伸缩腿双足机器人半被动行走控制研究

研究半被动伸缩腿双足机器人行走控制和周期解的全局稳定性问题.使用杆长可变的倒立摆机器人模型,以支撑腿的伸缩作为行走动力源,采用庞加莱映射方法分析了双足机器人行走的不动点及其稳定性.当脚与地面冲击时,假设两腿间的夹角保持为常数,设计了腿伸缩长度的支撑腿角度反馈控制率.证明了伸缩腿双足机器人行走过程不动点的全局稳定性.仿真结果表明,本文提出的腿伸缩长度反馈控制可以实现伸缩腿双足机器人在水平面上的稳定行走,并且周期步态对执行器干扰和支撑腿初始角速度干扰具有鲁棒性.     

膝踝协调驱动的平面双足机器人短跑运动规划

本文采用虚拟力控制方法规划双足机器人动态稳定的短跑运动,以解决仅脚尖着地时无有效支撑域的问题.然而,脚尖着地的方式却给支撑腿引入了1个冗余关节,导致在虚拟力控制时支撑腿内部运动的不确定.为解决该问题,在分析身体虚拟力和支撑腿各关节做功的基础上,以最大化虚拟力总驱动功率为目标,提出膝关节和踝关节协调驱动的条件和实现方法.该方法通过均衡膝和踝的驱动负担,既解决了支撑腿内部运动的不确定问题,又充分发挥了踝关节的驱动能力.在腿部其他关节驱动能力不变的情况下,通过短跑运动方式可以有效提高双足机器人的运动速度.最后,通过仿真实验验证了本方法的有效性.     

四足机器人对角小跑中机体翻转分析与姿态控制

为了解决四足机器人对角小跑运动中机体绕对角线翻转的问题,在理论分析翻转原因的基础上提出一种简单有效的姿态控制方法.首先建立四足机器人腿结构的运动学模型,通过数值运算与分析,得到机体翻转的根本原因,即支撑腿髋部前摆关节的反作用力矩产生了绕机体对角线的翻转运动.在此基础上,提出利用支撑腿的髋部侧摆关节力矩来平衡机体翻转的姿态控制方法,并分析讨论了姿态控制可能引起的机体侧向运动现象.最后进行动力学仿真试验,发现机器人在不施加姿态控制的情况下很容易失去平衡而翻到;而在应用了提出的姿态控制方法后,机器人能够实现稳定的小跑运动并且保持机体翻转角度在一个较小的范围内稳定波动.仿真试验对比证明了该姿态控制方法能有效控制机体翻转运动并保持机器人动态平衡.     

基于ZMP的仿人机器人跑步运动模式

采用小车-曲面桌子模型,提出了一种基于零力矩点(zero moment point,ZMP)的仿人机器人跑步运动模式.在单腿支撑阶段和飞行阶段,分别规划了仿人机器人的质心运动轨迹和双脚运动轨迹.在单腿支撑阶段,求解根据小车-曲面桌子模型建立的动力学方程,依据小车的运动轨迹规划出仿人机器人的质心轨迹;在飞行阶段,仿人机器人质心可看作抛物线运动,质心轨迹可通过水平方向上的匀速运动和竖直方向上的自由落体运动轨迹表示.分析了双脚与地面接触时的力及力矩约束.通过改变ZMP调整身体的倾斜角度,保持身体动态平衡.同时根据动力学方程分别求解出踝关节及其他关节的关节力矩.仿真实验结果表明:仿人机器人跑步时各关节角度和关节驱动力矩变化稳定,能够实现稳定的跑步,验证了方法的有效性.     

基于虚拟模型的四足机器人对角小跑步态控制方法

为提高四足机器人对角小跑运动的稳定性,实现机器人躯干6维运动方向控制的解耦,提出了一种基于虚拟模型的对角小跑步态控制方法.控制器主要包括支撑相虚拟模型控制和摆动相虚拟模型控制.在支撑相,建立了作用于躯干质心的虚拟力与对角支撑腿关节扭矩之间的数学关系,通过调整躯干虚拟力的大小控制躯干的高度与姿态,控制机器人前进速度和自转角速度.在摆动相,将机器人侧向速度控制引入到足端轨迹规划中,并通过虚拟的"弹簧-阻尼"元件驱动摆动足沿给定轨迹运动.此外,在控制器设计过程中,引入了状态机,用于监控机器人各腿的状态,并输出对角小跑步态相位切换指令.仿真实验结果表明,机器人能够以对角小跑步态在平地上进行全方位移动,跨越不平坦地形,并能够抵抗外部冲击,证明了文中控制方法的有效性和鲁棒性.     

