Impactless biped walking on a slope

Walking without impacts has been considered in dynamics as a motion/force control problem. In order to avoid impacts, an approach for both the specified motion of the biped and its ground reaction forces was presented yielding a combined motion and force control problem. As an application, a walker on a horizontal plane has been considered. In this paper, it is shown how the control of the ground reaction forces and the energy consumption depend on the gradient of a slope. The biped dynamics and the constraints within the biped system and on the ground are discussed. A motion control synthesis is developed using the inverse dynamics principle proven to be most efficient for human walking research, too. The impactless walking with controlled legs is illustrated by a seven-link biped. The “flying” biped has nine degrees of freedom, with six control inputs. During locomotion, the standing leg has three scleronomic constraints, and the trunk has three rheonomic constraints. However, there are three rheonomic constraints for the prescribed leg motion or three scleronomic constraints for reaction forces of the trailing leg, respectively. The nominal control action for impactless walking can be precomputed and stored. The model proposed allows the investigation of several problems: uphill and downhill walking, optimization of step length, stiction of the feet on the slope and many more. All these findings are also of interest in biomechanics.     

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.      

Control of statically unstable legged vehicles

Studies that consider a legged machine walking with a statically unstable gait as a controlled system of solids with variable constraints are generalized. The motion of such a system is described by both differential and difference equations. The method of optimization of periodic systems is used to synthesize control algorithms for such systems. It is demonstrated that if the dynamic processes due to constraint variation are taken into account in the synthesis of a control system, then it is possible to substantially increase the performances of control algorithms and to reduce loads on actuating mechanisms. S.P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 6, pp. 37–66, June, 2000     

A low-cost optimization framework to solve muscle redundancy problem

Prediction of muscle activations based on optimization procedures mostly leads to a prohibitive computational effort. To overcome this problem, an optimization framework by reformulation of the so-called method of extended inverse dynamics (EID) was developed. A planar, seven-segment model with sixteen muscle groups was used to represent human neuromusculoskeletal dynamics. The muscle activations were estimated based on two methods: EID, which treats the system dynamics (compatibility between muscular and skeletal torques), as an equality constraint, and the proposed method, which employs unconstrained system dynamics of EID (USDEID). The proposed method is based on the idea that the EID equality constraint, which is difficult to satisfy, can be eliminated by reformulation of the governing equations and optimization variables, which not only relaxes the optimization problem and leads to less optimization parameters, but also guarantees the full compatibility of the system dynamics. The comparison of simulation results of optimal muscle activations against experimental data showed a reasonable agreement for both methods during half of a gait cycle. Optimization results showed that USDEID is not only more accurate than EID in terms of the compatibility between the skeletal and muscular system dynamics, but also approximately eight times faster for ten random initial values. USDEID may be used to predict muscle activations, when the computational cost becomes prohibitive.     

An Efficient Technique in Shape Optimization*, †

A shape optimization method is presented for smoothing stress peaks that are caused by notch effects on unloaded edges of holes in plates or shell structures with linear-elastic, homogeneous, isotropic material under external forces. The optimization problem is first formulated as a functional whose integrand contains the difference between the stresses at the hole edge and the optimal stress. This mechanical problem is approximated by a sequence of purely geometric, substitute functionals. The substitute functional is discretized by means of splines and formulated as a nonlinear constrained optimization problem which is solved with a quasi-Newton method. The efficiency of the method is demonstrated on the basis of examples.     

非确定性结构静动态特性稳健优化设计

本文研究了考虑参数随机性的结构静动态特性稳健性优化设计问题的数学模型和数值求解。在考虑结构设计变量和其研究了考虑参数随机性的结构静动态特性稳健性优化设计问题的数学模型和数值求 解. 在考虑结构设计变量和其他参数随机分布的前二阶矩的条件下,采用基于二阶摄动法的 随机有限元方法对结构响应的平均值和方差进行近似求解. 在摄动法有限元分析的框架下, 提出以一般函数形式表达的结构性能的平均值和标准差及其灵敏度的计算格式. 将结构 稳健性优化设计问题构造为双目标优化问题,优化目标包含结构性能函数的期望值和标准 差,约束函数的变异也给予考虑. 优化问题采用基于函数梯度的算法进行求解. 文中给出的数值算例显示了方法的有效性.     

