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.     

A dynamic gait stabilization algorithm for quadrupedal locomotion through contact time modulation

In this paper, we propose a stabilization method for dynamic gaits of quadrupedal walking robots covering a wide range of speeds and various types of gait. Our stabilization method is based on adjusting the contact time between the four legs and ground. By modulating the contact time, the impact applied to the body can be controlled and stabilized. The stability provided by the proposed algorithm was proved in the sense of Lyapunov. The proposed algorithm also demonstrated robust performance under large external disturbances, and the performance was compared with other algorithms through simulations. Simulation results of bounding gaits under different ground conditions were compared, and the various types of stable gait implemented by the proposed algorithm are also presented.

     

考虑摆动腿动态的变长度柔性双足机器人步态切换控制研究

弹簧负载倒立摆模型是一种典型的双足行走模型,已经成为研究机器人类人行走的基础。本文在此模型的基础上进行了扩展,通过添加刚性躯干、脚质量及采用变长度伸缩腿,充分考虑了躯干及摆动腿动力学对机器人行走步态的影响。首先,利用欧拉–拉格朗日法推导了动力学方程。其次,设计了反馈线性化控制器来跟踪目标轨迹,以及调节摆动腿和躯干的姿态。第三,提出了步态切换策略,通过控制腿部长度和髋关节力矩来实现步态切换,从而改变平均行走速度。最后,通过计算机仿真验证了该方法的有效性。仿真结果表明：该控制策略能够有效地跟踪系统的期望轨迹及实现两种自然步态之间的切换,并形成稳定的极限环,实现机器人的稳定行走。

     

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.

     

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     

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.     

An approach to characterization of the agricultural self-propelled machines stability

This paper presents an analytical algorithm with appropriate software specified for the approximation of the allowed critical slope of the solid flat terrain that guarantees static and/or dynamic stability of the specified self-propelled agricultural machines and their aggregates. This algorithm assumes machine as a rigid body, having 3 or 4 contact points (defined by wheels or crawlers), under uniform motion at different constant velocities and radii of curvature trajectories. Using this algorithm, based on the principles of theoretical mechanics combined with 3D analytical geometry, the computer program SSPM (stability of the self-propelled agricultural machines) has been coded. This software is intended to facilitate the analysis, comparison and optimization of different configurations of self-propelled agricultural machines in operation on horizontal and sloped flat terrains at constant velocities and radii of trajectory with respect to their static and dynamic stability. It calculates critical pitch and roll angles of the self-propelled machine and the maximum allowed slope of the flat terrain under the given conditions. The algorithm and the appropriate SSPM software were experimentally verified using the platform and low-scale tractor model. Average difference between calculated and experimental critical values of roll and pitch angles were about 4°     

Self-stability of a simple walking model driven by a rhythmic signal

In this paper, we analyzed the dynamic properties of a simple walking model of a biped robot driven by a rhythmic signal from an oscillator. The oscillator receives no sensory feedback and the rhythmic signal is an open loop. The simple model consists of a hip and two legs that are connected at the hip. The leg motion is generated by a rhythmic signal. In particular, we analytically examined the stability of a periodic walking motion. We obtained approximate periodic solutions and the Jacobian matrix of a Poincaré map by the power-series expansion using a small parameter. Although the analysis was inconclusive when we used only the first order expansion, by employing the second order expansion it clarified the stability, revealing that the periodic walking motion is asymptotically stable and the simple model possesses self-stability as an inherent dynamic characteristic in walking. We also clarified the stability region with respect to model parameters such as mass ratio and walking speed.     

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.      

八脚机器爬虫运动仿真分析

采用叠层IPMC为片状脚,设计左右非对称分布的八脚机器爬虫模型,通过输入电压波形实现动力驱动.运用刚-柔混合技术,确定柔性体片状脚与刚性体地面接触模式,设计合理的行走步态,获得向前不间断的动力驱动.整个分析过程借助于ANSYS和ADAMS有限元分析软件完成,在ANSYS中建模,并获取32阶模态,通过ADAMS分析完成八脚机器爬虫的运动分析.经参数研究发现,较小的动力驱动和较高的驱动频率既能让机器爬虫保持一定速度,又能使其载重得到一定程度增加,且整体稳定性良好.     