复杂环境下仿人机器人有效支撑区域的感知

当主流的仿人机器人都采ZMP(zero moment point)理论作为稳定行走的判据.实时ZMP点落在支撑足与地面接触形成的多边形支撑区域内是仿人机器人实现稳定步行的必要条件.因此实现仿人机器人在复杂现实环境中稳定行走,必须要求机器人足部感知系统提供足够丰富的地面环境信息,从而可以准确获取支撑区域的形状以实现基于实时ZMP点的稳定控制.文中将柔性阵列力传感器应用于仿人机器人足部感知系统,提出了获取仿人机器人支撑区域形状的方法,而且通过实验验证了其可行性.     

下肢外骨骼机器人变步长步态规划方法

为了解决下肢外骨骼机器人连续步态规划问题,基于倒立摆模型提出了一种步态规划算法,并针对传统倒立摆模型无法变步长连续行走的问题提出了新的改进方法。将外骨骼机器人分成支撑腿和摆动腿两部分,分别采用D-H法进行运动学分析;利用倒立摆模型和固定函数法,进行等效质心与摆动腿末端轨迹规划;在相邻单脚支撑期之间插入双脚支撑期,使下肢外骨骼机器人在不断改变步行时,利用双脚支撑期进行位置和速度的切换,实现实时步态规划;将规划算法在SIMULINK中实现,并与ADAMS模型进行联合仿真,下肢外骨骼机器人在仿真环境下行走稳定,证明了算法的有效性。     

仿章鱼软体机器人形状控制

提出一种针对仿章鱼软体机器人的形状控制算法.由于软体机器人具有无限多自由度,所以无法使用针对刚体的机器人控制对软体机器人进行控制.根据软体机器人的运动特点,本文提出针对软体机器人的形状控制参数.通过对软体机器人的运动学建模,建立软体机器人控制参数与驱动线长度之间的函数关系,进而设计形状控制算法.通过李亚普诺夫理论,对形状控制算法的稳定性进行了分析.最后,通过实验验证了形状控制算法的有效性.     

基于虚拟模型控制的四足机器人缓冲策略

提出了一种基于虚拟模型控制的四足机器人缓冲策略.根据机器人落地过程中的触地状态和躯干纵向速度,将机器人的落地过程分为下落阶段、缓冲阶段和恢复阶段.在下落阶段,通过虚拟"弹簧-阻尼"元件驱动足端沿期望轨迹运动.在缓冲阶段和恢复阶段,控制器根据机器人下落过程中落地腿数目的不同,分别建立支撑腿与躯干质心虚拟力之间的数学关系,并通过施加在躯干质心的虚拟力的大小来控制躯干的位姿.躯干质心所施加的虚拟力通过主动变刚度控制实现,控制器根据机器人所处的落地阶段,给出合理的虚拟刚度和阻尼,从而减小机器人落地的冲击.由仿真实验可以看出,此缓冲策略是有效的.     

基于能量转换的仿人机器人摆动腿落地改进阻抗控制方法

针对没有缓冲装置的双足仿人机器人在快速运动中摆动腿落地会对机器人身体稳定性带来影响的问题,结合阻抗控制的控制特点,从能量转换的角度进行分析,提出了基于能量转换的仿人机器人摆动腿落地改进阻抗控制方法。以阻抗控制方法为基础,通过对机器人摆动腿落地时末端速度以及落地后质心速度的分析,结合在摆动腿落地这一过程中能量的转换关系,对机器人摆动腿各关节的力进行控制,从而达到机器人摆动腿缓冲落地的目的。最后,将此方法应用于机器人Nao,实验证明,机器人摆动腿落地时与地面的瞬时作用力减小,达到了缓冲落地的效果,同时也起到了预先控制的作用。     

