A free gait algorithm for quadrupedal walking machines

A free gait is a computer generated, rule-based gait for a walking machine to walk on rough terrain. Based on a given terrain map, the gait algorithm selects footholds for leg placements and determines the movements of legs and body. In the past, a few free gaits for hexapods have been developed. For quadrupeds, the only report on free gait was briefly mentioned in a paper by Hirose [Int. J. Robotics Res., 3(2) (1984)]. In this paper, a free gait algorithm for a quadrupedal walking chair is developed. For quadrupeds, the stability margin is small due to a small number of legs and the choices of a leg to be lifted are limited. Hence, deadlock situations may occur quite often. Many special techniques are incorporated into the algorithm in order to reduce deadlocks. This free gait algorithm adopts the wave-crab gaits as the primary gait because they are periodic and can provide good stability. The algorithm also adopts a non-periodic free gait to handle terrain with higher concentration of forbidden areas. This algorithm is evaluated under different terrain conditions using computer simulations. The results show that the performance is satisfactory on randomly generated rough terrain and needs improvement on manually generated rough terrain.     

Gaits and geometry of a walking chair for the disabled

The development of a walking chair is very important to a person with disability. This paper studies some fundamental issues of a practical walking chair, which are performance requirements, gaits and body geometry. According to the needs of a disabled person, the performance requirements of a walking chair are specified. The number of legs and leg mechanism are determined according to previous design experience. The three basic gaits for a quadruped to negotiate both structured and unstructured terrain, namely straight-line gaits, turning gaits and stair-climbing gaits, are then studied. Based on the results of gait study, the geometry of the walking chair is designed. Two geometric models are proposed and their performance is evaluated.     

The Effect of Limb Kinematics on the Speed of a Legged Robot on Granular Media

Achieving effective locomotion on diverse terrestrial substrates can require subtle changes of limb kinematics. Biologically inspired legged robots (physical models of organisms) have shown impressive mobility on hard ground but suffer performance loss on unconsolidated granular materials like sand. Because comprehensive limb–ground interaction models are lacking, optimal gaits on complex yielding terrain have been determined empirically. To develop predictive models for legged devices and to provide hypotheses for biological locomotors, we systematically study the performance of SandBot, a small legged robot, on granular media as a function of gait parameters. High performance occurs only in a small region of parameter space. A previously introduced kinematic model of the robot combined with a new anisotropic granular penetration force law predicts the speed. Performance on granular media is maximized when gait parameters utilize solidification features of the granular medium and minimize limb interference.     

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.      

Asymmetric three-link passive walker

Passive walkers are dynamically stable robots with a gait that resembles the human locomotion. These walkers can be studied to better understand the dynamic behavior of the human gait and design efficient active walkers and assistive devices. In this paper, we study the walking dynamics of a three-link passive walker with an asymmetrical structure where one leg has a knee while the other is knee-less. After finding a 2-periodic steady gait for the three-link walker with humanlike inertial parameters for both legs, the possibility of a gait with symmetrical step lengths is discussed where the half inter-leg angles at the beginning of every step are made equal by altering the physical parameters of the knee-less leg. We further study the gaits with symmetrical step lengths and show that by replacing one leg of a four-link symmetric walker with the knee-less leg of the three-link walker with the symmetrical half inter-leg angles, the dynamic behavior of the kneed leg remains unchanged. This approach can be adapted in the field of gait rehabilitation and prosthesis design to obtain a more symmetrical gait and preserve the motion of the healthy leg.

     

Adaptive control for discontinuous variable-order fractional systems with disturbances

This paper deals with the global asymptotic stabilization and finite-time stabilization issues for variable-order fractional systems with partial a priori bounded disturbances by designing an appropriate adaptive controller. Via the inductive method and Arzela-Ascoli theorem, the existence and uniqueness of the solution for the considered system is firstly verified under the proposed control strategy. By applying Lyapunov stability theory, non-smooth analysis and inequality technique, sufficient stabilization criteria are established under the framework of variable-order fractional Filippov differential inclusion. Finally, two numerical simulations are given to demonstrate the validity of the proposed method.

