tendency to refrain from making any purchase. This is represented by a utility premium that is required to trigger purchases. Inertia may induce consumers to wait even when it is optimal to buy immediately. We show that our model of inertia is consistent with well-established behavioral regularities, such as loss aversion and probability weighting in the sense of prospect theory, and hyperbolic time preferences. We embed this decision model within a dynamic pricing context. The firm has a fixed capacity of a particular product and sells it over two time periods to a market consisting of both rational and inertial consumers. We find that the depth of inertia (i.e., strength of inertial effects) always hurts seller profits but the breadth of inertia (i.e., the proportion of inertial consumers) may sometimes be beneficial. We offer practical recommendations for firms to influence both depth and breadth of consumer inertia.

Competing geometric and inertial effects on local flow structure in thick gravity-driven fluid films

Abstract: The formation and presence of eddies within thick gravity-driven free-surface film flow over a corrugated substrate are considered, with the governing equations solved semianalytically using a complex variable method for Stokes flow and numerically via a full finite element formulation for the more general problem when inertia is significant. The effect of varying geometry (involving changes in the film thickness or the amplitude and wavelength of the substrate) and inertia is explored separately. For Stokes-like flow and varying geometry, excellent agreement is found between prediction and existing flow visualizations and measured eddy center locations associated with the switch from attached to locally detached flow. It is argued that an appropriate measure of the influence of inertia at the substrate is in terms of a local Reynolds number based on the characteristic corrugation length scale. Since, for small local Reynolds numbers, the local flow structure there becomes effectively decoupled from the i...

Porous media characterization by the two-liquid method: effect of dynamic contact angle and inertia.

Abstract: The validity of using the Lucas-Washburn (LW) equation for porous media characterization by the two-liquid capillary penetration method was tested numerically and experimentally. A cylindrical capillary of known radius and contact angle was used as a model system for the tests. It was found that using the LW equation (i.e., ignoring inertia and dynamic contact angle effects) may lead to very erroneous assessment of the capillary radius and the equilibrium contact angle, for a relatively wide range of capillary radii and equilibrium contact angles. A correct assessment requires the application of a penetration kinetics equation that considers inertia and the dynamic contact angle.

A Compact Squeeze-Film Model Including Inertia, Compressibility, and Rarefaction Effects for Perforated 3-D MEMS Structures

Abstract: We present a comprehensive analytical model of squeeze-film damping in perforated 3D microelectromechanical system structures. The model includes effects of compressibility, inertia, and rarefaction in the flow between two parallel plates forming the squeeze region, as well as the flow through perforations. The two flows are coupled through a nontrivial frequency-dependent pressure boundary condition at the flow entry in the hole. This intermediate pressure is obtained by solving the fluid flow equations in the two regions using the frequency-dependent fluid velocity as the input velocity for the hole. The governing equations are derived by considering an approximate circular pressure cell around a hole, which is representative of the spatially invariant pressure pattern over the interior of the flow domain. A modified Reynolds equation that includes the unsteady inertial term is derived from the Navier-Stokes equation to model the flow in the circular cell. Rarefaction effects in the flow through the air gap and the hole are accounted for by considering the slip boundary conditions. The analytical solution for the net force on a single cell is obtained by solving the Reynolds equation over the annular region of the air gap and supplementing the resulting force with a term corresponding to the loss through the hole. The solution thus obtained is valid over a range of air gap and perforation geometries, as well as a wide range of operating frequencies. We compare the analytical results with extensive simulations carried out using the full 3D Navier-Stokes equation solver in a commercial simulation package (ANSYS-CFX). We show that the analytical solution performs very well in tracking the net force and the damping force up to a frequency f = 0.8fn where fn is the first resonance frequency) with a maximum error within 20% for thick perforated cells and within 30% for thin perforated cells. The error increases considerably beyond this frequency. The prediction of the first resonance frequency is within 21 % error for various perforation geometries.