Structural application of a shape optimization method based on a genetic algorithm

This paper presents a structural application of a shape optimization method based on a Genetic Algorithm (GA). The method produces a sequence of fixed-distance step-wise movements of the boundary nodes of a finite element model to derive optimal shapes from an arbitrary initial design space. The GA is used to find the optimal or near-optimal combination of boundary nodes to be moved for a given step movement. The GA uses both basic and advanced operators. For illustrative purposes, the method has been applied to structural shape-optimization. The shape-optimization methodology presented allows local optimization, where only crucial parts of a structure are optimized as well as global shape-optimization which involves finding the optimal shape of the structure as a whole for a given environment as described by its loading and freedom conditions. Material can be removed or added to reach the optimal shape. Two examples of structural shape optimization are included showing local and global optimization through material removal and addition. Received October 14, 1999     

A method for determination of optimal gaits with application to a snake-like serial-link structure

In this paper, we present a method of determining optimal gaits for shape actuated locomotion systems. This method is the synthesis of techniques for computing reduced equations for robotic locomotion systems and a numerical optimal control strategy. Symmetry reduction processes induce a form of locomotion system dynamics that reveals a cyclic-like coupling between group, shape, and momenta coordinates. This form allows one to focus on designing gaits, abandoning concern over shape dynamics. Using this vantage point we indicate how a numerical optimal control method based on Gaussian quadrature may be acclimatized to periodicity, thus providing optimal gaits. The method is demonstrated by means of its application to a snake-like serial-link structure or snake robot. This application provides scientific merit to hypotheses concerning observed locomotion phenomena amongst animals employing undulatory propulsive mechanisms.     

Support slimming for single material based additive manufacturing

In layer-based additive manufacturing (AM), supporting structures need to be inserted to support the overhanging regions. The adding of supporting structures slows down the speed of fabrication and introduces artifacts onto the finished surface. We present an orientation-driven shape optimizer to slim down the supporting structures used in single material-based AM. The optimizer can be employed as a tool to help designers to optimize the original model to achieve a more self-supported shape, which can be used as a reference for their further design. The model to be optimized is first enclosed in a volumetric mesh, which is employed as the domain of computation. The optimizer is driven by the operations of reorientation taken on tetrahedra with ‘facing-down’ surface facets. We formulate the demand on minimizing shape variation as global rigidity energy. The local optimization problem for determining a minimal rotation is analyzed on the Gauss sphere, which leads to a closed-form solution. Moreover, we also extend our approach to create the functions of controlling the deformation and searching for optimal printing directions.     

树结构与实例结合的形态创新设计方法

采用树结构和实例结合构建产品结构树模型，并以树的不完全分解进行包含形态特征的语义综合推理，从而对实例的组合进行导向及控制，探索了构造实用的形态创新设计系统的一种可能途径。并在Alias造型平台上二次开发实现了一个包含实例基元库及其它设计资源库的首饰形态创新设计系统。初步应用表明，系统在快速设计和引导设计等方面有较好的支持，提高了设计效率。     

Simultaneous design of components layout and supporting structures using coupled shape and topology optimization technique

The purpose of this paper was to study the layout design of the components and their supporting structures in a finite packing space. A coupled shape and topology optimization (CSTO) technique is proposed. On one hand, by defining the location and orientation of each component as geometric design variables, shape optimization is carried out to find the optimal layout of these components and a finite-circle method (FCM) is used to avoid the overlap between the components. On the other hand, the material configuration of the supporting structures that interconnect components is optimized simultaneously based on topology optimization method. As the FE mesh discretizing the packing space, i.e., design domain, has to be updated itertively to accommodate the layout variation of involved components, topology design variables, i.e., density variables assigned to density points that are distributed regularly in the entire design domain will be introduced in this paper instead of using traditional pseudo-density variables associated with finite elements as in standard topology optimization procedures. These points will thus dominate the pseudo-densities of the surrounding elements. Besides, in the CSTO, the technique of embedded mesh is used to save the computing time of the remeshing procedure, and design sensitivities are calculated w.r.t both geometric variables and density variables. In this paper, several design problems maximizing structural stiffness are considered subject to the material volume constraint. Reasonable designs of components layout and supporting structures are obtained numerically.     