     

基于MEMS加速度传感器的步态识别

针对最小采集约束条件和经历长时间跨度下识别率低的问题,提出一种基于MEMS加速度传感器的步态识别算法。该算法以右髋部位置采集加速度信号构造多个高斯差分尺度空间,利用局部关键点生成稀疏表示的步态特征位置模板,并采用模板融合来有效转换稀疏性步态周期特征,最后利用最近邻算法和投票机制对步态特征进行识别。在公开的含175名测试者的步态加速度数据集上进行测试,实验结果显示识别率为98.67%和认证率为99.89%,并进一步研究了测试集和训练集样本数目对识别效果的影响,验证了特征提取的有效性和稳定性。     

Double frictional receding contact problem for an orthotropic layer loaded by normal and tangential forces

With the increasing research in the field of contact mechanics, different types of contact models have been investigated by many researchers by employing various complex material models. To ascertain the orthotropy effect and modeling parameters on a receding contact model, the double frictional receding contact problem for an orthotropic bilayer loaded by a cylindrical punch is taken into account in this study. Assuming plane strain sliding conditions, the governing equations are found analytically using Fourier integral transformation technique. Then, the resulting singular integral equations are solved numerically using an iterative method. The weight function describing the asymptotic behavior of the stresses are investigated in detail and powers of the stress singularities are provided. To control the trustworthiness and correctness of the analytical formulation and to compare the resulting stress distributions and contact boundaries, a numerically efficient finite element method was employed using augmented Lagrange contact algorithm. The aim of this paper is to investigate the orthotropy effect, modeling parameters and coefficients of friction on the surface and interface stresses, surface and interface contact boundaries, powers of stress singularities, weight function and to provide highly parametric benchmark results for tribological community in designing wear resistant systems.

     

Synchronization control for networked mobile robot systems based on Udwadia–Kalaba approach

This paper addresses the problem of synchronization control for networked multi-mobile robot systems from the perspective of analytical mechanics. By reformulating the task requirement as a constrained motion problem, a unified synchronization algorithm for networked multi-mobile robot systems with or without leaders is proposed in combination with algebraic graph theory and the Udwadia–Kalaba approach. With the proposed algorithm, the networked mobile robot system can achieve synchronization from arbitrary initial conditions for the leaderless case and realize accurate trajectory tracking with explicitly given reference trajectories for the leader-following case. Numerical simulations of a networked wheeled mobile robot system are performed under different network structures and various trajectory requirements to show the performance of the proposed control algorithm.

     

基于机器学习的人体虚拟惯性测量组件构建方法

利用人体特征辅助行人导航与外骨骼机器人控制是近年来导航与机器人领域中的热点研究方向。针对惯性测量组件足部安装方式在过载较高时无法实现有效测量的问题,研究了一种基于机器学习的人体虚拟惯性测量组件构建方法。该方法以同步采集安装于足部与下肢其他部位的惯性测量组件的输出作为数据样本,通过遗传算法改进的误差反向传播(GA-BP)神经网络实现虚拟惯性测量组件的构建。为进一步改善训练效果,采用基于步态相位检测方法对训练样本进行筛选。基于Anybody与MATLAB的联合仿真结果表明,本文所研究的方法可实现采用安装于髋关节附近位置的惯性测量组件数据,有效模拟足部位置的惯性测量组件数据。该方法对未经训练的步态也有一定的适应性。本文所研究的方法可进一步应用于行人精确定位与外骨骼机器人控制等领域。     

A Note on a Walking Machine Model

The paper continues studies intended to find out whether it is possible to create a prototype walking machine with relatively simple components. In this connection, the control problem is solved for a two-dimensional model of biped machine. It has a torso and two telescopic legs. Each leg includes a ponderable section of constant length and an imponderable section of variable length. The machine, regarded as a system with variable constraints, implements a single-stance gait (one stance leg at a time) with a step of constant duration. The contact of the swing leg with the ground is analyzed within the framework of Carnot's theorem (perfectly inelastic impact). It is assumed that the force developed in the stance leg is due to the deformation of the leg's spring and that this deformation can be controlled. An algorithm is proposed to synthesize a control system that takes into account collisions occurring at reverse of the roles of the legs. This algorithm is based on methods of optimizing periodic systems. The algorithm is compared with approaches used by other authors     

