Yuji Harata

3-DOF passive dynamic walking of compass-like biped robot with semicircular feet generated on slippery downhill

The authors demonstrated that a stable passive compass gait can be generated on a slippery downhill, and showed that the 2-DOF constraint conditions for the contact point are not always necessary for it. The generated walking gait while sliding on the slope becomes 3-DOF increased by addition of the positional coordinate of the contact point. This paper then investigates the effects of semicircular feet on the 3-DOF passive compass gait. First, we develop the equations of a 4-DOF passive compass-like biped robot with semicircular feet that slides on a slippery downhill. Second, we derive the term of the sliding friction force and discuss the complexity and relationship with holonomic constraint condition. Third, we perform numerical simulations to observe the typical 3-DOF passive walking motion and change in the gait properties according to the foot radius.

A novel locomotion robot that slides and rotates on slippery downhill

This paper proposes a novel locomotion robot that slides and rotates on a slippery downhill by utilizing the dynamical effect of an actively-controlled wobbling mass. First, we introduce a 4-DOF seedlike robot model that consists of two identical arc-shaped body frames and a short link, and develop the equation of motion, friction dynamics, and control law for generating a wobbling motion. Second, we numerically show that a stable downward motion can be generated based on the effect of entrainment to the wobbling motion at high frequencies on a slippery downhill. Third, we analyze the fundamental properties of the generated motion, such as moving speed and ground reaction force, through numerical simulations. Throughout this paper, we show that the robots arc-shaped body frame can maintain kinetic energy or rotation motion without stopping on the high-frictional downhill, and that this property also enables the indirect control of the moving speed by utilizing the wobbling effect.

Parametric excitation-based inverse bending gait generation

In a gait generation method based on the parametric excitation principle, appropriate motion of the center of mass restores kinetic energy lost by heel strike. The motion is realized by bending and stretching a swing-leg regardless of bending direction. In this paper, we first show that inverse bending restores more mechanical energy than forward bending, and then propose a parametric excitation-based inverse bending gait for a kneed biped robot, which improves gait efficiency of parametric excitation walking.

Intrinsic Localized Modes of Harmonic Oscillations in Pendulum Arrays Subjected to Horizontal Excitation

The behavior of intrinsic localized modes (ILMs) is investigated for an array with N pendula which are connected with each other by weak, linear springs when the array is subjected to horizontal, sinusoidal excitation. In the theoretical analysis, van der Pol’s method is employed to determine the expressions for the frequency response curves for fundamental harmonic oscillations. In the numerical calculations, the frequency response curves are presented for N = 2 and 3 and compared with the results of the numerical simulations. Patterns of oscillations are classified according to the stable steady-state solutions of the response curves, and the patterns in which ILMs appear are discussed in detail. The influence of the connecting springs of the pendula on the appearance of ILMs is examined. Increasing the values of the connecting spring constants may affect the excitation frequency range of ILMs and cause Hopf bifurcation to occur, followed by amplitude modulated motions (AMMs) including chaotic vibrations. The influence of the imperfections of the pendula on the system response is also investigated. Bifurcation sets are calculated to examine the influence of the system parameters on the excitation frequency range of ILMs and determine the threshold value for the connecting spring constant after which ILMs do not appear. Experiments were conducted for N = 2, and the data were compared with the theoretical results in order to confirm the validity of the theoretical analysis.Copyright

Suppression of Period-Doubling Bifurcation in Passive Dynamic Walking With Delayed Feedback Control

This paper investigates the effect of period-doubling bifurcation on passive dynamic walking (PDW) of a compass-like biped robot which consists of three point masses and two legs. The gait pattern of the robot consists of a single-support phase and a double-support phase which occurs instantaneously. The support and swing legs are exchanged at the double-support phase. Period-doubling bifurcation of PDW occurs when the slope angle of the ground becomes large, and the robot walks with a long step and a short step, alternately. Hip torque is designed based on delayed feedback control (DFC) to suppress the bifurcation. The equation of motion for the robot is numerically integrated and the walking speed is calculated. The simulation results show an increase in walking speed after a period-two gait emerges. Then, DFC is applied to the gait and stabilizes it to a period-one gait. After a period-four gait emerges, DFC is also applied to the period-four gait and stabilize it to period-two and period-one gaits. By comparing the period-one gait with the period-four and the period-two gaits, it is shown that the period-two gait has the fastest mean walking speed. The effect of the robot parameters is investigated and it is shown that the fastest walking speed for the period-one gait can be obtained when a leg mass position is chosen to a certain value.© 2012 ASME

An optimization method for the reference trajectory of parametric excitation walking

In parametric excitation walking, up-and-down motion of the center of mass restores mechanical energy and sustainable gait is generated. Not only walking performance but also walking ability strongly depends on the reference trajectory of the center of mass. In this paper, we propose an optimization method for the reference trajectory, in which the reference trajectory is confined to the quartic spline curves and the parameters of spline curves are optimized by a local search method usually used in combinatorial optimization. We apply the proposed method to a kneed biped robot and find some remarkably interesting results by numerical simulations.