Brachistochrone with dry and arbitrary viscous friction

The brachistochrone problem in the case of dry (Coulomb) and viscous friction with the coefficient that arbitrarily depends on speed is solved. According to the principle of constraint release, the normal component of the supporting curve is used as control. The standard problem of the fastest descent from a given initial point to a given terminal point assuming that the initial velocity is zero is formulated. The Okhotsimskii-Pontryagin method is used to analyze the differential of the objective function. Necessary optimality conditions are found, and a formula for the optimal control that does not involve adjoint variables is derived from them. Differential equations that allow one to obtain extremals by solving a Cauchy problem are set up. Properties of these equations are investigated. A class of simple brachistochrones is distinguished, for which singular points constituting the terminal curve and the reachability domain in the vertical plane are found. Conditions for the existence of zero controls are obtained. For some friction laws, numerical results demonstrating the shape of the determined brachistochrones and optimal time are presented.     

Multiparametric shape optimal design of disks

The external boundary of a structure described by a set of design parameters undergoes shape modification. Arbitrary stress, strain and displacement functionals are defined within the domain of the structure and its first- and second-order sensitivities with respect to varying structural shape are discussed. The optimal shape design problem is then formulated and solved using the first- and second-order sensitivity information. The iterative analysis-redesign algorithm is formulated using the finite element method. Some illustrative examples are included.     

Accuracy tests for various sensitivity analysis methods with respect to shape variables in planar cantilever beams

Sensitivity information is required in the optimal design process. In structural optimization, sensitivity calculation is a bottleneck due to its complexities. Various schemes have been proposed for the calculation. Analytic and finite difference methods are the most popular at the present time; however, they have their advantages and disadvantages. The semi-analytic method has been suggested to overcome these difficulties. In spite of its excellence, the semi-analytic method has been found to possess numerical errors with respect to shape variables. In this research, the errors from each method are evaluated and compared using a shape variable. A planar beam is selected as an example since it has a mathematical solution. An efficient method is suggested for the structural optimization which utilizes the finite element method.     

Parameter-free optimum design method of stiffeners on thin-walled structures

In this paper, we present a shape optimization method for designing stiffeners on thin-walled or shell structures. Solutions are proposed to deal with a stiffness maximization problem and a volume minimization problem, which are subject to a volume constraint and a compliance constraint, respectively. The boundary shapes of the stiffeners are determined under a condition where the stiffeners are movable in the in-plane direction to the surface. Both problems are formulated as distributed-parameter shape optimization problems, and the shape gradient functions are derived using a material derivative method and an adjoint variable method. The optimal free-boundary shapes of the stiffeners are obtained by applying the derived shape gradient function to the $H^{1}$ gradient method for shells, which is a parameter-free shape optimization method proposed by one of the authors. Several stiffener design examples are presented to validate the proposed method and demonstrate its practical utility.     

The sample solution approach for determination of the optimal shape parameter in the Multiquadric function of the Kansa method

The Kansa method with the Multiquadric-radial basis function (MQ-RBF) is inherently meshfree and can achieve an exponential convergence rate if the optimal shape parameter is available. However, it is not an easy task to obtain the optimal shape parameter for complex problems whose analytical solution is often a priori unknown. This has long been a bottleneck for the MQ-Kansa method application to practical problems. In this paper, we present a novel sample solution approach (SSA) for achieving a reasonably good shape parameter of the MQ-RBF in the Kansa method for the solution of problems whose analytical solution is unknown. The basic assumption behind the SSA is that the optimal shape parameter is considered to be largely depended on the shape of computational domain, the type of the boundary conditions, the number and distribution of nodes, and the governing equation. In the procedure of the SSA, we set up a pseudo-problem as the sample solution whose solution is known. It is not difficult to obtain the optimal parameter of the MQ-RBF in the numerical solution of the pseudo-problem. The SSA suggests that the optimal shape parameter of the pseudo-problem can also achieve an approximately optimal accuracy in the solution of the original problem. Numerical examples and comparisons are provided to verify the proposed SSA in terms of accuracy and stability in solving homogeneous problems and non-homogeneous modified Helmholtz problems in several complex domains even using chaotic distribution of collocation points.