An explicit time domain solution for ground stratum response to harmonic moving load

Based on the thin layer method originally proposed in frequency domain, an explicit time domain semi–analytical solution has been developed for simulating three-dimensional layered ground responses to harmonic moving loads. The Fourier–Laplace transforms were applied to derive the transformed solution that satisfied the boundary conditions of horizontal infinities. The eigenvalue decomposition was performed with respect to Laplace parameter to express the ground motion corresponding to the eigenmodes. The formulation for each eigenmode incorporating the moving load expression was transformed back into time domain analytically, and the global system responses were given by means of the general mode superposition method. The proposed explicit time domain solution is suitable for studying various types of moving load acting on or inside the ground. In this paper a moving harmonic load with rectangular distribution was adopted to demonstrate the ground response simulation. Two illustrative examples for moving load with speeds below or above the ground Rayleigh wave velocity were presented to test the computational accuracy and efficiency of the proposed approach. A parametric study was also performed to investigate the influences of soil properties on the ground responses.The project is partially supported by the National Natural Science Foundation of China (50538010). The English text was polished by Yunming Chen.     

Parallel Iterative Solvers with Localized ILU Preconditioning for Unstructured Grids on Workstation Clusters

Incomplete Lower-Upper (0) (ILU(O)) factorization is a very effective preconditioning method of iterative solvers for large-scale linear sparse systems in scientific and engineering computations. However, this method requires global data dependency, which is not ideal for parallel computations in which locality is of utmost importance.

In this paper, the localized ILU(O) preconditioning method is implemented in various types of iterative solvers. This method provides data locality and good parallelization on each processor. The performance of the developed system was evaluated on a workstation cluster using MPI.

In 1997, the Science and Technology Agency of Japan (STA) began a five-year project to develop the Earth Simulator. Both hardware and software for various types of global earth simulation are to be developed under this project. The present study was conducted as part of the research on software for solid earth simulation. This simulation code, named GeoFEM, solves crust deformation, mantle convection, seismic wave propagation, etc., using the finite element method.     

Stability of quadruped robots’ trajectories subjected to discrete perturbations

In this paper, we study the stability of a mathematical model for trajectory generation of a qua-druped robot. We consider that each movement is composed of two types of primitives: rhythmic and discrete. The discrete primitive is inserted as a perturbation of the purely rhythmic movement. The two primitives are modeled by nonlinear dynamical systems. We adapt the theory developed by Golubitsky et?al. in (Physica D 115: 56?C72, 1998; Buono and Golubitsky in J. Math. Biol. 42:291?C326, 2001) for quadrupeds gaits. We conclude that if the discrete part is inserted in all limbs, with equal values, and as an offset of the rhythmic part, the obtained gait is stable and has the same spatial and spatiotemporal symmetry groups as the purely rhythmic gait, differing only on the value of the offset.     

Investigation on dynamic characteristics of a rod fastening rotor-bearing coupling system with fixed-point rubbing

The aim of this paper is to gain insight into the nonlinear vibration feature of a dynamic model of a gas turbine. First, a rod fastening rotor-bearing coupling model with fixed-point rubbing is proposed, where the fractal theory and the finite element method are utilized. For contact analysis, a novel contact force model is introduced in this paper. Meanwhile, the Coulomb model is adopted to expound the friction characteristics. Second, the governing equations of motion of the rotor system are numerically solved, and the nonlinear dynamic characteristics are analyzed in terms of the bifurcation diagram, Poincaré map, and time history. Third, the potential effects provided by contact degree of joint interface, distribution position, and amount of contact layer are discussed in detail. Finally, the contrast analysis between the integral rotor and the rod fastening rotor is conducted under the condition of fixed-point rubbing.