ZMP based neural network inspired humanoid robot control

This paper concerns ZMP-based control that is inspired by artificial neural networks for humanoid robot walking on varying sloped surfaces. Humanoid robots are currently one of the most exciting research topics in the field of robotics, and maintaining stability while they are standing, walking or moving is a key concern. To ensure a steady and smooth walking gait of such robots, a feedforward type of neural network architecture, trained by the back-propagation algorithm, is employed. The inputs and outputs of the neural network architecture are the ZMPx and ZMPy errors of the robot, and the x, y positions of the robot, respectively. The neural network developed allows the controller to generate the desired balance of the robot positions, resulting in a steady gait for the robot as it moves around on a flat floor, and when it is descending or ascending slopes. In this paper, experiments of humanoid robot walking are carried out, in which the actual position data from a prototype robot are measured in real-time situations, and fed into a neural network inspired controller designed for stable bipedal walking. In addition, natural walking motions on the different surfaces with varying slopes are obtained and the performance of the resulting controller is shown to be satisfactory.     

四连杆膝关节假肢的动力学建模与分析

相比于单轴式膝关节,四连杆膝关节具有更好的仿生特性和运动安全性,因而在下肢假肢研究中得到广泛关注. 本研究以一款四连杆膝关节被动假肢为研究对象,主要关注足-地交互作用力以及膝关节单边接触力等强非线性因素对下肢假肢步态的影响. 为此,采用 Kelvin-Voigt 模型和库伦模型描述足-地接触力和摩擦力,并采用 Kelvin-Voigt 模型描述膝关节单边接触力,从而基于第一类拉格朗日方程建立假肢动力学模型. 本研究以步态实验测得的髋关节运动数据为模型的驱动信号,针对假肢的步态特征进行了数值分析. 计算结果显示,当膝关节液压阻尼器的刚度较小时,强非线性作用力会使假肢产生显著的亚谐波响应,进而导致步态周期失谐. 进一步研究发现,提胯行为能够避免步态周期失谐,这也为残疾人行走时的提胯等代偿行为提供了一种新的力学解释. 为了评价假肢步态与健康人实测步态的一致性,本研究进一步定义了步态相关系数并分析了膝关节液压阻尼器刚度、阻尼参数对相关系数的影响. 结果表明,通过合理的刚度、阻尼参数设计,两者步态的相关系数可达到 0.9 以上,这为四连杆膝关节被动假肢进一步优化提供了理论支撑.      

LCP method for a planar passive dynamic walker based on an event-driven scheme

The main purpose of this paper is to present a linear complementarity problem (LCP) method for a planar passive dynamic walker with round feet based on an event-driven scheme. The passive dynamic walker is treated as a planar multi-rigid-body system. The dynamic equations of the passive dynamic walker are obtained by using Lagrange’s equations of the second kind. The normal forces and frictional forces acting on the feet of the passive walker are described based on a modified Hertz contact model and Coulomb’s law of dry friction. The state transition problem of stick-slip between feet and floor is formulated as an LCP, which is solved with an event-driven scheme. Finally, to validate the methodology, four gaits of the walker are simulated: the stance leg neither slips nor bounces; the stance leg slips without bouncing; the stance leg bounces without slipping; the walker stands after walking several steps.     

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.     