Vibration Suppression of Wind Turbine Blades Using Tuned Mass Dampers

Passive control of flapwise vibrations of a wind turbine blade is investigated when a single tuned mass damper (TMD) is attached to the blade. The blade is subjected to a wind pressure which changes linearly with height from the ground level due to the wind shear. The vibrations of the wind turbine blade are theoretically and numerically analyzed to determine the natural frequency diagrams, frequency responses, stationary time histories and their FFT results. It is found that several peaks appear near the specific rotational speeds in the response curves for the blade because of both the wind pressure and the parametric excitation terms. It is also demonstrated that the optimal single TMD can suppress the resonance peaks if the fixed point theorem is used to determine the optimal values of the parameters of the TMD. The influences of the mass and install position of the TMD on its performance are also examined.Copyright

Localization Phenomena in Pendulum Arrays Subjected to Vertical Excitation

Localization phenomena, also referred to as intrinsic localized modes (ILMs), are investigated in an N-pendulum array subjected to vertical harmonic excitation. The pendula behave nonlinearly and are connected with each other by weak linear springs. In the theoretical analysis, van der Pol’s method is employed to determine the expressions for frequency response curves for the principal parametric resonances, considering the nonlinear restoring moment of the pendula. In the numerical results, frequency response curves for N=2 and 3 are shown to examine the patterns of ILMs, and the influences of the connecting spring constants and the imperfections of the pendula. Bifurcation sets are also calculated to show the excitation frequency range and the conditions for the occurrence of ILMs. Increasing the connecting spring constant results in the appearance of Hopf bifurcation. The numerical simulations reveal the occurrence of ILMs with amplitude modulated motions (AMMs) including chaotic motions. ILMs were observed in experiments, and the experimental data were compared with the theoretical results. The validity of the theoretical analysis was confirmed by the experimental data.© 2014 ASME

Autoparametric Resonances of Elastic Structures Coupled With Two Sloshing Modes in a Square Liquid Tank

Nonlinear vibrations of an elastic structure coupled with liquid sloshing in a square tank subjected to vertical sinusoidal excitation are investigated. Previous studies examined the vibrations of a structure coupled with only one sloshing mode in a rectangular tank. However, square tanks are expected to work more efficiently as a vibration suppression device (Tuned Liquid Damper, TLD) because two sloshing modes, (1,0) and (0,1) modes, simultaneously appear when the internal resonance ratio 2:1:1 is satisfied. In reality, it is impossible to build a perfectly square tank. Therefore, a nearly square liquid tank is also considered when the tuning condition is slightly deviated. In the theoretical analysis, the fluid in the tank is assumed to be perfect. The modal equations of motion for seven sloshing modes are derived using Galerkin’s method, considering the nonlinear terms. The linear damping terms are then incorporated into the modal equations to consider the damping effect of sloshing. The frequency response curves are determined using van der Pol’s method (based on the harmonic balance method). From these response curves, the influences of the liquid level, the aspect ratio of the tank cross section, and the deviation of the tuning condition are investigated. For a square tank it is found that (1,0) and (0,1) modes are nonlinearly coupled. When the liquid level is high, there are three patterns for sloshing: (I) both (1,0) and (0,1) sloshing modes appear at identical amplitudes; (II) these two modes appear at different amplitudes; and (III) either (1,0) or (0,1) mode appears. Compared with the performance of a rectangular TLD, a square TLD works more efficiently when the liquid level is low. Small deviations of the tuning condition may cause amplitude modulated motion to appear. Bifurcation sets are also calculated to illustrate the influence of the system parameters on the performance of the TLD. Experiments were also conducted in order to confirm the validity of the theoretical results. These results were in good agreement with the experimental data.Copyright

Development and experiment of a kneed biped walking robot based on parametric excitation principle

Parametric excitation walking is one of methods to realize dynamic walking on a level ground. This method has first applied to a biped robot with telescopic legs and later to a robot with actuated knee joints. In parametric excitation walking, mechanical energy is increased by periodic up-and-down motion of the center of mass. While parametric excitation walking with telescopic legs has verified by an experimental robot, that with actuated knees has not yet as far as we know. The purpose of this paper is to present demonstration experiment of parametric excitation walking with a kneed biped robot. To do this, we develop an experimental kneed biped robot having four parallel legs with semicircular feet. In the experiment, the robot achieves walking on a level ground more than 15 steps. We also measure the movements of the robot during walking by a 3D motion capture and compare with simulation results.