     

Time series prediction using kernel adaptive filter with least mean absolute third loss function

In this paper, a novel kernel adaptive filter, based on the least mean absolute third (LMAT) loss function, is proposed for time series prediction in various noise environments. Combining the benefits of the kernel method and the LMAT loss function, the proposed KLMAT algorithm performs robustly against noises with different probability densities. However, an important limitation of the KLMAT algorithm is a trade-off between the convergence rate and steady-state prediction error imposed by the selection of a certain value for the learning rate. Therefore, a variable learning rate version (VLR–KLMAT algorithm) is also proposed based on a Lorentzian function. We analyze the stability and convergence behavior of the KLMAT algorithm and derive a sufficient condition to predict its learning rate behavior. Moreover, a kernel recursive extension of the KLMAT algorithm is further proposed for performance improvement. Simulation results in the context of time series prediction verify the effectiveness of the proposed algorithms.     

A new formulation for fictitious mass of viscous dynamic relaxation method

Abstract

In this article, a new relationship is proposed for the fictitious mass of viscous dynamic relaxation (DR) method. First, incremental equations are derived for DR steps. Using transformed Gershgörin theory, a new relationship is achieved for fictitious mass of viscous DR by formulating modified time step ratio. This procedure presents a new algorithm for the viscous DR method. To evaluate the numerical efficiency of the proposed method, some 2D and 3D truss and frame structures are analyzed with elastic linear and geometrically nonlinear behaviors. Results show that by using the proposed algorithm for fictitious mass, the convergence rate of the viscous DR method is improved so that the proposed algorithm presents the structural response with lower iterations in comparison with other common DR techniques.

Communicated by Joerg Fehr.     

Second-order coupled tristable stochastic resonance and its application in bearing fault detection under different noises

Bearing fault is the most likely to occur in mechanical fault, and stochastic resonance (SR), as a noise enhanced signal processing tool, can find mechanical faults as early as possible, so as to avoid larger problems. However, most of the existing research methods are based on the first-order Langevin equation. According to the previous studies of many scholars, the weak signal detection ability of the second-order system is better than that of the first-order system, and the coupled system also has better performance due to the addition of the control system. So, in order to detect the fault signal more easily, a second-order coupled tristable stochastic resonance system (SCTSR) based on the adaptive genetic algorithm (AGA) is proposed, it is an improvement on improving the first-order coupled tristable stochastic resonance system (FCTSR). First, based on the fourth-order Runge–Kutta algorithm (F-RK), the performances of monostable, bistable and tristable control systems to SCTSR are compared, it is verified that the monostable system has the best performance as SCTSR’s control system. Secondly, the equivalent potential function of SCTSR is derived, and the influences of each system parameters on it are researched. The output signal-to-noise ratio gain (SNRG) is chosen as a measure to verify that SCTSR’s performance is better than that of FCTSR, and the influences of parameters on SNRG are discussed. SCTSR and FCTSR are used to detect low-, high- and multi-frequency cosine signals combined with AGA. The simulation results are compared with the wavelet transform method, which proves the performance superiority of SR, and also prove that SCTSR is easier to detect weak signals and has a stronger de-noising ability. Finally, SCTSR and FCTSR are applied in bearing fault detection under Gaussian white noise and trichotomous noise. The results also prove that SCTSR can get larger peaks and SNRG, and it is easier to detect fault signals. This proves that SCTSR’s performance is superior that of other methods in bearing fault detection, and has better engineering application value.

     

A new tracking algorithm of PIV and removal of spurious vectors using Delaunay tessellation

 A new algorithm of Delaunay Tessellation Particle Tracking Velocimetry (DT-PTV in abbreviation) is proposed for tracking particles in images of a PIV system by making use of the Delaunay tessellation (DT). The algorithm is tested by using numerically simulated particle images. The calculation results based on DT are compared with those obtained by a conventional algorithm of Binary Image Cross-correlation method (BICC). The new algorithm shows higher performance of obtaining more identical particles in two consecutive images correctly with shorter computation time even if the images contain many particles. A further application of DT to elimination of spurious vectors is also discussed. Received: 24 November 1997/Accepted: 7 August 1998