DYNAMIC MODELING AND ANALYSIS OF THE LOWER LIMB PROSTHESIS WITH FOUR-BAR LINKAGE PROSTHETIC KNEE$^{\bf 1)}$

相比于单轴式膝关节,四连杆膝关节具有更好的仿生特性和运动安全性,因而在下肢假肢研究中得到广泛关注. 本研究以一款四连杆膝关节被动假肢为研究对象,主要关注足-地交互作用力以及膝关节单边接触力等强非线性因素对下肢假肢步态的影响. 为此,采用 Kelvin-Voigt 模型和库伦模型描述足-地接触力和摩擦力,并采用 Kelvin-Voigt 模型描述膝关节单边接触力,从而基于第一类拉格朗日方程建立假肢动力学模型. 本研究以步态实验测得的髋关节运动数据为模型的驱动信号,针对假肢的步态特征进行了数值分析. 计算结果显示,当膝关节液压阻尼器的刚度较小时,强非线性作用力会使假肢产生显著的亚谐波响应,进而导致步态周期失谐. 进一步研究发现,提胯行为能够避免步态周期失谐,这也为残疾人行走时的提胯等代偿行为提供了一种新的力学解释. 为了评价假肢步态与健康人实测步态的一致性,本研究进一步定义了步态相关系数并分析了膝关节液压阻尼器刚度、阻尼参数对相关系数的影响. 结果表明,通过合理的刚度、阻尼参数设计,两者步态的相关系数可达到 0.9 以上,这为四连杆膝关节被动假肢进一步优化提供了理论支撑.     

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.     

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．     

The test and simulation of ABS on rough,non-deformable terrains

It is well known that the performance of many antilock braking systems (ABS) deteriorate on rough, non-deformable surfaces due to a number of factors such as axle oscillations, wheel speed fluctuations and deficiencies in the algorithms. Rough terrain excitation further contribute to dynamic tyre effects such as loss of vertical contact and poor contact patch generation that leads to reduced longitudinal force generation. In this study, a slightly modified version of the Bosch ABS algorithm is implemented in Matlab/Simulink using co-simulation with a validated full vehicle ADAMS model that incorporate a valid high-fidelity FTire model. A non-ABS test vehicle is fitted with a commercial ABS modulator controlled by an embedded computer. The co-simulation model is validated with vehicle test data on both smooth and rough terrains. Initial results show that wheel speed fluctuations on rough terrain cause inaccuracies in the estimation of vehicle velocity and excessive noise on the derived rotational acceleration values. This leads to inaccurate longitudinal slip calculation and poor control state decisions respectively. It is concluded that, although the correlation is not yet as desired, the combined use of a simulation model and test vehicle can be a useful tool in the research of ABS braking on rough terrains.     

Interaction of surface radiation with combined conduction and convection from a discretely heated L-corner

Prominent results pertaining to the problem of multi-mode heat transfer from an L-corner equipped with three identical flush-mounted discrete heat sources in its left leg are given here. The heat generated in the heat sources is conducted along the two legs of the device before being dissipated by combined convection and radiation into air that is considered to be the cooling agent. The governing equations for temperature distribution along the L-corner are obtained by making appropriate energy balance between the heat generated, conducted, convected and radiated. The non-linear partial differential equations thus obtained are converted into algebraic form using a finite-difference formulation. The resulting equations are solved simultaneously by Gauss–Seidel iterative solver. A computer code is specifically written to solve the problem. The computational domain is discretised using 101 grids along the left leg, with 15 grids taken per heat source, and 21 grids along the bottom leg. The effects of surface emissivity, convection heat transfer coefficient, thermal conductivity and aspect ratio on local temperature distribution, peak device temperature and relative contributions of convection and radiation to heat dissipation from the L-corner are studied in detail. The point that one cannot overlook radiation in problems of this class has been clearly elucidated.     

3D-Simulation of human walking by parameter optimization

The simulation of human gait is a complex dynamical problem that requires accounting for energy consumption as well as dealing with a redundantly actuated multibody system. If muscle forces and generalized coordinates are parameterized, optimization techniques allow the simulation of the muscle forces and of the walking motion. An optimization framework is presented for non-symmetrical gait cycles found in the presence of one-sided gait disorders. The motion of each leg is independently parameterized for a whole walking cycle. The non-linear constraints used to fulfill the equations of motion and the kinematical constraints of the different walking phases are implemented in an efficient way. Fifth-order splines are used for the parameterization to reduce the oscillatory behavior coming from non-periodicity conditions. To achieve the computational performance required for three-dimensional simulations, the spline interpolation problem has been split in two parts, one is performed in a preprocessing stage and the other during the optimization. Numerical differentiation via finite differences is avoided by implementing analytical derivatives of the splines functions and of the contractile element force law. The results show good numerical performance, and the computational efficiency for 3D-simulations with one-sided gait disorders is highlighted.