高自由度双足机器人数学模型及步行控制研究

基于ZMP理论及位姿矩阵,采用了相对重心以及相对坐标系的数学描述方法,对17自由度双足机器人步行稳定性控制进行数学建模研究．所建立的数学模型能够描述机器人稳定性控制．并经过Matlab数学计算和仿真研究,验证了所建立的模型可以描述双足机器人的步行规律,在理论上达到了双足机器人步行稳定性的控制目的．最后通过VC 把整个模型封装成一个可视化系统,便于将所研究的模型应用到实际的控制中,为未来机器人的实时控制的研究提供了技术支持．     

弹簧刚度对被动步行的稳定性影响

由人类步行的生物力学研究得到启发,在被动双足步行机器人的髋关节处引入了扭簧,并通过仿真和试验研究了弹簧刚度对被动步行稳定性的影响.在仿真中,用胞映射方法计算被动步行机器人的吸引盆,并用吸引盆来衡量机器人的稳定性,研究了弹簧刚度对被动步行吸引盆大小的影响. 仿真结果表明, 吸引盆随着弹簧刚度的增大而增大. 在试验中,使机器人在各弹簧刚度参数下沿斜坡向下行走100次,记录下行走到头的次数作为稳定性的度量. 试验结果表明, 存在一个大小适中的弹簧刚度使机器人稳定性最大. 对弹簧提高机器人稳定性的原因进行了分析,对造成仿真与试验之间差异的原因进行了分析.      

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分析人体双足步行的动态稳定性以及跳跃运动的动力学过程. 讨论与竞走和跑步运动有关的 力学问题.     

带缩放式腿的四足步行机器人的三足支撑步行的动力学分析

本文讨论带缩放式腿的四足步行机器人的三足支撑步行运动。采用半逆解法预先规定运动学补充条件进行运动学分析,应用达朗伯原理和若丹原理进行动力学分析,并附加优化条件解决“超静定性”困难。所分析的结果用于计算一个具体机器人的动力学问题。     

人体步行的稳定性

本文讨论人体双足步行运动的动态稳定性。建立由躯干、双臂和双腿组成的多刚体人体模型，给出限制质心地面投影变化范围的动态稳定域。分析表明，对具有正常行走能力的人体，步行稳定性应取决于外部条件。地面粗糙程度、质心高度、步长、腿长和足长等是影响步行稳定性的重要因素     

动态规划求解空间双臂机器人非完整运动最优控制问题

通过自适应动态规划研究自由漂浮空间双臂机器人运动的最优控制问题．针对空间双臂机器人的非完整性运动,采用自适应动态规划(Adaptive Dynamic Programming, ADP)方法求解其最优控制问题．根据多体动力学理论,推导了载体位置、姿态均无控制条件下,双臂空间机器人满足的系统动量守恒关系的非完整约束方程,并将其转化为控制系统的状态方程,从而将双臂空间机器人的非完整运动规划问题转化为对非线性系统的控制问题．文中根据自适应动态规划网络结构,利用神经网络来近似性能指标函数,进而用龙格库塔法求解状态变量．并给出了适合该类问题的一种效用函数具体表达式,保证了空间双臂机器人到达期望位置后不再继续运动．实现了对空间双臂机器人非完整运动规划的最优控制．数值仿真实验验证了ADP对求解空间双臂机器人非完整运动规划最优控制问题的有效性．     

变长度弹性伸缩腿双足机器人动力学与控制

研究了半被动双足机器人的平面稳定行走的控制问题．基于弹簧质点模型，采用拉格朗日方法分别得到双足机器人单支撑阶段与双支撑阶段的动力学方程，对机器人系统的动力学方程求得周期解．应用非线性系统状态反馈线性化理论，在双足机器人的单支撑阶段和双支撑阶段中，通过控制双足机器人的腿长度，实现稳定的周期行走．在理论分析的基础上，对控制算法进行了仿真与研究．结果表明：在周期行走过程中，文中采用的变长度控制算法可以使双足机器人克服外界的干扰，并具有较强的抗干扰性．     

HUMAN-LIKE CONTROL FOR SEMI-PASSIVE BIPEDAL ROBOT WALKING WITH VARIABLE LEG STIFFNESS1)

研究了变刚度半被动双足机器人行走控制问题。采用仿人的行走控制策略,使用变刚度双足弹簧负载倒立摆模型,利用模型自稳定性,在双支撑阶段调整后腿刚度使机器人的能量保持在期望能量附近,在单支撑阶段调整摆动腿落地位置控制质点的高度和前向速度。仿真结果表明：本文采用的控制策略可以实现双足机器人在水平面上的稳定行走,无扰动时可以使机器人实现零输入的被动周期行走,有外部扰动时腿部变刚度控制可使机器人总能量恢复平衡并重新进入稳态行走,控制系统具有鲁棒性。     