离散变量结构形状优化设计的综合算法

提出一种离散变量结构形状优化设计的方法,该方法在优化过程中将两类变量统一考虑,根据两类变量的相对差商值确定搜索的变量;并且对形状变量施加了运动极限的限制,从而保证了收敛速度快,收敛平稳;将该算法应用于几个经典的结构优化算例：运算结果显示了该方法计算效率高,优化效果也比较满意．     

磁驱动单侧飞片实验的数值模拟

磁驱动单侧飞片实验的数值模拟通常可不考虑厚的阴极的运动状态和厚度方向上烧蚀宽度的影响,采用单侧计算模型进行模拟。为了理解磁驱动单侧飞片实验可采用单侧计算模型的原因,为磁驱动单侧飞片实验的单侧计算建模提供理论依据,建立了磁驱动单侧飞片实验的双侧计算模型,并对PTS-061、PTS-064磁驱动单侧飞片实验进行了模拟分析。在PTS-061、PTS-064实验中,飞片的电流加载面的位移随着时间的增加持续增大;厚的阴极的电流加载面的位移不随时间的增加持续增大,在磁驱动实验中后期基本保持不变。PTS-061实验结束时,飞片的电流加载面的位移为4.9 mm,阴极电流加载面的位移仅为1.7 mm。PTS-064实验结束时,飞片的电流加载面的位移为4.1 mm,阴极电流加载面的位移仅为0.9 mm。磁驱动单侧飞片实验能采用单侧计算模型模拟的原因,不是阴极板面保持位置不动,而是阴极电流加载面的位移不随时间持续增加;在磁驱动实验后期,飞片电流加载面位移对边界磁场的影响远大于阴极电流加载面的位移对边界磁场的影响。

     

基于高斯原理的非理想系统动力学建模

高斯原理给出了通过求函数极值、从可能运动中鉴别出真实运动的规则, 它可以使得多体系统动力学问题不需通过求解微分(代数)方程, 而是采用求解最小值的优化方法来解决, 从而提供了一种适用于优化算法的建模思路, 因此, 如何定义恰当的高斯拘束函数是动力学优化方法得以实现的前提. 对于理想系统而言, 约束对系统的作用可以通过约束方程来体现, 故高斯拘束可表达为系统质点加速度的函数, 系统的动力学问题因此可以描述为目标函数为高斯拘束函数、优化变量为质点加速度的约束最优化问题; 当系统中需要考虑干摩擦等非理想因素时, 部分相互作用不能被所定义的约束方程所涵盖而需要采用额外的物理规律来描述, 这种相互作用破坏了原有的针对理想系统的高斯拘束函数的极值特性. 基于变分类的高斯原理, 推导并证明了目标函数以理想约束力所表达的非理想系统的极值原理, 针对目前文献中用于非理想系统的高斯原理进行了讨论, 指出其实际为文中的极值原理在非理想约束力与理想约束力无明显关联时的一种特殊表达形式, 当非理想约束力与理想约束力有明显的函数关系(如库仑摩擦定律中滑动摩擦力与法向约束力间的线性关系)时, 该形式失效; 同时根据文中的极值原理, 得到了考虑库仑摩擦时非理想的多体系统动力学问题的优化模型. 例子中分析了优化模型及相应的线性互补性模型的关系, 分析发现在满足刚体滑动问题的唯一性条件下二者互为充分必要条件, 从而证明了文中优化模型的可靠性; 并采用优化计算方法进行了动力学模拟, 模拟结果显示了将高斯原理与优化算法相结合的可行性及有效性.      

摩擦与滚阻对被动行走器步态影响的研究

本文研究了圆弧足被动行走器支撑足与地面间的摩擦系数和滚阻系数对被动行走器步态的影响.首先分别利用扩展的赫兹接触力模型和LuGre摩擦模型描述了支撑足与地面接触点处的法向支撑力和切向摩擦力,并考虑了行走过程中支撑足所受的滚动摩阻;其次利用第二类Lagrange方程推导出了该系统的动力学方程,并通过与已有成果的对比确定了合适的LuGre摩擦模型参数;最后仿真分析了摩擦系数和滚阻系数对被动行走器步态的影响.研究发现:摩擦系数的改变虽然对被动行走器行走的平均速度、步幅,以及支撑足接触点处的最大法向接触力的影响较小,但摩擦系数的减小会改变其行走步态类型,如发生倍周期分岔甚至混沌现象;然而,滚阻系数的改变会对行走器行走的平均速度、步幅,以及支撑足接触点处的最大法向接触力的影响较大,尚未发现滚阻系数的改变会引起其行走步态的变化.     