A Method of Self-Adaptive Inertia Weight for PSO

Abstract: The particle swarm optimization algorithm (PSO) has successfully been applied to many engineering optimization problems. However, the most of existing improved PSO algorithms work well only for small-scale problems on low-dimensional space. In this new self-adaptive PSO, a special function, which is defined in terms of the particle fitness, swarm size and the dimension size of solution space, is introduced to adjust the inertia weight adaptively. In a given generation, the inertia weight for particles with good fitness is decreased to accelerate the convergence rate, whereas the inertia weight for particles with inferior fitness is increased to enhance the global exploration abilities. When the swarm size is large, a smaller inertia weight is utilized to enhance the local search capability for fast convergence rate. If the swarm size is small, a larger inertia weight is employed to improve the global search capability for finding the global optimum. For an optimization problem on multi-dimension complex solution space, a larger inertia weight is employed to strengthen the ability to escape from local optima. In case of small dimension size of solution space, a smaller inertia weight is used for reinforcing the local search capability. This novel self-adaptive PSO can greatly accelerate the convergence rate and improve the capability to reach the global minimum for large-scale problems. Moreover, this new self-adaptive PSO exhibits a consistent methodology: a larger swarm size leads to a better performance.

Motion capture based identification of the human body inertial parameters

Abstract: Identification of body inertia, masses and center of mass is an important data to simulate, monitor and understand dynamics of motion, to personalize rehabilitation programs. This paper proposes an original method to identify the inertial parameters of the human body, making use of motion capture data and contact forces measurements. It allows in-vivo painless estimation and monitoring of the inertial parameters. The method is described and then obtained experimental results are presented and discussed.

Chaotic vibrations in flexible multi-layered bernoulli-euler and timoshenko type beams

Abstract: NUMERICAL INVESTIGATIONS OF TRANSVERSALLY DRIVEN BEAMS ARE CARRIED OUT VERSUS CONTROL PARAMETERS, I.E. AMPLITUDE AND FREQUENCY OF AN EXTERNAL LOADING FOR A SERIES OF BOUNDARY CONDITIONS AND FOR TWO KINEMATICAL BEAM MODELS OF EULER-BERNOULLI AND TIMOSHENKO TYPES. NOVEL STIFF STABILITY BEAM LOSS IS DETECTED AND STUDIED. RELIABILITY OF THE OBTAINED RESULTS IS VERFIED VIA FEM (FINITE ELEMENT METHOD) AND FDM (FINITE DIFFERENCE METHOD). TRANSI-TIONAL AND CHAOTIC PHENOMENA EXHIBITED BY FLEXIBLE EULER-BERNOULLI BEAMS SUBJECTED TO AN IMPACT ACTION OF A ONE-DEGREE OF FREEDOM BODY WITH A GIVEN MASS AND VELOCITY ARE ANALYZED. IT HAS BEEN SHOWN, AMONG THE OTHERS, THAT INCLUSION OF TRANSVERSAL SHEARS AND ROTATION INERTIA ESSENTIALLY IN°UENCES NONLINEAR DYNAMICS OF THE STUDIED BEAMS SUBJECTED TO TRANSVERSAL AND SIGN-CHANGEABLE LOAD ACTIONS.

Slower is faster: fostering consensus formation by heterogeneous inertia

Abstract: We investigate an extension of the voter model in which voters are equipped with an individual inertia to change their opinion. This inertia depends on the persistence time of a voter’s current opinion (ageing). We focus on the case of only two different inertia values: zero if a voter just changed toward a new opinion, and ν otherwise. We are interested in the average time to reach consensus, i.e. the state in which all voters have adopted the same opinion. Adding inertia to the system means to slow down the dynamics at the voter’s level, which should presumably lead to slower consensus formation. As an unexpected outcome of our inertial voter dynamics, there is a parameter region of ν where an increasing inertia leads to faster consensus formation. These results rest on the heterogeneity of voters which evolves through the described ageing. In a control setting of homogeneous inertia values, we only find monotonously increasing consensus times. In this paper, we present dynamical equations for the mean field case which allow for analytical insight into the observed slower-is-faster effect.