柔性空间机器人姿态运动规划的混合优化策略

自由漂浮是空间机器人执行任务时常用的工作模式,其姿态规划是完成复杂空间任务的基础.针对自由漂浮柔性空间机器人姿态运动规划问题,提出一种由Gauss伪谱法求解可行解与直接打靶法求解更为精确的数值解相结合的混合优化策略.首先,利用假设模态法近似描述柔性臂杆的弹性变形,根据Lagrange方程建立空间机器人系统的动力学模型;然后,利用Gauss伪谱法将空间机器人非完整运动规划问题离散为非线性规划问题,求解在较少Legendre-Gauss(LG)点时状态变量和控制变量对应的可行解,可行解的求解采用从可行解到近似最优解的串行优化策略;最后,在LG点处离散控制变量,作为直接打靶法的初值,利用序列二次规划算法求解最优的控制输入,再通过数值积分得到空间机器人系统姿态运动优化轨迹.通过数值仿真,求解得到的姿态运动曲线光滑平稳,最优控制输入也能很好地满足各种约束条件.结果表明该混合优化策略具有很好的鲁棒性和有效性.     

基于步态切换的欠驱动双足机器人控制方法

由于高维、非线性、欠驱动等特点,3-D双足机器人的稳定性控制依然是一个研究难点.一些传统的控制方法,如基于事件的反馈控制方法和PD控制方法,抗扰动能力较弱,鲁棒性较差.通过观察,人类受到外部扰动影响时,会通过调整步态重新获得稳定性,相较之下仅依靠一个步态获得的稳定性是有限的.受此启发,本文针对上述问题提出一种基于步态切换的欠驱动3-D双足机器人控制方法.首先,以能耗最少为优化目标,通过非线性优化方法预先设计多组不同步长、步速的步态作为参考步态,以构建一个步态库;然后,通过综合考虑步态切换过程中的稳定性与能效,建立了多目标步态切换函数;最后,将该步态切换函数作为优化目标,并求解该最小化问题获得下一步的参考步态,从而实现步态切换,达到使用步态库-多轨迹方法来提高鲁棒性的目的.在仿真实验中运用该步态切换控制方法,欠驱动3-D双足机器人可实现相对高度在[-20,20]mm内随机变化的不平整地面上行走,而仅采用单步态控制策略则无法克服这样的外部扰动,从而说明了基于步态切换的欠驱动双足机器人控制方法的有效性.     

On formulas for the Rayleigh wave velocity in pre-stressed compressible solids

In this paper, formulas for the velocity of Rayleigh waves in compressible isotropic solids subject to uniform initial deformations are derived using the theory of cubic equation. They are explicit, have simple algebraic forms, and hold for a general strain energy function. Unlike the previous investigations where the derived formulas for Rayleigh wave velocity are approximate and valid for only small enough values of pre-strains, this paper establishes exact formulas for Rayleigh wave velocity being valid for any range of pre-strains. When the prestresses are absent, the obtained formulas recover the Rayleigh wave velocity formula for compressible elastic solids. Since obtained formulas are explicit, exact and hold for any range of pre-strains, they are good tools for evaluating nondestructively prestresses of structures.     

Green's function for SH-waves in a cylindrically monoclinic material

Green's function for SH-waves in a cylindrically monoclinic material is considered for impulsive and time-harmonic sources. Closed form expressions for the Green's function are derived for a few limited values of anisotropic parameters. A very interesting time development of the wave front shape is illustrated and the wave front singularity is discussed for the transient SH-wave. Contours of the displacement amplitude for the time-harmonic wave are also shown.     

Development of co-current air–water flow in a vertical pipe

Measurements of the cross-sectional distribution of the gas fraction and bubble size distributions were conducted in a vertical pipe with an inner diameter of 51.2 mm and a length of about 3 m for air/water bubbly and slug flow regimes. The use of a wire-mesh sensor obtained a high resolution of the gas fraction data in space as well as in time. From this data, time averaged values for the two-dimensional gas fraction profiles were decomposed into a large number of bubble size classes. This allowed the extraction of the radial gas fraction profiles for a given range of bubble sizes as well as data for local bubble size distributions. The structure of the flow can be characterized by such data. The measurements were performed for up to 10 different inlet lengths and for about 100 combinations of gas and liquid volume flow rates. The data is very useful for the development and validation of meso-scale models to account for the forces acting on a bubble in a shear liquid flow and models for bubble coalescence and break-up. Such models are necessary for the validation of CFD codes for the simulation of bubbly flows.     