连续体结构非概率可靠性拓扑优化

基于非概率可靠性 指标的定义,考虑材料、几何及荷载大小的不确定性,提出以结构体积最小化为目标、具有 位移非概率可靠性约束的三维连续体拓扑优化数学模型. 采用目标性能方法对优化模型进行 转换,给出目标性能值的伴随法灵敏度分析算法,利用数学规划法实现优化问题的求解. 数 值算例验证了所提出优化模型的正确性及算法的有效性,并指出相对于确定性优化而言,非 概率可靠性拓扑优化能够给出在考虑不确定参数和荷载条件下更合理的材料分布.     

DYNAMIC MODELING OF NONIDEAL SYSTEM BASED ON GAUSS'S PRINCIPLE$^{\bf 1)}$

高斯原理给出了通过求函数极值、从可能运动中鉴别出真实运动的规则, 它可以使得多体系统动力学问题不需通过求解微分(代数)方程, 而是采用求解最小值的优化方法来解决, 从而提供了一种适用于优化算法的建模思路, 因此, 如何定义恰当的高斯拘束函数是动力学优化方法得以实现的前提. 对于理想系统而言, 约束对系统的作用可以通过约束方程来体现, 故高斯拘束可表达为系统质点加速度的函数, 系统的动力学问题因此可以描述为目标函数为高斯拘束函数、优化变量为质点加速度的约束最优化问题; 当系统中需要考虑干摩擦等非理想因素时, 部分相互作用不能被所定义的约束方程所涵盖而需要采用额外的物理规律来描述, 这种相互作用破坏了原有的针对理想系统的高斯拘束函数的极值特性. 基于变分类的高斯原理, 推导并证明了目标函数以理想约束力所表达的非理想系统的极值原理, 针对目前文献中用于非理想系统的高斯原理进行了讨论, 指出其实际为文中的极值原理在非理想约束力与理想约束力无明显关联时的一种特殊表达形式, 当非理想约束力与理想约束力有明显的函数关系(如库仑摩擦定律中滑动摩擦力与法向约束力间的线性关系)时, 该形式失效; 同时根据文中的极值原理, 得到了考虑库仑摩擦时非理想的多体系统动力学问题的优化模型. 例子中分析了优化模型及相应的线性互补性模型的关系, 分析发现在满足刚体滑动问题的唯一性条件下二者互为充分必要条件, 从而证明了文中优化模型的可靠性; 并采用优化计算方法进行了动力学模拟, 模拟结果显示了将高斯原理与优化算法相结合的可行性及有效性.     

Dynamics and trajectory planning of a planar flipping robot

In this paper, a new planar one-legged robot model is firstly proposed, which, unlike previous one-legged robot with springy legs, consists of three revolute joints. Then a novel manner of one-legged locomotion (i.e., ballistic flip) is designed for this robot. A complete flipping gait cycle is composed of four phases: two stance phases and two flight phases. During flight phases, no active control is needed on the knee joint. Rotational motion and translational motion is decoupled from each other in flight phases. Landing of the robot is regarded as an inelastic impulsive impact. During stance phases, the robot model can be simplified as a two-degree-of-freedom rigid manipulator. Based on analysis of kinematics and dynamics of the flip robot, trajectory planning of cyclic flip gait is formulized as a problem of numerical optimization subject to nonlinear constraints such as positive reaction force of ground and finite torque of the joints. One potential application of the flipping robot is space exploration, which urgently requires the legged locomotive robots to be light-weighted and energy efficient.     

人体肌骨的多柔体系统动力学研究进展

人体肌肉骨骼系统简称肌骨系统, 包括骨骼、骨骼肌与关节连接, 其力学模型是典型的多柔体系统. 从多体动力学角度研究肌骨系统, 主要关注其在运动过程中的肌肉内力、关节力矩及产生的动力学影响, 属于动力学与生物力学的交叉融合. 肌骨系统的多体动力学模型已被广泛地应用于临床医学、竞技体育、军事训练、人机工程等诸多领域, 其仿真结果可为提高人体运动能力、降低关节载荷与能耗、避免运动损伤、加快康复进程等提供重要计算参考数据. 与此同时, 上述研究亦对肌骨动力学研究提出了许多新挑战. 本文综述了人体肌骨多柔体系统动力学相关研究进展, 包括骨骼肌功能解剖与生物力学建模、神经与肌肉控制理论、肌骨系统动力学问题与求解方法, 以及近年来肌骨多体动力学在步态分析、飞行员抗荷动作、口颌手术规划等领域的典型应用. 与工程领域的机械多体系统相比, 人体肌骨多体系统具有肌肉内力主动性与肌肉控制冗余性两大特征. 现有骨骼肌模型难以同时考虑肌肉的解剖结构、三维几何与肌力产生的生物化学机制. 已有大多数肌骨模型采用静态优化假设消除肌肉冗余性, 忽略了肌肉与肌腱内力平衡及兴奋收缩耦联机制. 此外, 目前仍缺乏实现肌骨模型个性化的无创在体测试手段. 未来, 人体肌骨多体动力学研究将会向更精确、智能、个性化的方向发展, 成为动力学与生物力学交叉的热点研究领域.      