Adaptive satellite attitude control in the presence of inertia and CMG gimbal friction uncertainties

Abstract: A nonlinear adaptive attitude controller is designed in this paper that compensates for dynamic uncertainties in the spacecraft inertia matrix and unknown dynamic and static friction effects in the control moment gyroscope (CMG) gimbals. Attitude control torques are generated by means of a four single gimbal CMG pyramid cluster. The challenges to develop the adaptive controller are that the control input is multiplied by uncertainties due to dynamic friction effects and is embedded in a discontinuous nonlinearity due to static friction effects. A uniformly ultimately bounded result is proven via Lyapunov analysis for the case in which both static and dynamic gimbal friction is included in the dynamic model, and an extension is provided that illustrates how asymptotic tracking is achieved when only dynamic friction is present in the CMG model.

Identification and quantification of stick-slip induced brake groan events using experimental and analytical investigations.

Abstract: To describe the brake creep-groan phenomenon and several types of stick-slip motions, we propose both analytical and experimental investigations for an automatic transmission equipped vehicle. A lumped torsional model is employed to approximate the dynamics of the real mechanical system. This model assigns inertia to the drive, brake rotor, brake caliper and tire/vehicle, and by appropriate algorithms the simulation time histories include the effects of the friction non-linearity coupling brake and rotor. We consider how to force this particular system, from what physical state, and finding appropriate parameters and solutions. Important computational issues, as related to the stick-slip or slip-stick transitions, are addressed with the algorithms. Driving forces are assigned with two functions, one appropriate for comparison with the test and the other to study stick-slip orbits, which have been found to have various types of motion depending on the controlling brake actuation parameters. Since the groan features a discontinuous friction force and finite-repeating motions some comparisons are made in the frequency and time-frequency domains. These demonstrate the expected stick-slip frequency and multiple orders.

On Tangential Friction Induced Vibrations in Brake Systems

Abstract: The basis for the analysis of friction in brake systems is the brake pad’s tribological interface. An investigation of this interface reveals friction intensive surface structures. These so-called “patches” are extremely hard and carry the main part of the friction power. By complex interaction processes of wear and heat these patches are generated permanently but leave the system after a certain period of time. So there is an equilibrium of flow of contact patches in the brake pad interface, with the outcome being a dynamic macroscopic friction coefficient, whose “inertia” can be well described by differential equations in the form of special balance equations. Systematic expansions of these balance equations even allow, for the first time, a simulation of different test cycles of the AK-Master test for friction materials with high accuracy. These friction force variations are generated by the dynamics of the local surface geometry and can explain physically effects of measurements, which were up to now described by control theoretic approximations [7, 8].

Kinematic and dynamic analogies between planar biped robots and the reaction mass pendulum (RMP) model

Abstract: In order to simplify dynamic analysis, humanoid robots are often abstracted with various versions of the inverted pendulum model. However, most of these models do not explicitly characterize the robotpsilas rotational inertia, a critical component of its dynamics, and especially of its balance. To remedy this, we have earlier introduced the reaction mass pendulum (RMP), an extension of the inverted pendulum, which models the rotational inertia and angular momentum of a robot through its centroidal composite rigid body (CCRB) inertia. However, we presented only the kinematic mapping between a robot and its corresponding RMP. Focussing in-depth on planar mechanisms, here we derive the dynamic equations of the RMP and explicitly compute the parameters that it must possess in order to establish equivalence with planar compass gait robot. In particular, we show that, a) an angular momentum equality between the robot and RMP does not necessarily guarantee kinetic energy equality, and b) a cyclic robot gait may not result in a cyclic RMP movement. The work raises the broader question of how quantitatively similar the simpler models of humanoid robot must be in order for them to be of practical use.