Long-wavelength dispersion of acoustic waves in transversely inhomogeneous anisotropic plates

Long-wavelength onset of the fundamental branches is described for a free anisotropic plate with arbitrary through-plate variation of material properties. Main attention is given to the flexural branch. Closed-form expressions for the leading-order dispersion coefficient of the velocity and displacement are derived for a generic case and exemplified for the various types of either continuous, or discrete, or periodic inhomogeneity and for the monoclinic symmetry. The relevance of the static averaging is examined in detail. The bounds for the slope of the flexural velocity branch are established. The upper fundamental branches are considered for the case when these are uncoupled inplane and shear horizontal ones.     

Boundary element simulations of spheres settling in circular,square and triangular conduits

Numerical simulations of a spherical particle sedimenting in circular, triangular and square conduits containing a viscous, inertialess, Newtonian fluid were investigated using the Boundary Element Method (BEM). Settling velocities and pressure drops for spheres falling along the centre-lines of the conduits were computed for a definitive range of sphere sizes. The numerical simulations for the settling velocities showed good agreement with existing experimental data. The most accurate analytic solution for a sphere settling along the axis of a circular conduit produced results which were almost indistinguishable from the present BEM calculations. For a sphere falling along the centre-line of a square conduit, the BEM calculations for small spheres agreed well with analytic results. No analytic results for a sphere falling along the axis of a triangular conduit were available for comparison. Extrapolation of the BEM predictions for the pressure drops, to infinitely small spheres, showed remarkable agreement with analytic results. For the circular conduit, the sphere's settling velocity and angular velocity were computed as a function of drop position for small, medium and large spheres. Excellent agreement with a reflection solution was achieved for the small sphere. In addition, end effects were investigated for centre-line drops and compared where possible with available experimental data and analytic results.Los Alamos National Laboratory, Los Alamos, New Mexico, USA.     

FRP筋粘结式锚具的界面径向弹性模量分析

建立了FRP(Fibre Reinforced Polymer)筋粘结式锚具粘结界面的Rib-scale模型和Bar-scale模型,然后利用Fourier-Bessel级数推导了FRP筋、混凝土以及钢套筒等在径向应力作用下的解析解.解析解与数值解吻合较好,验证了用Fourier-Bessel级数表达的解析解的有效性....     

The re-examination of the weakly nonlinear theory of hydrodynamic stability

The weakly nonlinear theory has been widely applied in the problem of hydrodynamicstability and also in other fields.However,although its application has been successful forsome problems,yet,for other problems,the results obtained are not satisfactory,especiallyfor problems like transition or the evolution of the vortex in the free shear flow,for whichthe goal of the theoretical investigation is not seeking for a steady state,but predicting anevolutional process.In this paper,we shall examine the reason for the unsuccessfulness andsuggest ways for its amendment.     

Renormalization Group Model of Large-Scale Turbulence in Porous Media

Renormalization group methods are used to develop a macroscopic (large-scale) turbulence model for incompressible flow in porous media. The model accounts for the large-distance and large-time behavior of velocity correlations generated by the momentum equation for a randomly stirred, incompressible flow. Utilizing the renormalization procedure, the transport equations for the large-scale modes and expressions for effective transport coefficients are obtained. Expressions for renormalized turbulent viscosity, which accounts for the ultraviolet subrange of the turbulent kinetic energy spectrum, are also obtained.     

On unsteady unidirectional flows of a second grade fluid

Some properties of unsteady unidirectional flows of a fluid of second grade are considered for flows produced by the sudden application of a constant pressure gradient or by the impulsive motion of one or two boundaries. Exact analytical solutions for these flows are obtained and the results are compared with those of a Newtonian fluid. It is found that the stress at the initial time on the stationary boundary for flows generated by the impulsive motion of a boundary is infinite for a Newtonian fluid and is finite for a second grade fluid. Furthermore, it is shown that initially the stress on the stationary boundary, for flows started from rest by sudden application of a constant pressure gradient is zero for a Newtonian fluid and is not zero for a fluid of second grade. The required time to attain the asymptotic value of a second grade fluid is longer than that for a Newtonian fluid. It should be mentioned that the expressions for the flow properties, such as velocity, obtained by the Laplace transform method are exactly the same as the ones obtained for the Couette and Poiseuille flows and those which are constructed by the Fourier method. The solution of the governing equation for flows such as the flow over a plane wall and the Couette flow is in a series form which is slowly convergent for small values of time. To overcome the difficulty in the calculation of the value of the velocity for small values of time, a practical method is given. The other property of unsteady flows of a second grade fluid is that the no-slip boundary condition is sufficient for unsteady flows, but it is not sufficient for steady flows so that an additional condition is needed. In order to discuss the properties of unsteady unidirectional flows of a second grade fluid, some illustrative examples are given.