有多余坐标完整系统的自由运动

对于完整力学系统,若选取的参数不是完全独立的,则称为有多余坐标的完整系统. 由于完整力学系统的第二类Lagrange 方程中没有约束力,故为研究完整力学系统的约束力,需采用有多余坐标的带乘子的Lagrange方程或第一类Lagrange 方程. 一些动力学问题要求约束力不能为零,而另一些问题要求约束力很小. 如果约束力为零,则称为系统的自由运动问题. 本文提出并研究了有多余坐标完整系统的自由运动问题. 为研究系统的自由运动,首先,由d'Alembert-Lagrange 原理, 利用Lagrange 乘子法建立有多余坐标完整系统的运动微分方程;其次,由多余坐标完整系统的运动方程和约束方程建立乘子满足的代数方程并得到约束力的表达式;最后,由约束系统自由运动的定义,令所有乘子为零,得到系统实现自由运动的条件. 这些条件的个数等于约束方程的个数,它们依赖于系统的动能、广义力和约束方程,给出其中任意两个条件,均可以得到实现自由运动时对另一个条件的限制. 即当给定动能和约束方程,这些条件会给出实现自由运动时广义力之间的关系. 当给定动能和广义力,这些条件会给出实现自由运动时对约束方程的限制. 当给定广义力和约束方程,这些条件会给出实现自由运动时对动能的限制. 文末,举例并说明方法和结果的应用.      

具有动应力和动位移约束的离散变量结构形状优化设计方法

讨论了动应力、动位移约束下离散变量状优化设计问题。首先用拟静力算法,将结构惯性力极值作为静载荷施加到结构上,求得结构的动位移和动内力,然后将考虑动应力约束和动作移约束的离散变量结构优化设计问题化为静应力和静位移约束的优化问题。在求解过程中,将单元内力作了一阶近似,并将多约束问题转化为单约束问题,然后利用两类变量统一考虑的离散变量结构形状优化设计的综合算法进行求解。     

国内全髋关节置换磨损测试及数值模拟研究进展

髋关节假体磨损及磨损颗粒所导致的无菌性松动是髋关节置换失败的重要原因. 本文作者对国内髋关节磨损研究时采用的运动学与力学曲线以及针对国人测绘的相应曲线进行了差异性分析,并对国内发表的全髋关节磨损体外模拟机测试试验及结果,数值模拟模型及结果进行了总结、对比和分析. 结果显示:1) 国人测绘的运动学与力学曲线不能直接用于全髋关节磨损评估的加载条件,国内关节力的测量方法仍有待进一步改进;2) 国内体外磨损测试的研究结论与国外发表的结论相似,但不同机构间的测试结果存在一定差异;3) 国内髋关节磨损仿真研究还处于起步阶段,仿真计算得到的磨损率普遍低于体外测试结果. 因此,建立基于国人行为力学的磨损评估标准、对磨损模型进行合理优化并采用有限元和骨肌多体动力学相耦合的分析方法对髋关节假体临床前磨损性能进行评估是未来的研究方向.      

Foot force distribution of walking machine with consideration of terrain properties

Determination of foot force distribution during walking is important to the simulation and control of the vehicle. This problem was often considered as an indeterminate problem and several optimization methods were proposed. The indeterminancy, which was due to the assumption of rigid bodies, can, however, be removed by incorporating the compliance equations into the equations of equilibrium. Based on such a compliant model, a s stiffness matrix method was developed to determine the foot force distribution. However, due to the complexity of the problem, the compliance of terrain in the stiffness matrix method was considered either negligible or as a linear spring model. In this paper, two realistic terrain models are incorporated into the stiffness matrix method to study the effect of terrain properties on foot force distribution during walking. These two terrain models are the three-parameter solid model and the four-parameter Burgers model. The former is a model of clay terrain while the latter is a model of a paddy field. These models are extended to three dimensions and then combined with the leg compliances to form the stiffness matrix of the system. The simulation results show that the terrain compliance has significant effect on foot force distribution. For example, it is observed that this compliance helps to distribute the foot forces evenly and to minimize the frictional angles.